Handbook of Macroeconomics, Volume 1C

( -Jt)

1 , implying that Q

=

Q

=

1 . Around the steady state,

the difterence between Qtt 1 and Q1 is second order. We therefore omit the rental term and express Equation (4.4) using Q11 1 rather than Q1+ 1 •

B.S. Bemanke et al.

1 358

that, in addition to operating firms, entrepreneurs supplement their income by working in the general labor market. Total labor input L 1 is taken to be the following composite of household labor, Ht . and "entrepreneurial labor", Ht": (4.6) We assume further that entrepreneurs supply their labor inelastically, and we normalize total entrepreneurial labor to unity 14. In the calibrations below we keep the share of income going to entrepreneurial labor small (on the order of .0 1 ), so that this modification of the standard production function does not have significant direct effects on the results. Let V, be entrepreneurial equity (i.e., wealth accumulated by entrepreneurs from operating firms), let Wt denote the entrepreneurial wage, and let w1 denote the state­ contingent value of w set in period t. Then aggregate entrepreneurial net worth at the end of period t, Nt+ 1 , is given by (4.7) with (4.8) where y V1 is the equity held by entrepreneurs at t 1 who are still in business at t. (Entrepreneurs who fail in t consume the residual equity ( 1 y)V1. That is, c,e ( 1 y) V1.) Entrepreneurial equity equals gross earnings on holdings of equity from t I to t less repayment of borrowings. The ratio of default costs to quantity borrowed, �

�

�

=

�

/)- fr�'

wRJQr-IKr dF(w) Qt - ! Kt Nt-1 �

reflects the premium for external finance. Clearly, under any reasonable parametrization, entrepreneurial equity provides the main source of variation in Nt+l · Further, this equity may be highly sensitive to unexpected shifts in asset prices, especially if firms are leveraged. To illustrate, let u;" == R� E1_ J {R1 } be the unexpected shift in the gross return to capital, and let �

1 4 Note that entrepreneurs do not have to work only on their own projects (such an assumption would violate aggregate returns to scale, given that individual projects can be of different sizes).

Ch. 21:

U1dp =

The Financial Accelerator in a Quantitative Business Cycle Framework

1 359

fow, cvQ1_ K1 d.F( cv) - E1 {f0w' cvQ1- J K1 dF( cv)} be the unexpected shift in the 1

1

conditional (on the aggregate state) default costs. We can express V1 as

(4.9) Now consider the impact of a unexpected increase in the ex post return to capital. Differentiating Equation (4.9) yields an expression for the elasticity of entrepreneurial equity with respect to an unanticipated movement in the return to capital: (4. 1 0) According to Equation (4. 1 0), an unexpected one percent change in the ex post return to capital leads to a percentage change in entrepreneurial equity equal to the ratio of gross holdings of capital to equity. To the extent that entrepreneurs are leveraged, this ratio exceeds unity, implying a magnification effect of unexpected asset returns on entrepreneurial equity. The key point here is that unexpected movements in asset prices, which are likely the largest source of unexpected movements in gross returns, can have a substantial effect on firms' financial positions. In the general equilibrium, further, there is a kind of multiplier effect, as we shall see. An unanticipated rise in asset prices raises net worth more than proportionately, which stimulates investment and, in turn, raises asset prices even further. And so on. This phenomenon will become evident in the model simulations. We next obtain demand curves for household and entrepreneurial labor, found by equating marginal product with the wage for each case:

Yt Ht

(4. 1 1 )

( 1 - a)Q- = Xt W� > (1 -

a)(

�

I - Q) e t

=

xl wte '

(4. 1 2)

where Wt is the real wage for household labor and W1e is the real wage for entrepreneurial labor. Combining Equations (4. 1), (4.7), (4.8), and (4. 1 2) and imposing the condition that entrepreneurial labor is fixed at unity, yields a difference equation for Nt+ l :

(4. 1 3)

Equation (4. 13) and the supply curve for investment funds, Equation (4.5), are the two basic ingredients of the financial accelerator. The latter equation describes how

1 3 60

B.S. Bernanke et al.

movements in net worth influence the cost of capital. The former characterizes the endogenous variation in net worth. Thus far we have determined wholesale output, investment and the evolution of capital, the price of capital, and the evolution of net worth, given the riskless real interest rate Rt+I , the household real wage Wt , and the relative price of wholesale goods 1/A't . To determine these prices and complete the model, we need to add the household, retail, and government sectors. 4.2. The complete log-linearized model

We now present the complete macroeconomic framework. Much of the derivation is standard and not central to the development of the financial accelerator. We therefOre simply write the complete log-linearized model directly, and defer most of the details to Appendix B. As we have emphasized, the model is a DNK framework modified to allow for a financial accelerator. In the background, along with the entrepreneurs we have described are households and retailers. Households are infinitely-lived agents who consume, save, work, and hold monetary and nonmonetary assets. We assume that household utility is separable over time and over consumption, real money balances, and leisure. Momentary utility, further, is logarithmic in each of these arguments 1 5. As is standard in the literature, to motivate sticky prices we modify the model to allow for monopolistic competition and (implicit) costs of adjusting nominal prices. It is inconvenient to assume that the entrepreneurs who purchase capital and produce output in this model are monopolistically competitive, since that assumption would complicate the analyses of the financial contract with lenders and of the evolution of net worth. To avoid this problem, we instead assume that the monopolistic competition occurs at the "retail" level. Specifically, we assume there exists a continuum of retailers (of measure one). Retailers buy output from entrepreneur-producers in a competitive market, then slightly differentiate the output they purchase (say, by painting it a unique color or adding a brand name) at no resource cost. Because the product is differentiated, each retailer has a bit of market power. Households and firms then purchase CES aggregates of these retail goods. It is these CES aggregates that are converted into consumption and investment goods, and whose price index defines the aggregate price level. Profits from retail activity are rebated lump-sum to households (i.e., households are the ultimate owners of retail outlets.) To introduce price inertia, we assume that a given retailer is free to change his price in a given period only with probability 1 - 8. The expected duration of any price change is 1 �1!" This device, following Calvo ( 1 983), provides a simple way to incorporate staggered long-term nominal price setting. Because the probability of changing price is independent of history, the aggregation problem is greatly simplified. One extra

Ch. 21:

The Financial Accelerator in a Quantitative Business Cycle Framework

1361

twist, following Bernanke and Woodford ( 1 997), is that firms setting prices at t are assumed to do so prior to the realization of any aggregate uncertainty at time t. Let lower case variables denote percent deviations from the steady state, and let ratios of capital letters without time subscript denotes the steady state value of the respective ratio. Further, let if>: denote a collection of terms of second-order importance in the equation for any variable z, and let t:f be an i.i.d. disturbance to the equation for variable z. Finally, let G1 denote government consumption, n1 = p1 - PH the rate of inflation from t 1 to t, and r;+ 1 = r,+ 1 + E {Pt+ 1 p1 } be the nominal interest rate. It is then convenient to express the complete log-linearized model in terms of four blocks of equations: ( 1 ) aggregate demand; (2) aggregate supply; (3) evolution of the state variables; and (4) monetary policy rule and shock processes. Appendix B provides details. -

-

( 1 ) Aggregate demand

(4. 1 4) (4. 1 5)

c� = n1 1 1 + · · · + ¢�' ,

(4. 1 6) (4. 1 7) (4. 1 8) (4. 1 9)

(2) Aggregate Supply (4.20) (4.2 1 ) (4.22) (3) Evolution of State Variables (4.23)

(4.24)

B.S. Bernanke et a!.

1 362 (4) Monetary Policy Rule and Shock Processes

(4.25) (4.26) (4.27)

with

D = 11

1w ()

w dF( w)R\

" ( 1 - a)(l - .Q)(Y/X) n _ (R IR - l )K k (rt + q,_, + kt ) + 1/Jt = Yt - x, , N N V=

'tjl(R"IR) 'tjl' (R"IR) '

cp =

( C/J(I!Kt I )' (f/J(I/K)-' )'' '

E

=

1

b)+ b ( )

(1 -

K =

-

a YI(XK)

1 -e -e

,

( 1 - e/)).

Equation (4. 1 4) is the log-linearized version of the resource constraint. The primary determinants of the variation in aggregate expenditures y1 are household consumption Ct . investment i1 , and government consumption g1 . Of lesser importance is variation in entrepreneurial consumption c� 1 6. Finally, variation in resources devoted monitoring cost, embedded in the term
Note that each variable in the log-linearized resource constraint is weighted by the variable's share of output in the steady state. Under any reasonable parametrization of the model, cf has a relatively low weight.

Ch. 2 1 : Th e Financial Accelerator in a Quantitative Business Cycle Framework

1 363

this model would be to incorporate household borrowing and associated frictions. With some slight modification, the financial accelerator would then also apply to household spending, strengthening the overall effect. Since entrepreneurial consumption is a (small) fixed fraction of aggregate net worth (recall that entrepreneurs who retire simply consume their assets), it simply varies proportionately with aggregate net worth, as Equation (4. 1 6) indicates. Equations (4. 1 7), (4. 1 8), and (4. 1 9) characterize investment demand. They are the log-linearized versions of Equations (4.5), (4.4) and (4.3), respectively. Equa­ tion (4. 1 7), in particular, characterizes the influence of net worth on investment. In 0: the absence of capital market frictions, this relation collapses to E1{r;� 1 } - rt+ 1 Investment is pushed to the point where the expected return on capital, E1{r�+ 1 }, equals the opportunity cost of funds rt+ 1 17. With capital market frictions present, however, the cost of external funds depends on entrepreneurs ' percentage equity holding, i.e., net worth relative to the gross value of capital, n11 1 - (q1 + k1 1 1 ) . A rise in this ratio reduces the cost of external funds, implying that investment will rise. While Equation (4. 1 7) embeds the financial accelerator, Equations (4. 1 8) and (4. 1 9) are conventional (log­ linearized) relations for the marginal product of capital and the link between asset prices and investment. Equations (4.20), (4.2 1 ) and (4.22) constitute the aggregate supply block. Equa­ tion (4.20) is the linearized version of the production function (4. 1 ), after incorporating the assumption that the supply of entrepreneurial labor is fixed. Equation (4.2 1 ) characterizes labor market equilibrium. The left side is the marginal product of labor weighted by the marginal utility of consumption 1 8 . In equilibrium, it varies proportionately with the markup of retail goods over wholesale goods (i.e., the inverse of the relative price of wholesale goods.) Equation (4.22) characterizes price adjustment, as implied by the staggered price setting formulation of Calvo ( 1 983) that we described earlier [along with the modification suggested by Bernanke and Woodford ( 1 997)] . This equation has the flavor of a traditional Phillips curve, once it is recognized that the markup x1 varies inversely with the state of demand. With nominal price rigidities, the retail firms that hold their prices fixed over the period respond to increased demand by selling more. To accommodate the rise in sales they increase their purchases of wholesale goods from entrepreneurs, which bids up the relative wholesale price and bids down the markup. It is for this reason that -x1 provides a measure of demand when prices are sticky. In turn, the sensitivity of inflation to demand depends on the degree of price inertia: The slope coefficient /(" can be shown to be decreasing in e, the probability an individual price stays fixed from period to period. One difference between Equation (4.22) and =

1 7 In the absence of capital market frictions, the tlrst-order condition from the entreprenew·'s partial equilibriwn capital choice decision yields E {R�+ 1 } = R1+ 1 • In this instance if E {R;'+ 1 } > R, 1 , the entrepreneur would buy an infinite amount of capital, and if E { R7+ 1 } < Rl+ he would buy none. When E{RJ+ 1 } = R,_,_ b he is indifferent about the scale of operation of his firm. 1 � Given logarithmic preferences, the marginal utility of consumption is simply --c, .

1,

1 364

B.S. Bemanke et al.

a traditional expectations-augmented Phillips curve is that it involves expected future inflation as opposed to expected current inflation. This alteration reflects the forward­ looking nature of price setting 1 9 . Equations (4.23) and (4.24) are transition equations for the two state variables, capital k1 and net worth n1 • The relation for capital, Equation (4.23), is standard, and is just the linearized version of Equation (4.2). The evolution of net worth depends primarily on the net return to entrepreneurs on their equity stake, given by the first term, and on the lagged value of net worth. Note again that a one percent rise in the return to capital relative to the riskless rate has a disproportionate impact on net worth due to the leverage effect described in the previous section. In particular, the impact of r� - r1 on n1+ is weighted by the coefficient yRKIN, which is the ratio of gross capital 1 holdings to entrepreneurial net worth. How the financial accelerator augments the conventional DNK model should now be fairly transparent. Net worth affects investment through the arbitrage Equation (4. 1 7). Equation (4.24) then characterizes the evolution of net worth. Thus, among other things, the financial accelerator adds another state variable to the model, enriching the dynamics. All the other equations of the model are conventional for the DNK framework [particularly King and Wolman's ( 1 996) version with adjustment costs of capital]. Equation (4.25) is the monetary policy rule 20 . Following conventional wisdom, we take the short-term nominal interest rate to be the instrument of monetary policy. We consider a simple rule, according to which the central bank adjusts the current nominal interest rate in response to the lagged inflation rate and the lagged interest rate. Rules of this form do a reasonably good job of describing the variation of short term interest rates [see Clarida, Gali and Gertler ( 1 997)]. We also considered variants that allow for responses to output as well as inflation, in the spirit of the Taylor ( 1 993) rule. Obviously, the greater the extent to which monetary policy is able to stabilize output, the smaller is the role of the financial accelerator to amplify and propagate business cycles, as would be true for any kind of propagation mechanism. With the financial accelerator mechanism present, however, smaller countercyclical movements in interest rates are required to dampen output fluctuations. Finally, Equations (4.26) and (4.27) impose that the exogenous disturbances to government spending and technology obey stationary autoregressive processes. We next consider two extensions of the model.

1 9 Iterating Equation (4.22) forward yields n:, = L'.,'f:"� o fY K(p;�k -·Pt+k) - With forward-looking price setting, how fast prices adjust depends on the expected discounted stream of future demand. 20 The interest rate rule may be thought of as a money supply equation. The associated money demand equation is given by m1 - p1 = c1 - ( -f, ) r;', • Note that under interest-rate targeting this relation simply 1 determines the path of the nominal money stock. To implement its choice of the nominal interest rate, the central bank adjusts the money stock to satisfy this equation.

Ch.

21:

4.2. 1.

The Financial Accelerator in a Quantitative Business Cycle Framework

1 365

Two extensions of the baseline model

Two modifications that we consider are: ( 1 ) allowing for delays in investment; and (2) allowing for firms with differential access to credit. The first modification permits the model to generate the kind of hump-shaped output dynamics that are observed in the data. The second is meant to increase descriptive realism. 4.2. 1 . 1. Investment delays. Disturbances to the economy typically appear to generate a delayed and hump-shaped response of output. A classic example is the output response to a monetary policy shock [see, e.g., Christiano, Eichenbaum and Evans ( 1 996) and Bernanke and Mihov ( 1 998)] . It takes roughly two quarters before an orthogonalized innovation in the federal funds rate, for example, generates a significant movement in output. The peak of the output response occurs well after the peak in the funds rate deviation. Rotemberg and Woodford ( 1 997) address this issue by assuming that consumption expenditures are determined two periods in advance (in a model in which non-durable consumption is the only type of private expenditure). We take an approach that is similar in spirit, but instead assume that it is investment expenditures rather than consumption expenditures that are determined in advance. We focus on investment for two reasons. First, the idea that investment expenditures take time to plan is highly plausible, as recently documented by Christiano and Todd (1 996). Second, movements in consumption lead movements in investment over the cycle, as emphasized by Bernanke and Gertler ( 1 995) and Christiano and Todd ( 1 996). For example, Bernanke and Gertler ( 1 995) show that in response to a monetary policy shock household spending responds fairly quickly, well in advance of business capital expenditures. ModifYing the model to allow for investment delays is straightforward. Suppose that investment expenditure are chosen j periods in advance. Then the first-order condition relating the price of capital to investment, Equation (4.3), is modified to

(4.28) Note that the link between asset prices and investment now holds only in expectation. With the time-to-plan feature, shocks to the economy have an immediate effect on asset prices, but a delayed effect on investment and output 2 1 . To incorporate the investment delay in the model, we simply replace Equation (4. 1 9) with the following log-linearized version of Equation (4.28):

In our simulations, we take j = 1 . 21

Asset prices move inunediately since the return to capital depends on the expected capital gain.

B.S. Bernanke et a/.

1 366

Heterogeneous firms. The baseline model assumes that all firms are alike ex ante, except for initial net worth. In practice, of course, there is considerable heterogeneity among firms along many dimensions, in particular in access to credit [see, e.g., the discussion in Gertler and Gilchrist ( 1 994)]. To see how heterogeneity affects the results, we add to our model the assumption that there are two types of firms, those that have easy access to credit, ceteris paribus, and those that (for various informational or incentive reasons, for example) have less access to credit. To accommodate two different types of firms, we assume that there are two types of intermediate goods (one produced by each type of firm) which are combined into a single wholesale good via a CES aggregator. Production of the intermediate good is given by 4.2. 1 . 2.

v

1 zt

= A·zlKtat H1Q1 (He )
z·

=

1

'

2

(4.29)

·

Aggregate wholesale output is composed of sectoral output according to Y:t =

l [a YiPt + ( 1 a)YP] 2 1 ( l p).

(4.30)

-

We also assume that capital is sector-specific, and that there are costs of adjusting the capital stock within each sector: (4.3 1 ) Let ji denote the number o f periods i n advance that investment expenditures must be chosen in sector i (note that the lag may differ across sectors): Then the link between asset prices and investment in each sector is given by

{

EI Qt,· l +jt _ ..

[rp' (K·

Ii, +Ji I

..

t, l+jl

) ] -! }

=

O

.

Note that the price of capital may differ across sectors, but that arbitrage requires that each sector generate the same expected return to capital

where

(

1 Pit a Y;, t+l Rki, t + l - x pw + Qi, I + I ( J 1+1 t � 1, 1 +1 _

and

b)) /

Qil ,

are the relative (wholesale) prices of goods produced in sectors

1

and 2 respectively.

Ch. 21:

The Financial Accelerator in a Quantitative Business Cycle Framework

1 367

As we discuss in the next section, it is easy to parametrize the model so that firms in each sector face differential costs of credit. Further, as we illustrate below, the financial accelerator can still be quite potent, even if only a portion of firms face significant capital market frictions. Indeed, there may spillover effects from constrained to non­ constrained firms. It is straightforward to log-linearize these equations and append them to the general model. Modified will be the aggregate supply block, to allow for the two types of intermediate output, and the law of motion for capital, to allow for two distinct types of capital.

5. Model simulations

In this section we present the results of some quantitative experiments to illustrate how the financial accelerator influences business cycle dynamics within the DNK framework. Specifically, we consider how credit-market imperfections amplify and propagate various shocks to the economy. We also examine the effects of allowing for delays in investment and of allowing for some firms to have better access to credit market than others. 5. 1.

Model parametrization

We choose fairly standard values for the taste and technology parameters. We set the quarterly discount factor f3 to 0. 99 (which also pins down the steady state quarterly riskless rate, R = {3- 1 ). We fix the labor supply elasticity, 'YJ, at 3 . 0, in keeping with much of the literature As is also within convention, the capital share, a, is 0. 35, and the household labor share, ( 1 - a)( l Q), is 0. 64. The share of income accruing to entrepreneurs' labor is accordingly equal to 0. 0 1 . The quarterly depreciation rate for capital, is assigned the usual value of 0.025. We take the steady­ state share of government expenditures in total output, GIY, to be 0.2, the approximate historical average. The serial correlation parameters for the technology and government expenditure shocks, p0 and [fi, are assumed to be 1 . 0 and 0.95, respectively. Finally, the elasticity of the price of capital with respect to the investment capital ratio, cp, is taken to be 0.25. There is no firm consensus in the l iterature about what this parameter value should be Reasonable assumptions about adjustment costs suggest that the value should lie within a range from 0.0 to 0.50.

22 .

-

b,

23.

22 In particular, we fix average hours worked relative to total hours available at a value that, in

conjunction with logarithmic preferences over leisure, generates the desired labor supply elasticity. King and Wolman ( 1 996) use a value of 2.0, based on estimates Jiom aggregate data by Chirinko ( 1 993). Because this value implies implausibly high adjustment costs, we do not use it. 23

B.S. Bernanke et al.

1 368

The non-standard parameters of our model pertain to the interplay between real and financial factors within the entrepreneurial sector 24 . Specifically, we choose parameters to imply the following three steady state outcomes: ( 1 ) a risk spread, R k - R, equal to two hundred basis points, approximately the historical average spread between the prime lending rate and the six-month Treasury bill rate; (2) an annualized business failure rate, F(w), of three percent, the approximate rate in the data; (3) a ratio of capital to net worth, %, of 2 (or equivalently, a leverage ratio of 0.5), the approximate value in the data. To obtain these steady state values we choose the "death rate" of entrepreneurs, 1 - y, to be 0.0272 (quarterly), we take the idiosyncratic productivity variable, log(w), to be log-normally distributed with variance equal to 0.28, and we set the fraction of realized payoffs lost in bankruptcy, /).. , to 0. 1 2 . We note that our choice for 11- is within the reasonable set of estimates for bankruptcy costs 25 . The final parameters to be selected are those related to the rate of price adjustment and to the policy rule. We let the probability a firm does not change its price within a given period, e, equal to 0. 75, implying that the average period between price adjustments is four quarters. In the policy rule, Equation (4.25), we set the autoregressive parameter, p, to 0. 9 and the coefficient on inflation equal to 0. 1 1 (implying a long-run rise in the nominal interest rate of one hundred and ten basis points in response to a permanent one hundred basis point increase in inflation.) These numbers are roughly in line with the evidence, allowing for the fact that there have been shifts in the actual feedback rule over time [see Clarida, Gali and Gertler ( 1 997)] . 5.2.

Results

In our experiments we consider four types of aggregate shocks: ( 1 ) a monetary policy shock, (2) a technology shock, (3) a government expenditure shock, and (4) a one­ time, unanticipated transfer of wealth from households to entrepreneurs. We first study the response of the economy to these shocks in our model, excluding and including the financial accelerator. We then consider the implications of allowing for investment delays and heterogeneous firms. 5.2. 1 .

Response to a monetary policy shock

The first experiment we consider is a monetary policy shock, specifically an unanticipated exogenous movement in the short-term interest rate. Analyzing the response of the model economy to a monetary policy disturbance provides a good way to evaluate our framework since a lengthy literature has produced a consensus of 24 Our parameter choices here follow closely Fisher ( 1 996) and Carlstrom and Fuerst ( 1 997).

25 See the discussion of bankruptcy costs in Carlstrom and Fuerst ( 1 997). They actually use a higher number than we do (0.20 versus 0 . 1 2).

Ch. 21:

The Financial Accelerator in a Quantitative Business Cycle Frarnework

1 3 69

"' c:i

N c:i

Log(GOP) Lo (GOP Deflator) 0

1

2

3

4

5

6

7

8

9

10

12

14

16

Quarters ,------------,

Prime Rate - Tbill CP Rate - Tbill Funds Rate

0

1

2

3

4

5

6

7

8

9

10

12

14

16

Quarters

Fig. 2. Impulse response t o a funds rate shock.

opinion about how the economy responds to this kind of shock 26 . Figure 2 summarizes this evidence, and also presents some new evidence on the behavior of several rate spread variables that proxy for premium for external funds, a key element of our model. The results in Figure 2 are based on a five-variable quarterly VAR that includes four "standard" macroeconomic variables - the log of real GDP, the log of the GDP deflator, the log of a commodity price index, the federal funds rate -- along with two rate spread variables. To identify the policy shock, we order the funds rate after the price and output variables, based on the view that monetary policy can respond contemporaneously to these variables but can affect them only with a lag. We order the spread variable after the funds rate based on the assumption that innovations in these variables do not contain any marginal information that is useful for setting current monetary policy. The two rate spread variables we consider are the difference between the six-month commercial paper rate and the six-month T-bill rate and the difference between the prime lending rate and the six-month T-bill rate.

2(' See, for example, Christiano, Eichenbaum and Evans ( 1 996), Bcrnankc and Gertler ( 1995), Bcrnankc and Mihov ( 1998), and Leeper, Sims and Zha ( 1 996).

1 370

B.S Bernanke et a!.

Figure 2 illustrates the impulse responses of several variables to a negative innovation in the federal funds rate. As is typically found in the literature, output declines after about two quarters, and the price level declines after about six quarters. The output decline, further, persists well after the funds rate reverts to trend. Finally, each of the spread variables rises fairly quickly, leading the downturn in output 27 . Figure 3 reports the impact of the same experiment, but this time using the model economy. As in all the subsequent figures, the time units on the graphs are to be interpreted as quarters. In each picture the hatched line designates the "baseline" impulse response, generated by fixing the external finance premium at its steady state level instead of allowing it to respond to changes in the capital-net worth ratio. In other words, the baseline simulations are based on a model with the same steady state as the complete model with imperfect credit markets, but in which the additional dynamics associated with the financial accelerator have been "turned off". The solid line in each picture indicates the response observed in the complete model, with the financial accelerator included. The figure shows the impact of an unanticipated 25 basis point (on an annual basis) decline in the nominal interest rate. Although the addition of credit-market frictions does not substantially affect the behavior of the nominal rate of interest, it does lead to a stronger response of real variables. In particular, with the financial accelerator included, the initial response of output to a given monetary impulse is about 50% greater, and the effect on investment is nearly twice as great. Further, the persistence of the real effects is substantially greater in the presence of the credit-market factors, e.g., relative to trend, output and investment in the model with credit-market imperfections after four quarters are about where they are in baseline model after only two quarters. The impact of the financial accelerator is mirrored in the behavior of the external finance premium, which is passive in the baseline model (by assumption) but declines sharply in the complete model, slowly reverting to trend. The unanticipated decline in the funds rate stimulates the demand for capital, which in turn raises investment and the price of capital. The unanticipated increase in asset prices raises net worth, forcing down the external finance premium, which in turn further stimulates investment. A kind of multiplier effect arises, since the burst in investment raises asset prices and net worth, further pushing up investment. Entrepreneurial net worth reverts to trend as firms leave the market, but the effect is slow enough to make the external finance premium persist below trend. This persistence in net worth and the external finance premium provides the additional source of dynamics. It is interesting to observe that the response of the spread in the model economy matches the VAR evidence reasonably well.

27

lt is worth noting that the impulse response of the prime-rate spread is twice as large as the impulse response of the commercial-paper spread. Since commercial paper issuers are h igh quality firms, this result is consistent with our model's implication that lower-quality borrowers experience larger spread movements in response to business cycle shocks.

With Financial Accelerator Without Financial Accelerator

'

CD d

With Financial Accelerator Without Financial Accelerator

"'

'

'·

"' d

0

1371

The Financial Accelerator in a Quantitative Business Cycle Framework

Ch. 21:

1

'·

2

- · - · - · - · -

3

4

5

6

7

8

- · - · - · - · ·

9

10

'·

0

12

0

1

'·

2

'·

3

4

Output

- - -

· -

5

6

7

8

9

10

12

Investment

- · - ·�

0 d

""' 0

9

"'

""' N

9

With Financial Accelerator Without Financial Accelerator

0

1

2

3

4

5

6

7

8

9

Nominal I nterest Rate

10

12

9

With Financial Accelerator Without Financial Accelerator

0

1

2

3

4

5

6

7

8

9

10

12

Premium

Fig. 3. Monetary shock -· no investment delay. All panels: time horizon in quarters.

It is worth emphasizing that this experiment generates substantial output persistence without relying on an unusually high labor supply elasticity, as is required for the baseline model [see, e.g., the discussion in Chari, Kehoe and McGrattan ( 1 996)]. The countercyclical movement in the premium for external funds (which is the essence of the financial accelerator) serves to flatten the marginal cost curve, as does making labor supply elastic in the baseline model. Overall, these results lend some supports to the claims of Bernanke and Gertler ( 1995), that credit-market effects can help explain both the strength of the economy's response to monetary policy and the tendency for policy effects to linger even after interest rates have retumed to normal. The fact that the model economy replicates the VAR evidence reasonably well is particularly encouraging. The one major point of discrepancy is that the response of output to a monetary shock is delayed in the data, but occurs immediately in the model economy 2 8 . We show shortly, however, that this problem can be fixed by allowing for investment delays.

n Tt is also true that the output response is large relative to the interest rate shock. This partly reflects the high degree of intertemporal substitution embedded in the household savings decision. It may also reflect unreasonably short investment delays.

B.S. Bernanke et al.

1 3 72 ·-, .----With Fin. Accelerator Without Fin. Accelerator

With Fin. Accelerator Without Fin. Accelerator

\

N

0

0

2

4

6

8

10

Technology Shock

12

0

\

2

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'·

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{()

0

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12

/

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Fig. 4. Output response - alternative shocks. All panels: time horizon in quarters.

5.2.2.

Shock to technology, demand, and wealth

figure 4 displays the effects on output of three alternative shocks: a technology shock, a demand shock (specifically a shock to government expenditures), and a redistribution of wealth between entrepreneurs and households. Once again, the hatched lines show impulse responses from the baseline model with the financial accelerator shut off, and the solid lines show the results from the full model. As the figure shows, the financial accelerator magnifies and propagates both the technology and demand shocks. Interestingly, the magnitude of the effects is about the same as for the monetary policy shock. Again, the central mechanism is the rise in asset prices associated with the investment boom, which raises net worth and thus reduces the external finance premium. The extra persistence comes about because net worth is slow to revert to trend. A positive shock to entrepreneurial wealth (more precisely, a redistribution from households to entrepreneurs) has essentially no effect in the baseline model, but has both significant impact and propagation effects when credit-market frictions are present. The wealth shock portrayed is equal in magnitude to about 1 % of the initial wealth of entrepreneurs and about 0.05% of the wealth of households. The transfer of wealth drives up the demand for investment goods, which raises the price of capital and thus entrepreneurs' wealth, initiating a positive feedback loop; thus, although the exogenous shock increases entrepreneurial net worth directly by only 1%, the total effect on entrepreneurs' wealth including the endogenous increase in asset prices exceeds 2%. Output rises by 1 % at an annual rate, and substantial persistence is generated by the slow decay of entrepreneurial net worth. Thus the addition of credit-market effects raises the possibility that relatively small changes in entrepreneurial wealth could be an important source of cyclical :fluctuations. This case is an interesting one, as it is reminiscent of (and motivated by) Fisher's ( 1 933) "debt-deflation" argument, that redistributions between creditors and debtors arising from unanticipated price changes can have important real effects. Indeed, Fisher argued

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that this kind of mechanism accounted for the depth and protractedness of the Great Depression 2 9 . The same kind of reasoning, further, helps explain why the recent spate of currency crises have had devastating real effects. To the extent loans from abroad are denominated in units of a foreign currency, an exchange rate collapse redistributes wealth from domestic borrowers to foreign lenders. 5. 2.3.

Investment delays and heterogeneous firms

We now suppose that investment expenditures must be planned one quarter in advance, as in Section 5 .2, and consider the effect of a monetary shock. As Figure 5 illustrates, an expansionary monetary policy shock (again, an unanticipated 25 basis point decline in the funds rate) now generates a hump-shaped response of output, as in the data. This hump-shaped response is considerably more accentuated when the financial accelerator is allowed to operate. The initial response of output is still too strong, suggesting that it may be desirable to build in other types of lags. On the other hand, the persistence of the response of output is considerably greater than in the case without investment delays, and comes much closer to matching the data. Interestingly, there remains an immediate response of the external funds premium as the data suggest. The reason is that asset prices rise immediately, in anticipation of the investment boom. We next consider the model with heterogeneous firms. We choose parameters so that firms in sector 2 face a steady-state premium for external finance of 3% per year, while firms in sector 1 face a premium of only 1 %. We set a = . 5 1 25 to generate an average steady-state premium of 2%. As a consequence of this assumption, roughly half of the economy's output is produced by credit-constrained firms, a breakdown which is in accord with the rough evidence summarized in Bernanke, Gertler and Gilchrist (1996). We set p = 0.9, implying that the goods produced in the two sectors are close substitutes. Assuming a high degree of substitutability biases the results against finding important aggregate effects of credit-market frictions in this setup; however, our results turned out to be not very sensitive to the choice of p. With sector-specific adjustment costs, the effective marginal cost of adjusting the aggregate capital stock is dramatically increased owing to the additional curvature implied by the two sector model. To achieve the same degree of overall capital adjustment as in the one-sector model we lower the adjustment cost elasticity cp from 0.25 to 0. 1 . Finally, we allow for a one-period delay in the investment of sector-2 firms and a two period delay for sector- 1 firms. This choice is based on the observation that credit-constrained firms tend to be smaller, and thus likely more flexible [see, e.g., Gertler and Gilchrist ( 1 994)] . All other parameters are the same as in the baseline DNK model. Figure 6 shows the results of a shock to monetary policy in the model with heterogeneous firms. The top left panel shows the response of output (the solid line),

29

Bcrnanke and Gertler ( 1 989, 1 990) argue that the financial accelerator mechanism provides a formal rationale for Fisher's debt-deflation theory of the Great Depression.

B.S. Bernanke et al.

1 374 co

0

With Financial Accelerator Without Financial Accelerator

With Financial Accelerator Without Financial Accelerator


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I

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Fig. 5. Monetary shock - one period investment delay. All panels: time horizon in quarters.

relative to the baseline case with the financial accelerator shut off (the hatched line). In response to an unanticipated fall in the funds rate, output rises by approximately the same amount as it did in the aggregative New Keynesian model with investment delays, both for the baseline model without credit-market frictions and for the complete model with differential access of firms to credit. One interesting difference is that the differential investment delays across sectors smooth out the hump-shaped response of output, adding to the overall persistence of the output response. Thus, the effect of credit-market frictions on the propagation of shocks is roughly the same in the one­ sector and two-sector versions of the model. The two-sector model also has cross-sectional implications, of course. The top and bottom panels on the right side of Figure 6 show the sectoral responses of output and investment. The solid line corresponds to the sector facing the relatively higher cost of external finance and the dotted line corresponds to the other sector. We find that, in response to an expansionary monetary policy shock, investment by firms with relatively poor access to external credit markets rises by nearly three times as much as the investment of firms with better access to credit. This "excess sensitivity" of the more constrained firms is consistent with evidence reported by Gertler and Gilchrist ( 1 994 ), Kashyap, Lamont and Stein ( 1 994), Oliner and Rudebusch ( 1 994), Morgan ( 1 998), and

The Financial Accelerator in a Quantitative Business C.)ICle Framework

Ch. 21:

With Financial Accelerator Without Financial Accelerator

1 375

Sector 2 Sector 1

"' 0

co 0 '·

N 0

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"' 0

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- - - - - --

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0

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Fig. 6. Monetary shock - multisector model with investment delays. All panels: time horizon in quarters. Aggregate output: models with and without financial accelerator; other panels: model with financial accelerator.

others. Although investment differs sharply across firms in the simulation, changes in output are similar for the two types of firms. Differing output effects could be produced, for example, by introducing inventories or inputs to production that must be financed by borrowing. Our finding that constrained firms' investment spending reacts more strongly to monetary policy contrasts with that of Fisher ( 1 996), who obtains an ambiguous result. We suspect that the main source of the difference in predictions is that, in our setting, borrowers ' net worth is endogenous and is a key channel through which monetary policy affects credit availability. In Fisher's model, in contrast, borrowers' equity positions are exogenously fixed and are unaffected by changes in policy.

6. A highly selected review of the literature

The theoretical and empirical literatures on credit-market imperfections are immense. Until recently, the great bulk of this research has been partial equilibrium in nature, e.g., theoretical analyses of equilibria in credit markets with asymmetric information

1 376

B.S. Bernanke et al.

and agency costs, or empirical studies of the effects of credit-market imperfections on various types of spending, including consumption, housing, business investment, and inventory investment. Some leading recent examples of the latter category are cited in the introduction; see, e.g., Bernanke, Gertler and Gilchrist ( 1 996) for additional references. Other surveys of these literatures which the reader may find useful include Gertler ( 1 988), Gertler and Hubbard ( 1 988), Jaffee and Stiglitz ( 1 990), Bernanke ( 1 993), Calomiris ( 1 993), Gertler and Gilchrist ( 1 993), Kashyap and Stein ( 1 994), Oliner and Rudebusch ( 1 994), Bernanke and Gertler ( 1 995), and Hubbard ( 1 995). To keep our survey of relevant literature brief, we limit consideration to the more recent work that, like the present research, studies the implications of credit-market frictions for macroeconomic dynamics. Even within this limited field our review must necessarily be selective; we focus on the work that bears the closest relationship to the model we have presented. In particular, we do not discuss the burgeoning related literature on the role of financial markets in economic growth [see, e.g., Levine ( 1 997) for a survey of this topic] or in economic development [see, e.g., Townsend ( 1 995)]. Nor do we consider research focusing on the role of banks in business cycles, primarily because there has been little work on the "bank lending channel" and related effects in an explicitly dynamic context 30 . We do believe however that the incorporation of a banking sector into our model would be a highly worthwhile exercise. Indeed, given that commercial banks borrow to order to fund investments in information-intensive, risky projects, and in this way bear resemblance to the entrepreneurs in our model, one could envision a relatively straightforward that allows for agency frictions int the intermediary sector. On the theoretical side, the two principal antecedents of the approach used in the present chapter are Bemanke and Gertler ( 1 989) and Kiyotaki and Moore ( 1 997). Bernanke and Gertler ( 1 989) analyze an overlapping-generations model in which borrowers/firms with fixed-size investment projects to finance face the "costly state verification" problem of Townsend ( 1 979) and Gale and Hellwig ( 1 985) 3 1 . As we discussed in detail in the presentation of our model above, the optimal contract in this setting has the features of a standard debt contract. As we noted earlier, the principal virtue of this setup, other than simplicity, is that it motivates an inverse relationship between the potential borrower's wealth and the expected agency costs of the lender­ borrower relationship (here, the agency costs are equated with monitoring/bankruptcy costs). In particular, a potential borrower with high net worth needs to rely relatively little on external finance; he thus faces at most a small risk of bankruptcy and a small

30 Interesting recent exceptions arc Gersbach ( 1 997) and Krishnamurthy ( 1 997). Holmstrom and Tirole ( 1 997) analyze the role of bank collateral and monitoring in a static context. Several papers have studied the role of banks in the context of "limited participation" models, see for example Fisher ( 1 996) and Cooley and Quadrini ( 1 997).] 3 1 Williamson ( 1987) also incorporates the costly state verification assmnption into a modified real business cycle model.

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premium on external finance. A borrower with less resources of his own to invest, in contrast, faces a high bankruptcy risk and a high external finance premium. In the Bernanke-Gertler model, shocks to the economy are amplified and propagated by their effects on borrowers' cash flows. For example, an adverse productivity shock lowers current cash flows, reducing the ability of firms to finance investment projects from retained earnings. This decline in net worth raises the average external finance premium and the cost of new investments. Declining investment lowers economic activity and cash flows in subsequent periods, amplifying and propagating the effects of the initial shock. B ernanke and Gertler show that this effect can generate serially correlated movements in aggregate output, even though the exogenous shocks to the system are i.i.d. They also show that in their model the dynamics of the cycle are nonlinear; in particular, the weaker the initial financial condition of borrowers, the more powerful is the propagation effect through cash flows. A number of subsequent papers have shown that this basic analysis can be extended and deepened without affecting the qualitative results: For example, Gertler ( 1 992) considers the case of multi-period financial contracts. Aghion and Bolton ( 1 997) give an extensive analysis of the short­ run and long-run dynamic behavior of a closely-related model. And Aghion, Baneijee and Piketty ( 1 997) show how the dynamics of this sort of model are affected when interest rate movements are endogenous (Bernanke and Gertler assume that the real interest rate is fixed by the availability of an alternative technology.) The model that we presented utilizes a number of the features of the B ernanke-Gertler model, notably the overlapping-generations assumption for entrepreneurs and the costly state verification model of intermediation. As in Bernanke and Gertler ( 1 989), our model here implies a central role for the endogenous evolution of borrowers ' net worth in macroeconomic dynamics. Other authors have developed dynamic macroeconomic models in which cash flows play a critical role in the propagation mechanism. Notably, Greenwald and Stiglitz ( 1 993) construct a model in which, as in Bernanke and Gertler ( 1 989), firms have access only to debt financing (equity finance is ruled out by assumption). Because bankruptcy is costly, firms are reluctant to become highly levered; their initial equity or net worth thus effectively constrains the quantity of funds that they can raise in capital markets. Greenwald and Stiglitz assume that there is a one-period lag between the use of variable inputs and the production of output. A firm that suffers a decline in cash flow is able to finance fewer inputs and less production. Lower production implies lower profits, which propagates the effects of the initial fall in cash flow. The Greenwald--Stiglitz model thus illustrates that financial factors may affect the level of inputs, such as employment or inventories, as well as the level of capital investment (as in Bernanke-Gertler). The basic intuition concerning how credit-market imperfections propagate the cycle is similar in the two models, however, The net worth of borrowers changes not only in response to variations in cash flow, but also (and often, more dramatically) to changes in the valuation of the real and financial assets that they hold. indeed, changes in asset values are taken by Fisher ( 1 933) and other classical writers on the subject to be the principal means by which

1 378

B.S. Bernanke et al.

financial forces propagate an economic decline. This element was added to the formal literature by Kiyotaki and Moore ( 1 997), who develop a dynamic equilibrium model in which endogenous fluctuations in the market prices of an asset (land, in their example) are the main source of changes in borrowers' net worth and hence in spending and production 32 . Kiyotaki and Moore analyze a stylized example in which land serves both as a factor of production and as a source of collateral for loans to producers. In this economy, a temporary shock (to productivity, for example) lowers the value of land and hence of producers' collateral. This leads in turn to tightened borrowing constraints, less production and spending, and finally to still further reductions in land values, which propagates the shock further through time 33. We consider the asset-price channel to be an important one, and it plays an important role in generating the significant quantitative effects we obtained in our calibration exercises 34. Turning from theoretical to empirical research, we note that there are very few examples of fully articulated macro models including capital-market imperfections that have been estimated by classical methods (the major exception being some large macroeconometric forecasting models, as noted in the introduction). The quantitative research most closely related to the present chapter uses the calibration technique. Our work here is particularly influenced by Carlstrom and Fuerst ( 1 997), which in turn draws from analyses by Fisher ( 1 996), Fuerst ( 1 995) and Gertler ( 1 995), as well as from the theoretical model of Bernanke and Gertler ( 1 989) discussed above. As we do in the model presented in this chapter, Carlstrom and Fuerst ( 1 997) study the optimal lending contract between financial intermediaries and entrepreneurs when verifying the return to entrepreneurs' projects is costly for the lender. They then embed the resulting representation of credit markets in an otherwise conventional real business cycle model. They find that the endogenous evolution of net worth plays an important role in the simulated dynamic responses of the model to various types of shock.

32 Suarez and Sussman ( 1 997) present a dynamic model in which asset price declines, induced by "fire

sales" by bankrupt firms, contribute to cyclical fluctuations. In the model we presented earlier, entrepreneurs do not obtain insurance against aggregate shocks because their indirect utility functions are linear in wealth (dne to the assumptions of risk neutrality and constant returns to scale), while households are risk-averse. Krishnamurthy ( 1 997) points out that in more general settings entrepreneurs are likely to want to obtain this kind of insurance, which raises the question of why the posited credit-market effects should be empirically relevant. Krishnamurthy's answer is that the ability of lenders or other insurers to insure against large aggregate shocks depends in turn on the insurers' own net worth, which may be reduced during a severe recession. He goes on to develop a model with implications similar to that of Kiyotaki and Moore ( 1 997), except that it is the net worth of lenders or insurers, rather than that of borrowers, that plays the crucial role. See Kiyotaki and Moore ( 1 998) for a related argument. 34 Another potentially interesting channel, emphasized by Kiyotaki and Moore (1998), involves the interdependency that arises from credit chains, where firms are simultaneously lending and borrowing. These authors show that small shocks can induce a kind of domino effect, due to the chain, that leads to big effects on the economy.

33

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1 379

An interesting finding of their research is that the model with credit-market frictions generates a hump-shaped output response, consistent with most empirical findings. Our model presented above has many features in common with that of Carlstrom and Fuerst ( 1 997). Putting aside some technical details, there are however two major differences between the two models. First, we consider a sticky-price setting in the Dynamic New Keynesian tradition, while Carlstrom and Fuerst restrict themselves to a model with flexible prices. Thus we are able to examine the interaction of credit-market frictions with shocks to monetary policy, or to other nominal variables. The second difference is more subtle but is also important: Carlstrom and Fuerst assume that the agency problem applies only to producers of investment goods, who produce capital directly from the output good. The output good is produced, using both capital and labor, by separate firms who do not face agency problems in external finance. As a result of these assumptions, in the Carlstrom-Fuerst model, changes in net worth affect the economy primarily by affecting the supply price of capital (when net worth is low, less capital is produced at any given price). In our model, in contrast, the agency problem applies to producers of final output, who own the economy's durable capital stock. Since borrowers own the economy's capital stock, changes in the price of capital directly affect their net worth; that is, our model more directly incorporates the asset price effects stressed by Kiyotaki and Moore ( 1 997). As a result, we find that credit­ market frictions amplify shocks to the economy to a greater degree than do Carlstrom and Fuerst. On the other hand, a clear virtue of Carlstrom-Fuerst model is that the credit-mechanism helps able to explain the real world auto-correlation properties of output.

7. Directions for future work

In subsequent research we hope to consider several extensions to the work so far: First, as noted above, we have not addressed the role of banks in cyclical fluctuations, despite considerable attention to banking in the previous theoretical and empirical literatures. There are several ways to incorporate a nontrivial role for banks into our framework; one possibility is to allow the financial intermediaries which lend to entrepreneurs to face financial frictions in raising funds themselves. In this case, the net worth of the banking sector, as well as the net worth of entrepreneurs, will matter for the models' dynamics. Second, an important institutional fact is that debt contracts in low-inflation countries are almost always set in nominal terms, rather than in real terms as in this chapter. It would be relatively easy to incorporate nominal contracting into this model, in order to evaluate whether the redistributions among debtors and creditors associated with unanticipated changes in the price level are of quantitative significance. Doing so would enable us to critically assess recent arguments that deflation may pose a serious threat to the US economy.

B.S. Bernanke et al.

1 3 80

Third, we have restricted the analysis to a closed economy. It would be interesting to extend the analysis to the open economy. By doing so it would be possible to analyze how a currency crisis may induce financial distress that is transmitted to the real sector 35. As we discussed in Section 5 , to the extent an exchange rate collapse redistributes wealth from domestic borrowers to domestic lenders (owing to the fact that loans are denominated in units of foreign currency), the model of our chapter predicts a contraction in real activity. Finally, in this chapter we have restricted the credit-market frictions to the investment sector. It would be interesting to study how the results might be affected if these frictions affect other components of spending, such as consumption, inventory investment, and housing.

Appendix A. The optimal financial contract and the demand for capital

In this appendix we provide a detailed analysis of the partial equilibrium costly-state­ verification problem discussed in Section 3 . We start with the case of no aggregate risk and show that under the assumptions made in the text, the optimal contract provides a monotonically increasing relationship between the capital/wealth ratio and the premium on external funds: QKIN 1jJ(RKIR) with 1jJ1 ( ) > 0. We also establish that the default probability ill is a strictly increasing function of the premium RKIR, implying that the optimal contract guarantees an interior solution and therefore does not involve quantity rationing of credit. This appendix also provides functional forms for the contract structure. In particular, for the case of the log-normal distribution we provide exact analytical expressions for the payoff functions to the lender and entrepreneur. In the final section of this appendix we extend the analysis to the case of aggregate risk and show that the previously established results continue to hold. =

-

A. I. The partial equilibrium contracting problem Let profits per unit of capital equal wR", where w E [0, oo) is an idiosyncratic shock with E(w) 1 . We assume F(x) = Pr [ w < x] is a continuous probability distribution with F(O) 0. We denote by f( w) the pdf of w. Given an initial level of net worth N , and a price of capital Q, the entrepreneur borrows QK N , to invest K units of capital in the project. The total return on capital is thus wRk QK. We assume w is unknown to both the entrepreneur and the lender prior to the investment decision. After the investment decision is made, the lender can only observe w by paying the monitoring cost {lWR" QK, where 0 < {l < 1 . Let the required return on lending equal R, with R < RK. =

=

-

35 See Mishkin ( 1 997) for a discussion of how the financial accelerator mechanism may be useful for

understanding the recent currency crises in Mexico and Southeast Asia.

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The optimal contract specifies a cutoff value w such that if w � w, the borrower pays the lender the fixed amount wRK QK and keeps the equity ( w - w)RK QK. Alternatively, if w < w, the borrower receives nothing, while the lender monitors the borrower and receives ( 1 - 11)wRK QK in residual claims net of monitoring costs. In equilibrium, the lender earns an expected return equal to the safe rate R implying

[w Pr(w � w) + ( 1 - fi)E(wl w

<

w) Pr (w < w)]RKQK

=

R(QK - N).

Given constant returns to scale, the cutoff w determines the division of expected gross proftts RK QK between borrower and lender. We define T(w) as the expected gross share of profits going to the lender:

T(W)

= law wf(w) dw + w �w=f(w) dw,

and note that

r' (w) = 1 - F(w),

r" (w) = -f(w),

implying that the gross payment to the lender is strictly concave in the cutoff value

w. We similarly define fiG(w) as the expected monitoring costs: fiG (w) = /1 and note that

flG' (w)

=

l(i) wf(w) dw 0

,

f1Wf(w).

The net share of profits going to the lender is T(w) - f.l G ( w ), and the share going to the entrepreneur is 1 - T(w), where by definition T(W) satisfies 0 < T(W) < 1 . The assumptions made above imply:

T(w) - fiG(w) > 0 for w E (0, oo) and lim

w ---> 0

T(w) - fiG(w) = o,

_lim

(1) ··----+ 00

T(w) - fiG(w) =

1

-

fi.

We therefore assume that R"(I - /1) < R, otherwise the firm could obtain unbounded profits under monitoring that occurs with probability one 36. 36 The bound on F(w) can be easily seen from the fact that both F(w) - E(wlw

< lii) Pr(w < ril) 1 w Pr( w ;;:, w) and 1 - F (w) (E( w!w ;;:, w) - w) Pr( w ;;:, w) are positive. The limits on r(w) - p.G(Cii) can be seen by recognizing that G(w) = E(wl w < w) Pr(w < w) so that limw� oc G(w) = E(w) = l . =

B.S. Bernanke et a!.

1 382

37.

Let h(w) ::::: (f(w)/(1 - F(w)), the hazard rate. We assume that wh(w) is increasing in w There are two immediate implications from this assumption regarding the shape * of the net payoff to the lender. First, differentiating T(w) - f.1 G(w), there exists an w such that

r' (w) -- f.l G' (w) = (1 - F(w)) o - f.1wh (w)) �

o

for

-* w> < w ,

implying that the net payoff to the lender reaches a global maximum at w* . The second implication of this assumption is that

r'(w)G" (w) - T" (w)G' (w) =

d(wh(w)) dw

( l -F(w)f > 0 for all

W.

These two implications are used to guarantee a non-rationing outcome. The optimal contracting problem with non-stochastic monitoring may now be written as

max(l - T(w))R" QK K, W

subject to

[T(w) - f.lG(w)] R" QK = R(QK - N).

It is easiest to analyse this problem by first explicitly defining the premium on external funds s = R"IR and then, owing to constant returns to scale, normalizing by wealth and using k = QKIN the capital/wealth ratio as the choice variable Defining A as the Lagrange multiplier on the constraint that lenders earn their required rate of return

38.

37

Any monotonically increasing transformation of the normal distribution satisfies this condition. To see this, define the inverse transformation z z(w), z' (w) > 0, with z - N(O, I). The hazard rate for the standard normal satisfies h(z) = ifl(z)/(1 -
wh(w)

_

wifl(z(w)) ( I -
Differentiating wh(w) we obtain

d(wh(w)J dw

-

,

= h(z(w)) + wh (z(w)) z (w) > o,

,

where the inequality follows from the fact that the hazard rate for the standard normal is positive and strictly increasing. 3x It is worth noting that the basic contract structure as well as the non-rationing outcome extends in a straightf01ward manner to the case of non-constant returns to capital, as long as monitoring costs remain proportional to capital retums.

The Financial Accelerator in a Quantitative Business Cycle Framework

Ch. 21.

1 383

in expectation, the first-order conditions for an interior solution to this problem may be written: w : T' (W) - A[T ' (W) - flG' (W)] = 0,

k : [ ( 1 - T(W)) + A(T(W) - flG(W))] s - A = 0, A : [T(w) - flG(w)] sk - (k - 1 ) = o. Since T(W) - flG(w) is increasing on (0, w*) and decreasing on (w*, oo) the lender would never choose w > w* . We first consider the case 0 < w < w* which implies an interior solution 39. As we will show below, a sufficient condition to guarantee an

,

interior solution is

1 - s* · T( w*) - fiG( w*) We will argue below that s ) s* s<

=

cannot be an equilibrium. Assuming an interior solution, the F.O.C. with respect to the cutoff w implies we can write the Lagrange multiplier A as a function of w:

= T'(W)r'(w) - flG' (w)

A(w) -

Taking derivatives we obtain _

A1(w)

=

!l

-

[r'(w)G"(w) - r"(w)G'(W'J] [T'(W) - flG'(W)]2

>

0

for W E (0, w*),

where the inequality follows directly from the assumption that Taking limits we obtain lim A(w) = W---+ 0

1,

lim

W ---+ W*

wh(w)

is increasing.

A(W) = +oo.

Now define

A(Ci5) ( 1 - T(w) + A(T(w) - flG(w)) ; then the F.O.C. imply that the cutoff w satisfies (A. l ) s = p(w) so that p(w) i s the wedge between the expected rate of return on capital and the safe _

p(w)

=

(

return demanded by lenders. Again, computing derivatives we obtain

p, (W) = p(W)

1 - r(w) A' (w) A(w) 1 - T(w) + A(T(w) - flG(w)

and taking limits: lim

p(w) =

1,

lim

"'*

) 1 1 :;:--, p(w) = s* < -(T( w*) - fiG(w*)) -

-

>0

=

for

__

____

w E (O, w* ) ,

1 ,u Thus, for s < s*, these conditions guarantee a one-to-one mapping between the optimal cutoff w and the premium on external funds s. By inverting Equation (A. l ) we may w --> 0

39

Obviously,

w=0

w

_,

cannot be a solution if s > l .

B.S. Bernanke et a!.

1 384

express this relationship as 05 = w(s), where w'(s) > 0 for s E ( l , s*) . Equation (A. l ) thus establishes the monotonically increasing relationship between default probabilities and the premium on external funds. Now define

lJf(w) = l +

A(F(w) �J,G(W)� . 1 F(W) �

�

Then, given a cutoff 05 E (0, w*) the F.O.C. imply a unique capital/wealth (and hence leverage) ratio:

k = lJf(W).

(A.2)

Computing derivatives we obtain

I.JI'(w)

=

A' C) r ) ( lJf(w) 1 ) + 1 ' C lJf(w) A(� r7w) �

�

>

o

for w E (0, w* ),

and taking limits: Jim I.JI(W) = 1 , w�o

_ lilll_ lJf(w) = +oo. OJ --+

w*

Combining Equation (A. l ) with Equation (A.2) we may express the capital/wealth ratio as an increasing function of the premium on external funds:

k = 1/J(s),

(A.3)

with

1/J' (s)

>

0 for s E ( l , s*).

Since limrv -+ u! * I.JI (w) = +oo and limu; -+ rv * p(w) = s*, as s approaches s* from below, the capital stock becomes unbounded. In equilibrium this will lower the excess return s. Now consider the possibility that the lender sets w = oi*. The lender would only do so if the excess return s is greater than s* . In this case, the lender receives an expected excess return equal to

(r(w*) �J,G(w* )) sk · k

=

s s* �--k > 0. s* · ·

Since the expected excess return is strictly positive for all k, the lender is willing to lend out an arbitrary large amount, and both the borrower and lender can obtain unbounded profits. Again, such actions would drive down the rate of return on capital

Ch. 21:

The Financial Accelerator in a Quantitative Business Cycle Framework

in equilibrium, ensuring s w E co, w*) .

<

1 385

s* and guaranteeing an interior solution for the cutoff

A.2. The log-normal distribution In this section, we provide analytical expressions for F(W) and F(W) - {lG(w), for the case where w is distributed log-normally40. Under the assumption that ln(w) N(- � a2, a2) we have E(w) = 1 and �

where cPO is the c.d.f. of the standard normal and z is related to w through = (ln(w) + 0. 5a2)/a. Using the fact that 1 - F(w) (E(w l w � w) - w) Pr(w � w), we obtain z

=

F(w)

=

cP(z - a ) + w [ l

-·

z

cP( ) ]

and F(w) - fl G(w)

=

(l - {l)cP(z -- a) + w[l -
A.3. Aggregate risk To accommodate the possibility . of aggregate risk, we modify the contracting framework in the following manner. Let profits per unit of capital expenditures now equal uwR" where w represents the idiosyncratic shock, u represents an aggregate shock to the profit rate, and E(w) = E(u) 1 . Since entrepreneurs are risk neutral, we assume that they bear all the aggregate risk associated with the contract. Again, letting k s = � the ex ante premium on external funds, and k = QKJN, capital per dollar of self-financing, the optimal contracting problem may be now be written: =

m� E{( l - F(W)) usk + A [(T(w) k, w

{tG(w)) usk - (k

- 1 )] } ,

where A is the ex post value (after the realization of the aggregate shock u) of the Lagrange multiplier on the constraint that lenders earn their required return and E { } refers to expectations taken over the distribution of the aggregate shock u. We wish to establish that with the addition of aggregate risk, the capital/wealth ratio k is a still an increasing function of the ex ante premium on external funds. Define 40

Since the log-normal rs a monotonic transformation of the normal, it satisfies the condition

d(wh(711))/dw > o.

1 386

B.S. Bernanke et al.

Y(w)

= I - r(w) + Jc(F(w) - p,G(w)). The first-order conditions for the contracting

problem may be written as

w : r' (w) - Jc [r '(w) -- p,G' (w)] k : E {Y(w) us - Jc(W)}

= 0,

A : (F(W) - p,G(W)) us -

(k- l)

=

o,

=

0.

Again, under no rationing, the first-order condition with respect to w defines the function Jc(W). This function is identical to Jc(W) defined in the case of no aggregate risk. The constraint that lenders earn their required rate of return defines an implicit function for the cutoff w = w(u, s, k) 4 1 . Computing derivatives we obtain ( r (W) -· - p, G(W) )=::-'--_,_=-==': (r'(W) - p,G'(w)) s

aw

"CC: -c:':-

as

0

<

and ow

-

ak

=

1 (r'(w) - p,G'(w)) (us)

> 0·

To obtain a relationship of the form = 1/J(s), 1/J' (s) > 0 we totally differentiate the first-order condition with respect to capital:

k

{

E uf'(w) ds + usY' (ill)

Rearranging gives

dk

{ {

(a-a; a-a; )

E (usY'(W) -- Jc'(w))

ds

_

ds +

ow

---

as

_

E (A'(w) - usY' (W))

dk

+ u l{w)

a} w

}

- Jc' (ill)

(a-a; a; ) } ds +

c-

dk

=

0.

ak

Using the fact that Y ' (w)

=

Jc' (w) (r(w) - p,G(w))

4 1 As a technical matter, it is possible that the innovation in aggregate returns is sufficiently low that w(p,, s, k) > w* , in which case the lender would set w = w* and effectively absorb some of the aggregate risk. We rule out this possibility by assumption. An alternative interpretation is that we solve a contracting problem that is approximately co!Tect and note that in our parametrized model aggregate shocks would have to be implausibly large before such distortions to the contract could be considered numerically relevant.

Ch. 21:

The Financial Accelerator in a Quantitative Business Cycle Framework

1 3 87

we obtain

A. '(w) - Y'(w) us = A.'(w) [ 1 - ( T(w) - p,G(w)) us] = A-'(w)k- 1 , implying that dk/ds simplifies to the expression dk ds

E

{ usY(w) - A.'(w) �} { '( ) �;} E A w

Since awl as < 0, awlok > 0, and A' (w) > 0, the numerator and denominator of this expression are positive, thus establishing the positive relationship between the capital/wealth ratio k and the premium on external funds s. Appendix B. Household, retail and government sectors

We now describe the details of the household, retail, and government sectors that, along with details of the entrepreneurial sector presented in Section 4, underlie the log-linearized macroeconomic framework. B. l.

Households

Our household sector is reasonably conventional. There is a continuum of households of length unity. Each household works, consumes, holds money, and invests its savings in a financial intermediary that pays the riskless rate of return. C1 is household consumption, M/P1 is real money balances acquired at t and carried into t + 1 , H, is household labor supply, � is the real wage for household labor, T1 is lump sum taxes, D1 is deposits held at intermediaries (in real terms), and fit is dividends received from ownership of retail firms. The household's objective is given by

(8 . 1 ) The individual household budget constraint is given by

Ct = Wt H, - T, + llr + RrDr - Dt+ 1 +

(Mt-1 - M1) . P,

(8 .2)

The household chooses C" D1+ 1 , H1 and M/P, to maximize Equation (8 . 1 ) subject to Equation (B.2). Solving the household's problem yields standard first-order conditions for consumption/saving, labor supply, and money holdings: (8 .3)

B.S. Bernanke et al.

1 388

= 1 ' Ct ( R�+� - ) - ' = Pt R 1

Wt C1

s1

1

(B.4)

H1 '

M,

t+l

1

(B.5)

where R7+ 1 is the gross nominal interest, i.e., . zt+1

_ =

Pn1 Rt+l -Pt n

-

1.

Note that the first-order condition for M/P1 implies that the demand for real money balances is positively related to consumption and inversely related to the net nominal interest rate. Finally, note that in equilibrium, household deposits at intermediaries equal total loanable funds supplied to entrepreneurs: Dt = B t . B.2.

The retail sector and price setting

As is standard in the literature, to motivate sticky prices we modify the model to allow for monopolistic competition and (implicit) costs of adjusting nominal prices. As is discussed in the text, we assume that the monopolistic competition occurs at the "retail" level. Let Y1(z) be the quantity of output sold by retailer z , measured in units of wholesale goods, and let P1(z) be the nominal price. Total final usable goods, Y{, are the following composite of individual retail goods:

Y{

= [1

1

l

Yt(z)lE- 1 )/E dz

EI(E- 1 )

(B.6)

with E > 1 . The corresponding price index is given by

P1

=

[1

I

P1(z)< 1

]

c) dz

I /( 1 E)

(B.7)

Final output may then be either transformed into a single type of consumption good, invested, consumed by the govemment or used up in monitoring costs. In particular, the economy-wide resource constraint is given by

(B. S ) where q is entrepreneurial consumption and gate monitoring costs.

fl .f;"' w dF(w) R7Q1 1 K1 reflects aggre­

The Financial Accelerator in a Quantitative Business Cycle Framework

Ch. 21:

1 3 89

Given the index (B.6) that aggregates individual retail goods into final goods, the demand curve facing each retailer is given by

Y1 (z) =

( p��) y-c Y{.

(B.9)

The retailer then chooses the sale price P1(z), taking as given the demand curve and the price of wholesale goods, P;'. To introduce price inertia, we assume that the retailer is free to change its price in a given period only with probability 1 - 8, following Calvo ( 1 983). Let P;' denote the price set by retailers who are able to change prices at t, and let �*(z) denote the demand given this price. Retailer z chooses his p1ice to maximize expected discounted profits, given by

[

oc

L ekEl- I

At,k

k-0

-

]

p * pw l t+k * (z) pt+k yt+k

(B. l O)

'

where the discount rate A1 ,k = f3C/(Ct+k ) is the household (i.e., shareholder) intertemporal marginal rate of substitution, which the retailer takes as given, and where P;' = P/Xr is the nominal price of wholesale goods. Differentiating the objective with respect to Pt' implies that the optimally set price satisfies CXJ

L ekEt- 1

k-0

{ ( )-c Pt* Al,k Pt+k

[- - (--=-) E ]}

p1* �+* k (z) Pt+k

E

pw t+ k 1 Pl+k

-

=

0.

(B. l l )

Roughly speaking, the retailer sets his price so that in expectation discounted marginal revenue equals discounted marginal cost, given the constraint that the nominal price is fixed in period k with probability e". Given that the fraction 8 of retailers do not change their price in period t, the aggregate price evolves according to (B. l 2) where P1* satisfies Equation (B. l l). By combining Equations (B. l l) and (B. l 2), and then log-linearizing, it is possible to obtain the Phillips curve in the text, Equation (4.22). B.3.

Government sector

We now close the model by specifying the government budget constraint. We assume that government expenditures are financed by lump-sum taxes and money creation as follows:

Gt =

Mt - Mt- 1

PI

+ TI ·

The government adjusts the mix of financing between money creation and lump-sum taxes to support the interest rate rule given by Equation (4.25).

1 390

B.S. Bernanke et al.

This, in conjunction with the characterization in Section 5 of the entrepreneurial sector and the monetary policy rule and shock processes, completes the description of the model.

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The Financial Accelerator in a Quantitative Business Cycle Framework

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Chari, VV, P.J. Kehoe and E.R. McGrattan ( 1 996), "Sticky price models of the business cycle: can the contract multiplier solve the persistence problem?", Staff Report 2 1 7 (Federal Reserve Bank of Miuneapolis). Chirinko, R.S. ( 1 993), "Business fixed investment spending: a critical survey of modelling strategies, empirical results, and policy implications", Journal of Economic Literature 3 1 : 1 875-1 9 1 1 . Christiano, L.J., and R. Todd ( 1996), "Time to plan and aggregate fluctuations", Federal Reserve Bank of Minneapolis Quarterly Review, Winter, 1 4-27. Christiano, L.J., M. Eichenbaum and C.L. Evans ( 1 996), "The effects of monetary policy shocks: evidence from the flow of funds", Review of Economics and Statistics 78: 1 6-34. Clarida, R., J. Gali and M. Gertler ( 1 997), "Monetary policy rules and macreconomic stability: evidence and some theory", unpublished paper (New York University, March). Cooley, T.F., and V. Quadrini ( 1 997), "Monetary policy and the financial decisions of firms", unpublished paper ( University of Rochester, December). Cummins, J.G., K.A. Hassett and R.G. Hubbard ( 1 994), "A reconsideration of investment behavior using tax refonns as natural experiments", Brookings Papers on Economic Activity 1 994(2) : 1 -74. Deaton, A. ( 1 99 1 ), "Saving and liquidity constraints", Econometrica 59: 1 2 2 1 - 1 248. Eberly, J.C. ( 1 994), "Adjustment of consumers' durable stocks: evidence from automobile purchases", Journal of Political Economy 1 02:403-436. Eckstein, 0., and A. Sinai ( 1 986), "The mechanisms of the business cycle in the postwar era", in: R.J. Gordon, ed., The American Business Cycle: Continuity and Change (University of Chicago Press for NBER, Chicago, IL). Engelhardt, G. ( 1996), "Consumption, down payments, and liquidity constraints", Journal of Money, Credit and Banking 28:255-76 1 . Fazzari, S.M., R.G. Hubbard and B.C. Petersen ( 1988), "Financing constraints and corporate investment", Brookings Papers on Economic Activity 1 988( 1 ) : 1 4 1-195. Fisher, I. ( 1 933), "The debt-deflation theory of great depressions", Econometrica 1 :337-357. Fisher, J.D.M. ( 1 996), "Credit market imperfections and the heterogeneous response of firms to monetary shocks", Working Paper WP-96-23 (Federal Reserve Bank of Chicago, December). Fuerst, T. ( 1 995), "Money and financial interactions in the business cycle", Journal of Money, Credit and Banking 27: 1321-1338. Gale, D., and M. Hellwig ( 1 985), "Incentive-compatible debt contracts: the one-period problem", Review of Economic Studies 52:647-664. Gcrsbach, H. ( 1997), "Financial intermediation, capital spillovers, and business fluctuations", unpublished paper (Alfred-Weber-Institut, University of Heidelberg, November). Gertler, M. ( 1 988), "Financial structure and aggregate economic activity: an overview", Journal of Money, Credit and Banking 20(3):559-588. Gertler, M. (1 992), "Financial capacity and output fluctuations in an economy with multiperiod financial relationships", Review of Economic Studies 59:455-472. Gertler, M. ( 1 995), "Comment on 'Money and financial interactions in the business cycle"', Journal of Money, Credit and Banking 27: 1 342--1 3 5 3 . Gertler, M . , and S. Gilchrist ( 1993), "The role o f credit market imperfections i n the monetary transmission mechanism: arguments and evidence", Scandinavian Journal of Economics 95:43-64. Gertler, M., and S. Gilchrist ( 1994), "Monetary policy, business cycles, and the behavior of small manufacturing firms", Quarterly Journal of Economics 59:309-340. Gertler, M., and R.G. Hubbard ( 1988), "Financial factors in business fluctuations", in: Financial Market Volatility (Federal Reserve Bank of Kansas City) 33-72. Gilchrist, S., and C.P. Himmelberg ( 1995), "Evidence on the role of cash flow for investment", Journal of Monetary Economics 36:541-572. Goodfiiend, M., and R.G. King ( 1 997), "The new neoclassical synthesis", NBER Macroeconomics Annual, 23 1-282. Gourinchas, P.-O., and J. Parker (1 995), "Consumption over the lifecycle", mimeograph (MIT).

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Rotemberg, J.J., and M. Woodford ( 1997), "An optimization-based econometric framework for the evaluation of monetary policy", NBER Macroeconomics Annual, 297-345. Sharpe, S. ( 1994), "Financial market imperfections, firm leverage, and the cyclicality of employment", American Economic Review 84: 1 060-1074. Suarez, J., and 0. Sussman ( 1 997), "A stylized model of financially-driven business cycles", unpublished paper (CEMFI and Ben-Gurion University, September). Taylor, J.B. ( 1993), "Discretion versus rules in practice", Carnegie-Rochester Conference Series on Public Policy 39: 1 95-21 4 . Townsend, R.M. ( 1979), "Optimal contracts and competitive markets with costly state verification", Journal of Economic Theory 2 1 :265-293 . Townsend, R.M. ( 1995), "Financial systems in northern Thai villages", Quarterly Journal of Economics

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Chapter 22

POLITICAL ECONOMICS AND MACROECONOMIC POLICY* TORSTEN PERSSON

Institute for International Economic Studies, Stockholm University, S-1 06 91 Stockholm, Sweden. E-mail: [email protected]. GUIDO TABELLINI

IGIER, Bocconi University, via Salasco 3/5, 20136 Milano, Italy. E-mail: guido. tabellini@uni-bocconi. it Contents

Abstract Keywords 1 . Introduction Part A. Monetary Policy

2. Credibility of monetary policy 2. 1 . A simple positive model of monetary policy 2.2. Ex ante optimal monetary policy 2.3. Discretion and credibility 2.4. Reputation 2.5. Notes on the literature

3 . Political cycles 3 . 1 . Opportunistic governments 3 . 1 . 1 . Moral hazard in monetary policy 3 . 1 .2. The equilibrium

3 . 1 .3. Adverse selection 3.2. Partisan governments 3.2. 1 . The model 3 .2.2. Economic equilibrium 3.2.3. Political equilibrium 3.3. Notes on the literature

1 399 1 399 1 400 1 404 1 405 1405 1 407 1 409 1412 1415 1416 1416 1417 1418 1 420 1 422 1 422 1 423 1 423 1 425

* We are grateful to participants in the Handbook conference at the Federal Reserve Bank of New York, to our discussant Adam Posen and to Roe! Bcctsma, Jon Faust, Francesco Lippi, Ken Rogoff; Lars Svensson and Jolm Taylor for helpful comments. The research was supported by Harvard University, by a grant from the Bank of Sweden Tercentenary Foundation and by a TMR Grant from the Europcm1 Commission. We are grateful to Christina Lonnblad and Alessandra Startari for editorial assistance.

Handbook (){Macroeconomics, Volume 1, Edited by JB. Taylor and M. WooqfiJrd © 1999 Elsevier Science B. V All rights reserved 1 397

T. Persson and G. Tabellini

1 398

4. Institutions and incentives 4. 1 . Fixed exchange rates: simple rules and escape clauses 4.2. Central bank independence 4.3. Inflation targets and inflation contracts 4.4. Notes on the literature Part B. Fiscal Policy

5. Credibility of fiscal policy 5. 1 . The capital levy problem 5 . 1 . 1 . The model 5 . 1 .2. The ex ante optimal policy 5 . 1 .3 . Equilibrium under discretion 5 . 1 .4. Extensions 5.2. Multiple equilibria and confidence crises 5.3. Public debt management 5.4. Reputation and enforcement 5.5. Notes on the literature

6. Politics of public debt

6. I . Political instability in a two-party system 6. 1 . 1 . Economic equilibrium 6 . 1 .2. The political system 6. 1 .3 . Equilibriun1 policy 6. 1 .4. Endogenous election outcomes 6. 1 .5. Discussion 6.2. Coalition governments 6.2. 1 . Equilibrium debt issue 6.2.2. A stronger budget process

6.3. Delayed stabilizations 6.4. Debt and intergenerational politics 6.5. Notes on the literature Part C. Politics and Growth

7. Fiscal policy and growth 7. 1 . Inequality and growth 7.2. Political instability and growth 7.3. Property rights and growth 7.4. Notes on the literature

References

1 426 1 427 1 429 1 432 1437 1439 1 440 1 440 1 440 1441 1 442 1 444 1 445 1 446 1 448 1 449 1450 1 45 1 1 45 1 1452 1 452 1 454 1456 1 45 7 1458 1 460 1 46 1 1 463 1 464 1 466 1 466 1 467 1 469 1 472 1 472 1 473

Ch. 22:

Political Economics and Macroeconomic Policy

1 399

Abstract

This chapter surveys the recent literature on the theory of macroeconomic policy. We study the effect of various incentive constraints on the policy making process, such as lack of credibility, political opportunism, political ideology, and divided government. The survey is organized in three parts. Part I deals with monetary policy in a simple Phillips curve model: it covers credibility issues, political business cycles, and optimal design of monetary institutions. Part II deals with fiscal policy in a dynamic general equilibrium set up: the main topics here are credibility of tax policy, and political determinants of budget deficits. Part III studies economic growth in models with endogenous fiscal policy.

Keywords

politics, monetary policy, fiscal policy, credibility, budget deficits

JEL classification: E5, E6, H2, H3, 01

1 400

T. Persson and G. Tabellini

1 . Introduction

Traditional macroeconomic policy analysis asks the posttlve question of how the economy responds to alternative, but exogenous, policy actions or rules. Knowing these responses, the analyst can go on to the normative problem of policy advice. The best action or rule is selected, given a specific objective function. But as macroeconomists, we should also be able to shed light on a more ambitious set of questions. Why is it that we observe such different inflation rates across countries and time? Why did we not observe peace-time accumulations of government debt until the seventies, and why did they arise only in some countries? Why are growth rates so different in different parts of the world? To answer such questions, we need a positive theory, explaining why different countries choose different macroeconomic policies. Early steps towards such a theory were taken about twenty years ago; the credibility problem in macroeconomic policy was introduced by Kydland and Prescott ( 1 977) and Calvo ( 1 978), and the first models of electoral and partisan motivations in policymaking were suggested by Nordhaus ( 1 975) and Hibbs ( 1 977). The literature did not really take off until ten years later. But since then "political economy", or "political economics" as we prefer to call it, has been one of the most active fields in macroeconomics - as well as in other branches of economics 1 • With its emphasis on institutions as important determinants of policy, this literarure has taken the normative analysis one step further, replacing the question: Which policies should be followed? with the question: What policymaking instirutions produce better policy outcomes? In surveying this literatllre, we split the material into three parts: Part I deals with monetary policy, Part II with fiscal policy, and Part III with growth. Following the conventional approach in the literature, this division is based both on substance and on methodology. The monetary policy part relies on quadratic loss functions over macroeconomic outcomes and on models incorporating rational expectations, but assuming an ad hoc Phillips Curve. The fiscal policy and growth parts have better microfoundations: agents' preferences, technologies and endowments govern their economic and political interactions in simple, but complete, two-period general equilibrium models. Each part emphasizes the credibility and politics of policymaking, and includes a normative evaluation of different institutions. The general approach of this line of research is to explain deviations in observed economic policies from a hypothetical social optimum by appealing to specific incentive constraints in the decision problem of optimizing policymakers. The positive analysis focuses on identifying the relevant incentive constraints, while the normative analysis focuses on institutional reforms which may relax them. Despite the separation into three parts, several common themes run throughout the chapter, reflecting similar incentive constraints. It is useful to summarize already here the natllre of these incentive constraints, when they arise, and their positive and normative implications.

1

Many recent contributions have been collected in Persson and 'Iabellini ( 1 994a).

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Desirable policies may suffer from lack of credibility when policy decisions are taken sequentially over time (under "discretion") and the government lacks a non­ distorting policy instrument, so that the socially optimal policy (the optimal policy in the absence of the incentive constraint) yields a second-best outcome. Lack of credibility has several positive implications, and arises both in monetary and in fiscal policy. When the government takes private expectations embodied in private economic decisions as given, it neglects the policy effects running through expectation formation. This way, equilibrium average inflation or wealth taxes become too high. Moreover, in a Natural Rate world, monetary policy and inflation respond to all shocks, and not only to those over which the monetary authority has an information advantage, as the optimal policy should do. Losing control of private expectations also makes the government a prospective victim of confidence crises: runs on public debt, capital flight, or speculative attacks on the currency. All these events stem from the same fundamental problem: the government is forced to react to self-fulfilling private expectations. Finally, lack of credibility breaks a Modigliani-Miller theorem of government finance, in the same way as incentive constraints in the relationship between owners and managers break the Modigliani-Miller theorem of corporate finance. The composition of the outstanding public debt into nominal or real securities (i.e. indexed to the price level) affects the propensity of a government to rely on unexpected inflation as a source of government revenue. Similarly, the maturity composition of government debt affects the likelihood of debt runs or the interest rate policies that future governments want to pursue. Thus, public debt management can relax future incentive constraints and thereby affect private sector expectations. Lack of credibility also has implications for institution design. First, it makes delegation to an independent policymaker desirable. Second, it makes it desirable to restrict the tasks of the policymaker. Rather than pursuing loosely defined social welfare, the central bank should target a specific variable, such as inflation, or the money supply, or the exchange rate. If a sufficiently rich incentive mechanism -- a complete contract - can be designed and enforced, the credibility problem can be eliminated completely. If state-contingent payments are not feasible, however, or if narrowly defined tasks are inappropriate, as in fiscal policy, incentive mechanisms are necessarily incomplete. But in order to gain credibility, strategic delegation of the decision-making authority to a policymaker with "distorted" preferences may still be desirable. This insight has been exploited in monetary policy, to advocate the benefit of an independent and "conservative" central bank. It also applies to the election of a conservative policymaker facing the task of selecting a wealth tax, or to the delegation of certain policy choices to a foreign government, as in the case of multilateral exchange rate arrangements, or currency boards 2 . 2 International competition i s another institutional device for coping with credibility which is

emphasized in the literature but not in this survey. Tax competition, or exchange rate competition, contribute to overcoming a domestic credibility problem because they can reduce the ex-post incentives to unilaterally increase tax rates or inflation.

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T Persson and G. Tabellini

A second incentive constraint is political opportunism, by which we mean that the incumbent government is prepared to introduce distorted policies to increase its chances of re-election. This incentive constraint typically applies when politicians value holding office per se and voters, although rational, are uninformed. We study the consequences of political opportunism in monetary policy only, but the empirical implications for fiscal policy have been spelled out in the literature. The main prediction is an electoral cycle in aggregate demand policies: the incumbent government has an incentive to stimulate the economy just before elections to appear more competent in the eyes of uninfonned voters, thus boosting of the probability of re-election. This always leads to an electoral cycle in inflation which, depending on the information advantage of the government, could also increase output volatility at the time of elections. The nonnative implications tend to reinforce those of the credibility literature: central bank independence and monetary or inflation targets reduce the scope for electoral cycles in monetary policy. Other, deeper reforms, such as who should have the right to call the elections and at what time, remain to be investigated. Political ideology may shape policy formation if different parties pursue different "partisan" (i.e. ideological) platforms once in office, and if the election outcome is uncertain. Political polarization and political instability thus induce another incentive constraint, which also gives rise to an electoral cycle in aggregate demand, output or public spending. But here the cycle takes place after, rather than before, elections and reflects the winning party's desire to influence economic outcomes. In a dynamic context, this incentive constraint may generate "strategic myopia". The government in office realizes that it may be replaced by a policymaker with different ideological preferences. This gives an incentive to accumulate public debt or postpone investment, so as to influence the future behavior of the opponent. Political ideology also implies strategic manipulation of state variables to influence the voters; for instance, an extremist incumbent may restrain his own future behavior by appropriate institutional reforms to increase his own electability. The strategic manipulation of future opponents and voters are both stronger, the more unstable and polarized the political system. From a normative point of view, the benefits of delegation and targeting in monetary policy are further reinforced. More generally, there may be advantages of institutional checks and balances and institutions that moderate political conflict and policy extremism. The discussion, so far, applies to a single decision-maker facing static or dynamic incentive constraints. Often, however, decision-making power is dispersed among several political actors. This creates another incentive constraint, which we may call divided government. Examples include coalition governments, soft budget constraints on public enterprises or local governments, veto rights held by key individuals in government or by organized groups in society, or the lobbying activities of special interests. Divided government arises almost exclusively in fiscal policy. In a static context its central implication is over-spending, as every decision-maker fully internalizes the benefits of public spending but only a fraction of the cost: this is the so called "common pool" problem. In a dynamic context, myopic behavior emerges: each decision-maker has an incentive not only to over-spend, but also to spend

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sooner rather than later. Leaving tax revenues for tomorrow can be counter-productive, because they are partly appropriated by other decision-makers. Hence, models of divided government also predict debt accumulation and/or under-investment. In some circumstances, the dispersion of veto rights delays stabilization in an unsustainable fiscal situation. The most straightforward institutional remedy is to centralize power in the hands of a single decision-maker (a prime minister, or a president, or the Secretary of the Treasury). Alternatively, one might rely on two-stage budgeting, with a decision on aggregate items (total spending, or total borrowing) preceding the decision on how spending is allocated. Such budgetary solutions entail a trade-off between an allocative distortion (a lopsided spending result from centralized decision-making power) and an aggregate distortion (over-spending resulting from inadequate centralization). At a deeper political level, the incentive constraints induced by divided government and political ideology can be traded off. Political reforms that centralize power in the hands of single parties or individuals also exacerbate polarization between the maj ority and the opposition, and may thus imply that political instability becomes a more binding incentive constraint. The last incentive constraint considered in this chapter arises when there is income heterogeneity, so that tax policies are motivated by pressure for redistribution. The positive implication is that the overall size of government is determined by the extent of inequality in pre-tax income or, in the case of social insurance policies, by inequality in risk. This, in turn, has implications for the link between inequality and measures of economic performance. But the redistributive motive is also an important force shaping the composition of spending or the structure of taxation. Public financial policies that redistribute along different dimensions become non-equivalent, because they are supported by different coalitions of voters. For instance, public debt and social security redistribute across generations in the same way; nevertheless in a political equilibrium they give rise to different allocations, because they redistribute between rich and poor in different ways. A similar non-equivalence result holds with regard to alternative instruments of geographic redistribution. As in the case of lacking credibility, an incentive constraint on policy formation breaks the Modigliani-Miller theorem of government finance. Some of the topics covered in this survey partly overlap with a companion survey, Persson and Tabellini ( 1 999). There we cover the literature on public economics and public choice, dealing with static allocation issues in fiscal policy, rather than the intertemporal policy issues emphasized here. Neither do we cover the literature on monetary and fiscal policy in an international context, which is surveyed in Persson and Tabellini ( 1 995). Each part starts with a separate introduction, in which we highlight a number of empirical regularities, motivating the sections to follow, and provide a more detailed road map. We comment on the original literature both as we go along and in separate "Notes on the Literature" at the end of each section.

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T Persson and G. Tabellini

Part A. Monetary Policy

The empirical evidence for the (democratic) OECD countries in the post-war period suggests the following stylized facts: (i) Inflation rates vary greatly across countries and time. But there is a common time pattern: in most countries inflation was low in the 1 960s, but very high in the 1 970s; it came down in the 1 980s and 1 990s in all countries, though at different speeds and to different extents 3 . (ii) Inflation rates are correlated with real variables, such as growth or unemployment, in the short run. But there is little evidence of a systematic correlation over longer periods. Across countries, average inflation and average growth tend to be negatively correlated or not correlated at al1 4 . (iii) There is little evidence of systematic spillover effects between monetary and fiscal policy. Specifically, higher budget deficits are not systematically associated with higher inflation rates 5. (iv) Inflation increases shortly after elections; budget deficits tend to be larger during election years; there is also some (not very strong) evidence that monetary policy is more expansionary before elections. On the other hand, real variables such as growth or unemployment are not systematically correlated with election dates. (v) Output displays a temporary partisan cycle just after elections: newly appointed left-wing governments are associated with expansions, right-wing governments with recessions. This cycle tends to occur in the first half of the inter-election period and is more pronounced in countries with two-party systems. Inflation displays a permanent partisan cycle: higher inflation is associated with left-wing governments 6. (vi) Average inflation rates and measures of central bank independence are negatively correlated; this holds up when controlling for other economic and institutional variables (even though the correlation is less robust). There is also some evidence that fixed exchange rates are associated with lower inflation. Real variables, on the other hand, have no systematic correlation with the monetary regime (although the variance of the real exchange rate is lower under fixed than floating exchange rates) 7. These stylized facts will be taken as the starting point for Part I. Fact (i) clearly calls for a positive model of inflation. Fact (ii) is not well understood and the profession 1

Sec, for instance, Bordo and Schwartz ( 1 999). Time-series evidence (for the USA) can be found in Stock and Watson (1 999), whereas (broad) cross-country evidence can be found in Barro ( 1 997) and in Fischer ( 1 99 1 ). 5 See for instance Grilli et a!. ( 1 99 1 ). This fact no longer applies if one considers the interwar period or developing countries. In particular hyperinflations are typically associated with fiscal problems. 6 Statements (iv) and (v) are suggested by the comprehensive study by Alesina and Roubini ( 1 997). 7 See Grilli et a!. ( 1 99 1), Cukiennan ( 1 992), Jonsson ( 1 995), Eijffinger and de Haan ( 1996), Mussa ( 1 986), Baxter and Stockman ( 1 989). The robustness of these findings has been questioned by Posen ( 1 993, 1 995), however.

4

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is still searching for a satisfactory model of the j oint determination of nominal and real variables. But it suggests that a plausible model would encompass the natural rate hypothesis that the Phillips curve is vertical and monetary policy is neutral in the long run, while preserving some scope for aggregate demand policies to affect output in the short run. Fact (iii) suggests that abstracting from fiscal policy may not be a bad first approximation. Facts (iv) and (v) indicate that political variables might be important ingredients in successful positive models of inflation and macroeconomic policy. Fact (vi) finally suggests that the institutional features of the monetary regime ­ particularly the statutes regulating the central bank - should also play a role in a successful model. In Section 2 we formulate and discuss a model of macroeconomic policy and inflation which has been the workhorse in much of the recent literature. We illustrate how credibility problems in monetary policy may arise and how these may be fully or partly resolved by reputation. Section 3 extends the simple model with political institutions and incentives. We illustrate how political business cycles and partisan cycles, consistent with the stylized facts above, may come about. Designing monetary institutions to tackle the distortions created by credibility problems and political cycles is the topic of Section 4.

2. Credibility of monetary policy

In this section, we first formulate and discuss a model of macroeconomic policy and inflation, in the spirit of Kydland and Prescott ( 1 977), Fischer ( 1 977) and Barro and Gordon (1983a), which has been the starting point for much of the recent literature. In subsection 2 . 1 we set up the model and make general comments. Subsection 2.2 derives a normative benchmark. In subsection 2.3 we emphasize how the credibility problems tied to the central banks' ability to temporarily boost the economy result in excessively high equilibrium inflation - the celebrated "inflation bias". Subsection 2.4 briefly illustrates how reputation may provide full or partial solutions to such credibility problems, drawing on the work by Barro and Gordon ( 1 983b ), Backus and Driffill (1 985), Canzoneri ( 1 985) and others that - in turn - borrow heavily from the literature on repeated games. 2. I. A

simple positive model of monetary policy

The demand side of our model economy is represented by Jr =

m + v + /1,

(2. 1 )

where :n: i s inflation, m i s the money growth rate, v is a demand (or velocity) shock, and 11 is a "control error" in monetary policy. Letting output enter the implicit money demand function underlying Equation (2. 1 ) complicates the algebra, but does not yield

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important additional insights. The supply side of the model assumes that nominal wage setting (unilaterally by firms, unilaterally by labor unions, or bilaterally by bargaining between these actors) aims at implementing an exogenous, but stochastic, real wage growth target w 8 . Letting nc denote rationally expected inflation, nominal wage growth w then becomes W=

W + JTe.

(2.2)

Employment (or output growth),

x,

satisfies

x = y - (w - n) - E, where y is a ( potentially stochastic) parameter, and E is a supply shock. Combining this relation with Equation (2.2), we obtain an expectations-augmented short-run Phillips curve X

=

{) + (JT - J!e )

-

E,

(2.3)

where 8 = y w can be interpreted as the stochastic natural rate of employment (output growth). We assume that all shocks are i.i.d., orthogonal to each other, have 2 (unconditionally) expected values of zero, well-defined variances a� , a, , and so on. The timing of events is as follows: (0) rules of the monetary regime may be laid down at an institution design stage; ( 1 ) the value of e is observed both by the private sector and the policymaker; (2) ne is fonned, given the infonnation about 8; (3) the values of v and E are observed; (4) the policymaker determines m; (5) fJ. is realized together with n and x. The assumed timing captures the following concerns: Some shocks, related to the labor market, are commonly observable and can therefore be embodied in private­ sector wage-setting decisions, here captured by expectations formation. Other shocks can only be embodied in policy. This distinction is best interpreted as reflecting the ease with which monetary policy decisions are made, relative to the laborious wage-setting process, but could also reflect a genuine information advantage of the policymaker (which is perhaps only plausible for financial sector shocks). Of course, it is this advantage that allows monetary policy to stabilize the economy. Finally, there is some unavoidable noise in the relation between policy and macroeconomic outcomes. -

x As is well-known, the "surprise supply" formulation we end up with below could also be derived from a model of price-setting finns, or from a Lucas-style "island model".

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Clearly, Equation (2. 1) and the assumed information implies that rationally expected inflation is JTc = E(n

I

8)

= E(m I

8),

(2.4)

where E is the expectations operator. Substituting Equations (2. 1 ) and (2.4) into (2.3), we have

x = fJ + m - E(m I

fJ) +V+fJ,-E.

(2 .5)

The model thus entails the usual neutrality result: only unanticipated aggregate demand policy affects real variables. But if policy responds to shocks, it can still stabilize employment. 2.2.

t.x

ante optimal monetary policy

We follow the rational expectations literature in thinking about policy as a rule. Suppose society has the quadratic loss function

E[L(n, x)] = �E[(n - n*)2 + A-(x - x* f ],

(2.6)

where n* and x* are society's most preferred values for inflation and employment, and A is the relative weight on fluctuations in these two variables. As the objective is quadratic in macroeconomic outcomes, which in tum are linear in the shocks, the optimal policy rule is of the form (2.7) that is, policy potentially responds to all shocks observable to the policymaker. Suppose furthermore that the policymaker can make a binding commitment to the rule (2. 7) at the institution design stage (0), i.e. before the observation of e. Clearly, since E( = E( = 0, this implies private sector expectations:

v) E)

(2.8) By Equations (2. 1 ), (2.5), (2.7) and (2.8), macroeconomic equilibrium under the rule lS

+k8 8+ (P + 1) v+eE+ + l)V+fJ,+ (kE -l)E.

n=

k

X=

fJ + (e

f.l,

(2.9) (2. 1 0)

What is the optimal rule? Substitute Equations (2.9) and (2. 1 0) into (2. 6), take expectations over all shocks, and set the derivatives of the resulting expression with regard to the intercept and the slope coeflicients in Equation (2.7) equal to zero. The following results emerge:

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Jt* and k iJ = 0. The optimal rule provides an "anchor for inflationary k expectations". Expectations are right where society wants them to be, namely at the preferred rate of inflation: E(Jt I 8) = Jt* . The optimal rule is thus neither conditional on the observable shock to the natural rate, 8, nor on society' s output target, x* . Such conditionality would be embodied in expectations; it would therefore do nothing to stabilize employment, only add costly noise to inflation. (ii) ku = - 1 . Demand (velocity) shocks are fully stabilized. As policy also operates via aggregate demand, a complete stabilization of demand shocks nullifies their effects on inflation as well as on employment. (iii) k" = A/( 1 + A). Supply shocks are stabilized according to the policymaker's trade­ off between inflation and employment fluctuations. The higher the weight on employment, the more these shocks are stabilized. The optimal state-contingent policy rule can thus be written as (i)

=

m = Jt *

-

V+

A E + A)

---

(1

.

Macroeconomic outcomes -- indexed by R

Jt R XR

=

A Jt * + l+ J: H· ,U ,

= 8-

1

--

l +A

E + ,U.

-·

when the rule is followed are (2. 1 1) (2. 1 2)

Results such as these have been - and continue to be - very influential for academic economists ' thinking about policy. They suggest that delivering low inflation and stable employment is essentially a technical (not a strategic) problem: inflation can be kept low by clearly announcing a rule aiming at low average inflation. Demand shocks should be completely stabilized. The inflation and employment consequences of supply shocks should be traded off according to society's preferences. Control errors are unavoidable, but can perhaps be reduced by better forecasting or operating procedures in monetary policy. Even though this picture is too rosy for a realistic positive model of macroeconomic policy, it still provides a useful normative benchmark that we can use to evaluate the outcome in the positive models below. In the remainder of the chapter, we simplify the stochastic structure by setting v = ,u = 0. Demand shocks, as we saw, present no problem for the policymaker in this class of models, provided that they can be identified in time and that there are no other policy goals such as interest-rate smoothing. Control errors do present problems, but are unavoidable 9 . With these simplifications, there is no meaningful 9 Abstracting from control errors is innocuous as long as the public can monitor monetary policy perfectly and as long as policymaker competency and efforts are exogenous. Below, we comment on where control errors would matter. Moreover, in a richer (dynamic) setting with expectations entering the aggregate demand function, demand shocks and control errors may give rise to incentive problems similar to those discussed below.

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distinction in the model between m and Jr. For simplicity, we therefore assume that the policymaker sets .1r directly. Why don't we eliminate the shocks to the natural rate (), with a similar motivation? The answer is that such shocks do not affect the solution under commitment, whereas they do affect policy in an interesting way under alternative assumptions about the policymaking process. 2.3.

Discretion and credibility

In reality, decisions on monetary policy are taken sequentially over time, rather than once and for all. Assuming ex ante commitment to a state-contingent policy rule rhymes badly with this practice. In our static model, reality is better captured by an alternative timing: policy is chosen under "discretion" when the policy instruments are set at stage (4) above, after wages have been set (ne formed) and shocks have been realized. This adds an ex post incentive compatibility condition to our positive model: policy has to be optimal ex post - when it is actually enacted. This additional credibility constraint makes the solution less advantageous for the policymaker (and society). The policymaker still sets n (that is, m), seeking to minimize the loss in Equation (2.6). But all uncertainty has been resolved at the new decision stage, so the expectations operator is redundant. Consider how the loss is affected by a marginal expansion, for given nc and E. Using Equations (2.3) and (2.6), we have 1 dL(n,x) dx * = (n - n ) + A ( () + (n - ne) - E - x * ), = LJ[(n, x) + Lx (n, x) dn dn

(2. 1 3)

where a subscript denotes a partial derivative. By Equation (2. 1 3), the benchmark policy rule is not incentive compatible under discretion. Suppose that wage setters believed in an announcement of that rule, implying that ne = n * . Using the optimal-rules outcome in Equations (2. 1 l }-(2. 1 2), and evaluating the derivative m Equation (2. 1 3) at the point prescribed by the ex ante optimal policy rule, we get

If preferred employment (output) exceeds the natural rate (if x* :.- 8), an expansion reduces the loss, rendering the ex ante sub-optimal policy rule ex post inoptimal. Once wages have been set, the marginal inflation cost - the first term on the RHS of Equation (2. 1 3) - is always smaller than the marginal employment benefit - the second term on the RHS 1 0 . Thus, the ex post incentive-compatibility constraint is binding and the low-inflation rule is not credible. 10 To make this more clear, consider the case when E ·� 0, such that the optimal rule prescribes the policy nR :rc* , implying x! = e. Then, by Equation (2. 1 3 ) the marginal inflation cost is actually zero (to first order), whereas the marginal employment benefit is positive (if x* > 8). =

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A credible policy must simultaneously fulfill two conditions: (i) the policy is ex = 0, given Jfe and c:; (ii) expectations are rational, i.e. Jfe = E(n I 8). In game-theoretic terms, those are the conditions for a Nash Equilibrium in a game with many atomistic private wage setters (desiring to minimize the deviation of the realized real wage w n" , from the targeted real wage w) moving before the policymaker 1 1 . Condition (i) requires that the expression in Equation (2. 1 3) equals zero. Taking expectations of that expression, condition (ii) can be expressed as E(n I 8) = n* + A(x* - 8). Combining the two conditions, we get

post optimal, �;

-

nD

=

n * + A(x* - 8) +

_A-_ E

(2. 1 4)

1 +A '

where the D superscript stands for discretion. The employment outcome remains as in Equation (2. 1 2) except that f1 = 0 by assumption. If we assume x* 8 > 0, the discretionary policy outcome in Equation (2. 1 4) and the commitment outcome in Equations (2. 1 1 )-(2. 1 2) illustrate the celebrated "inflation bias" result: equilibrilUll inflation is higher under discretion than under commitment to a rule, whereas employment is the same, independently of the policy regime. The bias is more pronounced the higher is A (the more valuable is employment on the margin) and the higher is x* relative to 8 (the higher is preferred employment relative to the natural rate); both factors contribute to a greater "temptation" for the policymaker to exploit his short-run ability to boost employment by expansionary policy once wages are fixed. Since the natural rate 8 is random, whereas the employment target x* presumably is constant (or at least more stable than 8), inflation is also more variable under discretion than under the rule. The inflation bias is due to two key assumptions. The first is the sequential timing of monetary policy decisions. The second is the assumption that the employment target is higher than the natural rate, that is: x* 8 > 0. This asslUllption must reflect a lack of policy instruments : some distortion in the labor or product market keeps employment too low. The government does not remove this distortion; either because it does not have enough policy instruments or because the distortion is kept in place by some other incentive problem in the policy-making process. These assumptions capture important features of monetary policymaking in the real world. In this static model, the policy response to the supply shock E is not distorted: shocks are stabilized in the same way under discretion and commitment. This equivalence does not, however, carry over to a dynamic model where employment (but not the employment target) is serially correlated. In such a dynamic model, the future inflation bias depends on current employment (since the future equilibrium employment depends on current employment). To reduce the future inflation bias, the -

-

11 The equilibrium would also apply identically to a simultaneous game between the government and a single trade union. If the union moved before the government, the equilibrium might differ slightly, but the fundamental incentive problem would not be affected.

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policymaker thus responds more aggressively to supply shocks under discretion than under commitment. Moreover, the systematic inflation bias increases, as an ex post expansion today expands both current and future employment 1 2 . The "distortion" i n the policymaking process can b e described as follows: under discretion, the policymaker (correctly) fails to internalize the mapping from actual policy to expected policy. He is not being foolish: he really cannot influence private sector expectations. This is what we mean when saying that a (low inflation) policy "lacks credibility". Yet, actual policy maps into expected policy in equilibrium when private agents have rational expectations. Under commitment, on the contrary, the policymaker internalizes this equilibrium mapping; indeed announcing the optimal policy rule brings rationally expected inflation down precisely to the preferred rate of inflation. The conclusions are pretty stark. First, a desirable policy rule does not become credible just by announcing it; is thus pointless to recommend a non­ credible policy rule. Second, the inability to commit to a policy rule has obvious costs. Institutional reforms that give policymakers greater commitment ability can thus be desirable. This simple model of monetary policy credibility is often criticized with reference to the plausible objection that "real world policymakers are not trying to surprise the private sector with unexpected inflation". But this criticism misses the point of the analysis. The model does not predict that the policymaker tries to generate policy surprises in equilibrium. On the contrary, in equilibrium the policymaker would like to bring inflation down but refrains from doing so as his lack of credibility would turn any anti-inflationary policy into a recession. In other words, the model predicts an inertia of expectations to a suboptimally high inflation rate, and a difficulty in curbing these expectations down to the socially efficient rate. What the model does rely on, however, is an assumption that the policymaker would want to generate policy surprises outside of equilibrium to a more favorable outcome. Is this a plausible positive model of inflation? Some observers, like McCallum ( 1 996), apparently do not think so. A convincing rebuttal should address the question already posed by Taylor ( 1 983), who - in his discussion of Barro and Gordon ( 1 983b) - asked why society has not found ways around the credibility problem in monetary policy, when it has found ways around the credibility problem of granting property rights to patent holders. This question is best addressed in connection with a closer discussion of the institutions of monetary policymaking, so we come back to it in Section 4. What are the observable implications of the analysis so far? One implication is that a binding credibility problem would show up by the central bank reacting to variables that entered the private sector's information set (before policy is set), whereas the

1 2 Svensson ( l997a) proves this result formally, drawing on earlier work by Lockwood el al. ( 1 998) and Jonsson ( 1 997). See also Obstfeld ( 1 997b) for a related result in a dynamic model of seignorage. Beetsma and Bovenberg ( 1 998) show that stabilization bias arises also when monetary and fiscal policy are pursued by different authorities with diverging objectives.

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reaction function would not include such variables under commitment. Hence, the unconditional variance of inflation is higher under discretion. If the credibility problem is caused by a high A, the model indeed predicts a positive correlation between average inflation and the variance of inflation, in conformity with international evidence. The discretionary model also suggests a plausible explanation of the secular trend in inflation experienced by the industrialized countries and mentioned in the introduction. The 1 950s and 1 960s were a period without serious supply shocks and with a low natural rate of unemployment (low variance of E, high realizations of 8), which made it easy to keep inflation low. Enter the 1 970s with severe supply shocks (high realizations of E) pushing up the natural rate (to capture this in the model would require serial correlation in employment) and inflation; we may then interpret the rise in inflation as the result of policymakers maintaining their earlier high employment objectives (x * staying constant or falling by less than 8). The gradual decline in inflation from the mid- 1 980s and onward, despite continued high natural rates (in Europe), can be understood to derive from policymakers gradually adapting their employment ambitions to the structural problems in the labor market (x * drifting downwards over time) and from the institutional reforms in central banking arrangements in a number of countries in the recent decade. Naturally, learning from past policy mistakes is also likely to have played an important role. To date, time-series implications of this type have received too little attention in the credibility literature 1 3 . Instead, the literature has focused on normative issues o f institutional reform, and to some extent on explaining cross-sectional differences in macroeconomic outcomes by different institutions. 2.4. Reputation

One can criticize the simple model discussed so far for being static and failing to capture the repeated nature of policymaking. Specifically, the model rej ects repeated interaction with the public and hence ignores reputational forces. A branch of the literature has studied reputational forces in detail. The main result is that a link from current observed policy to future expected policy can indeed discipline the policymaker and restore credibility. With repeated interaction, a policymaker operating under discretion faces an intertemporal trade-off: the future costs of higher expected inflation, caused by expansion today, may more than outweigh the current benefits of higher employment. To illustrate the idea, consider the model of subsection 2.3, repeated over an infinite horizon. The policymaker's intertemporal loss function, from the viewpoint of some arbitrary period s, can be written as

Es

[�

]

(/ sL(nr , Xr) ,

(2. 1 5 )

l.l See, however, the recent papers b y Parkin ( 1 993), Barro and Broadbent ( 1 997) and Broadbent ( 1 996).

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where D is a discount factor. To simplifY the algebra, we assume the static loss function to be linear, not quadratic, in employment:

L(n, x) = �n2 - A.x.

(2. 1 6)

With the simpler loss function, the ex ante optimal policy rule is simply to have zero inflation all the time and to accept employment x = () - E (since n * = 0 and employment volatility is not costly), while the static equilibrium under discretion has inflation equal to A and employment still at X = e - E. We now show that, even under discretion, reputation can indeed create strong enough incentives to enforce zero inflation. As an example, assume that wage setters set wages on the basis of the following expectations:

n,e _-

{A 0

iff nu = n;, otherwise.

u = t - l , . . . , t -- T,

(2 . 1 7)

Equation (2. 1 7) says that wage setters trust a policymaker who sticks to zero inflation in period t to continue with this same policy in the next period. But if they observe any other policy in period t, they lose this trust and instead expect the discretionary policy to be pursued for the next T periods. A policymaker confronted with such expectation formation, in effect, faces a non-linear incentive scheme: he is "rewarded" for sticking to the rule, but he is "punished" if deviating from it. Consider a policymaker that enjoys the trust of the public (i.e. Jr5c = 0). When is the punishment strong enough to outweigh the immediate benefit of cheating on the rule? To answer formally, note that the optimal deviation (found by minimizing the static loss function, given E and nse = 0) is simply ns = A, thus implying employment xs = A + Bs - £5 . After some algebra, the current benefit from cheating can then be expressed as (2. 1 8) Due to the simpler loss function, the benefit is independent of the realizations of 8 and E. The punishment comes from having to live with higher expected and actual inflation in the next T periods. Why higher actual inflation? As the expectations in Equation (2. 1 7) are consistent with the static Nash Equilibrium outcome in subsection 2.3, it is indeed optimal for the policymaker to bear the punishment if it is ever imposed. In other words, the private sector's expectations will be fulfilled, both in and out of equilibrium 1 4. Thus, the cost of a deviation is

c = Es.

[

T

1 "' � 0 -s(L(A' t�s+ l

l

( 1 - iV)

et - EI ) -- L(O' eI - Et )) = 15 ---),_2 ( 1 - D) '

(2. 1 9)

1 4 By this argument the analysis identifies a sequentially rational (subgame perfect) equilibrium. For other expectation formation schemes, in which expectations changed more drastically after a deviation, we would have to impose a separate incentive-compatibility constraint, namely that it is indeed optimal to carry out and bear the ptmishment after a deviation [see Persson and Tabellini ( 1990, ch. 3) on this point].

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which is clearly stationary if we assume that e is i.i.d. over time. Obviously, the policymaker finds it optimal to stick to the zero-inflation rule as long as B � C. Inspection of Equations (2. 1 9) and (2. 1 8) reveals that this is more likely the higher the discount factor (5 and the longer the horizon T for which inflationary expectations go up after a deviation. Many extensions of this basic framework are feasible; and some have been pursued in the literature. For instance, if we retained the quadratic loss function of the previous subsection, the benefit of cheating would be an increasing function of the actual realization of e, while the cost would depend on the variance and the expected value of e. As a result, even with reputation, equilibrium inflation would continue to depend on the actual realization of e: a high value of e makes the incentive­ compatibility condition more binding, as it increases the benefit B but not the cost C. The lowest sustainable inflation rate (defined by the condition that B = C) would be an increasing function of e. Thus, reputation would reduce average inflation but would not change the main positive implications of the model of the previous section. Canzoneri ( 1 985) studied a framework with shocks to inflation that are unobservable to private agents both ex ante and ex post; an example could be the f.l shocks in Equation (2. 1 ) above. If observed inflation exceeds some threshold, such monitoring problems give rise to temporary outbreaks of actual and expected inflation, because the public cannot clearly infer whether high inflation is due to large shocks or to deliberate cheating. Backus and Driffill ( 1 985), Barro ( 1 986), Tabellini ( 1 985, 1 987) and Vickers ( 1 986) studied reputational models where the private agents are uncertain about the policymakers "type" (as his A in the model above). They use the information embodied in current observations of policy to learn about this type, and the policymaker sets policy optimally with a view to this private learning process. Such models illustrate how a "dovish" policymaker (someone with a high A or without access to a commitment technology) can temporarily borrow the reputation of a "hawkish" policymaker (someone with a low A or with access to a commitment technology). They also illustrate how a hawkish policymaker may have to impose severe output costs on the economy to credibly establish a reputation. This differs from the equilibrium considered above, where the policymaker merely maintains a reputation he is lucky enough to have. Cukierman and Meltzer ( 1 986) also studied credibility and private learning but in a richer dynamic setting, where parameters in the central bank's objective function vary stochastically over time. The central insight of the reputation literature is that ongoing interaction between a policymaker and private agents can mitigate the inflation bias and restores some credibility to monetary policy. Whether the problem is entirely removed is more controversial, however, and depends on details of the model and the expectations formation mechanism. Even though the insight is important, the reputation literature suffers from three weaknesses. As in the theory of repeated games, there is a multiple­ equilibrium problem, which strikes with particular force against a positive model of monetary policy. Moreover, the problem of how the players somehow magically

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coordinate on one of the many possible equilibria is worse when the game involves a large number of private agents rather than a few oligopolists. Finally, the normative implications are unclear. The existence of reputational equilibria with good outcomes is not helpful to a country where inflation is particularly high at a given moment in time. The lack of suggestions for policy improvements is another reason why researchers largely turned away from reputational models, towards an analysis of the policy incentives entailed in different monetary policy institutions 1 5. 2.5. Notes o n the literature

Textbook treatments of the general material in this section can be found in Persson and Tabellini ( 1 990, Chs. 1-4), and in Cukierman ( 1 992, Chs. 9-1 1 , 1 6), both covering the literature up to around 1 990. The literature on credibility in monetary policy starts with Kydland and Prescott ( 1 977), who included a brief section with the basic insight of the static model in subsection 2.3. B arro and Gordon ( l 983a) formulated a linear­ quadratic version and pushed its use as a positive model of monetary policy. Calvo ( 1 978) studied the credibility problem of monetary policy in a dynamic model, where the short-run temptation to inflate arises for public-finance reasons. Obstfeld ( 1 997b) provides an insightful analysis of the credible policies in a dynamic seignorage model. Dynamic models of the employment motive to inflate were developed by Lockwood and Philippopoulus ( 1 994), Lockwood et al. ( 1 998), and Jonsson ( 1 997). Parkin ( 1 993) argues that the great inflation of the 1 970s can be explained by an increase in the natural rate in the kind of model dealt with here. Ball ( 1 996) points to indirect evidence that many disinflationary episodes in the 1 980s lacked credibility. Barro and Gordon ( l983b) started the theoretical literature on reputation in monetary policy, drawing on the work on trigger strategies in repeated games with complete information. Backus and Driffill ( 1 985), Tabellini ( 1 985, 1 987) and Barro ( 1 986) developed incomplete information models of reputation, emphasizing how a dovish policymaker can borrow a reputation from a super-hawkish policymaker who only cares about inflation and not at all about employment. Vickers ( 1 986) instead emphasized how a policymaker who seriously wants to fight inflation may have to engage in costly recessionary policies in order to signal his true identity to an incompletely informed public. Reputation with imperfect monitoring of monetary policy was first studied by Canzoneri ( 1 985). Grossman and Van Huyck ( 1 986) and Horn and Persson ( 1 988) studied reputational models dealing with the inflation tax and exchange rate policy, respectively. Rogoff ( 1 987) includes an insightful discussion about the pros and cons of the reputational models of monetary policy.

15 Some interesting recent work, however, suggests an institutional interpretation of some of these reputational equilibria arguing that some institutional arguments are more conducive to reputation building than others; see Jensen ( 1 997), al Nowaihi and Levine ( 1 996) and Herrendorf ( 1 996). The ideas arc related to Schottcr ( 1 9 8 1 ) and to the view that international institutions may facilitate cooperation in trade policy [see Staiger ( 1 995) for a survey].

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3. Political cycles

The empirical evidence for the democratic OECD countries during the post-war period suggests systematic pre-electoral expansionary policies - fact (iv) in the introduction ­ as well a post-election partisan cycle in real variables and inflation -- fact (v). These "facts" vary somewhat depending on the country and the time period considered, and their robustness has not been checked with the same standards as, say, in the modern macroeconometric literature attempting to identify innovations in monetary policy 1 6 . But they are interesting enough t o motivate this line o f research. The empirical evidence also indicates that there is so-called "retrospective voting": the likelihood of election victory for the incumbent government or legislature depends largely on the state of the economy; as expected, a higher growth rate boosts the re­ election probability of the incumbent 17. It is then tempting to "explain" fact (iv) the political business cycle - by opportunistic governments seeking re-election by taking advantage of the voters' irrationality. But how can we claim that the same individuals act in a rational and forward-looking way as economic agents, but become fools when casting their vote? One of the puzzles any rational theory of political business cycles must address is thus how to reconcile retrospective voting with the evidence of systematic policy expansions before elections. This puzzle is addressed in subsection 3 . 1 , under the assumption that voters are rational but imperfectly informed, and that the government is opportunistic and mainly motivated by seeking re-election. This section builds on work by Lohman ( 1 996), Rogoff and Sibert ( 1 988) and Persson and Tabellini ( 1 990). The correlations between macroeconomic outcomes and the party in office are easier to explain, provided that we are willing to assume policymakers to be motivated by ideology (have preferences over outcomes) and, once in office, prepared to carry out their own agenda. These assumptions lead to a theory of "partisan" political business cycles, which is summarized in subsection 3 .2, following the pioneering work by Alesina ( 1 987). 3. 1. Opportunistic governments Throughout this section, we discuss political business cycles in the simple monetary policy model of Section 2, as does most of the literature. But the ideas generally apply to aggregate demand management, including fiscal policy. We deal in tum with "moral

!(, Faust and Irons ( 1999) criticize the literature on partisan cycles in the USA for failing to control for simultaneity- and omitted-variable bias and argue that the support for a partisan cycle in output is much weaker than what a cursory inspection of the data would suggest. Mishra ( 1 997) uses modern panel data estimation techniques trying to control for similar biases in a panel of 1 0 OECD countries. He finds strong support for a post-electoral pa1iisan cycle and weaker support for a pre··electoral cycle. 17 See, for instance, Fair ( 1 978).

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hazard" and "adverse selection", where the labels refer to the informational asymmetry between voters and the elected policymaker. 3. 1.1. Moral hazard in monetary policy

The model in this first subsection is adapted from Lohman ( 1 996), whose work builds on that by Persson and Tabellini ( 1 990) and Holmstrom ( 1 982). Its main insight is that elections aggravate the credibility problem of monetary policy, because they raise the benefit of surprise inflation for the incumbent. Consider a version of the model in subsection 2.4. Voters are rational, have an infinite horizon and are all identical. Their preferences are summarized by a loss function defined over inflation and employment, identical to Equations (2. 1 5) and (2. 1 6) above - and are thus linear in employment. Political candidates have the same objectives, defined over output and inflation, as the voters. In addition, they enjoy being in office: their loss is reduced by K units each period they hold office. Candidates differ in their ability to solve policy problems. One candidate may be particularly able to deal with trade unions, another to deal with an oil-price shock, a third is better able to organize his administration. This competence is reflected in output growth (employment): a more competent candidate brings about higher growth, ceteris paribus. To capture this, we write the Phillips curve exactly as in Equation (2.3), except that we set 8 to zero; we thus consider only E shocks, but change their interpretation. Throughout this section, E captures the competence of the incumbent policymaker, not exogenous supply shocks. We assume that the competence -rj1 fJH , where of a specific policymaker follows a simple MA-process: £1 rJ is a mean zero, i .i .d. random variable, with distribution F(-) and density JO (in this formulation a positive realization of rJ leads to high output). Competence is assumed to be random, as it depends on the salient policy problems, but partially lasting, as the salient policy problems change slowly and as competence may also depend on talent. Serially correlated competence is the basis of retrospective voting: as competence lasts over time, rational voters are more likely to re-elect an incumbent who brought about a high growth rate. In the very first period of this repeated game, we assume fJo = 0. The timing in a given period t is as follows. The previous period's policy instrument and inflation JT1_ 1 are observed. Wages (and expected inflation) are determined. The policymaker sets the policy instrument for t. Competence is realized and output growth x1 is observed by everybody. Finally, if t is an election year - which happens every other year - elections are held. Two remarks should be made about these assumptions. First, unlike in Section 2, the policymaker does not have any information advantage over private agents : when policy is set, the current competence shock rj1 is unknown to everyone, including the incumbent. The voters do not face an adverse selection problem in that the policymaker cannot deliberately "signal" his competence. This assumption distinguishes the model in Lohman ( 1 996) from the earlier work by Rogoff and =

-

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Sibert ( 1 988), Rogoff ( 1 990) and Persson and Tabellini ( 1 990). The voters still face a moral hazard problem: through his monetary policy action, the incumbent can appear better than he really is. The voters understand these incentives, but can do nothing about them, as policy is unobservable. A model of this kind was first studied by Holmstrom ( 1 982) in a standard principal-agent set-up, where the agent has career concerns. subsection 3 . 1 .3 discusses the alternative, and more complicated, setting when the policymaker is better informed about his own competence than the voters. Second, at the time of the elections, voters only observe output growth and wages (expected inflation), but not inflation or policy. This assumption is not as bad as it may first appear. Inflation typically lags economic activity. And even though monetary policy instruments are immediately and costlessly observed, this information is meaningless unless the voters also observe other relevant information that the policymaker has about the state of the economy. To properly understand an expansion of the money supply six months before the elections, voters would have to know the policymaker's forecasts of money demand and other relevant macroeconomic variables. Assuming that policy itself is unobservable is just a convenient shortcut to keep the voters signal-extraction problem as simple as possible 1 8 . Finally, we make two other simplifying assumptions. Once voted out of office, an incumbent can never be reappointed. The opponent in any election is drawn at random from the population and his pre-election competence is not known. Thus the expected competence of any opponent is zero. 3.1.2. The equilibrium

First, consider wage-setters. They have the same information as the policymaker and can thus compute equilibrium policy and perfectly predict inflation. Hence, in equilibrium :rr = :;re in every period. Next, consider voters. By observing output and knowing the previous period shock to competence, 1]1_ 1 , they can correctly infer the current competence of the incumbent by using Equation (2.3): 1]1 = x1 - 1Jt- l 1 9. The equilibrium voting rule is then immediate. Voters always prefer the policymaker with the highest expected competence. As the opponent has zero expected competence, the voters re-elect the incumbent with probability one if and only if x1 > 111-1 , as in this case 1}1 > 0 (if x1 = 1Jr-- I , we can assume that the voters randomize, as they are indifferent). To an outside econometrician, who observes x1 but not 11t- I , 18

As Lohman ( 1 996) observes, however, this asswnption is not easily made consistent with a surprise supply formulation (like in Section 2) where employment (output growth) is determined by realized real wages in a one-sector setting. Lohman instead formulates her model as a Lucas island model where firms observe fhe local inflation but not economy-wide inflation (the policy instrument). 19 Voters know that n = ne Also, recall that in period 0 we have, by asswnption, '1/o 0. Hence in period 1 : x 1 = ry 1 , and output fully reveals the policymaker's competence. Knowing ry 1 , in period 2, voters can infer ry2 from x2 = ry2 + ry 1 , and so on. =

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this voting rule appears consistent with retrospective voting: the probability of re­ election, Pr(1Jt- I ::;; x1) = F(xt), increases with output growth in the election period. Next, consider the policymaker's optimization problem. In off-election years, he can do nothing to enhance future re-election probability, as competence shocks last only one period and are observed with the same lag. Hence, the equilibrium inflation rate minimizes the static loss in Equation (2. 1 6) with respect to :rr , subject to Equation (2.3) and taking :n;e as given. As in subsection 2.4, this yields :rr1 A. On-election years entail different incentives: by raising output growth through unexpected inflation, the incumbent policymaker would increase his election probability. In equilibrium, wage­ setters correctly anticipate these incentives, and raise expected inflation accordingly, so that output continues to grow at its natural rate. To formally derive these results, we first compute the equilibrium probability of re-election from the point of view of the incumbent. Recall that he is re-elected iff [x1 > 1]1 _ J ], or - by Equation (2.3) and our definition of f - iff [1]1 > n1e - n1 ] . When setting policy, the incumbent has not yet observed 1]1 • His perceived probability of re­ election is 1 - Prob(171 ::;; :rr1e - :rr1 ) = 1 - F(:rr1e - :rr1 ), where F(-) is the cumulative distribution of 1]. This probability is clearly an increasing function of unexpected inflation. Next, we need some additional notation. Let V11 and VN be the expected equilibrium continuation values of reappointment and no reappointment, at the point when policy in an on-election year is chosen. Furthermore, let fc be equilibrium inflation during on-election years, to be derived below. Simple algebra establishes that: =

K(l + <5)

1 - 82 ( 1 - F(O)) '

(3 . 1 )

where 1 - F(O) is the equilibrium probability of re-election perceived by the incumbent in all future elections (he recognizes that future inflation surprises are not possible in equilibrium). Intuitively, the expected value of winning the elections - the difference vR - v N - depends on K, the benefits from holding office, but not on the equilibrium policies, A and fr, since those are the same irrespective of who wins. Note also that these continuation values do not depend on the policymaker's competence, as competence is not known when policy is set. We are now ready to formulate the problem of an incumbent during an on-election year. The incumbent takes expected inflation as given and chooses current inflation to mm1m1ze

(3.2) The first two terms in Equation (3.2) capture the expected loss in the current period. The last two terms capture the expected value of future losses, as determined by reappointment or not in the upcoming elections. Taking the first-order condition for a

T Persson and G. Tabellini

1 420

given ne and then imposing the equilibrium condition n = ne yields the equilibrium inflation rate during on-election years: n

=

A+

of(O)( vN -

vR )

=

A +K

80 + o)f(O) 1 - 82 ( 1 - F(O)) '

(3 .3)

where the last equality follows from Equation (3 . 1 ). The LHS of Equation (3.3) is the marginal cost of inflation. The RHS is the marginal benefit: A is the usual benefit of higher output growth, present at all times; the second term is the additional on-election-year benefit; higher output growth increases the chance of re-election. This additional benefit of surprise inflation undermines credibility and makes policy more expansionary during on-election years. Thus, equilibrium inflation right after the election is higher, the more the policymaker benefits from holding office, as measured by K, and the more surprise inflation raises the probability of reappointment, as measured by the density f(O). Finally, as the incentives to inflate before elections are perfectly understood by private agents, expected inflation is also higher, and equilibrium output growth is not affected. Thus, the equilibrium is consistent with stylized fact (iv) in the introduction. Elections aggravate the credibility problem, as the incumbent cares even more than usual about output growth.

3. 1.3. Adverse selection What happens when policy is instead chosen after the incumbent has observed the realization of current competence rlt, but the sequence of events is otherwise exactly as before? In this setting, studied by Rogoff and Sibert ( 1 988), Rogoff ( 1 990) and Persson and Tabellini ( 1 990), the policymaker enjoys an information advantage over wage-setters, who do not know the realization of r}1 when forming expectations. Output fluctuations can still reveal the policymaker's type, but in a less straightforward fashion: voters have to deal with an adverse selection problem, where output can be used as a deliberate signal of the incumbent's competence. To cope with this more intricate problem, we postulate that in each period IJ can only take one of two values: 17 > 0 and r] < 0 with probabilities P and ( 1 - P), respectively. As before, fJ is i.i.d. and has an expected value E(IJ) = PYj + ( l - P)!J. 0. We refer to an incumbent with a high (low) realization of 1J as competent (incompetent). The opponent's competence is still unknown to everyone. In the moral hazard model, all incumbent types choose the same action, because ex ante they were all identical. Here, a more competent incumbent has stronger incentives to surprise with higher inflation. There are two reasons for this. First, a more competent incumbent cares more about winning the elections, since he knows that he can do a better job than his opponent. Second, a more competent incumbent also has a lower cost of signalling his competence through high output growth. Here, we only sketch the arguments needed to characterize the equilibrium. A full derivation is provided by =

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Persson and Tabellini ( 1 990, Ch. 5). As a first step, compute the expected net value

of winning the elections: (3 .4) Comparing Equations (3 . 1 ) and (3 .4) , the net value of winning now depends on the competence of the incumbent: a competent incumbent knows he is more likely to bring about higher future output growth than his opponent, and hence values office more. A incompetent incumbent realizes the converse - and is less eager to be re-elected 20 . The equilibrium inflation rate trades off this net value of winning against the short-run cost ofsignalling. Both types want to appear competent and are prepared to artificially boost the economy through unexpected inflation to increase the chances of winning. But the competent type can signal at a lower cost: he needs to inflate less to produce any level of output growth. As the value of winning is also higher for the competent type, a "separating equilibrium" generally emerges: rational voters re-elect the incumbent only if output growth exceeds a minimum threshold. The threshold is so high that only a competent incumbent finds it optimal to reach it through unexpected inflation. The incompetent type instead prefers to keep inflation low, knowing he will not be re-elected. Recall that wage-setters have to form inflation expectations without knowing which incumbent type they face. ex post, they will always be wrong, even though their ex ante inflation forecast is rational. If the incumbent is incompetent, he chooses the short-run optimal inflation rate (n = A in the model), which is lower than expected; hence, the economy goes through a recession. If the incumbent is competent, inflation is higher than expected and the economy booms. How do the conclusions of this model compare with the stylized facts? Clearly, retrospective voting applies: voters reward pre-electoral booms with reappointment and punish pre-electoral recessions. Output is not systematically higher before elections; on average, inflation is higher just after the elections, but this cycle is weaker than in the moral hazard model, as only the competent type now raises equilibrium inflation. Overall, the predictions of this model are not inconsistent with the stylized facts. Which model is more satisfactory? The moral hazard model has more clear-cut predictions and makes less demanding assumptions about the rationality of the voters. Moreover, multiplicity of equilibria is an additional problem in the adverse selection model. With enough data, one could discriminate between the two models: output 20 We assmne that K is sufficiently high that even an incompetent inc.umbcnt values being re-elected. Note also that here the equilibrinm probability of winning future elections coincides with P, the probability of a high realization of fJ. That is, in equilibrimn a competent incumbent is always reappointed and an incompetent one is not This is a feature of all separating equilibria, that will be discussed below; some equilibria may exist that are not separating, but we neglect them here. Persson and Tabellini ( 1 990) contains a more general discussion of this issue.

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volatility before the elections and inflation volatility after the elections are higher only in the adverse selection model. Note that these two models also have different normative implications. With moral hazard, the political cycle is entirely wasteful, whereas it conveys valuable information to voters in the adverse selection model 2 1 . 3.2. Partisan governments

The prior section relied on two crucial assumptions. All voters are alike and policymakers are opportunistic: their main purpose is re-election to enjoy the rents from office. Elections serve only one purpose: to select the most competent policymaker. But voters are not alike, and policymakers are also motivated by their own "ideological" view of what ought to be done and which group of voters to represent. Therefore, elections serve another goal: they resolve conflicts and aggregate preferences. The policy outcome then hinges on the partisan interests of the elected government. In monetary policy, and more generally aggregate demand policies, one crucial concern is the relative weight assigned to stabilizing output. For left-wing governments output and employment may weigh more heavily than prices; if so, they will also pursue more expansionary aggregate demand policies than right-wing governments. Elections thus create uncertainty about economic policy. This uncertainty is greater in a two-party system with very polarized parties. It may create a post-· electoral cycle in the policy instruments, and a resulting macroeconomic cycle. We now extend our simple monetary policy model to illustrate these ideas, showing how one can account for stylized fact (v) in the introduction. The ideas originate with the work of Alesina ( 1 987, 1 988). 3.2. 1. The model

Consider the same model as in the previous section, but suppose that individual voters differ in their relative evaluation of output and inflation. The preferences of voter i are still described by an intertempora1 loss function like (2. 1 5), but the static loss of individual i has an idiosyncratic relative weight on output: (3 .5) Two political candidates or parties, called D and R, have the same general loss function as the voters, with relative weights }._D > AR. The D candidate thus cares more 2 1 Rogoff (1 990) shows in a closely related adverse selection model of fiscal policy that society may

actually be worse off if one tries to curtail pre-election signalling through, say, a balanced budget amendment (the loss of losing the information may more than outweigh the gain of eliminating the distortions associated with signalling). In a recent paper, however, al Nowaihi and Levine ( 1 998) demonstrate that political cycles can be avoided and social welfare increased by delegating monetary policy to an independent central bank faced with an inflation contract of the type discussed in subsection 4.3 below.

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about output growth and less about inflation than the R candidate. The candidates' preferences are known by everybody, but the outcome of the election is uncertain. For simplicity, there are no competence or supply shocks: output growth is described by Equation (2.3), without any f so that X = e + :n; - :n;e , The timing of events is as follows: Wages are set at the beginning of each period. Elections are held every other period, just after wages are set for that period. Thus, wage contracts last through half the legislature and cannot be conditioned on the election outcome. Finally, to capture the electoral uncertainty about policy, we assume that candidates can only set policy once in office. In other words, electoral promises are not binding and the policy must be ex post optimal, given the policymaker's preferences. 3.2.2. Economic equilibrium Under these assumptions, voters are perfectly informed and the state of the economy does not reveal anything to them. Hence, policymaker I chooses the same inflation rate in office whether it is an on- or off-election period. Given the assumed timing, it is easy to verity that n1 }/ , I = D, R. In off-election periods, this inflation rate is perfectly anticipated by wage-setters, and output grows at the natural rate: x = 0. But just before the elections, wage-setters do not know which policymaker type will win. Suppose they assign probabilities P and ( 1 - P) to the events that D and R win. During on-election periods, expected inflation is thus :n;e = A,R + P(J.cD - A,R). If party R wins, it sets :n; = AR < :n;c and causes a recession in the first period of office: output is x -P(J.cD - J.cR). If D wins, the opposite happens: actual inflation is higher than expected and a boom occurs: x = ( 1 - P)(J.cD - J.cR). Thus, uncertain election outcomes may cause economic fluctuations. But thi s political output cycle occurs after the election and is due to different governments having different ideologies, in contrast to the previous model where the political output cycle is due to signalling and occurs before elections. Interpreting these ideological differences along a left-right political dimension, we get a possible explanation for stylized fact (v). The model predicts that left-wing governments stimulate aggregate demand and cause higher inflation throughout their tenure, while the opposite happens under right-wing governments. An election victory of the left brings about a temporary boom just after the elections; victory of the right is instead followed by a recession. These partisan effects are more pronounced under a more polarized political system (i.e. with large differences between J.cD and J.cR in the model), or more generally if the elections identify a clear winner, like in two-party systems. Alesina and Roubini ( 1 997) argue that these predictions are consistent with the evidence for industrial countries. =

=

3.2. 3. Political equilibrium The partisan model focuses on the role of party preferences in elections. Voters anticipate what each party would do if elected, and choose the party closest to their

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ideal point. Thus, the probability that one party or the other wins is entirely determined by fluctuations in the distribution of voters' preferences for the two parties. Moreover, as electoral promises are not binding and voters are rational and forward-looking, the policy platforms of the two candidates do not converge towards the median voter. In the model, voters face a trade-off. If R wins, inflation is lower but output is temporarily lower, while the opposite happens if D wins. How voters evaluate this trade-off depends on their relative weight parameter ).i . Computing the losses to a generic voter after an R and a D victory, respectively, and taking differences, it is easy to verify that voter i strictly prefers R to win if (3 . 6) The probability (1 - P) that R wins is the probability that the relative weight of the median voter Am satisfies inequality (3.6). Electoral uncertainty thus ultimately relies on the identity of the median voter being unknown, because of random shocks to the voters' preferences or to the participation rate. Ceteris paribus, right-wing governments enjoy an electoral advantage: because all policymakers suffer from an inflation bias, a high value of ). is a political handicap 22 . Inequality (3 .6) implies that a voter whose ideological view is right in between R and D [that is, such that ).i = !(A.11 + ).D)] votes for the right-wing candidate. This suggests that an incumbent can act strategically to increase its chances of re-election. Specifically, a right-wing government can make its left-wing opponent less appealing to the voters by increasing the equilibrium inflation bias. This could be done by reducing wage indexation, by issuing nominal debt (to raise the benefits of surprise inflation), or by creating more monetary policy discretion, via a less disciplining exchange rate regime or weaker legislation regarding central bank independence, or even by current monetary policy if unemployment is serially correlated. These ideas have their roots in the literature on strategic public debt policy, further discussed in Section 6 below. On the normative side, electoral uncertainty and policy volatility are inefficient, and voters would be better off ex-ante by electing a middle-of-the-road government that enacted an intermediate policy. But in the assumed two-party system, there is no way of eliminating this unnecessary volatility. The stark result that there is no convergence to the median position, is weakened under two circumstances. One, studied by Alesina and Cukierrrian ( 1 988), is uncertainty about the policymaker type. Then each candidate has an incentive to appear more moderate, so as to raise the probability of winning the next election. The second, studied by Alesina ( 1987), is repeated interactions. Then the two candidates can sustain self-enforcing cooperative agreements: a deviation from a moderate policy would be punished by the opponent who also reverts to more extreme behavior once in office. Alternatively, cooperation could be enforced by the voters

22

This observation is related to the argument about the benefits of appointing a conservative central banker discussed in subsection 4.3 below.

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punishing a government that enacted extreme policies. Naturally, there is the same problem of multiple equilibria as in the reputational equilibria of subsection 2.4. Institutional checks and balances can also moderate policy extremism. In a presidential system, for instance, actual policies often result from a compromise between the legislature and the executive. The model of partisan policymakers suggests that the voters would take advantage of these institutional checks and balances to moderate the behavior of the maj orities. Alesina and Rosenthal ( 1 995) argue that the voters ' attempt to moderate policy extremism can explain split ticket voting in Presidential systems (i.e., the same individuals voting for different parties in Presidential and Congressional elections) and the mid-term election cycle (the party who won the last general elections loses the interim election).

3. 3. Notes on the literature Alesina and Roubini ( 1 997) present existing and new evidence on electoral cycles in OECD countries. They also survey the theoretical work on political cycles in aggregate demand policy. Alesina and Rosenthal ( 1 995) focus on the United States in particular. The evidence for a partisan cycle is scrutinized by Faust and Irons ( 1 999) (for the USA) and by Mishra ( 1 997) (for a panel of OECD countries). Fair ( 1 978), Fiorina ( 1 9 8 1 ) and Lewis-Beck ( 1 988) discuss the evidence on retrospective voting i n the USA and elsewhere. The first models of political business cycles with opportunistic government are due to Nordhaus ( 1 975) and Lindbeck (1 976). The first theory of a partisan political cycle is due to Hibbs ( 1 977). All these papers relied on the assumption that private agents are backward-looking, both in their economic and voting decisions. The model of an opportunistic government and adverse selection with rational voters, summarized in subsection 3 . 1 .3, was developed by Rogoff and Sibert ( 1 988) in the case of fiscal policy, and adapted to monetary policy by Persson and Tabellini ( 1 990). Rogoff ( 1 990) generalized the fiscal policy results to two-dimensional signalling by the incumbent. Ito ( 1 990) and Terrones ( 1 9 89) considered political systems in which the election date is endogenous and chosen by the incumbent himself, after having observed his own competence. The moral hazard model studied in subsection 3 . 1 . 1 is very similar to a principal­ agent problem with career concerns developed by Holmstrom ( 1 982). It was studied in the context of monetary policy by Lohman ( 1 996) and, in a somewhat different set-up, by Milesi-Ferretti ( 1 995b). Ferejohn ( 1 986) and Barro ( 1 973) study a more abstract moral hazard problem where an incumbent is disciplined by the voters through the implicit reward of reappointment. The model of partisan politics with rational voters is due to Alesina ( 1 987, 1 988). This model is extended by Alesina et al. ( 1 993) and by Alesina and Rosenthal ( 1 995) to allow for ideological parties who also differ in their competence. Milesi-Ferretti ( 1 994) discusses how a right-wing incumbent might increase his popularity by reducing the extent of wage indexation; similar points with regard to nominal debt and the choice of

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an exchange rate regime were investigated by Milesi-Ferretti ( 1 995a,b). Jonsson ( 1 995) discusses strategic manipulation of monetary policy for political purposes when there is autoregression in employment. Uncertainty about the policymaker's ideological type is considered in Alesina and Cukierman ( 1 988). The role of moderating elections, in theory and in the US data, is studied by Alesina and Rosenthal ( 1 995).

4. Institutions and incentives

Theoretical work on institutions and incentives in monetary policy has developed over the last ten years. Below, we give a selective account of key ideas in that development. We do not follow the actual course of the literature over time, but we exploit what, in retrospect, appear to be the logical links between different ideas. The main issue is how the design of monetary institutions can remedy the incentive problems discussed in Sections 2 and 3 . Even though we focus on lack of credibility, some results extend to the political distortions of Section 3 . The ideas in this section rely on a common premise: institutions "matter". A constitutional or institution-design stage lays down some fundamental aspects of the rules of the game, which cannot be easily changed. Once an independent central bank has been set up, an international agreement over the exchange rate has been signed, or an inflation target has been explicitly assigned to the central bank, it has some such staying power, in the sense that changing the institution ex post is costly or takes time. This premise is questioned by some critics [in particular by McCallum ( 1 996) and Posen ( 1 993)], who argue that some of the proposed institutional remedies discussed in this section "do not fix the dynamic inconsistency" that is at the core of this literature, they "merely relocate it". The criticism is correct, in that the institutions are assumed to enforce a policy which is ex post suboptimal from society's (or the incumbent gov­ ernment) point of view. Hence, there is always a temptation to renege on the institution. But the staying power of institutions need not be very long to be effective. In the model that dominates the literature, what is needed is a high cost for changing the institution within the time horizon of existing nominal contracts. Beyond the contracting horizon, expectations would reflect any constitutional change, which removes the distinction between ex post and ex ante optimality. As already remarked in subsection 2.4, the cost of suddenly changing the institution could also be a loss of reputation. By focusing political attention on specific issues and commitments, institutions alert private individuals if governments explicitly renege on their promises. To pick up the thread from Section 2, one purpose of successful monetary institutions is to make monetary policy a bit more like patent legislation. In our view, real-world monetary institutions do have such staying power. They can be changed, but the procedure for changing them often entails delays and negotiations between different parties or groups that were purposefully created when the institution was designed. We thus think that the premise of the literature is generally appropriate. But it would be more convincing to derive

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the institutional inertia as the result of a well-specified non-cooperative strategic inter­ action between different actors, something the literature - so far - has failed to do 23 . 4. 1. Fixed exchange rates: simple rules and escape clauses

Pegging the value of the exchange rate to gold or to some reserve currency has been a common device, particularly in smaller countries, to anchor inflationary expectations, discipline domestic price and wage setting, or prevent political interference in monetary policy. Such attempts have met with mixed success. Among the industrialized countries during the post-war period, the Bretton Woods system and ( part of) the European Exchange Rate Mechanism (ERM) were reasonably successful. But unilateral attempts of some European countries to peg their exchange rates in the 1 970s and 1 980s often ended up in failure: with lack of credibility generating a spiral of repeated devaluations, domestic wages and prices running ahead of foreign inflation. What can explain such differences? To shed light on this question, let us study a slight modification of the static model in Section 2. A small open economy is specialized in the production of a single good which is also produced by the rest of the world. The central bank controls :rr through the exchange rate, given a foreign inflation rate denoted :rr* . The rest of the model, including the expectations-augmented Phillips curve (2.3), the rational-expectations assumption, the objective function of the policy maker (2.6), and the timing of events are as in subsection 2.2 or 2.3; except that we assume not only 8, but also :rr * to be known when wages are set (:rrc are formed). Note that :rr* denotes both foreign and target inflation, as pegging the exchange rate to a low-inflation currency can be seen as an explicit or implicit attempt to target a low inflation rate. Under discretion, the model is formally identical to that in subsection 2.3 and thus generates the inflation and employment outcomes in Equations (2. 1 2) and (2. 1 4). As E(:rr) > :rr* , the model is consistent with the idea of a devaluation spiral, fuelled by low credibility among wage-setters and a devaluing exchange rate. Consider now the following institution. At stage (0), society commits to a simple rule of holding the exchange rate fixed, or of letting it depreciate at a fixed rate k. There is commitment, in the sense that the rate of depreciation k is chosen at the start of each period, and cannot be abandoned until one period later. The rule is simple, because it cannot incorporate any contingencies. In practice, simple commitments of this kind can be enforced by multilateral agreements such as the Bretton Woods system or the ERM, where the short-run interests of other countries are hurt if one country devalues. Policy commitments to complex contingent rules would require implausible assumptions on verifiability and foresight. 23 Jensen ( 1 997) in fact studies a simple model - related to the contracting solution to be studied

in subsection 4.3 - where the government can renege on the initial institution at a continuous (non­ lump sum) cost. ln this setting institution design generally improves credibility, but cannot remove the credibility problem completely.

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What is the optimal rule? As the depreciation rate is known in advance of wage setting and expectation formation and is not contingent on the E shocks, it is neutral with respect to real variables. Hence, the optimal rule has k = 0. Under this simplicity constraint, a fixed exchange rate is thus the optimal commitment. This results in the following equilibrium outcome: J£:8 = JC * , XS = e - E, where the S superscript stands for simple rule. Is the simple rule better than discretion? It depends. The rule brings about lower average inflation, but employment is more variable. A formal comparison of the two regimes can be made by substituting Equations (2. 1 2)-(2. 14), and the previous expression for n8 and x8 , into Equation (2.6) and taking expectations of the difference in their payoffs. Recalling that E( e) = 0, this gives

The first two terms on the RHS capture the benefit of credibility under the simple rule the sum of the squared average inflation bias and its variance. The last term is the loss from not being able to stabilize employment. A simple rule is better than discretion if the gain of credibility is larger than the loss of stabilization policies. This trade-off between credibility and flexibility is a recurrent theme in the literature on institution design. The benefit of the simple rule is further enhanced if, under discretion, monetary policy is also distorted by the electoral incentives discussed in Section 3 . Another monetary regime, often advocated though harder to enforce, i s a commit­ ment to a k% money growth rule. Suppose we add a simple quantity-theory equation to our model, where money demand depends on output growth (or employment), so that n + x = m + v. The policy instrument is m, like in Section 2. Under a simple money growth rule, velocity shocks u destabilize employment and prices. A simple exchange rate peg, on the other hand, automatically offsets velocity shocks. But a money supply rule might better stabilize supply shocks; as these destabilize both output and prices, the price response acts as an automatic output stabilizer. In the limit, if A = 1 , a k% money rule mimics the optimal policy response to a supply shock 24 . The assumption that an exchange rate peg, once announced, cannot be abandoned until next period, may be too stark. Multilateral exchange rate agreements often have escape clauses: European countries have temporarily left the ERM or realigned their central parities when exceptional circumstances made it difficult to keep the exchange rate within the band. An escape clause can be thought of as follows. Define normal times as a range of possible realizations of the unobservable supply shock: E E [eL (e), (e)]. Inside th:s interval, the central bank remains committed to the simple rule. During exceptional times, defined by the complementary event, an

Eu

24 A literature dating back to the 1 970s has studied the choice between altemative rules in richer models - for surveys, see Genberg ( 1 989) and Flood and Mussa ( 1 994). Recent contributions to the comparison of exchange rate versus money based stabilizations of inflation are surveyed by Calvo and vegh ( 1 999).

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escape clause is invoked. The central bank abandons the simple rule and pursues a discretionary (ex post optimal) policy, given inflationary expectations. At normal times, the exchange rate is fixed and output is destabilized by (small) supply shocks. There is also a peso problem: as the escape clause will be invoked with positive probability, expected inflation is always positive. Normal times with actual inflation at zero, thus has some unexpected deflation and employment below the natural rate. At exceptional times, on the other hand, the central bank abandons the rule and sets an ex post optimal policy to stabilize (unusually large) supply shocks. But less inflation is now needed compared to the regime with pure discretion, because expected inflation is lower. Hence, a simple rule with an escape clause strikes a better balance between credibility and flexibility, by allowing for flexibility when it is most needed. Indeed, Flood and Isard ( 1 989) have shown that a rule with an escape clause always dominates pure discretion and, if supply shocks are sufficiently volatile, it also dominates a simple rule. As Obstfeld ( 1 997a) has stressed, however, escape-clause regimes can give rise to multiple equilibria. Intuitively, expected inflation depends on how often the escape clause is invoked. At the same time, the ex post decision whether or not to invoke the escape clause depends on expected inflation. As higher inflationary expectations make it more tempting to abandon the rule, high inflationary expectations may become self-fulfilling. How can a regime with an escape clause be implemented? In a multilateral exchange rate regime where realignments have to be approved by an international body, the bounds would depend on the bargaining power of the devaluing (revaluing) country, which, in tum, would depend on the details of the institution (the prospective sanctions, the procedure for making the decisions, etc.). In a domestic context, we could suppose that at the institution design stage (before 8 is realized) society sets a pair of fixed costs [cL(8), cu (8)] incurred whenever the escape clause is invoked. These costs would capture the public image loss for the central banker from not fulfilling his mandate, or the costs for the government of overriding a central bank committed to the simple rule. They would implicitly define bounds EL( 8) and Eu ( 8), that leave the central bank indif­ ferent between sticking to the simple rule and bearing the cost of no stabilizing policies, or paying the cost and invoking the escape clause. In neither of these interpretations it is reasonable to assume that the costs could be calibrated very carefully ex ante. For instance, costs may have to be state-dependent or symmetric; cL( 8) = d", cu ( 8) = cu or cu = cL = c. Such plausible constraints would prevent society from reaping the full value of the escape-clause regime, but still generally improve on the discretionary outcome. Flood and Marion ( 1 997) point out that an important consideration behind the ex ante choice of c might be to prevent multiple equilibria. 4.2. Central bank independence The first example of strategic delegation in monetary policy is the independent and conservative central banker, suggested by Rogoff ( 1 985). To illustrate the idea in our simple model, we continue to make a formal distinction between society and the central bank. Society's true preferences take the form (2.6). At the institution design stage (0)

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of the model, society appoints a central banker. The central banker is independent: once appointed, society can no longer interfere with his decisions. (Towards the end of this subsection, we ask how reasonable this assumption really is.) Prospective central bankers have loss functions of the form (2.6), but differ in their personal values of A 25 . The appointment thus boils down to the choice of a parameter, say AB. The private sector observes AB and forms its inflationary expectations accordingly. The appointed central banker sets monetary policy freely at stage ( 4), according to his own private preferences. As already discussed in subsection 2.3, this choice gives the equilibrium outcomes

Note that the outcomes do not only depend on the realized shocks, but also on the bankers ' preferences. These expressions illustrate a basic trade-off in the strategic del­ egation: a central banker more hawkish on inflation, i.e. someone with a lower As, has more credibility in keeping inflation low, but is less willing to stabilize supply shocks. To formally study delegation, consider society's expected loss function, as a function of the central banker type: (4. 1 ) where the expectation i s taken over e and E , for any AB. Next, insert the expressions for equilibrium inflation and employment into Equation (4. 1 ) and take expectations. The derivative of the resulting expression with regard to AB is dE[L(A8 )]

oR

*2 �� = A (x + Oo ) + (AB - A)(l

OE

+ AB)} ·

(4.2)

The first term is the expected credibility loss of choosing a central banker with a higher A8. The second term measures the expected stabilization gain. The optimal appointment involves setting this expression equal to zero. Evaluating the derivative (4 .2) at the extreme points implies that A > AB > 0 26 Thus, by optimally choosing an independent central banker, society strikes a different compromise between credibility and flexibility than in the fixed exchange rate regime. 25 This suggests a heterogeneity in the population with regard to the relative weight placed on inflation versus employment, which our formal model abstracts from. As discussed in Section 3, however, such heterogeneity can he formally introduced in the model without any difficulties. Alesina and Grilli ( 1 992) indeed show that strategic delegation of the type to be discussed below would take place endogenously in a model where heterogeneous voters elect the central banker directly. 26 Equation (4. 7) is a fourth-order equation in J..B , which is difficult to solve. But as the derivative is negative at )./1 = 0, positive for all }..'1 > i\., and the second-order condition is fulfilled for any i\.B in the interval (0, i\.), we know that the solution must be inside the interval (0, i\.).

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But it is still a compromise: it is optimal to appoint a central banker who is more conservative on inflation than society itself (to address the inflation bias), but still not ultraconservative (to preserve some of the benefits of stabilization). Note also that fluc­ tuations in the inflation bias arising from observable 8 shocks remain. If A 8 could be chosen after the realization of 8, society would want to meet a more serious incentive problem - a smaller 8 - with a more hawkish central banker - a smaller AB. In practice, the extent of the incentive problem is serially correlated over time, so that making appointments at discrete points is probably a good way of dealing with this problem. Like in the escape-clause model, we could give society or government the option of overriding the central bank decision in exceptional circumstances. The override option could involve firing the central banker, introducing ad-hoc legislation or an explicit override clause under a prespecified procedure (the latter arrangement is indeed observed in the central bank legislation of many countries). An implicit escape clause mitigates the ex post suboptimality of central banlc behavior, inducing even a conservative central banker to stabilize extreme supply shocks to the same extent as society would do 27 . This option should not be overemphasized, however; escape clauses can hardly be optimally designed ex ante. Moreover, as already noted in the introduction, if the government has an override option, why does it not use it all the time to get the policy it wants ex post? We may also note that having an independent central bank also protects society from the distortions introduced by the electoral business cycles discussed in Section 3 . In this case, however, only independence is required, and no special emphasis on inflation relative to other macroeconomic goals. Waller ( 1 989) was probably first in formulating a model of central bank independence under partisan politics 2 8 . Waller and Walsh ( 1 996) study the optimal term length of central bankers in the context of partisan cycles, where society's objectives may change over time. The literal interpretation that society picks a central banker type is not very satisfactory: individual priorities or attitudes towards inflation and employment are often unknown and vaguely defined. Moreover, individual attitudes are probably less important than the general character and tradition ofthe institution itself. A better inter­ pretation is that, at the constitutional stage, society drafts a central bank statute spelling out the "mission" of the institution. Thus, the parameter AB reflects the priority assigned to price stability relative to other macroeconomic goals. As instrument independence is a necessary condition for delegation to work, we should expect such a strategic setting of goals to work better if combined with institutional and legislative features, lending independence to the central bank and shielding it from short-run political pressures. In this interpretation, the model yields observable implications: countries or time periods in which the central bank statute gives priority to price stability and protects central bank independence should have lower average inflation and higher employment 27

This is indeed proved by Lohman (1 992). Fratianni et a!. ( 1 997) formally analyze the role of central bank independence in the absence of a traditional credibility problem, but in the presence of explicit electoral incentives. 28

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(or output) volatility - since if ).,8 < A, stabilization policies are pursued less vigorously. Moreover, electoral business cycles in inflation or output should be less pronounced with greater central bank independence. By now, a number of studies have constructed measures of central bank independence based on central bank statutes, also taking the priority given to the goal of price stability into account 29. Cross­ country data for industrial countries show a strong negative correlation between those measures of central bank independence and inflation, but no correlation between output or employment volatility and central bank independence. Thus, central bank independence seems to be a free lunch: it reduces average inflation, at no real cost. Different interpretations of this result have been suggested. Alesina and Gatti ( 1 996) note that an independent central bank could reduce electorally induced output volatility, as would be predicted by the models of Section 3 , and Lippi ( 1 998) provides evidence that could support this proposition. Posen ( 1 993, 1 995) argues that the cross-country correlation between central bank independence and lower inflation is not causal, and suggests that both may be induced by society's underlying preferences for low and stable inflation. Finally, Rogoff ( 1 985) also suggests another interpretation of the model: the conservative central banker might be interpreted as a targeting scheme supported by a set of punishments and rewards. Having a conservative central banker is formally equivalent to having an additional term in inflation in his loss function, (XB X)(JT - ;r * )2 , where XB > X · The central banker thus has the same objective function as everybody else, but faces additional sanctions if actual inflation exceeds the target. In this simple model, a conservative central banker is thus equivalent to an inflation target 30. This alternative interpretation has been picked up by a more recent literature, asking which targets are more efficient, and more generally how a targeting scheme should be designed to optimally shape the central bank ex-post incentives. -

4.3. Inflation target, and inflation contracts Central banks have traditionally operated with intermediate targets, like money or the exchange rate. In the 1 990s, several central banks started to target inflation: whereas some central banks imposed the procedure on themselves, the transition has been mandated by some governments 3 1 . Such targeting schemes have recently been studied 29 See in particular Bade and Parkin ( 1 988), Grilli et al. (J 991 ), Ales ina and Summers ( 1 993 ), Cukierman

( 1 992) and Eijffmger and Schaling ( 1 993). Rogoff ( 1985) compares an inflation target to other nominal targets, such as money and nominal income. He shows that strategic concerns of the type considered here, can indeed overturn the ranking of intermediate targets, based on parameter values and relative variance of shocks, in the traditional non-strategic literature on monetary targeting. 31 A substantial literature discusses real-world inflation targeting. Sec in particular Leiderman and Svensson ( 1 995), Haldane (1 995), McCallum ( 1 996), Mishkin and Posen ( 1 997) and Almeida and Goodhart ( 1 996). In practice, an inflation target means that the central bank is using its own inflation forecast as an intermediate target; see Svensson ( 1 997b) for instance.

30

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from the point of view of the theory of optimal contracts. Society, or whoever is the principal of the central bank, presents its agent - the central bank - with punishments or rewards conditional on its performance. The question is what constitutes an optimal contract, and what kind of behavior it induces on the agent. We illustrate the basic ideas of this recent literature in our simple model of credibility. The optimal contract can easily be modified so as to implement the optimal monetary policy even in the presence of political distortions, but we do not pursue this extension. Much of the discussion in this subsection is based on results in Persson and Tabellini ( 1 993) and Walsh ( 1 995a). The central bank holds the same quadratic preferences as everybody in society. It operates under discretion, setting policy at stage (4). At the constitutional stage (0), the government formulates a publicly observable complete contract for the central bank which formulates state-contingent punishments (or rewards) conditional on realized in:flation: P(n ; 8, E) = Po( 8, E) + P I ( fJ, E) Jt + �P2 ( 8, E) n2 .

(4.3)

Our goal is to optimally set the terms p;(8, E), i = 0, 1 , 2, that define the contract. We only include up to second-order terms in the contract, since that is sufficient for our purposes. Units are normalized so that, at stage (4), the central bank minimizes the sum of the loss function and its punishment with respect to inflation: L(n, x) + P(:rr ; e, E). Going through the same steps as in subsection 2.3 (deriving the central bank optimum condition for inflation, given the contract and expected inflation, solving for rationally expected inflation, and combining the resulting expressions), we get the equilibrium condition (4.4) The benchmark optimum in Equation (2. 1 1 ) can be implemented by setting p2 (8, E) = 0 and p 1 (8, E) = p1 (fJ) = .A(x* - 8). Since the constant p0(fJ, f) does not affect any of the central bank marginal incentives, it can be set freely - for instance, it can be set negative enough that the participation constraint is satisfied: the central bank leadership finds it attractive enough in expected terms to take on the job. Thus a remarkably simple linear performance contract - imposing a linear penalty on inflation - removes the inflation bias completely. The credibility-flexibility trade-off has disappeared: average inflation is brought down to the target, at no cost of output volatility. Once the simple contract has been formulated, the central bank has the right incentives to implement ex ante optimal policy. Note that the optimal contract is not conditional on f; this is because the marginal incentives to stabilize the economy are correct under discretion (in the terminology of Section 2, there is an inflation bias but no stabilization bias). But the slope of the penalty for in:flation is conditional on 8; as the incentive to inflate the economy also varies linearly with 8. To see the intuition for this result, think about the punishment for inflation as a Pigovian corrective tax. As

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discussed in subsection 2.3, the distortion we want to address is that the central bank does not internalize the effect of its policy on inflationary expectations, when acting ex post. Since expected inflation E(n I 8) is a linear projection of Jr, a linear penalty for inflation makes the central bank correctly internalize the marginal cost of its policy 3 2 . To see this formally, substitute Equation (2.3) into the objective function (2.6) and calculate the equilibrium marginal cost of expected inflation in state 8 as:

dE[L(n, x) I & = (x * _ = ] Jc &) Pt ( & dne

'

E).

That there is no credibility-flexibility trade-off with an optimal contract contrasts with the previous subsection, where - under a quadratic inflation target - lower expected inflation was associated with distorted stabilization policy. A quadratic inflation target is thus not an optimal contract. The Rogoff ( 1 985) targeting solution, discussed at the end of the last section, is equivalent to an inflation contract with P2 = ( X8 - X), P I = ( X8 - X) JT *, and po = 1 (X8 - X)(n*)2 . This clearly gives the central banker incorrect marginal incentives. Nevertheless, the optimal linear inflation contract can be reinterpreted as similar to an inflation target. As the intercept can be set freely, we can write the optimal contract as

P (n; 8) =Po +pt (8)(n - n*);

(4. 5)

the central banker is punished linearly, but only for upward deviations from society's preferred inflation rate. Walsh ( 1 995b) shows that the marginal penalty on inflation can be interpreted as resulting from an arrangement where the governor of the central bank faces a probability of being fired which increases linearly in inflation. Such an arrangement resembles the Price Targeting Agreement in force in New Zealand since 1 990. Other looser interpretations would be to associate the penalty with altered central-bank legislation, a lower central-bank budget, or a loss of prestige of the institution and the individuals heading it, for failing to deliver on a publicly assigned or self-imposed "mission". Naturally, it may be impossible to specifY the penalty exactly as a linear function of inflation. But to approximate an optimal incentive scheme, the punishment for upward deviations from an inflation target should not increase too rapidly with the size of the deviation. In fact, if the central banlc is risk averse, the optimal contract entails a diminishing marginal penalty on inflation (to reintroduce linearity in the incentive scheme). Svensson ( 1 997a) has proposed an alternative interpretation of inflation targets, related to - but somewhat different from - the optimal performance contract interpretation. In his formulation the central bank is not assumed to have any generic 9

Indeed, linearity of the optimal contract is preserved for any general loss functions, and not JUS( for

the quadratic one .

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preferences over macroeconomic outcomes; instead society can impose a specific quadratic objective function on the central bank of the form in Equation (2.6). Suppose that society manages to assign a loss function with a lower goal for inflation, say :reB ( 8) rather than :rc* , to the central banlc Then the optimal central bank goal for inflation is :rr;B ( 8) = :rc * - A,(x* - 8). Pursuing this goal would eliminate the inflation bias, without giving up on stabilization policies. That is, the lower inflation goal is equivalent to our previous setting with a central bank minimizing L + P, where L is society's loss function and P is an inflation contract of the form in Equation (4.3), with parameters A-(x* - 8) and P o = HA-(x* - 8)2 - 2:rc* A-(x* - 8)] . This representation 0, P1 P2 of an inflation target suggests an alternative explanation for the empirical observation discussed in the previous subsection. A lower :reB is associated with lower inflation but not with higher output variability, as in the data. It is not without problems to associate this scheme with real-world institutions, however. Suppose that the optimal inflation rate for society, :rc*, is about 2%, and that the average inflation bias, A-(x* - 8), is about 5% (not an outrageous number, given the recent monetary history of many European countries). The central bank should then be given an inflation goal, :rcB(8), of -3%. But in equilibrium, the central bank would not take any action to bring inflation below 2%, which may present it with some problems when explaining its policy to the public. A second, more important, problem relates to enforcement. How can we ensure that the central bank accepts to evaluate the costs and benefits of the policy according to the imposed objective function, rather than according to society's preferences? A plausible answer is that the central bank is held accountable for its actions and that there is a performance based scheme of rewards or punishments that makes the central bank behave in the desired fashion. But then we are back to the performance contract interpretation of inflation targets explicitly suggested by Equation (4.5) 33 . A natural question is whether to base the contract on inflation or on other measures of performance, such as money, the exchange rate, or nominal income. Persson and Tabellini ( 1 993) show that if the central bank is risk neutral, if the constraints faced by the central bank (i.e. the behavioral equations of the economy) are linear, as assumed so far, and if the marginal penalties under the contract can be contingent on 8, there is an equivalence result: alternative targets yield the same equilibrium. With relevant non-linearities, however, an inflation-based contract is simpler; to replicate the ex ante optimal policy with other measures of performance, the contract must be contingent on a larger set of variables, such as shocks to money demand, or to the money multiplier. In this sense, an inflation target dominates targeting schemes based on other nominal variables: simplicity implies enhanced accountability and thus easier enforcement. Intuitively, the whole purpose of optimal contracts is to remove an inflation bias. This is most easily done by means of a direct penalty on inflation, rather than in a =

=

33 The best assignment if society could really freely impose an objective function on Cl:l, would be to set x*(8) = 8, thereby e liminating the inflation bias completely.

T Persson and G. Tabellini

1 43 6

more round about way, by targeting other variables that are only loosely related to inflation. What happens if the contract cannot be made state-contingent, so that p0, P1 and p2 in Equation (4.3) each have to be constant across 8? This question and its answer are related to the problem in Herrendorf and Lockwood ( 1 997), who study delegation in a model with observable shocks, and to the problem in Beetsma and Jensen ( 1 998), who study delegation via an optimal contract when the central banker's preferences are tmcertain ex ante. To find the optimal incomplete contract in this case, we first plug the solution for Jr in Equation ( 4.4) with the slope coefficients constant, as well as the associated solution for x, namely

X = A-

1 + pz

1

+ A + P2 E ,

into the quadratic objective function. We then take expectations of the resulting expression over A and E and maximize with regard to p 1 and p2 . After tedious but straightforward algebra, we can write the optimality conditions as ( 1 + Pz P pz ___-::-"'-_ -- _-=( l + .A. + pz )3

(4.6)

These conditions are both intuitive. It is easy to show that the first condition says E(n) = ;r* : unconditionally expected inflation should coincide with society's preferred rate of inflation. The second condition says that the coefficient on the quadratic term in the contract should be a positive increasing function of the relative importance of observable to unobservable shocks (the left-hand side is increasing in pz ). Thus, when fluctuations in the observable incentives to inflate cannot be handled by a state­ contingent linear punishment, the constrained optimum gives up a little bit on (first­ best) stabilization in order to diminish the costly fluctuations in Jr. As p1 contains a term in ;r*, we can rewrite the optimal non-state contingent contract P(n) = Po + P 1 n + pz (n - n *i ,

with p2 given by Equation (4.6) and p 1 = (h' +p2 n'). According to this expression, the central bank should be targeting society's preferred rate of inflation and face an extra reward for low inflation. It is perhaps not too far-fetched to interpret the inflation targeting schemes enacted in the 1 990s in many countries as an instance of this arrangement 3 4. The simple contracting model discussed here has been extended in several directions. lf some shocks are observable, but not verifiable and hence not contractible, the central In the model of Beetsma and Jensen ( 1 99g) with uncertain CB preferences, the optimal inflation target may instead be above society's target.

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bank can be required to report the value of these shocks. Persson and Tabellini ( 1 993) show that the optimal contract is related both to the inflation outcome and to the central bank announcement; it is structured in such a way as to induce optimal behavior as well as truth telling. Policy announcements matter not because they convey information to the private sector (that already observes everything), but because they change central bank incentives, by providing a benchmark against which performance can be assessed ex post 35. Walsh ( 1 995a) shows that the optimal contract can also handle costly effort by the central bank. Dolado et al. ( 1 994) as well as Persson and Tabellini ( 1 996) extend the contract approach to the international policy coordination problems that arise when central banks fail to internalize the international externalities of their monetary policies. al Nowaihi and Levine ( 1 998) show how delegation via inflation contracts may eliminate political monetary cycles. McCallum ( 1 996) and others have argued that the contracting solution makes little sense, because it just replaces one commitment problem with another: who enforces the optimal contract? This question reintroduces the general question about institutional reforms raised at the beginning of this section, although it might apply more forcefully to a more ambitious incentive scheme such as the optimal contract. As in the case of the fixed-exchange rate regimes of subsection 4. 1 , enforcement is more likely if agents have heterogenous ex post benefits of inflation and agents hurt by inflation are given a prominent role in the enforcement. Interestingly, Faust ( 1 996) argues that a desire to balance redistributive interests for and against surprise inflation was a clear objective in the mind of the framers of the Federal Reserve. As stated before, we also do believe that changing institutions takes time. The public image of a policymaker who emphatically announces an inflation target, would be severely tarnished, if he explicitly abandoned it shortly afterwards. This is one of the main reasons why in the real world inflation targets can alter the ex post incentives of policymakers. The emphasis of the contracting solution on accountability and transparency is helpful for thinking more clearly about these issues, and about the trade-offs that emerge if the reward scheme cannot be perfectly tailored to mimic the optimal contract. We cannot demand much more than that from simple theoretical models. But where the literature should go next is probably not to other variations of the objective function in the simple linear-quadratic problem. Instead it would be desirable to model the different steps and the incentives in the enforcement procedure as a well-defined extensive-form, non-cooperative game. 4. 4. Notes on the literature The literature on institutions in monetary policy has been surveyed in textbook forn1 by Persson and Tabellini ( 1 990), Cukierman ( 1 992) and Schaling ( 1 995). In the reputational model of Cukiennan and Liviatan ( 1 99 1 ), by contrast, announcements matter because they convey information about the policymaker's type.

35

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The formal theoretical literature on central bank independence starts with Rogoff ( 1 985), whose analysis of the conservative central banker is the basis of the model in subsection 4.3, although the treatment of society's problem as a principal-agent problem is suggested by Barro and Gordon ( 1 983b) in an anticipatory footnote. Giavazzi and Pagano ( 1 988) discuss the commitment ability in multilateral fixed exchange rate regimes, although their analysis is carried out in a richer dynamic framework than the simple model of subsection 4. 1 . Flood and Isard ( 1 98 9) introduce the formal analysis of the rules with escape clauses. Lohman ( 1 992) discusses the implementation of an escape clause, by costly government override, in a monetary policy model that also includes delegation to a Rogoff-type central banker. Obstfeld ( 1 997a) applies an escape-clause model in his analysis of realignments within the ERM, emphasizing the possibility of multiple equilibria. Bordo and Kydland ( 1 995) argue that the classical gold standard worked like a rule with escape clauses. Flood and Marion ( 1 997) include an insightful discussion of escape-clause models and speculative attacks. The optimal contracting solution to the credibility problem, in subsection 4.3, was developed by Walsh ( 1 995a) and by Persson and Tabellini ( 1 993), and was further extended by Beetsma and Jensen ( 1 998) and by Herrendorf and Lockwood ( 1 997). Insightful recent general discussions about the appropriate institutional framework for monetary policy can be found in Fischer (1 995), McCallum ( 1 996) and Goodhart and Vinals ( 1 994). Cukierman and Lippi ( 1 998) study theoretically and empirically how the optimal central banking arrangement varies with the structure of labor markets. The early real-world experience with inflation targeting is surveyed in Leiderman and Svensson ( 1 995). More recent surveys include Haldane ( 1 995) and Mishkin and Posen ( 1 996). A number of studies - including Bade and Parkin ( 1 988), Alesina ( 1 988), Grilli et al. ( 1 99 1 ), Cukierman ( 1 992) and Eijffinger and Schaling ( 1 993) - have developed empirical measures of central bank independence and studied their relation to inflation and other macroeconomic outcomes in a cross-section of countries during the last few decades. Capie et al. ( 1 994) study historical evidence on inflation before and after major central bank reforms in twelve countries since the end of the 1 9th century. Jonsson (1 997) uses pooled time-series and cross-section data from the OECD countries since the early 1 960s and finds that the negative relation between central bank independence and inflation is robust to the control of a number of other institutional and economic variables. Posen ( 1 993) criticizes this kind of finding and argues that it is caused by an omitted variable problem, the causal variable for both independence and inflation being the resistance against inflation in the financial community. A survey of empirical studies is found in Eijffinger and de Haan ( 1 996). Each subsection above refers to additional relevant studies on specific topics.

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Part B. Fiscal Policy

This part of the chapter focuses mainly on intertemporal aspects of fiscal policy, such as government debt issue and taxation of wealth. A companion piece [Persson and Tabellini ( 1 999)] surveys the research on static "public finance" problems. The main stylized facts regarding the intertemporal aspects of post-war fiscal policy in the industrialized countries include: (i) Tax rates on capital vary considerably across countries and fluctuate over time, with an upward trend. In many countries, estimates of effective tax rates on capital are quite high and often higher than tax rates on consumption or labor 36. (ii) Many countries have accumulated large debts, even in peace time. For most countries, debt accumulation in the post-war period started in the early 1 970s. The cross-sectional pattern of deficits is far from homogeneous; some countries have been endemically in deficit and built up massive debts, whereas others have not 37. (iii) Large deficits and debts have been more common in countries with proportional rather than maj oritarian and presidential electoral systems, in countries with coalition governments and frequent government turnovers, and in countries with lenient rather than stringent government budget processes 38. It is difficult to account for these regularities by the theory of optimal taxation or, more generally, any theory that assumes policy to be set by a benevolent social planner. According to Charnley ( 1 986), the optimal capital tax should decline over time, asymptotically approaching zero, as the long-run elasticity of investment is very high compared to that of other tax bases. Similarly, Barro's ( 1 979) tax-smoothing model of deficits can successfully explain war-time deficits, but not the persistent accumulation of debt that has occurred in many industrial countries since the 1 970s. Moreover, the correlations between policies and political institutions suggest that political and institutional factors play an important role in shaping fiscal policy. In this second part of the chapter, we survey some recent literature that speaks to these stylized facts on the basis of positive models of fiscal policy. As in monetary policy, these recent contributions try to explain departures from socially optimal outcomes by various incentive constraints in the policy formation process. In Section 5 we discuss credibility again, abstracting from politics and individual heterogeneity. In Section 6 we add politics to our basic model of fiscal policy and discuss alternative explanations for large government borrowing. 36 Mendoza et a!. ( 1 996), building on earlier work by Mendoza et a!. ( 1 994), compute effective tax rates for a sample of 1 4 industrial countries, during the period 1 965- 1 99 1 . For the most recent six-year period, the average capital tax rate for these countries was close to 40%, higher than both the average labor tax rate and the average consumption tax rate. Furthem1ore, the average tax rate on capital was higher than that on labor and consumption during every five-year period since 1 965, and kept rising over time. 37 See for instance Elmendorf and Mankiw (1 999) and Alesina and Perotti ( 1 995b ). Jx See von Hagen and Harden (1 995), Alcsina and Perotti ( 1 995b), Grilli et a!. ( 1 99 1), Roubini and Sachs ( 1 989).

T Persson and G. Tabellini

1440 5. Credibility of fiscal policy

We first discuss the ex post incentive compatibility constraints that imply a lack of credibility for desirable tax policies. Many insights parallel those in monetary policy. But by adding microeconomic foundations, we can now make more meaningful welfare statements. And by adding an explicitly dynamic setting, we can investigate how state variables link policy decisions over time. As in monetary policy, sequential (or discretionary) decision-making and a lack of policy instruments may imply that the government lacks credibility and loses control of private sector expectations. The economy gets trapped in a third-best equilibrium, where the government relies excessively on a highly distorting policy instrument. The most obvious example is the "capital levy problem". But credibility problems are not confined to capital taxation: they are the norm rather than the exception in a dynamic economy. These issue are discussed in subsection 5 . 1 . Subsection 5.2 treats another consequence of lack of credibility: the possibility of multiple equilibria and confidence crises, features often observed in countries with high public debts. In a dynamic economy current policy credibility depends on previous policy decisions; for instance, it depends on the size and denomination of the outstanding public debt; this new dimension is discussed in subsection 5 . 3 . Finally, as in monetary policy, reputation can mitigate the adverse effects of the ex post incentive constraint and institutions can be designed to relax it. These remedies are briefly discussed in subsection 5.4. 5. 1 . The capital levy problem

According to the standard theory of optimal taxation, capital should be taxed at a much lower rate than labor or consumption. Moreover, the tax rate on capital income should generally decrease over time and approach zero asymptotically. The reason is that the elasticity of investment tends to be higher than those of labor supply and consumption, and it is even higher over longer horizons, as there are more opportunities for intertemporal substitution. This prescription sharply contrasts with stylized fact (i) above. Lack of credibility offers a reason why even a benevolent government can end up with such a suboptimal tax structure 39. 5. 1. 1 . The model

Consider a two-period closed economy, t = 1 , 2, with one storable commodity. A representative consumer has preferences defined over consumption in both periods, c1, and leisure in the second period, x, represented by

u = U(c t ) + c2 + V(x).

(5. 1 )

In the first period, the consumer either consumes his exogenous and untaxed endowment, e, or invests a non-negative amount in a linear storage technology with 39

The next two subsections draw on Persson and Tabellini ( 1 990, ch. 6).

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unitary gross returns. In the second period, he devotes his unitary time endowment to labor l, or leisure time x, and consumes all his income and wealth after having paid taxes. His budget constraints are

c 1 + k = e, c2 = (1 - 8) k + ( 1 - r) l,

(5.2) (5.3)

where k is the investment in the storage technology, 8 and T are the capital and labor income tax rates, and the real wage is unity. Finally, the government must finance a given amount of second-period per-capita public consumption, g. Thus, the government budget constraint is g

= r l + fJk.

(5.4)

Taxes are only paid in the second period, and lump-sum (i.e. non-distorting) taxes are not available. We follow the public-finance tradition of treating the set of available Ramsey taxes as exogenous; but ultimately, the non-availability of ( personalized) lump-sum taxes must be due to some heterogeneity that can only be imperfectly observed by the government. What is the optimal tax structure in this economy? And what is the equilibrium tax structure if the government lacks credibility? We address both questions in turn. 5. 1.2. The ex ante optimal policy

To derive a normative benchmark, we assume that at the start of period I -- before any private decision is made - the government commits to a tax structure (8, r) for period 2. The decision is observed by the private sector, and cannot be changed. There is no uncertainty, and period-2 public consumption, g, is known already in period 1 . We first describe how the private sector responds to the tax rates. The private sector first-order conditions are:

Uc (e - k) � 1 - &;

Vx ( l - l)

= 1 -- r,

(5.5 )

where the equality in the first condition applies at an interior optimum with positive investment. Each tax rate thus drives a wedge between the relevant marginal rates of transformation and substitution. Optimal policy seeks to minimize the resulting distortions. Inverting these two expressions, we obtain the private sector savings function k = Max[O, K( l - 8)], where K( l - 8) = e - U; 1 ( 1 - 8), and labor supply function l = L(l - r) = 1 - Vx 1 ( 1 - r). The partial derivatives Ko and Lr are both negative. By the separability and quasi-linearity of the utility function, each tax base depends on its own tax rate only. For future reference, it is useful to define the

1442

T Persson and G. Tabellini

elasticities of these two tax bases with respect to their own net of tax returns, as Ek( 8) and Et( r), respectively 40 . The optimal tax structure maximizes consumer welfare, subject to the private sector and government budget constraint (5 .2)-(5.4), and the private sector first-order conditions (5.5). Solving this optimization problem yields the following version of the Ramsey Rule 4 1 :

e

r (5.6) E, ( r). E" (e) = 1-r Equation (5.6) implicitly defirles the ex ante optimal tax structure. What are its general properties? First, optimal tax rates are higher on the more inelastic tax base. Second, it is always optimal to tax both bases, as long as both elasticities are finite and strictly positive. Finally, both tax rates move in the same direction if the revenue requirements change; higher public consumption drives up both tax rates, in proportion to their elasticities. If, as empirically plausible, labor supply is much more inelastic than investment, the optimal tax rate on labor is much higher than that on capital. As taxes are distorting, the economy reaches a second best - not a first best.

1-e

5. 1.3. Equilibrium under discretion

Suppose instead that the policy decision is taken at the start of period 2, after period- 1 investment decisions have been made. This timing is much more plausible, as a sovereign country can change its tax structure at any time, under a normal legislative procedure. Under this timing, however, every tax structure promised in period 1 is not credible. A credible tax structure must be optimal ex post; from the vantage point of period 2. More precisely, a credible equilibrium tax structure satisfies three requirements. (i) Individual economic decisions are optimal, given the expected policies and the decisions of all other individuals in the economy. (ii) The tax structure is ex post optimal, given outstanding aggregate capital and individual equilibrium responses to the tax structure. (iii) Individual expectations are fulfilled and markets clear in every period. Let us consider each of these requirements. (i) Optimal individual behavior is still summarized by the functions K and L and by the corresponding elasticities. But the investment function and the corresponding elasticity are now defined over the expected, not the actual, capital tax rate, as the tax structure is decided in period 2, after the investment decision. Thus, k = K ( l ee) and E�c( ee). We call this elasticity the ex ante elasticity of investment, since it is defined over ee rather than e -

0

40 These elasticities are, respectively: fJ

' (8)

41

=

( 1 - 8)

df(

--- -··---

K

d(l - 8)

=

u,

---

K Ucc

> 0'

c1(r)

=

(1 - r)

dL

d(l - r)

- - - -----

See Persson and Tabellini ( 1 990, ch. 6), for a derivation.

L

= - - > 0.

Vx

L V...,

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(ii) The ex post optimal tax structure also continues to be described by the Ramsey Rule (5 .6), but with one important proviso. The investment elasticity that enters Equation (5.6) is the ex post elasticity, that is the elasticity with respect to the actual tax rate e, since that is what the government is choosing. By the argument at point (i), this ex post elasticity is zero: k depends on ee, not on e. Equation (5 .6) then implies that for any given capital stock k the ex post optimal capital tax rate, e*, must satisfy e * = Min[ l , g/k].

(5.7)

The optimal labor tax rate r follows from the government budget constraint. In particular, r = 0 if e* = g/k < 1 . This result is very intuitive. When tax policy is chosen, the supply of capital is completely inelastic at k, whereas the supply of labor continues to have a positive elasticity, as it is chosen by the private sector after observing tax policy. Hence, the government finds it ex post optimal to set either a fully expropriating capital tax rate of I , or a tax rate sufficiently high to finance all of public consumption with capital taxes, driving labor taxes to 0. (iii) Rational individuals correctly anticipate government policy. Hence, ee = e* and k = K ( l - e*). Combining this last result with Equation (5 .7), the equilibrium tax rate is defined by e* = Min[ 1 , g/K(1 - e*)]. We illustrate the possible equilibria in Figure 1. The solid curve is the ex ante revenue function for different values of e. Tax revenues first grow with the tax rate, but at a decreasing rate, since the tax base slu·inks as e rises. Once we reach the "top of the Laffer Curve", tax revenue begins to shrink, as the reduction in the tax base more than offsets the higher tax rate. If g is sufficiently high (higher than point G) only one equilibrium exists, in which 8* = 1 and k = 0 ( point C in the diagram). Irrespective of private expectations, the government fully expropriates any outstanding capital stock. Anticipating this, nobody invests. It is easy to verify that all three requirements for an equilibrium are fulfilled. Private individuals optimize and have correct expectations about policy. And the government also optimizes, for even with no capital outstanding, e = I is (weakly) optimal, as confirmed by Equation (5 .7). This equilibrium is disastrous: there is a prohibitive tax on capital, but still a large tax on labor which is the only available tax base. Yet, the government can do nothing to change the outcome. No promise to tax capital at a rate lower than 1 would be believed, because it would not be ex post optimal for the government to fulfill it. If g is below point G in Figure 1 , this disastrous outcome continues to exist together with two other equilibria. Suppose that government spending corresponds to the horizontal line in Figure 1 . Then points A and B are also equilibrium outcomes. At point A, every consumer expects ee = eA and invests K( 1 eA). Hence, the government can just finance g by setting 8 exactly at (JA, while keeping the labor tax equal to 0. Thus, the government is at an ex post optimum. The same argument establishes that point B is also an equilibrium. -

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T Persson and G. Tabellini

8 K( l - 8) G A

B

c

0

L--------�-+

()

Fig. 1 .

These equilibria are clearly Pareto ranked: A i s better than B which i s better than C. They are all worse than the ex ante optimal tax structure, since they tax capital too heavily and labor too lightly (except at point C where both bases are taxed too heavily). If the government is unable to commit, the economy is trapped in a third-best, or worse, allocation. 5. 1 . 4. Extensions

Results similar to those above, apply to the taxation of other forms of wealth, in particular to public debt and real money balances; in the case of money, naturally, the tax takes the form of inflation. The logic is always the same. Once an investment decision has been made, the tax base is fixed and it becomes ex post optimal to tax it as much as needed, or as much as possible. Moreover, credibility problems are not confined to wealth taxes, but are generic in a dynamic economy with sequential policy decisions. The reason is that the ex post and ex ante elasticity of tax bases generally differ from each other. In general this difference is not as stark as with wealth taxes, where the ex post elasticity is zero. In the case of other tax bases than wealth, we can no longer conclude that the optimal tax rate is always higher ex post than ex ante. To gain some intuition for why, consider an increase in a labor tax rate in a given period t. If the tax increase is unanticipated, the household substitutes from labor into leisure in the current period. But if the tax increase was anticipated in period t - 1 , some intertemporal substitution has already taken place: the household works less in period t, but has already worked more in period t - 1 . We cannot generally tell whether an anticipated or an unanticipated tax hike is more distorting, however. Intertemporal substitution increases the distortion at time t, the period of higher taxes, as the tax base is more elastic. But this greater distortion is offset by a larger tax base in period t - 1 , when the household is working more in

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anticipation of higher future taxes. In general, therefore, we can say that optimal tax 2 rates are different, but not whether they are higher ex ante or ex post 4 . We close this discussion with two remarks. First, characterizing the equilibrium with sequential government decisions is relatively easy in a two-period economy, and doable in a finite-horizon economy. But it becomes very difficult in an infinite-horizon economy43 . Second, so far we have considered a representative consumer economy in which the government lacks a non-distorting tax and has incentives to raise revenues in less distorting ways. Lump-sum taxation may, however, not be enough to avoid lack of credibility. If the government also has distributive goals, but not enough lump-sum taxes and transfers to reach its desired income distribution, the optimal tax policy may still lack credibility despite the availability of (non-personalized) lump-sum taxation. What matters ultimately is thus a scarcity of policy instruments relative to objectives. 5.2. Multiple equilibria and confidence crises When discussing reputational equilibria in monetary policy, we argued that multiple equilibria indicated an incomplete theory. Here, multiplicity of equilibria instead reflects an indeterminacy in the economy, and helps explain the occurrence of sudden speculative attacks or capital flights that have plagued many economies. Absent a commitment technology, policy is driven by private expectations rather than the other way around. Equilibria under discretion thus become intrinsically fragile, as investors face a difficult coordination problem. The ex post optimal policy depends on aggregate investment. But aggregate investment depends on the simultaneous decisions of many atomistic individuals, which in turn depend on expectations about policy. Thus, there is a strategic complementarity. A single investor expecting nobody else to invest also finds it optimal not to invest: he realizes that aggregate capital will be small, and hence full expropriation is inevitable. Thus, individual expectations are self-fulfilling and, as they are not nailed down by any economic fundamentals, can fluctuate widely. The resulting policy uncertainty is yet another drawback of a discretionary policy environment. These problems arise in many policy decisions. Consider public-debt repayment in a two-period economy, and suppose that in the second period debt can be partially defaulted or taxed away, at a cost proportional to the size of the default. Calvo ( 1 988) shows that we then get multiple equilibria. In a good equilibrium, every investor expects the debt to be fully repaid and demands a low interest rate. To avoid the cost of default, the government indeed services the outstanding debt. In a bad equilibrium, every investor expects partial default and demands a higher interest rate. The cost of servicing this debt is now higher, and with distorting taxes the government prefers a partial default; hence, default expectations are self-fulfilling. The equilibrium with default is Pareto inferior, as the net amount serviced is the same, but default costs are borne.

42 43

For a further dl.scussion, see Persson and Tabellini ( 1990, ch. 8). See also the survey by Krusell et al. ( 1 997).

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T Persson and G. Tabellini

Another example, studied by Velasco ( 1 994) and Giavazzi and Pagano ( 1 990), concerns exchange-rate crises in a high public debt economy. By assumption, the cost of outright default is prohibitive, but the outstanding debt could be monetized away. In a good equilibrium, investors expect the exchange rate peg to be viable and the domestic interest rate equals the foreign interest rate; at this low interest rate, it is optimal to service the outstanding public debt by tax revenue alone. In a bad equilibrium, investors expect the peg to collapse. They demand a higher interest rate, which raises the cost of servicing the debt through tax revenue; at the higher interest rate, it becomes optimal to fulfill the expectations, the peg is abandoned and the debt is partially monetized through higher inflation 44. Related coordination problems arise in sequential (as opposed to simultaneous) investment decisions. Alesina et al. ( 1 990) and Cole and Kehoe ( 1 996a,b) study an infinite-horizon economy with a large public debt. Like in Calvo ( 1 988), default is costly, but the cost is assumed to be a lump sum cost. In the good equilibrium, the debt is rolled over forever at low interest rates, and distorting taxes are raised to pay interest on the debt. In the bad equilibrium, there is a debt run, as nobody wants to buy the outstanding debt for fear that - next period - investors will refuse to roll it over. Faced with such a situation, it is indeed ex post optimal for the government to default on the debt, rather than repaying it all at once. Thus the investors' fears are indeed rational and self-fulfilling. Here, the coordination problem thus concerns investment decisions at different points in time. 5.3. Public debt management

The papers discussed in the previous subsection have implications for debt man­ agement policies, as the occurrence of a confidence crisis depends on the maturity structure or currency denomination of outstanding debt. For instance, the debt-run equilibrium discussed by Alesina et al. ( 1 990) disappears if the outstanding debt has a long enough maturity, whereas it is more likely with a short-maturity debt that must be rolled over every period. Similarly, the results in Giavazzi and Pagano ( 1 990) suggest that issuing foreign currency debt can reduce the risk of capital flight, as investors are already protected against depreciation. More generally, public debt management policies alter the future incentives of the monetary and fiscal authorities in many subtle ways, even if the ex ante and ex post elasticities of all tax bases are the same. This point was first noted in the seminal paper by Lucas and Stokey ( 1 983) with regard to the maturity structure of public debt. They start from the observation that fiscal policy typically alters real interest rates. The resulting wealth effect can benefit or harm the government, depending on the composition of its balance sheet. With a lot of long-term debt, a higher long-term 44 A high cost of servicing the debt is not the only reason why an exchange rate peg may not be credible. ln a related argument, Bensaid and Jeanne ( 1997) show that multiple equilibria can arise if raising the interest rate to defend an exchange-rate peg is too costly for the government.

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real interest rate depreciates the outstanding debt and acts like a non-distorting capital levy. Alternatively, if it has long-term assets and short-term liabilities, the government benefits from a policy that reduces the short-term real interest rate. Under sequential decision making, the government's ex ante optimal policy may not be credible: the government may have an incentive to deviate from it ex post, in order to change the value of its outstanding assets and liabilities. Conversely, these incentives give an additional role for public debt management policies: if the maturity and contingency structure of the debt is rich enough, it can be revised over time so as to maintain credibility of the ex ante optimal tax policy under sequential decision making, even if ex ante and ex post elasticities of relevant tax bases differ from each other 45 . Naturally, these results only hold if the economy is closed or large enough to affect intertemporal world prices. Not only the maturity structure of the public debt shapes policy incentives. Its composition into nominal and indexed debt plays a similar role, as the real value of the former, but not the latter, depends on the price level 46 . Based on this observation, Persson et al. ( 1 987) show that the capital-levy incentive for the government to dilute the real value of its outstanding nominal liabilities - such as the money stock - can be relaxed if the government holds claims on the private sector, denominated in nominal terms. If the nominal claims and liabilities are balanced, the ex ante Ramsey solution may be sequentially sustained. But nominally denominated liabilities can also offer valuable insurance against unanticipated fluctuations in government spending, if the government does not have access to contingent debt. Calvo and Guidotti ( 1 990) study the choice between nominal and indexed debt as a trade-off between credibility and flexibility. The upshot is thus that the structure of the public debt becomes a strategic variable that can be manipulated by a government to relax incentive constraints which it will meet in the future. As a result, the "government capital structure" again becomes non­ neutral, even if a Modigliani-Miller theorem about the irrelevance of the government financial structure would apply in the absence of these incentive constraints. In this section, we have only considered governments that continue to make decisions in the future with full certainty. But the idea of using public financial policies strategically to influence future fiscal policy decisions, obviously extends to the case which is more relevant for real-world democracies (dictatorships), where elections (coups and revolutions) shift the identity and policy preferences of governments over time. Strategic public financial policies have indeed received attention in the literature on the politics of public debt that we survey in Section 6.

45

"Rich enough" generally means that there are as many government debt instruments as there are policy instruments. 46 Public debt denominated in foreign currency is similar to indexed debt in this regard, but will not be considered here.

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Reputation and enforcement

As in monetary policy, repeated interaction creates incentives to maintain a reputation, which may mitigate the capital-levy problem. Suppose that future expected capital tax rates depend on the current tax structure. Even though existing capital is taken as given by the government, it still perceives future investment to respond to current tax rates, through expected future tax rates, and this discourages overtaxation. Chari and Kehoe ( 1 990) have studied this reputation mechanism in an infinitely repeated version of the simple two-period model of subsection 5 . 1 . The equilibrium with reputation comes arbitrarily close to the ex ante optimal Ramsey rule, under appropriate assumptions about the government discount factor and the length of the punishment period. Kotlikoff et al. ( 1 988) show that a related enforcement mechanism may be available in an overlapping-generations economy. A misbehaving government is not deterred by investors' expectations, but by the threat that future generations of tax payers will withdraw their intergenerational transfers to a generation that breaks "the social contract" by overtaxing capital. Naturally, multiplicity of equilibria remains in both models. When we consider default on public debt, however, reputational equilibria encounter additional difficulties. Suppose that a defaulting government is "punished" by savers, who refuse to buy public debt in the future. The punishment thus consists of not being able to smooth tax distortions overtime, in the face of fluctuating public spending or tax bases. Is this sufficiently strong to deter default? Bulow and Rogoff ( 1 989) argue that it is not. Suppose that a defaulting government can never borrow again, but can nevertheless still invest budget surpluses in assets earning the market rate of return (for instance, by accumulating reserves of a foreign asset). Then, a simple arbitrage argument implies that the government is always better off defaulting rather than repaying its debt 47 . Thus, simple reputation models cannot explain public debt repayment. There must be other reasons why governments honor their debts: either reputational spillovers across policy instruments, or other costs in a default, such as distress in the banking system, arbitrary redistributions, or sanctions credibly enforced by the international community. In Part I, we discussed various institutional reforms that might raise the credibility of desirable policies. In the case of fiscal policy, such reforms are less effective, however, as the tasks of a sovereign legislature cam10t be narrowly defined. Nevertheless, some institutional devices could mitigate the capital-levy problem. Political delegation to a conservative policymaker is one way. International tax competition is another. As discussed in a companion survey [Persson and Tabellini ( 1 995)], capital controls or international tax agreements that limit tax competition exacerbate the domestic credibility problems, and could thus be counterproductive. 47 Bulow and Rogoff ( 1989) develop their argument in the case of sovereign loans that finance consumption or investment, with no tax distortions, for arbitrary concave utility and production function. But their result generalizes to a model with tax distortions.

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5. 5. Notes on the literature Much of this section is based on Persson and Tabellini ( 1 990, chs. 6-8). There is a large game-theoretic literature on dynamic games with sequential decision-making. What started this line of research are again the papers by Kydland and Prescott ( 1 977) and Calvo ( 1 978). The book by Basar and Olsder ( 1 982) provides a game-theoretic analysis of these problems in an abstract setting. The "capital levy problem" has a long history in economics. Eichengreen ( 1 990) provides a historical account. It has been formally analyzed (although with numerical solutions) in a two-period economy by Fischer ( 1 9 80). An early treatment of surprise inflation to tax real money balances is Auernheimer ( 1 974), but Calvo ( 1 978) is the classic here. A large literature deals with speculative attacks and multiple equilibria. In this section we have only focused on multiple equilibria that arise when policy is endogenous and there is a credibility problem. Confidence crises on public debt have been studied by many authors; in particular by Calvo ( 1 98 8), Alesina et al. ( 1 990), Cole and Kehoe ( 1 9 96a,b) and Giavazzi and Pagano ( 1 990). Multiple equilibria with discretionary monetary policy have also been extensively treated in the literature, in particular by Obstfeld ( 1 997a), Bensaid and Jeanne ( 1 997), Chari et al. ( 1 996) and Velasco ( 1 994). Reputation and capital taxation is discussed by Kotlikoff et al. ( 1 988), Chari and Kehoe ( 1 990) and, more recently, by Benhabib and Rustichini ( 1 996), while Grossman and Van Huyck ( 1 988) and Chari and Kehoe ( 1 993) applied reputation to a model of public debt repayment. The idea that reputation can fail in the case of sovereign debt repayment is due to Bulow and Rogoff ( 1 989), whereas Chari and Kehoe ( 1 993) show that enforcement problems on both sides of the market can restore a role for reputation. Reputational spillovers across contracts are discussed by Cole and Kehoe ( 1 994). Political delegation and capital levies are modeled in Persson and Tabellini ( 1994c) and discussed by North and Weingast ( 1 989) in a fascinating historical context. The literature on international tax competition and credibility is surveyed by Persson and Tabellini ( 1 995). The credibility of optimal tax structures in a general intertemporal context and without capital has been studied by Lucas and Stokey ( 1 983). Their seminal paper discusses both debt management and the credibility of tax policy. Subsequently, Persson and Svensson ( 1 9 84) and Rogers ( 1 987) reinterpret and clarify some of the general issues concerning the credibility of optimal intertemporal taxation. The debt management implications of the Lucas and Stokey paper are also generalized and interpreted, by Chari et al. ( 1 992) and by Persson and Svensson ( 1 986). Persson et al. ( 1 987) extend the Lucas and Stokey result to a monetary economy, whereas M. Persson et al. ( 1 997) show that the temptation to generate surprise inflation may be much stronger than the theoretical literature suggests, once the full set of nominal rigidities in public expenditure and tax programs are taken into account. Rogers ( 1 987) discusses strategic debt management and credible tax policy in an economy with endogenous

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government consumption, while Rogers ( 1 986) considers distributive goals. Missale and Blanchard ( 1 994) study how the maturity structure required to make a low-inflation policy incentive compatible varies with the level of debt. Calvo and Guidotti ( 1 990) study the credibility-flexibility trade-off in the optimal decomposition of public debt into indexed and non-indexed securities. Finally, Missale et al. ( 1 997) as well as Drudi and Prati ( 1 997) have studied public debt management as a signal of the government resolution to enact stabilization policies.

6. Politics of public debt

As noted in the introduction to Part II, many industrial countries have accumulated large debts in peace time. Moreover, debt and deficits appear to be correlated with specific political and institutional features. The goal of this section is to survey the literature that addresses these issues. We begin with the idea that deficits may be a by-product of political instability. Section 5 emphasized that governments can manipulate their debt structure to resolve their own future credibility problems. Subsection 6. 1 takes up this thread, showing how the debt level itself can be used strategically to bind the hands of succeeding governments with different political preferences, in a way first suggested by Alesina and Tabellini ( 1 990) and Persson and Svensson ( 1 989). This idea typically applies to political systems with two parties and a government that clearly represents the view of a cohesive political majority. The debt level can also be used to enhance the incumbent government's re-election probability, in a way first suggested by Aghion and Bolton ( 1 990) and also discussed in Section 3. We construct a simple two-period example that incorporates both of these mechanisms. The remainder of the section then looks at political systems with more dispersed political powers, as in the case of coalition govermnents or powerful political interest groups. In subsection 6.2, we discuss why such a situation may be particularly prone to generate deficits. The argument is a dynamic version of the common-pool problem formulated by Levhari and Mirman ( 1 980) - in the context of natural resources and applied to government debt by Velasco ( 1 999). In subsection 6.3 we follow the approach of Alesina and Drazen ( 1 99 1 ), showing how the struggle between powerful groups, about who will bear the cost of necessary cuts in spending, may lead to a war of attrition delaying the elimination of existing deficits. In both these subsections, we reduce the full-blown dynamic models found in the literature to simple two-period examples. In subsection 6.4, finally, we discuss briefly how the politics of intergenerational redistribution may trigger government deficits, as suggested by Cukierman and Meltzer ( 1 989), Tabellini ( 1 99 1 ) and others.

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6. 1. Political instability in a two-party system 6. 1.1. Economic equilibrium

Consider a two-period economy without capital, but otherwise similar to that of subsection 5. 1 . A continuum of individuals have identical preferences over consumption and leisure. First we describe their preferences over private economic outcomes and their private economic behavior, for a given economic policy. Individual preferences over public policy and different parties are described later. Preferences over private economic outcome are given by the utility function: (6. 1 ) Every consumer faces the same constraints. Leisure and labor i n period t , must sum to unity. Budget constraints are

x1

and

/1 ,

where 7:1 is a labor tax rate, R is the gross interest rate, and b is the holding of public debt - the only available form of saving. By the absence of discounting and the linearities in the utility function, an interior equilibrium for b requires R = 1 . Recognizing this, we can write the equilibrium consolidated budget constraint as

Solving the consumer problem, leads to labor supply functions L ( l r1) identical to those of subsection 5 . 1 . Public spending only takes place in period 2 . Let g denote total per capita public consumption. Using R = 1 , the government budget constraints are -

It is useful to re-express private utility as an indirect utility function defined over the policy variables b and g. Private equilibrium utility is only a function of the two tax rates r1 and r2 • From the government budget constraints, these tax rates can be expressed as functions of b and g. Thus we can rewrite Equation (6. 1 ) as J(b, g) = Max[c 1 + c2 + V(x1) + V(x2)]. This indirect utility function has intuitive properties. First, Jg < 0, is the private marginal cost of government spending which is increasing in g : Jgg < 0. Second, Jb is the private marginal cost of government debt. The symmetry of labor supply implies (6.2) That is, when tax rates an� equal over time, tax distortions are optimally smoothed out (J& = 0). But if more (less) than half the revenue necessary to finance g is raised in

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period 1 , so that b < -�g (> - �g), private utility could be enhanced by higher (lower) debt issue. Finally, as taxes are distortionary and as higher b adds to the government's tax bill in period 2, the cross-derivative Jbg is negative 48 . 6. 1.2. The political system Individuals belong to two different groups, which we label d and r, of given sizes s and ( 1 - s). The two groups are identified with the supporters of two political parties: D and R. Individuals and parties differ in their preferred allocation of public spending over two types of public consumption: gd and g,.. The two types of public consumption each require one unit of output, but they provide different utilities to the two parties and their individual supporters. For simplicity we assume that individuals belonging to group d (r) only care about gd (g�") and that each party only cares about the utility of its own supporters. If elected, party l thus maximizes the utility function

J

=

J(b, g) + H(g;).

(6.3)

Thus, party I correctly internalizes the welfare effects of economic policy on private economic outcomes, according to the indirect utility function J defined over debt and total spending, and evaluates the benefits of public consumption for its constituency according to the (concave) H function, defined over g;. Political parties are "outcome motivated" rather than "office motivated". It is easy, however, to amend the model with a separate benefit of holding office, as in Section 3 . Finally, we assume that relative group size s i s a random variable, the realization of which determines the election outcome. We define P = Pr(s � 0.5) as the probability, from the viewpoint of period 1 , that party R wins. This electoral uncertainty can be due to a random participation rate, or to uncertainty about the relative popularity of parties on other policy dimensions. Below we suggest an explicit model for P, but for now we take it as exogenous. 6. 1.3. Equilibrium policy Events in the model unfold as follows: ( 1 ) One of the parties holds office in period 1 ; this party sets debt (tax) policy b. (2) Economic decisions in period 1 are made. (3) The elected party takes office and sets public spending. (4) Economic decisions in period 2 are made. As before, we consider a sequentially rational equilibrium, and we characterize it by backward induction.

48

Note that our formulation of the model rules out credibility problems of the type discussed in Section 5. The assmned preferences imply that labor supply functions depend on the current after-tax wage only, so that there is no difference between ex ante and ex post elasticities. Also, incentives for debt repudiation do not arise, because the government is a creditor and has no opportunity to manipulate the equilibrium interest rate.

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Optimal private decisions at stages (2) and (4) are already subsumed in the indirect utility function. Suppose party I holds office in period 2. It chooses g so as to maximize its objective in Equation (6.3), given the outstanding debt level b. The first-order condition for good i is (6.4) Thus party I spends on good i only (good } * i has only costs and no benefits) and equates the marginal cost of supplying good i to its marginal benefit (to group i). Clearly, this condition defines a reaction function gi = G(b) which is the same for both parties. Since higher debt implies higher period-2 tax distortions, any government type is less willing to spend on public goods if it inherits a higher public debt; hence: Gb < 0. We can look at the period- ! incentives to issue debt at stage ( 1 ) . The identity of that government does not matter for the results, but to fix ideas we suppose that party D is the incumbent. Its expected payoff, given the expected election outcome, depends on debt policy according to the incentive constraint imposed by equilibrium policy choices in period 2 :

E(uJJ (b)) = J(b, G(b)) + ( 1 - P) H(G(b)]. Optimal debt policy thus has to satisfy (6. 5) where the second equality follows once we impose condition (6.4). Condition (6.5) has an intuitive interpretation. To strengthen the intuition, first consider the special case in which party R stands no chance at winning - that is, P = 0 for any b. Then Equation (6.5) reduces to Jh = 0. In words, a government that is certain of re-election chooses the efficient debt policy, smoothing completely over time the tax distortions from the financing of its preferred public good. When re-election is not certain, however, other incentives come into play. The larger is the probability that the opponent will win, the more party D deviates from the efficient debt policy, as is evident from the second term. As this term is positive, party D sets Jh < 0 whenever P > 0. A positive probability of losing the election leads to excessive debt issue - or more precisely to an insufficient surplus today [recall Equation (6.2)] . Whereas the incumbent government fully internalizes the benefits of borrowing associated with tax smoothing, it does not fully internalize the cost of lower public spending in the future, because these costs are borne only if the government is re-elected. Thus, the over-issue of debt is larger the slimmer is the re-election probability. To express the intuition in an alternative way: it is optimal for the party-D government to tie the hands of a prospective party-R government, as that party will spend on a good not valued by the natural constituency. This strategic motive, creating

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facts for a successor with different preferences, was first stressed by Persson and Svensson ( 1 989) and Alesina and Tabellini ( 1 990). 6. 1. 4. Endogenous election outcomes As mentioned already in Section 3, governments also manipulate state variables to increase their chances of re-election. We now modifY our model to show how this incentive applies to public debt, illustrating an idea first stressed by Aghion and Bolton ( 1 990). Consider the same model, but suppose that parties and individuals also differ along a second not explicitly modeled dimension capturing aspects of public policy that do not directly affect the economy. Specifically, we assume that individual utility depends on the identity of the party holding office, in addition to the public good it provides. But we allow individuals belonging to the same group to have different preferences over policymakers in this second dimension. Thus, we postulate the following overall preferences for individual j in group i, for i = D, R: �

uii = J(b, g) + H(i) + (ai + f3) K D ,

�

(6.6)

where H(-) is the same concave function as in Equation (6.3), and the dummy variable KJJ equals 1 if party D holds office in period 2, and 0 if party R holds office. The parameter ai is distributed around a mean value of 0 in the population of each group, according to the symmetric and unimodal distribution function F(·). In period 1 the precise value of f3 is not known, but only its expected value E(/3). The ai parameter thus measures an idiosyncratic "ideological" (and exogenous) bias for party D, and to the extent that f3 is positive, party D enjoys a popularity advantage. That is, individuals evaluate public consumption according to their group affiliation, and each party cares about its natural constituency. But voters also trade off the economic benefits obtained from their party against other (exogenous or non­ economic) aspects of public policy, according to the parameters a and /3. These "non­ economic" determinants of political preferences are not related to group affiliations in any precise way. This specification of political preferences implies that group affiliation does not completely determine how individuals vote, so that the vote share of each party is endogenous . Finally, we assume that the relative size of the two groups, given by s, is now a fixed parameter, not a random variable. The timing of events is as before, except that just before the date of elections the realization of aggregate popularity, /3, becomes known. What determines the election outcome? At the time of elections, debt policy b is given by previous decisions. Consider voter j in group d. She votes for party R if and only if J(b, g) + H(G(b)) + ai + f3 > J(b, g), or if ai > �(H(G(b)) + ()) . Thus, unless party D is generically unpopular ({3 < 0), only group-d individuals with a strong idiosyncratic ideological bias against party D vote for party R. Next, consider voter j in group r. She votes for party R if and only if J(b,g) + ai + f3 > J(b, g) + H(G(b)),

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or if ai > H(G(b)) - {3 . Not surprisingly, a group-r voter is more likely to support party R, since she draws economic benefits from its election. Combining these conditions and using the law of large numbers, we get the total vote share for party R:

SR(b, {3) = sF (-H(G(b)) - {3) + ( 1 - s) F(H( G(b)) - {3), where f3 is a random variable; everything else is known or chosen by the incumbent government. Thus, before knowing the realization of {3, the probability that R wins is

P(b) = Pr [SR(b, {3) ): 0.5]. (i We want to know how this probability depends on public debt. As a preliminary step, note that dSR

db = Hg Gb[( l - s)f( H(G(b)) - {3) - sf(-H( G(b)) - {3)], where f is the derivative (density) of F. As Hg Gb is negative, the sign hinges on the expression in square brackets. Consider first the case f3 = 0. By symmetry of F, we see that the vote share of party R goes up for any f3 if s > (1 - s). Intuitively, higher b leads to lower future spending, which increases party R 's advantage among voters in group d, but it reduces it among voters in group r. If group d is larger, the former effect prevails. Consider next the case in which s = ( 1 - s) = � - Then, by symmetry and unimodality of F, the vote share for R goes up as b increases if and only if f3 < 0. Again the voters in group d are more important, not because the whole group is larger, but because at the margin the voters in group d are more mobile when party D is generally unpopular. It follows from this discussion that P6 > 0 is more likely the larger is s and the smaller is E(f3). That is, from the point of view of a party-D incumbent, issuing more debt reduces the probability of re-election (Ph > 0) if its economic policies benefit a large group of voters (s is large) or if it is unpopular among all the voters ({3 < 0). It is now easy to characterize the equilibrium debt issued by a party-D government Going through the same steps as in the previous subsection, the optimality condition for public debt - the analog of (6.5) - is

(6.7) The first two terms on the left-hand side of Equation (6.7) are identical to those in Equation (6.5) and have the same meaning. The government trades off the efficiency considerations of public debt (captured by Jb) and the strategic effects on the future spending decisions of its opponent (captured by PHg G6). The last term captures the effect of debt on the re-election probability. If issuing debt enhances the re-election

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chances for party D, so that Pz, < 0, this effect adds to the incentives to issue debt, but when P6 > 0 it pulls in the opposite direction. From the previous discussion we know that ?6 < 0 is more likely when s is small and when E(/3) > 0. Intuitively, a party-D government whose spending policies benefit only a small "minority" -- one for which s is small - enhances it re-election chances by constraining its own future spending, that is by issuing more debt, since this makes him more attractive to swing voters in the larger group r. Similarly, a party-D government whose non-economic policies are generically popular finds it more beneficial to go after swing voters in the opposition party's natural constituency, group r.

6. 1. 5. Discussion What happens if the disagreement between the two parties is not as extreme as we assumed, so that both parties always spend on both goods, gd and gr , although the preferred composition of public spending differs across parties? The answer depends on the shape of the utility function: more debt forces future spending cuts, but which public good is cut the most depends on preferences. If lower total spending is associated with a more similar mix of the public goods by the two parties, Tabellini and Alesina ( 1 990) show that more instability (a lower probability of re-election) still leads to larger equilibrium debt 49. The model thus yields the empirical prediction that political polarization (i.e. sharp disagreement between the majority and the opposition) and political instability (i.e., frequent government turnovers) lead to larger debt accumulation. The simple idea that political instability causes government to behave myopically can be applied in more general models. Adding government spending in period 1 does not change the argument in any respect. Similarly, the results go through if policies are chosen directly by the voters, rather than by the government, as long as there is a probability that the current maj ority will be replaced by a future majority with different preferences. In fact, the prediction is more general and really applies to any intertemporal aspect of public policy, such as the choice of public investment [Glazer ( 1 989) and Part Ill below], or the implementation of tax reforms [Cukierman et a!. ( 1 992)] . If political disagreement concerns the overall size of public spending, rather than its composition, the result that public debt policy is economically inefficient continues to apply. But ·now the direction of the inefficiency depends on which government is in office. Persson and Svensson ( 1 989) show that a conservative government facing a more liberal opposition has an incentive to borrow, to force future spending cuts if the liberal is elected; but a liberal government has the opposite incentives and under­ issues debt (runs an excessively large surplus). Hence the empirical prediction that on average left-wing governments are more disciplined than their opponents, because they are more willing to raise tax revenue. Tabellini and Alesina ( 1 990) formulate this condition in index of the function H.

49

a

precise way, referring to the concavity

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As we saw in the introduction to this part, the general idea that government turnover is positively associated with debt issue is consistent with the stylized facts. Some of the models' specific predictions regarding public debt issue have been taken to the data by Ozier and Tabellini ( 1 99 1 ) for developing countries and by Lambertini ( 1 996) for industrial countries, with supportive results in the first paper but not in the second one 5°. Stretching the model somewhat, it also predicts that minority governments would be more prone to issue debt, as the two strategic effects pull in this direction for a government with a small natural constituency (a small s tends to raise P and to make Pb negative) 5 1 . For a government with popular candidates, the two effects pull in opposite directions, though. The specific positive implications concerning the effect of debt on re-election probabilities are not necessarily robust, but depend on the assumptions about voters' preferences in Equation (6.6). But the general idea, that public financial policies can also be used to manipulate the relative popularity of the two parties, is sound and has many other applications besides public debt. Clearly, these determinants of economic policy would be even more important if parties were also opportunistic, i.e., also cared about staying in office per se. Finally, note that all of these predictions are confined to a two-party system, and in particular to a political system in which a government, once elected, behaves as a single decision-maker. We now turn to coalition governments.

6.2.

Coalition governments

To see why coalition governments may issue debt, consider a two-period, two-group, two-party model, similar to that in the previous section. As tax distortions are not central to the argument here, we assume taxes to be exogenous and lump-sum. Furthermore, we abstract from elections and popularity and instead assume that the two parties share office, both in period I and period 2. Public spending occurs in each period. As before, the two groups have sharply different preferences over the composition of public consumption. We can write the utility of a typical group-i individual as

where y and r are exogenous per capita incomes and per capita taxes assumed to be equal over time.

50 Petterson ( 1 997) test the Persson-Svensson and Alesina-Tabellini models of strategic debt issue on panel data from Swedish municipalities. He finds suppoti for the fom1er model but not for the latter. 5 1 Questioning the stylized fact cited in the Introduction to Part II, Edin and Ohlsson ( 1 99 1 ) argue that minmity governments, rather than coalition governments, are associated with larger debt issue.

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To simplify further, let us assume that s = ! , so groups (or parties) equal size. The government budget constraints are

d

and

r are of

It is easy to see that in this setting the optimal cooperative policy (giving equal weight to the two groups) would set b = 0, and g; = ! r for i = d, r and t = 1 , 2, since that would smooth the benefits of government spending optimally across groups and time. This is not the equilibrium outcome, though, if groups do not cooperate. In each period, the coalition partners simultaneously and non-cooperatively propose a spending level for their constituency. Period-2 debt is always honored. If jointly feasible, these proposals are implemented; if infeasible, each group gets a share of the feasible spending level in proportion to its proposal. More precisely, using p(g{) to denote the proposal of group i in period t we assume that 5 2

i

g1 1

g2

= =

{ {

p(g\ )' if (p(g\) + p(g{)) � 2 r, p(g · + 1 ) . 2 r otherwise , p(g\ ) p(g{ ) p(g;) if (p(gD + p(gi )) � r - b, , p(g2 ) . ( r - b) otherwise. 2+ {

(6.8)

p(g ) p(g )

Clearly, this model implicitly assumes a weak budget process, where each of the coalition partners is given responsibility for one separate part of the government budget, and none of them has responsibility for the overall budget constraint. We can also interpret the model as referring to a very weak government where spending ministers are in the hands of powerful interest groups. Given the relation between proposals and outcomes in Equation (6.8), there is a unique Nash equilibrium in period 2: each party proposes that the whole remaining pool of government resources, r - b, be allocated to its own group. Bidding for the whole pie in period 2, by setting p(gD = ( r - b), is costless. Such a proposal is a dominant strategy, as any lower proposal reduces the share of group i. Equilibrium spending thus satisfies

(6.9)

6.2. 1 . Equilibrium debt issue In period 1 the situation is different, because insisting on high spending eats up future resources. This cost is not high enough, though, to prevent equilibrium over-issue of

52 We also assume that no group can bid for more than the total available resources. Thus, p(g\ ) � 2 r and p(g]_) � r - b for i = r , d.

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debt. To see this, consider how debt links spending in periods 1 and 2. Given future equilibrium spending in Equation (6.9) and the budget constraints (6.7), we can write the objective of party I in period 1 as

d

=

2(y - r) + H(g\ ) + H[r -- (g( + g{ )/2] .

When contemplating its spending proposal and taking party J 's proposal as given, party I thus does not internalize more than half the cost of current spending. The optimal proposal satisfies

As the proposals of both parties are identical, they are clearly feasible: the second expression in parentheses is positive, satisfying the feasibility constraint in Equa­ tion (6.9). They are thus implemented and the equilibrium spending profile for group i satisfies

As g( > g; for i = d, r, it follows from Equation (6.8) that b > 0. This result is an instance of the familiar common pool argument: as the property rights to future income are not well defined, each of the parties only internalizes a fraction of the cost of current spending and debt issue. The result is a collective irrationality, which departs radically from the cooperative solution. Naturally, with N > 2 groups the problem becomes even worse, because now each party only internalizes liN of the future costs of debt issue. This model can be generalized in several directions. Velasco ( 1 999) studies a genuine multi-period model. This gives richer debt dynamics, including the possibility of delayed endogenous stabilizations. Chari and Cole ( 1 993) study a two-period model which combines ideas from this and the previous subsection. Legislators facing a free-rider problem that drives spending too high try to constrain future spending and avoid collective irrationality by issuing more debt. Lizzeri ( 1 996) applies a related idea to a very different model of redistribution, originally formulated by Myerson ( 1 993). He considers a two-period economy where elections are held every period. Candidates can make binding promises before elections, over how to redistribute the available resources across voters and over time. Rational voters reward myopic behavior, however, favoring a candidate who promises to distribute all resources today. The reason is that resources left for the future can be taken away by the opponent if the first-period incumbent is not re-elected 53 . 03 The common pool problem has also been extensively studied in a static context. Persson and Tabcllini ( 1999) smvey that literature.

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stronger budget process

The over-issue of debt is obviously caused by a flawed government budget process, where each party of the coalition (each group) is given decision-making authority over part of the budget, but nobody is given decision-making authority over the aggregate outcome. Which institutional reforms could address this problem? A natural idea is to centralize decision-making authority completely to one of the parties (or perhaps to reform the electoral system, to make majority governments, rather than coalition governments, more likely). If the same party fully controlled all spending decisions, it would indeed appropriately internalize the cost of overspending and of debt issue. Such centralization of decision-making power could be abused, however. In the model of subsection 6. 1 , party I would spend all the revenue evenly over time on its own group, if it had the power to do so. The allocation of spending across time would thus be fine, but the allocation across groups would be terrible. Moreover, in such a world, electoral uncertainty would re-introduce the incentives for debt issue considered in that section. This problem could be mitigated by institutional "checks and balances", for instance by splitting agenda-setting power between the two groups, giving, say, party D agenda-setting power over the budget size and party R agenda-setting power over its allocation 54. It turns out that a simple institution can implement the socially optimal allocation in the model. The solution is to split the decision in stages. First public debt is chosen. Then the allocation of g1 across different types of public goods is sequentially determined, first in period 1 and then in period 2, with a separate budget constraint for each period. Suppose that the allocation of spending is made according to Equation (6.8), except that (r + b) replaces 2 r in the expression for first-period spending on the RHS of Equation (6. 8). It is easy to see that both groups now agree to a balanced budget (b = 0), as any other choice would be inefficient for both of them. Since there is unanimity, any mechanism for choosing b would give the same result. Interestingly, the empirical evidence in von Hagen ( 1 992), von Hagen and Harden ( 1 995) and Ales ina et al . ( 1 996) suggests that certain features of the budget process makes it less likely that countries run into public debt problems. One of the indicators that make up the index of budget stringency in their work is precisely whether the budget process entails a decision on the overall budget, before the decision on its allocation 5 5 .

5 4 The effects o f some o f these checks and balances are investigated i n a different set u p by T. Persson

et al. ( 1997). 55 Hallcrberg and von Hagen ( 1 997) argue that countries with majoritarian electoral systems (and which thus are more likely to have one-party governments) have chosen to centralize power to the finance minister in the budget process, whereas cotmtries with proportional electoral systems (more likely to have coalitions and minority governments) instead have tried to limit their deficits by adopting fonnal budget targets.

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6.3. Delayed stabilizations In this section we do not focus on why budget deficits arise, but on why it may take time to get rid of them once they have arisen. Following Alesina and Drazen ( 1 99 1), we illustrate the possibility of delayed stabilizations when two parties in a coalition government, or two powerful interest groups, both have an incentive to let the other party bear the brunt of the necessary adjustment. Alesina and Drazen's continuous­ time model built on the biological war-of-attrition model of Riley ( 1 980) and on the public-goods model of Bliss and Nalebuff ( 1 984). We adapt their analysis to our simple two-period setting. In the model of the previous section, assume that aggregate government spending has got stuck at a level higher than aggregate tax revenue. In particular, assume that gd + gr = g = r + /3, with f3 > 0. As before, tax revenue is exogenously fixed at the same level in each period. We study two possible outcomes: (i) Stabilization is delayed, in which case gf + g]' = g1 = r + {3, b = {3, and gf + g2 = g2 = r - {3 . (ii) Stabilization occurs in period 1 , in which case aggregate overspending is cut by f3 so that g1 = r = g2 and hence b = 0. The allocation of spending cuts across the two groups in case (ii) depends on how stabilization came about. We return to this question below. We are interested in the probability that stabilization is delayed, and what factors make delay more likely. To simplify the algebra, we assume that the utility of group i is linear in g; . We assume that the costs of debt policy enter additively in the utility function. They can be thought of as either a suboptimal spending allocation over time, or other costs associated with debt issue - perhaps part of the deficit is financed by a distortionary inflation tax. We thus write utility of group i as (6. 1 0) The parameter K; measures the cost to group i of postponing the stabilization. A crucial assumption is that this cost is private information to group i. Group j only knows that Ki is distributed on the interval [0, K'] according to the distribution function F(Ki) . The corresponding parameter K.i has the same distribution, but the realizations of Ki and KJ are independent. All political action takes place at the beginning of period 1 , when each party, simul taneously and non-cooperatively, makes a proposal p1 of whether to stabilize (p1 = s) or not (p1 = n). If both parties propose n, the stabilization is delayed. But if at least one party proposes s, stabilization takes place. If only one party "gives in" and proposes s, that party bears the main burden of the necessary cutbacks. Specifically, we assume: g\ (n, n)

=

�( r -f- {3),

gf (s, n) = g; (n, s) =

gi (n, n) =

! r - a, gf (n, s) = g; (s, n) = ! r + a, g; (s, s) = ! r, i = d, r, t =

�( r - {3), t = 1 , 2, t = 1 , 2,

l , 2,

i = d, r, (6. 1 1 )

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where gi(pD,�) denotes how spending on group i depends on the two proposals, and where a > 0 measures the advantage of not giving in. Implicit in Equation (6. 1 1) is the idea that the political process gives veto rights to some party or interest group. Thus, this model applies to countries ruled by coalition governments, or more generally to a situation where the executive is weak and faces effective opposition by organized interests in the legislature or outside of Parliament. Consider one of the parties, say party D. It compares expected utility when proposing n, denoted by E[ud I pd = n], and when proposing s, denoted by E[ud I pd = s]. Let q = Pr [p' = s] be the probability that party R proposes s (q is determined in equilibrium). Then, Equations (6. 1 0)-(6. 1 1) and some algebra imply

E [ud I p" = n] - E [ u" I p" = s] = a - ( 1 - q) Kd b.

(6. 1 2)

Thus, it is more advantageous to propose n if the gains from not giving in are large (a is large), if the costs of deficit finance for group d is low (kd is low), and if the probability that party R proposes s is high (q is high). Clearly, party D says no whenever K" is below some critical number K. But, since party R faces an identical decision problem, it also proposes n whenever K' < K. Thus it must be the case that ( 1 - q) = F(K). Using that and setting the expression in (6. 1 2) equal to zero, we can implicitly define the equilibrium value of K by:

KF(K) = a!(3. The LHS of this expression is increasing in K. Therefore, K = K ( a, (3), with Ka > 0 and Kr1 < 0. We can now answer the main questions, namely how often we would observe a delayed stabilization and what factors make equilibrium delay more likely. Delayed stabilization requires that both groups propose n. As Kd and K' are independently distributed, the unconditional probability of observing delay is

( 1 - q)(l - q) = F(K( a, {3)) F(K(a , (3 )). The likelihood of delay is thus increasing in a , the gain from winning the war of attrition when the other party gives in first. If we interpret a as a measure of cohesion in the political system, this result thus says that delayed stabilizations and prolonged deficits are more likely in polarized political systems. Note that if a = 0, there is never any delay; postponing adjustment only implies losses for each party. The likelihood of delay is also decreasing in {3, the initial fiscal problem. The model is consistent with the general idea that a worse fiscal crisis makes adjustment more likely; here we get that result because the expected cost of waiting becomes individually larger with a higher (3. Thus, the model supports the general idea that financial crises and times of economic distress resulting from budgetary instability are catalysts of reforn1, and

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should not be feared too much [Drazen and Grilli ( 1 993)]. The mechanism causing delay in the model, namely a conflict over how to distribute the losses from cutbacks in government programs, also rhymes well with casual observation. Finally, the model can be used to study the consequences of financial aid to developing countries and conditionality [Casella and Eichengreen ( 1 995)] . To be effective, external financial aid should not ease the pain of an unsustainable situation (in terms of our model, it should not reduce /3), for this would simply delay the stabilization. Effective financial aid should instead be conditional on a stabilization taking place and shrink over time if the stabilization is postponed, to increase the incentives to give in early for the rivaling parties.

6.4. Debt and intergenerational politics The models in this section all focus on how debt redistributes tax distortions, or benefits of government spending, over time. But they ignore another role of debt: redistribution across generations. They also all assume any outstanding debt to be honored by the government that inherits it. But as we have seen in Section 5, this requires a strong form of commitment. Reputational or institutional forces facilitate commitments, but then they should really be part of the argument; such forces may also not go all the way. In conventional representative-agent macroeconomics, debt issue and pay-as-you­ go social security are identical policies. Several authors have addressed the political determinants of such policies in a median-voter setting without altruism - see Browning ( 1 975) for an early contribution, Boadway and Wildasin ( 1 989), and Cooley and Soares ( 1 999). In these papers, future social-security policies are honored by assumption (at least in the next period); i.e. commitment is assumed. Working agents not too far from retirement favor introducing pay-as-you-go social security, as this allows them to free ride on younger agents. Old-age agents are, of course, also in favor. Therefore a majority of voters typically favors social security and equilibrium policy depends, in a predictable way, on age-earning profiles and the population growth rate. Cukierman and Meltzer ( 1 989) analyze budget deficits in a similar way, but introduce inter-generational altruism. The degree of altruism varies across households: some households leave positive bequests, but others are bequest-constrained. Non­ constrained voters, who can undo any intergenerational redistribution, are only concerned with the general equilibrium effects of the policy, and not on how it redistributes across generations. But a budget deficit is favored by the bequest­ constrained voters, because it allows them something they cannot do privately redistribute resources towards themselves. In a median voter equilibrium, the size of the budget deficit depends of the efficiency effects and the number of bequest-constrained voters. Even though these contributions introduce important aspects of politics, they still hinge on the commitment assumption. At any moment social security strictly benefits

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only a minority (the retired) but imposes a cost on a majority (the workers). A similar problem exists for debt. Why then does the majority not repeal the policy? Reputational concerns may help, if honoring the current program enhances the probability that it will be honored in the future. But as we have already discussed in Section 5, this argument is not without problems. Tabellini ( 1990, 1 99 1 ) suggests one should allow intra-generational heterogeneity in income, when thinking about these questions. Pure intergenerational policies rarely exist, at least when generations are altruistically linked. Social security programs thus redistribute not only from kids to parents, but also from rich to poor. Similarly, public debt default would have both intergenerational and intragenerational effects (as the rich are likely to hold more debt). A policy redistributing across generations may therefore be upheld in equilibrium, without ex ante commitments, by a coalition of voters that contains members of different generations who belong to similar income groups. But the coalitions that form ex post to support existing social security and outstanding debt are different. Social security is supported by the old and the kids of poor parents, whereas debt is supported by the old and the kids of rich parents. These two intergenerational policies are thus not equal under heterogeneity and lack of commitment. As in Section 5, incentive constraints in policymaking violate the Modigliani-Miller theorem of government finance. Majority voting is not the only way of thinking about how the policy preferences of different generations get aggregated in the political process. In many societies, different age-groups - the old, in particular ·- have well-organized interest groups that lobby and take other political action to support policies benefitting their members. Rotemberg ( 1 990) discusses the repayment of government debt as the outcome of bargaining between living generations. Grossman and Helpman ( 1 996) formulate a dynamic model of intergenerational redistribution where policy commitments are again not feasible. In the model, pressure groups of living generations make contributions to the government conditional on the support given to their members. The model has multiple expectational equilibria, which remind of the equilibria in capital taxation studied in Section 5 . But it is the expectations of the current government - rather than the expectations of private agents - about the policy of the next government that introduce the self-fulfilling property. One can easily end up in a very bad equilibrium, where the pressure groups get engaged in a very stiff and costly competition for policy favors and where capital formation suffers.

6.5.

Notes on the literature

A huge literature deals with the politics on government deficits. Here we only refer to the more recent contributions, that typically study general equilibrimn models with rational voters and politicians. A broader survey of the public choice literature is Mueller ( 1 989). Much of the modern macroeconomic literature on public debt is surveyed in Alesina and Perotti ( 1 995a).

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The idea that political instability induces a government to use public debt strategically, to influence the future policies of its opponent, was first independently studied by Alesina and Tabellini ( 1 990) and Persson and Svensson ( 1 989). The model of subsection 6. 1 is related to Alesina and Tabellini ( 1 990), while Persson and Svensson (1989) studied a model where parties disagree on the overall size (as opposed to the composition) of public spending. Since then, many other papers have applied this idea to intertemporal fiscal policy. In particular, Tabellini and Alesina ( 1 990) provide a generalization of these results, Alesina and Tabellini ( 1 989) study capital flight and external borrowing, Tabellini ( 1 990) looks at these models in the context of international policy coordination, Glazer ( 1 989) applies the same idea to the choice of duration in public investment, Cukierman et al. ( 1 992) analyze tax reforms from this point of view and provide empirical evidence that political instability is associated with more inefficient tax systems, and Roubini and Sachs ( 1 989), Grilli et al. ( 1 99 1 ), Ozier and Tabellini ( 1 99 1 ) and Lambertini ( 1 996) analyze the empirical evidence. Finally, the result that public debt policies also affect the re-election probability was first studied in this context by Aghion and Bolton ( 1 990). Modeling the voters' preferences as entailing a trade-off between economic and non-economic dimensions, as we do in subsection 6. 1 , is a common strategy in some of this literature - see in particular Lindbeck and Weibull ( 1 987). The dynamic "common pool" problem has a long history. It has been studied in industrial organization, where it refers to dynamic games among oligopolists facing an exhaustible resource, such as an oil field or a fishery [Levhari and Mirman ( 1 980), Benhabib and Radner ( 1 992)] . In fiscal policy, it was studied by Tabellini ( 1 987) in a dynamic game of monetary and fiscal policy coordination, and by Velasco ( 1 999) in a setting more similar to that of this model. This idea is also at the core of the more empirically oriented literature on budgetary procedures, such as Alesina and Perotti ( 1 995a), von Hagen and Harden ( 1 995), and Hallerberg and von Hagen ( 1 997). There is also an interesting (mainly empirical) line of research, that has investigated the effects of various restrictions on government borrowing. Most of this literature has studied the variety of institutional arrangements in US states. See for instance Bohn and Inman ( 1 996), Poterba ( 1 994), and Eichengreen and von Hagen ( 1 996). The model of delayed stabilizations is due to Alesina and Drazen ( 1 99 1), who in turn have elaborated on earlier ideas by Riley ( 1 980) and Bliss and Nalebuff ( l 984). Since then, the model has been extended in several directions, among others, by Drazen and Grilli ( 1 993), Casella and Eichengreen ( 1 995) and Alesina and Perotti ( 1 995b). Finally, a large literature deals with intergenerational redistribution. Besides the papers quoted in the previous subsection, a separate line of research has investigated the sustainability of social-security systems in reputational models [Kotlikoff et al. ( 1 988), Boldrin and Rustichini ( 1 996)] .

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Part C. Politics and Growth

Distorted fiscal policies, such as those emerging from the political equilibria in Part II, are likely to affect economic performance. It is therefore natural to ask whether political factors and political institutions are correlated with long-run economic growth. Here, too, there are some stylized facts. Most notably, after controlling for the conventional determinants of growth: (i) Inequality in the distribution of income or wealth is significantly and negatively correlated with subsequent growth in cross-country data. On the other hand, the evidence on the effect of growth on the distribution of income (the Kuznets curve) is quite mixed, both in cross section and time series data 56. (ii) Political instability, as measured by more frequent regime changes, or political unrest and violence, is significantly and negatively correlated with growth in cross-country data 57. (iii) Better protection of property rights is positively and significantly correlated with the growth. Whereas political rights and the incidence of democracy are strongly correlated with the level of income, there are no robust findings regarding the effect of democracy on economic growth. 58 A recent literature has tried to explain these regularities in a setting where both economic growth and fiscal policies are endogenous. Section 7 surveys this literature.

7.

Fiscal policy and growth

Subsection 7 . 1 illustrates how income inequality can produce a negative effect on investment and growth, because it provides stronger incentives for redistributive policies that hurt growth-promoting investment. This idea was suggested by Alesina and Rodrik ( 1 994) and Persson and Tabellini ( 1 994b). As in these papers - and a great deal of subsequent work - we rely on a simple median-voter model inspired by Roberts ( 1 977) and Meltzer and Richards ( 1 98 1 ). Subsection 7.2 then illustrates how political instability can hurt growth, by inducing the incumbent government to follow more myopic policies, as in the work by Svensson ( 1 996) and Devereux and Wen ( 1 996). The argument here is closely related to that on strategic debt policy in subsection 6. 1 . Finally, subsection 7.3 briefly discusses how poor protection of property rights may hurt investment and growth, as in Tomell and Velasco ( 1 992) 56 This finding was first obtained by Alesina and Rodrik ( 1 994) and Persson and Tabellini ( l 994b). For a recent and comprehensive survey of the empirical evidence on inequality and growth, see Perotti ( 1 996). 57 On this point see Alesina et a!. ( 1 996) and Barro ( 1 99 1 ). 58 On the relation between property rights and growth see Knack and Keefer ( 1 995). A survey of the voluminous literature on the links fi·om democracy to growth can be found in Przeworsk:i and Limongi ( 1 993),

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and Benhabib and Rustichini (1996). The underlying ideas are closely related to the dynamic common-pool problem discussed in subsection 6.2.

7. 1. Inequality and growth Consider again a two-period economy inhabited by a continuum of heterogenous agents. Everyone has the same quasi-linear preferences over private consumption in periods 1 and 2 and over government ( per capita) consumption in period 2. The utility of consumer i is:

(7. 1 ) The budget constraints are

(7.2) where ki is private investment, r and e lump-sum and capital taxes, and A(I) the gross return to private capital, which is increasing in public investment l . We abstract from credibility problems; the government can commit to these policy instruments before private capital accumulation. Finally, ei is the endowment of agent i. These endowments are distributed in the population with mean e and a distribution function for the idiosyncratic part F( e' - e). To proxy empirical income distributions, we assume that F is skewed to the right: the median value of ei - e, labeled e111 - e and defined by F(e111 - e) = �' is negative. Assuming a balanced budget in every period, the government budget constraint in per capita terms is: l

=

T,

(7.3) (7.4)

g = 8A(I) k,

where k denotes per capita (average) capital. Following the approach of subsection 5. 1 , we can derive equilibrium private investment from Equations (7. 1)--(7.3) as

k' = e - l - u; 1 (A(/ )(1 -- 8)) + (ei - e) = K( O , I) + (ei - e),

where the common investment function satisfies K0 < 0 and K1 > 0. lt is again convenient to express the utility from private consumption as an indirect utility function defined over the policy variables:

Ji ( O , I, ei ) = Max[ U(c\ ) + c� ] = U(e - I- K(O, I)) + ( I - O)A(I) K( O , I) + A(/) ( l - O)(ei - e) = J( O , l) + A(/) ( 1 - O )(e' - e). By the envelope theorem, the direct welfare cost of the capital tax negative. Moreover, the welfare effect of public investment, .1] = U -

c

J0

=

+ (1

(7.5)

A(l) K is 8) - A1K, is

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T Persson and G. Tabellini

monotonically decreasing in I (by Ucc < 0 and A11 < 0). Substituting Equation (7.5) into (7 . 1 ) and using (7 .3), we obtain individual-i policy preferences over the two policy instruments 8 and I:

u; = J'(B, I, e') + H(8A(I) K(8, I)). These policy preferences are linear in the idiosyncratic variable e; . They therefore fulfill a monotonicity (single-crossing) condition, such that the preferred policy of the agent with endowment em will be a Condorcet winner, even though the policy space is two-dimensional. If we imagine that policy decisions are taken at the begitming of period 1 by direct democracy, the winning proposal is thus the policy preferred by this decisive voter. If the second-order conditions are fulfilled 59, the equilibrium values for I and 8 thus satisfY J1

+ Hg 8(KAI + AK1) + (em - e)( l - 8)A1

Je + HgA(K + 8Ke) - (em - e)A = 0.

=

0,

(7.6)

To understand these conditions, first assume that the distribution is symmetric, so that em = e. Then the third terms in both conditions are zero, and Equation (7.6) characterizes the optimal policy for the average agent, which - by quasi-linear preferences - would be chosen by a utilitarian planner. The first condition says that it is optimal to provide more public investment than would maximize private indirect utility (i.e. J1 < 0) due to the beneficial effects on the future tax base and hence on public spending (if public debt were allowed this result would be different). The second condition equates the average private marginal cost of raising revenue (Je < 0) with the marginal benefit it generates via public consumption . But if em < e, redistributive effects come into play. The decisive voter's capital falls short of average capital by exactly (em - e). This implies that I is smaller and 8 is higher than in the hypothetical planning solution. The reason is that the decisive V<'ter does not benefit from public investment as much as the average capital holder, and he also does not suffer as much from capital taxes. To see this formally, notice that the third term in the first equation of (7.6) is negative and the third term in the second equation is positive. By the second-order conditions, l has to be lower and 8 has to be higher than in the social planner's solution. We thus see that inequality hampers growth via two different channels. The growth rate from period 1 to period 2, given by [A(J) K(8, !)/e] - 1 , is increasing in I (both directly and indirectly) and decreasing in 8. Furthermore, the higher is inequality, as measured by the distance between median and average income, the lower is growth as equilibrium public investment is smaller and capital taxation - as well as government consumption - is higher. "" As in all optimal taxation problems, this assumption is not necessarily innocuous, but can involve restrictive assumptions on underlying f1.mctional forms.

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Alesina and Rodrik ( 1 994) and Persson and Tabellini ( 1 994b) developed this kind of reduced-form prediction in related but explicitly dynamic models. Whereas Persson and Tabellini (as we have done) focused on the size distribution of income, Alesina and Rodrik focused on the functional distribution of income between labor and capital. Both papers also took the reduced-form prediction to the data - here Alesina and Rodrik too look at the size distribution of income. And they indeed found a strong negative effect of inequality on growth in a cross section of post-war data from a broad sample of countries 60 . These papers stimulated a body of subsequent work scrutinizing both the empirical and the theoretical argument. Whereas the reduced-form relation from inequality to growth indeed seems empirically robust, the structural links implied by the theory have not generally found support in later empirical work 6 1 • Thus, it has been hard to identify both the implied link from inequality to redistribution and the link from redistribution to growth, as emphasized in the recent surveys by Perotti ( 1 996) and Benabou ( 1 996). The model in this section suggests that these links could be pretty subtle, however (with opposite effects of inequality on government consumption and investment, for example, and ambiguous effects on total government spending). Moreover, the failure to find a robust link from tax rates and redistribution to economic growth is a problem for conventional growth theory, not just for political theories of growth. The literature has also searched for other reasons why inequality and growth may be inversely related. Perotti ( 1 996) stresses that one link may run via political instability or via other, non-political, channels such as education. Benabou covers a whole range of recent theoretical work showing that the links between income distribution, policy and growth may run in different directions. For instance, redistribution may promote growth when agents are credit constrained, or when it promotes education.

7.2. Political instability and growth We now modify the previous model as follows. First, every private agent has the same first-period endowment: that is, e; = e and the average investment function K(fJ, I) applies for everyone. Instead, as in subsection 6. 1 , agents belong to two different groups, d and r, and public spending is of either of two types: g" (benefitting only group d) or g,. (benefitting only group r). Second, and again following subsection 6. 1 , policy is not set by majority rule but by an incumbent government D that acts so as to maximize the utility of group-d agents. The incumbent may be replaced by an alternative government R in the future.

"0 Persson and Tabellini ( 1 994b) also found a similar relation in a small historical panel of industrialized countries with data going back to the late 1 9th century. " 1 Later empirical work based on better data has also questioned an empirical finding by Persson and Tabcllini ( 1994b) that was interpreted as giving indirect support for the theory, namely that the relation between inequality and growth was only present in democracies and not in dictatorships.

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For simplicity, we take the re-election probability ( 1 - P) as exogenous. It is natural to interpret P as a measure of political instability. Third, to introduce a meaningful policy choice in period 2, policies are chosen sequentially. Thus, public investment I is chosen in period 1 , before private capital, and the capital tax rate 8 is chosen in period 2. To avoid the capital-levy problem discussed in Section 5, we assume that in period 2 the private sector can still avoid some of the tax, though at a cost, by reallocating some of its accumulated capital to a non-taxed asset with a lower return. We could think of this as tax avoidance, or capital flight. A convenient formulation, following Persson and Tabellini ( 1 992), is to rewrite the period-2 budget constraint as

C2 = ( 1 - 8)A(I)(k -f) +f - M(f), where M(f) is a concave and increasing function of the amount f shielded fi:om taxation and where we have recognized that everybody makes the same savings decision. It is easy to show that average savings are still given by the function K(8,I) and that tax avoidance is given by the function F(8, !) with F0 > 0 and F1 < 0 62 . The government's tax base can thus be written as a function K(8, !) = A(I) K(8, !) - F(8, !). The ex ante properties of this function (that is from the viewpoint of period 1) are the same as before: decreasing in 8 and increasing in I. I n period 2, when K and I are given from previous decisions, the ex post tax base

K.2 ( 8, !)

is still decreasing in 8 but with a smaller slope (intertemporal substitution possibilities are eliminated). The bottom line after these modifications is similar to the previous section: we can write the ex ante indirect utility of an agent in group i as

u1 = 1(8, !) + H(g; ) = 1 (8, !) + H(8K(8, !)).

(7.7)

-2 -2 162 + Hg (K + 8K0) = 0,

(7.8)

We can also define ex post indirect utility (for given K and J) as 12 (8, !) + H(8K\ 8, !)). Both 1(8, !) and 1 2 (8, I) have the same qualitative properties as the corresponding function in subsection 7 . 1 . Any government holding power in period 2 spends all revenue on the public good favored by its own constituency. The ex post optimal tax rate is given by the condition: which has the same interpretation as the second condition in Equation (7.6). Thus, both prospective governments will set the same tax rate. Condition (7.8) implicitly defines the optimal tax rate as a function of past public investment 8(!), with slope

-2 2 K 8 -- lei + Hgg-2Iii · I 2 + HggK ee lee r,J The first.,order condition for optimal tax avoidance is for the consumer to set A (I )(1 - H) M1(f) = 0. When this condition is inverted, we get the desired tax avoidance function.

-

I -+

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1 47 1

Unless H i s very concave, 81 > 0 , a s the numerator i s positive and the denominator is negative (by the second-order condition). Public investment enlarges the tax base and this drives up the optimal tax rate. The incumbent party-D government in period 1 chooses I so as to maximize

E(u" ) = PJ( H(I ), J ) + ( 1 - P) [J( H(I), J) + H ( H(I)K( H(l), J ))] = J ( H(J) , I) + ( 1 - P)[H ( H(J )K( H(I), J ))]. We can rewrite the first-order condition to this problem with Equation (7.8), recognizing that f{j K at the equilibrium tax rate. Some additional Ju and K2 algebra gives =

=

(7.9) Suppose first that D is certain to be re-elected: P 0. Then the optimal choice of I boils down to the familiar weighting of private welfare (the first term) against government revenue (the second term), where the latter are fully internalized as the government is certain to remain in office. The resulting condition is the same as the second condition in Equation (7.6) of the previous subsection, adjusted for the different timing of tax policy and for the lack of heterogeneity. But when re-election is uncertain, P > 0, future government revenue is less valuable and policy myopia sets in. As the third term in Equation (7. 9) is negative, a higher probability P of losing office makes public investment less attractive and reduces it in equilibrium. Higher instability not only draws down public investment, but reduces growth in this model. Second-period income, c2 + g = A(J) K( H, I) - M(F(8, I)), unambiguously goes down as I falls. The direct negative effects of lower public investment and the indirect negative effects of higher waste due to more tax avoidance always outweigh the positive effects of the smaller equilibrium capital tax. Much of the informal discussion of why political instability is harmful for growth seems to suggest a direct effect of uncertainty or unpredictability on private investment. We know, however, that uncertainty in returns has ambiguous effects on private investment. Here a different mechanism is at work: political instability induces more myopic fiscal policies, which in turn cause lower public investment and growth. This is related to Svensson ( 1 998), who shows that political instability may make a forward­ looking government abstain from improvements in the legal system that enforce private property rights. He also finds empirical support for this idea. Political instability [as measured by Alesina et al. (1 996)] indeed reduces the protection of private property rights [as measured by the same index as in Knack and Keefer ( 1 995)] in a wide cross­ country sample. And controlling for property-rights protection, political instability drops out of a cross-country investment regression. The theoretical paper by Devereux and Wen ( 1996) emphasizes a somewhat different mechanism: political instability induces incumbent governments to leave smaller assets to their successors, thereby forcing them to tax capital at a higher rate; the expectation of higher taxes drives down private investment, which leaves a smaller tax base for the successor government. =

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7. 3. Property rights and growth As mentioned in the introduction, the data support the idea that poor enforcement of property rights is harmful for investment and growth. This idea is also derived from some recent theoretical work. Benhabib and Rustichini ( 1 996) study a growth model where two groups try to redistribute consumption towards themselves at the expense of the economy's capital stock. They show how such incentives may arise both at low and high levels of income, and how they may be exacerbated by greater inequality in the two groups' incomes. Their model abstracts from the political mechanism and the channels of redistribution, however. Tornell and Velasco ( 1 992) focus on redistribution through the fiscal policy process in a linear (Ak) growth model. Their argument, as Benhabib and Rustichini's, is another instance of the common pool problem discussed in subsection 6.3. The common pool is now a part of the economy capital stock rather than the government tax base, but the incentive to over-exploit this common pool is the same. Because the redistribution is supposed to take place via the government policy process, the poorly enforced property rights are closely related to weak government. Tornell ( 1 995) studies a related model, but allows for endogenous property rights. In particular, property rights can be created and destroyed at a cost. He shows that the economy can go through a cycle with low property-rights protection at low and high levels of income. If so, this pattern is perfectly foreseen and leads to gradually falling growth rates at intermediate levels of income. Lane and Tornell (1 996) show that an exogenous positive shock due to productivity or the terms of trade may actually reduce the growth rate in an economy with powerful interest groups and poorly defined property rights. The mechanism is again a coordination failure between the interest groups, whereby the initial increase in the incentives to invest is more than outweighed by an increase in redistributive transfers. Svensson ( 1 996) produces a related result, where the incentives of the interest groups to hold back on their demand for transfers vary negatively with government income.

7.4.

Notes on the literature

Beyond the papers cited in the text, early contributions to the theory of income distribution, investment and growth were made by Perotti ( 1 993), who studied human capital accumulation, and tax-financed subsidies in the presence of borrowing constraints, by Bertola ( 1 993) who studied tax policy and the functional distribution of income, by Glomm and Ravikumar ( 1 992) who studied private versus public provision of education, and by Saint-Paul and Verdier ( 1 993) who also studied redistributive policies that finance public education in a setting with wealth-constrained individuals. Perotti ( 1 996) and Benabou ( 1 996) provide additional references to recent empirical work. Finally, Caballero and Hammour ( 1 996) focus on the rents created by factor specificity and how the distribution of those rents affects the incentives to invest. As stated in the text, few theoretical models spell out the mechanisms whereby political

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instability is harmful for growth. As emphasized by Benabou ( 1 996), there is thus scope for new work to provide better theoretical underpinnings for the empirical findings. Sharper theory is also needed to sort out the empirical channels whereby politics interacts with growth. This is not going to be easy, however, given the strong empirical correlations between inequality, instability and lacking enforcement of property rights. We want to end with a methodological note. In this section, as in the previous one, we have relied exclusively on simple two-period examples. This avoids a major difficulty: a full-fledged treatment of the dynamic interactions between collectively chosen policy decisions and income distribution rapidly becomes analytically complex. As a result, the dynamic models studied in the literature have often relied on simplifying assumptions: dynamic links are assumed away in the model's economic structure, voting only takes place at an initial point in time rather than sequentially over time, or agents are assumed to be myopic and ignore some of the dynamic implications of their actions. The clearest formulation of a general solution concept for dynamic political models with heterogenous agents is made in Krusell and Rios-Rull (1996). This paper also makes a contribution by showing how the endogenous build-up of vested interests, as agents acquire monopoly skills in operating new technologies, can lead to a growth cycle: the political majority at different points in time will shift between less and more growth-promoting policies. Krusell et al. ( 1 997) survey parts of the literature on politics and growth from a methodological angle. They also show how to go from their proposed solution concept to quantitative (numerical) applications.

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McCallum, B.T. ( 1 996), "Crucial issues concerning central bank independence", Working Paper No. 5597 (NBER). Meltzer, A.H., and S. Richards ( 1 98 1), "A rational theory of the size of government", Journal of Political Economy 89:9 1 4-927. Mendoza, E . , A. Razin and L. Tesar ( 1994), "Effective tax rates in macroeconomics: cross-country estimates of tax rates on factor incomes and consumption", Journal of Monetary Economics 34: 297-323. Mendoza, E., G.-M. Milesi-Ferrctti and P. Asea ( 1996), "On the ineffectiveness of tax policy in altering long-run growth: Harberger's superneutrality conjecture", Discussion Paper No. 1 378 (CEPR). Milesi-Ferretti, G.-M. ( 1 994), "Wage indexation and time consistency", Journal of Money, Credit and Banking 26:941-950. Milesi-Ferretti, G.-M. ( 1 995a), "Do good or do well? Public debt management in a two-party economy", Economics and Politics 7:58-74. Milesi-Ferretti, G.-M. ( 1 995b), "The disadvantage of tying their hands: on the political economy of policy commitments", Economic Journal 1 05 : 1 381-1402. Mishkin, F.S., and A. Posen (1 996), "Experiences with inflation targeting as a strategy for the conduct of monetary policy", mimeograph (Federal Reserve Bank of New York). Mishkin, F.S., and A. Posen (1 997), "Inflation targeting: lessons from four conntries", Federal Reserve Bank of New York Economic Policy Review 3:9-1 1 0 . Mishra, D . (1 997), "An unbiased reexamination o f political cycle in OECD countries", mimeograph (University of Maryland). Missale, A., and O.J. Blanchard (1 994), "The debt burden and debt maturity", American Economic Review 84:309-3 1 9. Missale, A., F. Giavazzi and P. Benigno ( 1 997), "Managing the public debt in fiscal stabilizations: theory and practice", Working Paper (IGIER). Mueller, D. ( 1 989), Public Choice II (Cambridge University Press, Cambridge). Mussa, M . (1 986), "Nominal exchange rate regimes and the behavior of real exchange rates", Carnegie­ Rochester Conference Series on Public Policy 25: 1 1 7-2 1 4 . Myerson, R . ( 1993), "Incentives to cultivate favored minorities under alternative electoral systems", American Political Science Review 87:856-869. Nordhaus, W. ( 1 975), "The political business cycle", Review of Economic Studies 42: 1 69-190. North, D., and B. Weingast ( 1989), "Constitutions and commitment: the evolution of institutions governing public choice in seventeenth-century England", Journal of Economic History 69:803-832. Obstfeld, M. (1 997a), "Destabilizing effects of exchange rate escape clauses", Journal of International Economics 43 : 6 1--77. Obstfeld, M. ( 1997b), "Dynamic seigniorage theory: an exploration", Macroeconomic Dynamics 1 : 588-6 14. Ozier, S., and G. Tabellini ( 1 99 1 ), "External debt and political instability", Working Paper No. 3772 (NBER). Parkin, M. ( 1 993), "Inflation in North America", in: K. Shigehara, ed., Price Stabilization in the 1 990s (Macmillan, London) 47-93. Perotti, R. ( 1 993), "Political equilibrium, income distribution and growth", Review of Economic Studies 60:755- -776. Perotti, R. ( 1 996), ''Growth, income distribution and democracy: what the data say", Journal of Economic Growth 1 : 149-1 88. Persson, M., T. Persson and L.E.O. Svensson ( 1 987), "Time consistency of fiscal and monetary policy", Econometrica 5 5 : 1 4 1 9-143 1 . Persson, M., T. Persson and L.E.O. Svensson ( 1 997), "Debt, cash flow and inflation incentives: a Swedish example", in: M. King and G. Calvo, eds., The Debt Burden and it Consequences for Monetary Policy (MacMillan, London) 28-62.

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Persson, T., and L.E.O. Svensson ( 1984), "Time consistent fiscal policy and government cash flow", Journal of Monetary Economics 14:365-374. Persson, T., and L.E.O. Svensson ( 1 986), "International borrowing and time-consistent fiscal policy", Scandinavian Journal of Economics 88:273-295 . Persson, T. , and L.E.O. Svensson ( 1 989), "Why a stubborn conservative would run a deficit: policy with time-inconsistency preferences", Quarterly Journal of Economics 1 04:325-345 . Persson, T., and G. Tabellini (1 990), Macroeconomic Policy, Credibility and Politics (Harwood Academic Publishers, Chur). Persson, T., and G. Tabellini ( 1992), "The politics of 1 992: fiscal policy and European integration", Review of Economic Studies 59:689-701 . Persson, T. , and G. Tabellini ( 1 993), "Designing institutions for monetary stability", Carnegie-Rochester Conference Series on Public Policy 39:53-89. Persson, T., and G. Tabellini, eds ( 1 994a), Monetary and Fiscal Policy. vol. 1, Credibility; vol. II, Politics (MIT Press, Cambridge, MA). Persson, T., and G. Tabellini ( 1994b), "Is inequality harmful for growth?", American Economic Review 84:600-621 . Persson, T., and G. Tabellini ( 1 994c), "Representative democracy and capital taxation", Journal of Public Economics 55:53-70. Persson, T., and G. Tabellini ( 1 995), Double-edged incentives: institutions and policy coordination, in: G. Grossman and K. Rogoff, eds., Handbook of International Economics, vol. III (North-Holland, Amsterdam) 1 973-2030. Persson, T., and G. Tabellini ( 1996), "Monetary cohabitation in Europe", American Economic Review, Papers and Proceedings 86: 1 1 1 --1 1 6. Persson, T., and G. Tabellini (1 999), "Political economics and public finance", in: A. Averbach and M. Feldstein, eds., Handbook of Public Economics (Elsevier Science, Amsterdam) forthcoming. Persson, T., G. Roland and G. Tabellini ( 1 997), "Separation of powers and political accountability", Quarterly Journal of Economics 1 1 2 : 1 1 63-1202. Petterson, P ( 1 997), "An empirical investigation of the strategic use of debt", mimeograph (Uppsala University). Posen, A. ( 1 993), "Why central bank independence does not cause low inflation: there is no institutional fix for politics", min1eograph (Harvard University). Posen, A. ( i 995), "Declarations are not enough: financial sector services of central bank independence", in: B.S. Bernanke and J.J. Rotemberg, eds., NBER Macroeconomics Annual 1 995 (MIT Press, Cambridge, MA) 253-274. Poterba, J.M. ( 1994), "State responses to fiscal crises: natural experiments for studying the effects of budget institutions", Journal of Political Economy 1 02 :799-821 . Przcworski, A., and F. Limongi ( 1 993), "Political regimes and economic growth", Journal of Economic Perspectives 7:5 1 �70. Riley, J. (1 980), "Strong evolutionary equilibrium and the war of attrition", Journal of Jheoretical Biology 82:383-400. Roberts, K. (1 977), "Voting over income tax schedules", Journal of Public Economics 8:329-340. Rogers, C. ( 1 986), "The effects of distributive goals on the time inconsistency of optimal taxes", Journal of Monetary Economics 1 7:25 1 --270. Rogers, C. (1 987), "Expenditure taxes, income taxes, and time-inconsistency", Journal of Public Economics 32:2 1 5-230. Rogoff, K. ( 1 985), "The optimal degree of commitment to an intermediate monetary target", Quarterly Journal of Economics I 00: 1 1 69-1 1 90. Rogoff; K. ( 1987), "A reputational constraint on monetary policy", Carnegie-Rochester Conference Series on Public Policy 24: 1 15-165. Rogoff, K . (1 990), "Equilibrium political budget cycles", American Eronomic Review 80:21-36.

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Rogoff, K., and A. Sibert ( 1 988), "Elections and macroeconomic policy cycles", Review of Economic Studies 5 5 : 1-16. Rotemberg, J.J. (1 990), "Constituencies with finite lives and the valuation of government bonds", mimeograph (MIT). Roubini, N., and .T. Sachs ( 1989), "Political and economic determinants of budget deficits in the industrial democracies", European Economic Review 33:903-933 . Saint-Paul, G., and T. Verdier ( 1 993), "Education, democracy and growth", Journal o f Development Economics 42:399-407. Scha1ing, E. (1 995), Institutions and Monetary Policy: Credibility, Flexibility, and Central Bank Independence (Edward Elgar Publishers, Aldershot). Schotter, A. ( 1 98 1), The Economic Theory of Social Institutions (Cambridge University Press, Cambridge). Staiger, R. (1995), "International rules and institutions for cooperative trade policy", in: G. Grossman and K. Rogoff, eds., Handbook of International Economics, vol. III (North-Holland, Amsterdam) 1495-1 5 5 1 . Stock, J.H., and M.W. Watson (1 999), "Business cycle fluctuations in US macroeconomic time se1ies", ch. 1 , this Handbook. Svensson, J. (1 996), "Collusion and interest groups: foreign aid and rent dissipation", mimeograph (The World Bank). Svensson, J. (1 998), "Investment, property rights and political instability: theory and evidence", European Economic Review 42: 1 3 17-1341. Svensson, L.E.O. (1 997a), "Optimal inflation targets, 'conservative' central bankers and linear inflation contracts", American Economic Review 87:98- 1 14. Svensson, L.E.O. (1997b), "Inflation forecast targeting: implementing and monitoring inflation targets", European Economic Review 4 1 : 1 1 1 1-1 1 46. Tabellini, G. ( 1985), "Accommodative monetary policy and central bank reputation", Giomalc Dcgli Economisti 44:389-425. Tabellini, G. (1 987), Money, debt and deficits in a dynamic game, Journal of Economic Dynamics and Control 1 0:427-442. Tabellini, G. (1 990), "A positive theory of social security", Working Paper No. 3272 (NBER). Tabellini, G. ( 1 991 ) "The politics of intergenerational redistribution", Journal of Political Economy 99:335-357. Tabellini, G., and A. Alcsina ( 1 990), "Voting on the budget deficit", American Economic Review 80:37-39. Taylor, J.B. (1 983), "Rules, discretion and reputation in a model of monetary policy: Comments", Journal of Monetary Economics 1 2 : 1 23-125. Terrones, M. ( 1989), "Macroeconomic policy choices under alternative electoral structures", mimeograph (University of California at Berkeley). Tornell, A. (1 995), "Economic growth and decline with endogenous property 1ights", mimeograph (Harvard University). Tornell, A., and A. Velasco (1 992), "The tragedy of the commons and economic growth: why docs capital flow from poor to rich countries", Journal of Political Economy 1 00 : 1 208-123 1 . Velasco, A . ( 1994), "Are balance of payment crises rational?", Working Paper (New York University} Velasco, A. (1 999), "A model of endogenous fiscal deficit and delayed fiscal reforms", in: J. Poterba and J. von Hagen, eds., Fiscal Institutions and Fiscal Performance (University of Chicago Press, Chicago, IL) 37-58. Vickers, J. (1 986), "Signalling in a model of monetary policy with incomplete infonnation", Oxford Economic Papers 38:443-55. von Hagen, J. (1 992), "Budgeting procedures and fiscal performance in the European communities", Economic papers No. 96 (European Commission). ,

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von Hagen, J., and I. Harden ( 1 995), "National budget processes and fiscal performance", European Economy, Reports and Studies 3. Waller, C. ( 1989), "Monetary policy games and central bank politics", Journal of Money, Credit and Banking 2 1 :422-43 1 . Waller, C., and C.E. Walsh (1 996), "Central bank independence, economic behavior, and optimal term limits", American Economic Review 96: 1 1 39-1 1 53 . Walsh, C.E. ( 1995a), "Optimal contracts for central bankers", American Economic Review 85: 1 50-167. Walsh, C.E. ( 1995b), "Is New Zealand's Reserve bank act of 1 989 an optimal central bank contract?", Journal of Money Credit and Banking 27: 1 179-1 1 9 1 .

Chapter 23

ISSUES IN THE DESIGN OF MONETARY POLICY RULES* BENNETT T. McCALLUM Carnegie Mellon University and National Bureau of Economic Research Contents

Abstract Keywords 1 . Introduction 2. Concepts and distinctions 3 . Special difficulties 4. Choice of target variable 5. Choice of instrument variable 6. Issues concerning research procedures 7. Interactions with fiscal policy 8. Concluding remarks References

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The author is indebted to Peter B. Clark, Todd Clark, Charles Evans, Robert Flood, Marvin Goodfriend, Charles Goodhart, Andrew Haldane, Robert Hetzel, Lars Jommg, Allan Meltzer, Edward Nelson, Christopher Sims, Lars Svensson, John Taylor, John Whittaker, and especially Michael Woodford for helpful suggestions and CJiticisms. Handbook of Macroeconomics, Volume I, Hdited by JB. Taylor and M. Woodford © 1999 Elsevier Science B. V. All rights reserved 1483

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Abstract

This chapter begins with a number of important preliminary issues including the distinction between rules and discretion in monetary policy; the feasibility of committed rule-like behavior by an independent central bank; and optimal control vs. robustness strategies for conducting research. It then takes up the choice among alternative target variables - with the most prominent contenders including price level, nominal income, and hybrid (inflation plus output gap) variables - together with the issue of growth-rate vs. growing-level target path specifications. One conclusion is that inflation and nominal income growth targets, but not the hybrid target, would have induced fairly similar policy responses in the US economy over 1 960- 1 995. With regard to instrument choice, the chapter argues that both nominal interest rate and monetary base measures are feasible; this discussion emphasizes the basic conceptual distinction between nominal indeterminacy and solution multiplicity. Accordingly, root-mean-square-error performance measures are estimated for interest rate and base instruments (with nominal income target) in the context of a VAR model. Other topics emphasized in the chapter include the operationality of policy-rule specifications; stochastic vs. historical simulation procedures; interactions between monetary and fiscal policies; and the recently-developed fiscal theory of the price level.

Keywords

Jl!.L classification:

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1 . Introduction

The topic of rules for the conduct of monetary policy has a long and distinguished history in macroeconomic analysis, with notable contributions having been made by Thornton ( 1 802), Bagehot ( 1 873), Wicksell ( 1 907), Fisher ( 1 920, 1 926), Simons ( 1 93 6), M. Friedman ( 1 948, 1 960), and others 1 . A major reorientation in the focus of the discussion was provided as recently as 1 983, however. In particular, Barra and Gordon ( 1 983a) built upon the insights of Kydland and Prescott ( 1 977) in a manner that put an end to the previously widespread notion that policy rules necessarily involve fixed settings for the monetary authority's instrument variable. This step served to separate the "rules vs. discretion" dichotomy from the issue of "activist vs. non­ activist" policy behavior and thus opened the door to possible interest in policy rules on the part of actual monetary policymakers - i.e., central bankers. In fact there has been a great increase in apparent interest in rules by policymakers during recent years - say, 1 990- 1 996. Evidence in support of that claim is provided by several studies conducted at the Federal Reserve's Board of Governors of the rule introduced by John Taylor ( 1 993b), such as Brayton et al. ( 1 997) and Orphanides et al. ( 1 998), as well as by discussions of this rule in speeches by members of the Board [e.g., Blinder ( 1 996)] . In the United Kingdom, interest by the Bank of England in Taylor's rule as well as an alternative due to McCallum ( 1 988, 1 993a) is clearly indicated in an article by Stuart ( 1 996) that attracted considerable attention in the British press. Numerous analytical studies of these rules 2 have been conducted by central bank economists from a number of conntries 3 . To some extent this upsurge in interest is related to the arrival of inflation targeting as a leading candidate for the provision of a practical guideline for monetary policy, significant applications having been introduced during 1 990- 1 993 in Canada, New Zealand, Finland, Sweden, and the United Kingdom 4. There are, to put it mildly, numerous issues concerning monetary policy rules on which professional agreement is far from complete, even among academics - that is, even neglecting the split between academic and central-bank views, which itself has probably diminished in recent years. The main purpose of this chapter is to survey the most critical of these issues. The first to be discussed, which concerns the fundamental nature of policy rules and an independent central bank's capacity to

1 For other early rule proposals, sec Laidler ( 1 996) and Humphrey ( 1 992). Also sec Jonung ( 1979) for an interesting discussion of the Swedish experience of the 1 930s. 2 Including proposals of Meltzer (1 984, 1 987), Hall ( 1 984), Hall and Mankiw ( 1994), Feldstein and Stock ( 1 994), and Gavin and Stockman ( 1 990). 3 An incomplete list of notable studies would include those mentioned above plus Hess, Small and Brayton ( 1993), Clark ( 1994), Croushore and Stark ( 1 995), Dueker ( 1 993), Dueker and Fischer ( 1 995), Estrella and Mishkin ( 1997), Judd and Motley ( 1 9 9 1 , 1 992), Haldane and Salmon ( 1 995), King ( 1 996), and Jefferson ( 1 997). Many more have been added since this chapter was written, most featuring Taylor's rule. 4 There is a sizable and growing literature on inflation targeting that will be mentioned below.

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behave in accordance with a rule - i.e., the commitment problem - is reviewed in Section 2. Next, Section 3 takes up some special difficulties that bedevil all attempts to design good policy rules and also to study ones previously proposed, namely, the lack of agreement (especially among academics) concerning models of monetary policy effects - and the associated social costs of inflation and unemployment - plus the existence of ongoing changes in economic structure relevant to monetary policymaking (e.g., improvements in payments technology). Two major substantive areas of rule design, the specification of target and instrument variables, are then taken up in Sections 4 and 5. In the first of these, the choice among basic target variables - such as exchange rate, price level, or nominal income measures - is considered along with the desirability of specifying target paths in trend­ stationary or difference-stationary form (i.e., levels vs. growth rates). In the second, the classic dispute between advocates of interest-rate and monetary-base (or bank reserve) instruments is reviewed, brief discussions being given of the rather extreme views that one or the other is actually infeasible as an instrument. The following pair of sections, 6 and 7, take up a number of analytical issues involving the study of candidate rule specifications. Among these are the design of simulation exercises; issues involving operationality (i.e., feasibility of specified instruments and information sets); and the interaction of monetary and fiscal policy rules. Finally, a brief conclusion is included as Section 8 . Since the author has been writing o n the subject o f monetary rules for well over a decade, it would be futile to pretend that the chapter's discussion will be entirely "balanced" or "unbiased". What is intended, rather, is that important alternative points of view are mentioned and presented with reasonable accuracy even where agreement is lacking. Another recent overview is provided by Clarida, Gali and Gertler ( 1 999). 2 . Concepts and distinctions

The crucial point that a policy rule can be activist has already been mentioned. Of course this is a matter of definition; thus the use of a terminological system that does not permit rules to be activist - i.e., to involve policy instrument settings that are conditional on the state of the economy - cannot be ruled out on strictly logical grounds. But since the publication of Barro and Gordon ( 1 983a), standard usage in the profession has been virtually unanimous in permitting activist rules and in basing the "rules vs. discretion" distinction on the manner in which (typically activist) instrument settings are determined. Roughly speaking, discretion implies period-by­ period reoptimization on the part of the monetary authority whereas a rule calls for period-by-period implementation of a contingency formula that has been selected to be generally applicable for an indefinitely large number of decision periods. The foregoing distinction is satisfying and straightforward to apply in the context of the simple "workhorse" model that features a surprise Phillips curve as utilized by Kydland and Prescott ( 1 977), Barro and Gordon ( 1 983a,b), and a host of subsequent

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writers. When it comes to practical application to the behavior of actual central banks, however, the distinction is not so easily drawn. Suppose that a particular central bank, which presumably cares about both inflation and unemployment outcomes, is observed regularly to be more stimulative when recent unemployment is high and/or current macroeconomic shocks threaten to increase unemployment. How does one decide whether this central bank's behavior should be classified as discretionary or rule-based but activist? Within a simple model one can calculate the settings implied by each type of behavior, or simply observe whether inflation exceeds its target value on average (i.e., whether the discretionary inflation bias is present). But such steps are not possible for an actual central bank, because there will typically not be any clear-cut agreement concerning the nature and magnitude of shocks that have occurred in specific historical periods or even (in many cases) agreement as to the prevailing target inflation rate expressed in precise quantitative terms - even for analysis within the central bank itself. Taylor ( 1 993b) explicitly addressed the problem of distinguishing "rule-like" from discretionary behavior in practice, recognizing that no actual central bank would be likely to follow literally a simple formula for its instrument settings but contending that the distinction could be of importance nevertheless 5 . The key, Taylor suggested, is that rule-like behavior is systematic in the sense of "methodical, according to a plan, and not casual or at random". Clearly, being systematic is a necessary condition for rule-like behavior, but even those central bankers who defend discretionary behavior do not think of it as unsystematic. Accordingly, McCallum ( 1 993b) argues that being systematic is not sufficient and points out that discretionary behavior in the workhorse model can, even with the inclusion of random shock terms, be accurately represented by systematic application of a simple formula. The needed additional criterion, McCallum suggests, is that the monetary authority "must also design the systematic response pattern [so as] to take account of the private sector's expectational behavior" (p. 2 1 7), i.e., to optimize once, not each period. Taking such account is basically what Barro and Gordon ( 1 983a) specified in their characterization, within the workhorse model with rational expectations, of policy according to a rule. There is then no attempt to exploit temporarily given inflationary expectations for brief output gains 6. Qualitative knowledge of the policymaking process of an actual central bank may then be sufficient in some cases to determine whether or not policy responses are designed to try to exploit temporarily given expectations.

5

Taylor, like Judd and Motley ( 1992), envisions the genuine possibility that central banlc policy committees would enrich their considerations by referring to the instrument settings suggested by a numerical rule, e.g., taking them as a starting point for their policy deliberations. 6 It may be asked why a one-time optimization will not involve the exploitation of expectations that happen to exist at the time. But my meaning of systematic implies that the same actions are specified each time the same conditions are faced, so the response pattern cannot be different for the "first" or "first few" periods. Basically, the optimization calculation must be made from the perspective of a dynamic stochastic steady state.

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It is interesting to note, parenthetically, that although Milton Friedman has never embraced the concept of activist rules, in one of his most carefully considered arguments on behalf of nondiscretionary monetary policy the crucial advantage of a rule is said to be that decisions are made in the form of a policy applicable to many distinct cases, not on a case-by-case basis, with such a form of policymaking having favorable effects on expectations. In particular, Friedman ( 1 962) suggests that monetary policymaking is in important ways analogous to freedom-of-speech issues, in the sense that adopting a rule that applies in general will on average lead to different and preferable - outcomes than those generated by decision making on a case-by-case basis. After presenting the analogy and remarking on "our good fortune of having lived in a society that did adopt the self-denying ordinance of not considering each case of [contested] speech separately" ( 1 962, p. 24 1), Friedman contends that: Exactly the same considerations apply in the monetary area. If each case is considered on its [individual] merits, the wrong decision is likely to be made in a large fraction of cases because the decision-makers are . . . not taking into account the cumulative consequences of the policy as a whole. On the other hand, if a general rule is adopted for a group of cases as a bundle, the existence of that rule has favorable effects on people's attitudes . . . and expectations that would not follow even from the discretionary adoption of precisely the same [actions] on a series of M Friedman (1962, p. 241) separate occasions.

Thus we see that the logic of Friedman's argument is basically the same as that identified by Barro and Gordon ( 1 983a) and is entirely compatible with "activism," i.e., conditioning clauses in the rule 7 . A controversial issue i s whether it i s feasible for an independent central bank to behave in a rule-like fashion. The most straightforward point of view is that expressed by Taylor ( 1 983, 1 993b), McCallum ( 1 995b, 1 997b), Kydland and Prescott ( 1 977), and Prescott ( 1 977), namely, that an independent central bank is perfectly free to choose its instrument settings as it sees fit. Since it will generate superior outcomes on average if it does so in a rule-like manner, and is presumably capable of understanding that, the well-managed central bank will in fact behave in such a manner. This requires it to adopt instrument settings that are different, however, from those that would appear optimal if it were making a fresh optimization calculation each period (i.e., not considering the cases as a group). Thus many authors have suggested that, since there is no tangible "commitment technology" to guarantee that future choices will be made similarly, independent central banks are inevitably destined to behave in a discretionary fashion, making a fresh optimization calculation each period. One of the strongest explicit statements of this position has been made by Chari, Kehoe and Prescott ( 1 989, p. 303), as follows: "We should emphasize that in no sense can societies choose between commitment [and] time-consistent [i.e., discretionary] equilibria. Commitment technologies are like technologies for making shoes in an Arrow-Debreu

7 An example of a conditioning clause in the freedom-of-speech example would be one petiaining to cases of false alam1s shouted in "crowded theaters".

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model - they are either available or not". But while this form of language is rather extreme, the position taken is probably more representative of academic thought over (say) 1 984- 1 994 than is the pragmatic Taylor-McCallum position. That is, most analyses of the consequences of various issues simply presume, often without explicit justification, that central bank behavior will be of the uncommitted discretionary type 8 . In many cases it i s contended that there i s a necessary tradeoff between commitment and flexibility, which the Taylor-McCallum position denies. The justification typically given, explicitly or implicitly, for the assumption of (suboptimal) discretionary behavior is that although rule-like behavior is superior on average, it remains true that within each period prevailing expectations are "given" so each extra bit of inflation or monetary ease will add output or reduce unemployment, implying that the discretionary choice would typically be superior from the perspective of that single period. Furthermore, the public understands this feature of policy choice, according to the usual position, so individuals will expect the central bank to behave discretionarily, thereby making the discretionary action preferable (from the single­ period perspective). But to conclude that the central bank will therefore consistently choose the discretionary outcome is analytically to adopt a particular equilibrium concept - see Chari, Kehoe and Prescott ( 1 989). The solution concept preferred by Taylor, McCallum, Lucas ( 1 976, 1 980), and Prescott ( 1 977) is simply rational expectations in a competitive model with a monetary authority that behaves as a Stackelberg leader vis-a-vis the private sector 9. To the present writer the latter concept seems more plausible 1 0 , but the key point here is that neither of the two modes of central bank behavior -· rule-like or discretionary - has as yet been firmly established as empirically relevant or theoretically appropriate. Also, it would seem to be indisputable that there is nothing tangible to prevent a central bank from behaving in a rule-like

B A particularly striking example of the importance of this assumption is provided by Svensson ( 1 996), who argues that in the workhorse model, extended to include persistence of output or unemployment in the surprise Phillips relationship, price-level targeting will lead to less inflation variability (as well as less price-level variability) than will inflation targeting. This dramatic result depends, however, upon the presence of discretionary behavior on the part of the monetary authority. It docs not obtain if the central bank is behaving in a rule-like fashion. Svensson ( 1 996) recognizes this point but his discussion emphasizes the discretionary case. Y This exposition docs not explicitly refer to the rcputational models pioneered by Barro and Gordon ( l983b) the reason being that the author finds these models implausible. Of course the argument here advanced relies upon reputational effects, but does not utilize the type of equilibria featured in the reputation literature. 10 Empi1ically it is - unlike the usual position - consistent with the "free lunch" finding that increased CB independence provides improved inflation performance without increased output employment variability. On this finding, see Fischer ( 1 995) or Debelle and Fischer ( 1 995, p. 201 ). It should be noted, incidentally, that my hypothesis is quite different from that of Mervyn King ( 1 996), who suggests that CBs do not aim for output in excess of the natural rate value (as they do in the workhorse model). The latter implies, since inflation and output desires are reflected in separate terms in King's loss fi.mction, that actual CBs would not want to keep output above the natural rate value euen if they could do so without generating any inflationary tendency. ,

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fashion 1 1 so that there is no necessary (i.e. , inescapable) tradeoff between "flexibility and connnitment", as has often been suggested 1 2 . This position does not deny that central banks are constantly faced with the temptation to adopt the discretionary policy action for the current period; it just denies that succumbing to this temptation is inevitable. In practice, adoption of rule-like decision making procedures is one mechanism for combating these temptations.

3. Special difficulties

To economists who do not specialize in monetary or macroeconomic issues, it may seem surprising or perhaps a matter for professional embarrassment that a large volume of debate can be sustained on the subject of monetary policy rules. Surely, the argument would go, it should not be terribly difficult to conduct an optimal control exercise using some reasonably good macroeconometric model and thereby discover what an optimal monetary policy rule would be. This would have to be done for a number of different economies, of course, but the problems involved are in principle almost negligible and in practice are easily surmountable. Admittedly, the model would have to be one that is structural - policy invariant - so as not to be subject to the Lucas critique ( 1 976), but that necessity has been well understood for many years by now 1 3 . In fact, however, such an argument fails entirely to recognize one basic and fundamental difficulty that underlies a large fraction of the issues concerning monetary policy rules. This difficulty stems from the lack of professional agreement concerning the appropriate specification of a model suitable for the analysis of monetary policy issues. There are various aspects of such a model that different researchers would emphasize. Many would suggest that money demand theory is quite undeveloped and inadequate for policy analysis. The viewpoint taken in McCallum ( 1 997a), by contrast, contends that it is the dynamic connection between monetary policy actions and real aggregative responses that is the main source of difficulty 14• Others, including 1 1 In the workhorse model, policy settings of both the committed and discretionary type may be expressed as resulting from policy feedback equation of the form n, a0 + a1E1_ 1 n1 + a2 u1, with different coefficient values. Here E1 1 n1 represents prevailing expectations and u1 is a current macroeconomic shock. There is nothing tangible to prevent ai choices that represent conunitment. 1 2 The absence of any inescapable tradeoff is implicit in the central bank contracting approach pioneered by Walsh (1995) and Persson and Tabellini (1993). Taylor ( 1979) conducted an optimal policy exercise in the context of a dynamic macro model with rational expectations ahnost 20 years ago. 1 4 In this reference, the argument is stated as follows. It is not just that the economics profession does not have a well-tested quantitative model of the quarter-to-quarter dynamics, the situation is much worse than that: we do not even have any basic agreement about the qualitative nature of the mechanism. This point can be made by mentioning some of the leading theoretical categories, which include: real business cycle models; monetary misperception models; semi-classical price adjustment models; models with overlapping nominal contracts of the Taylor variety or the Fischer variety or the Calvo-Rotemberg =

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King ( 1 993) and Fuhrer ( 1 997) would point to weaknesses in modeling investment or consumption behavior, and of course empirical understanding of exchange rates and other open-economy influences is widely regarded as highly unsatisfactory. But whatever the particular model component that is singled out for special criticism, it seems extremely hard to avoid the conclusion that agreement upon macroeconomic model specification is predominantly absent - and that different models carry highly different alleged implications for monetary policy. The upshot, clearly, is that in practice one cannot simply conduct an optimal control exercise with an "appropriate" model. That approach simply collapses in response to the question "What is the appropriate model?" In light of this mundane but fundamental difficulty, the research strategy recommended by several writers including Blanchard and Fischer ( 1 989, p. 582), McCallum ( 1 988, 1 997a), and to some extent Brunner ( 1 980) - is to search for a policy rule that possesses "robustness" in the sense of yielding reasonably desirable outcomes in policy simulation experiments in a wide variety of models. In effect, the same type of approach is collectively utilized by the various teams of researchers participating in the Brookings projects directed by Ralph Bryant [Bryant et al. 1 988, 1 993)] 1 5 . It i s worth mentioning briefly that the research strategy based on robustness may serve to some extent as a protection against failures of the Lucas-critique type. That critique is best thought of not as a methodological imperative regarding model building strategies, but as a reminder of the need to use policy-invariant relations in simulation studies and especially as a source of striking examples in which policy invariance is implausible. The construction of a policy-invariant model faces a major difficulty, however, in the above-mentioned absence of professional agreement about model specification. Thus it would seem sensible to consider a variety of models in the hope that one will be reasonably well specified - and therefore immune to the critique - and search for a rule that will perform satisfactorily in all of them 1 6 . Of course, there is no need for such a project to be carried out by a single researcher; furthermore, attempts to make each contending model policy invariant would enhance the effectiveness

type; models with nominal contracts set as in the recent work of Fuhrer and Moore; NAIRU models; Lucas supply function models; MPS-style markup pricing models; and so on. Not only do we have all of these basic modeling approaches, but to be made operational each of them has to be combined with some measure of capacity output a step that itself involves competing approaches - and with several critical assmnptions regarding the nature of different types of unobservable shocks and the time­ series processes generating them. Thus there are dozens or perhaps hundreds of competing specifications regarding the precise nature of the connection between monetary policy actions and their real short-term consequences. And there is little empirical basis for much narrowing of the range of contenders. 1 5 For the optimal-design point of view, see Fair and Howrey ( 1 996). 1 6 From the perspective of the robustness approach, there is something to be said in favor of expressing "satisfactorily" in terms of nominal variables - even though individuals are concerned ultimately with real magnitudes - because the relationship between monetary policy instruments and nominal variables may be less subject to Lucas-critique difficulties than is the case with real variables. An argument to this effect is attempted in McCallum (1 990b, pp. 2 1 -22).

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of the overall proj ect. Thus there is no necessary conflict between a robustness­ oriented strategy and studies by individual researchers that involve construction of single models [e.g., Ireland ( 1 997), Rotemberg and Woodford ( 1 997)] . The lack of professional agreement over model specification also makes it difficult to reach any firm conclusions about the proper goals of monetary policy, as is discussed at the end of this section, before the related but more pragmatic issue of target variables is taken up. Other issues that are of greater technical interest but less fundamental importance - for example, issues concerning operationality and the simulation teclmiques appropriate for investigating a rule's properties - will be considered below, in Section 6. In any discussion of monetary policy, but especially in ones involving the design of rules, it is useful to adopt a terminology regarding goals, objectives, targets, instruments, etc., that clearly reflects basic conceptual distinctions and at the same time is reasonably orthodox (or at least non-idiosyncratic). With those criteria in mind, we shall below use the word goals to refer to the ultimate but typically non­ operational objectives of the monetary authority, and the term target to refer to an operational variable that takes precedence in the actual conduct of policy. The leading contenders for a central bank's target variable would be some comprehensive price index, nominal GDP or some other measure of nominal spending, a monetary aggregate, or a foreign exchange rate - with growth rates rather than (growing) levels perhaps pertaining in the case of the first three. The choice among target variables will be considered in some detail in Section 4. At the opposite end of the scale from goals are instrument variables, i.e., the variables that central banks actually manipulate more or less directly on a daily or weekly basis in their attempts to achieve specified targets. For most central banks, some short-term interest rate would be regarded as the instrument variable, but some analysts continue to promote the monetary base (or some other controllable narrow aggregate) in that capacity. It must be said that a term such as "operating target" would probably be nearer to standard for central bank economists or even policy-oriented academics, and there is a sense - to be described momentarily - in which it is more accurate than "instrument variable". But in an article such as the present one it would seem desirable to employ a terminology that promotes a clear distinction between target and instrument variables. Thus we seek to avoid ambiguous usage such as "interest rate targeting" to refer to a central bank's weekly instrument (or operating target) settings, rather than its policy-governing target variable. The sense in which "operating target" would be preferable to "instrument" is as follows. Many actual central banks choose not to manipulate their interest rate instruments in a literally direct fashion but rather to conduct open-market operations only once a day with quantities chosen so as to be expected to yield a market-influenced interest rate that lies within (or close to) some rather narrow band. The USA's Federal Reserve, for example, typically enters the Federal Funds market only once a day (normally around 1 0:30--10:45 a.m.) so the end-of-day or daily average value of the Federal Funds rate (FF rate) can depart from the open-market desk's "target value" by

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20-30 basis points on any given day. Thus writers such as Cook and Hahn ( 1 9 89) or Rudebusch ( 1 995) will distinguish between "actual" and "target" values at the daily level. But the Fed keeps the FF rate within a few basis points of its operating target on average over periods as short as a week. Thus there is little harm, in a study such as the present one, in using the term instrument variable and pretending that the Fed controls its interest instrument directly. There is, it should be said, a significant amount of debate over the feasibility of a central bank's using one variable or another as its instrument (even in our sense). Those issues will be taken up in Section 5 . In our terminology, then, a policy rule might b e thought o f a s a formula that specifies instrument settings that are designed to keep a target variable close to its specified target path. If r 1 and x1 were the instrument and target variables, then, the simplest prototype rule might be of the form (3 . 1 ) which specifies that the instrument setting should be decreased if x1 fell short of its target value x; in the previous period. Somewhat more realistic examples involving more variables and other timing patterns will be considered below. Some writers have taken the position that the specification of a policy rule is complete when a target variable has been selected and a target path (or perhaps a tolerance range) has been designated. Hall and Mankiw ( 1 994, p. 79), for example, recommend that the central bank behave so as to keep each period's externally­ generated forecast of future nominal income equal to a value given by a selected target path, but beyond that "we see no need to tell it how to go about achieving the peg." Also, Svensson ( 1 997a) distinguishes between "instrument rules" and "target rules" and expresses a preference for the latter, which specify target values but not instrument settings 1 7 . The position taken in the present chapter, however, is that a monetary policy rule is by definition a formula that specifies instrument settings, with the choice of a target variable and path constituting only one ingredient. For some particular target choices it might be the case that the problem of designing instrument settings would be extremely simple or uninteresting, but in general such will not be the case. McCallum's series of rule studies ( 1 988, 1 993a, 1 995a), for example, was undertaken partly in response to a claim by Axilrod ( 1 985) - who was at the time a principal monetary policy advisor at the Fed's Board of Governors - that the achievement of nominal GNP targets was technically infeasible. From this practical perspective, the investigation of a rule expressed in terms of a feasible instrument variable becomes 1 7 As a related matter, Svensson has suggested that behavior conforming to a rule of the form (3. 1 ) should not b e referred t o a s involving a x 1 target; that terminology should b e reserved (he suggests) to cases in which the central bank's instrument is set so as to make E1x1 1i = x�+j · But a rule such as (3 . 1 ) with A(x7 - E1 x10 i) on the right-hand side leads t o equivalent behavior i n the limit as A-->oo, and s o is v : a compatible but more general formulation.

1 494

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an essential portion of the selection of a desirable target. For there is little point in designating a particular target if in fact it is not achievable. Svensson's ( 1 997a) preference for what he terms target rules is not based on any lack of interest in the instrument�target relationship, but stems (apparently) from a point of view that does not recognize the difficulty emphasized above, namely, the absence of a satisfactory model of the economy. Thus Svensson presumes that any change in knowledge about the economy's workings will typically require some change in an instrument rule, whereas "with new information about structural relationships . . . a target rule implies automatic revisions of the reaction function" [Svensson ( 1 997a), pp. 1 1 36-1 1 3 7]. Indeed, if the central bank were conducting policy by conducting optimal control exercises each period with a single model, it would be true that changes in the latter would typically entail changes in the implied instrument rule. But under the presumption presented above, that it would be unwise to design a rule optimally on the basis of any single model, Svensson's conclusion does not follow. Instead, if an instrument rule has been designed so as to work reasonably well in a wide variety of models, then new information about the economy's structure is unlikely to entail any change in rule specification even when the rule designates instrument settings. Terminologically, moreover, it seems best to distinguish between the choice of policy rules and policy targets. The selection of a target variable is an extremely important aspect of systematic policy-making and may involve sophisticated analysis, as in the work of Svensson. But nevertheless a target is just that, a target. A rule, by contrast, is a formula that can be handed to a central banker for implementation without any particular knowledge of the analysts' views about model specification or obj ectives. In any event, in what follows it will typically be presumed that the term monetary policy rule refers to a formula or guide such as Equation (3 . 1 ) for period-by-period setting of instrument values in response to specified conditions. In evaluating candidate formulas such as Equation (3 . 1 ), it would clearly be desirable to have at hand an established specification of the appropriate ultimate goals of monetary policy. In that regard there exist important issues, such as whether a CB should keep actual or expected inflation close to some normative value, what that normative value is, and precisely how variability of output - or is it output relative to capacity (measured how?) or consumption? - should be weighed in relation to the inflation criterion. Now, in optimizing models that are specified at the level of individuais' tastes and technology, such as ireland ( 1 997) and Rotemberg and Woodford ( 1 997), the answers to such questions are unambiguous and implicit in the solution to the optimal control problem. But again the fundamental difficulty mentioned above intrudes in a crucial manner, for these answers will depend non­ negligibly upon the specification of the model at hand 1 8 . Consequently, the marked

1g One rather prominent issue is whether there exists some externality that makes the appropriate output reference value greater than the natural-rate value that is relevant for price and wage behavior. Another crucial issue concerns the validity or invalidity of strict natural-rate hypothesis, i.e., the proposition that

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absence of professional agreement regarding model specification implies that there can be (at least at present) no consensus as to the CB goals that are appropriate from the perspective of an economy's individuals. In practice, nevertheless, there seems to be a substantial amount of agreement about actual (not ideal) CB objectives; namely, that many CBs strive to keep expected inflation close to zero (allowing for measurement error) and to keep output close to a capacity or natural-rate value that is itself a variable that grows with the capital stock, the labor force, and technical progress 1 9 . Although it cannot be established that these objectives are optimal, it would seem to this writer that they probably provide a fairly good specification of appropriate CB macroeconomic goals.

4. Choice of target variable After a long dose of preliminaties, let us now finally turn to substantive issues in the design of a monetary rule. In this section we shall be concerned with the choice of a target variable - both its identity and the question of whether its path should be specified in growth-rate or level form. For the reasons just outlined, our discussion will be pragmatic rather than theoretical in nature. In recent years, the most fashionable target variable for the monetary authority has been a nation's inflation rate - in other words, a comprehensive price-level variable with its target path set in growth-rate terms. A great deal has been written about inflation targeting in policy-oriented publications, and substantial scholarly efforts have been contributed by Almeida and Goodhart ( 1 996), Bernanke and Mishkin ( 1 997), Goodhart and Vinals ( 1 994), McCallum ( 1 997a), and others, as well as the individual authors represented in books edited by Leiderman and Svensson ( 1 995) and Haldane ( 1 995). Other leading target-variable choices are aggregate spending magnitudes such as nominal GNP or GDP - often in growth rate form - and a "hybrid" variable that sums inflation and real output measured relative to some sort of trend or reference value 20 . All of these choices presume, however, that the economy in question does not have its monetary policy dedicated to an exchange rate target, so a brief prior discussion of exchange rate policy should be appropriate.

output cannot be kept above its natural-rate value permanently by any monetary policy strategy, even one that features a permanently increasing (or decreasing) rate of inflation [Lucas ( 1 972)]. 19 This variable capacity value may, however, exceed the natural-rate value, as mentioned in footnotes I 0 and 1 8, and as is typically assumed in the CB credibility literature. 20 The magnitude of inflation rates depends upon the length of a single time period whereas the percentage (or fractional) deviation of output from its reference path does not. The usual convention with this hybrid variable is to add percentage inflation rates measured for annual periods to percentage output deviations. It would be equivalent to use inflation over a quarter plus one-fourth of the relative output deviation. Use of fractional units for both variables would also be equivalent, with appropriate adjustments in the response coefficient. This last convention will be utilized below.

1 496

B. T. McCallum

Perhaps the most basic of all monetary policy choices is whether or not to adopt a fixed exchange rate. The principal considerations involved in this choice are those recognized in the optimal currency area literature began by Mundell ( 1 96 1 ) and extended by McKinnon ( 1 963) and Kenen ( 1 969). Basically, these all boil down to the question of whether the microeconomic (i.e., resource allocation) advantages of an extended area with a single medium of exchange outweigh the macroeconomic (i.e., stabilization policy) disadvantages of being unable to tailor monetary policy to local conditions 2 1 . Some analysts [e.g., Bruno ( 1 993), Fischer ( 1 986)] have contended that there are some macroeconomic advantages of a fixed exchange rate 22 but the arguments seem actually to be based on political or public-relations considerations, not economic costs and benefits 23 . Thus in the case of small economies for which large fractions of their market exchanges are intemational in character, and which tend frequently to experience the same macroeconomic shocks as their neighbors and trading partners, it is clearly advantageous to forgo the flexibility of an independent monetary policy by keeping a fixed exchange rate (and co1111o11 n currency) with a specified currency or basket of currencies 24 . And at the other extreme, the macroeconomic advantages of a floating exchange rate would seem to be clearly dominant for pairs of nations such as the USA, Japan, and the prospective European monetary union. The main point of the previous paragraph is that the advantages that might lead a nation to choose to have a fixed exchange rate, and thus to dedicate its monetary policy actions to that criterion, are basically either microeconomic or political in nature. Thus the type of considerations involved are quite different than those that are involved in the selection among macroeconomic target variables such as inflation, nominal spending growth, or the above-mentioned hybrid variable. Because of the scope of the present chapter, we shall henceforth focus our attention on the latter type of choice 25 .

21

I f a set o f countries i s t o have permanently fixed exchange rates, i t would seem that fi·om a purely economic perspective there are extra benefits (reduced transaction costs) with no extra costs of having a common currency. (No ongoing costs, that is; there may obviously be significant changeover costs, as in the EMU example.) As for rates that are fixed, but not permanently, the European experiences of 1 992 and 1 993 support Friedman's ( 1953) classic argument that such an arrangement is tmdesirable because of the self�destructive speculative impulses that are encomaged. 22 From the monetary-policy perspective, a moving peg or narrow band falls into the same category as a fixed exchange rate, since it entails the dedication of monetary policy to its maintenance. 23 This statement is applicable to much of the literature relating to the planned European monetary lmion, of course. 24 A relatively clear-cut example is provided by Luxembomg, which has had a monetary union with Belgimn since 192 1 (except for an intenuption during World War II), Belgian francs serving as a legal tender in both nations. Luxembourg also issues franc notes and coins, but has kept these interchangeable with their Belgian counterparts. 25 It should be recognized, however, that it would be possible to consider a target that consists of a weighted average of (say) exchange rate changes and inflation. This example could alternatively be thought of as an inflation target with an unusual specification of the price index to be utilized.

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In the literature on this subject, which is large, the most popular approach is to determine how well the various targets would perform in terms of yielding desirable values of postulated social and/or policy-maker objective functions, with these pertaining primarily to root-mean-square (RMS) deviations from desired values of variables such as inflation or real GDP relative to capacity 26 . Such studies may be conducted with theoretical or estimated models, but in either case need to take account of the various types of macroeconomic shocks that may be relevant - need to take account, that is, of the variance, covariance, and autocovariance magnitudes of the shock processes. Some of the leading examples of theoretical studies are those of Bean ( 1 983), West ( 1 986), Aizenman and Frenkel ( 1 986), Henderson and McKibbin ( 1 993), Frankel and Chinn ( 1 995), Ratti ( 1 997), and Ireland ( 1 998), while well­ known simulation studies with estimated models have been conducted by Taylor ( 1 979, 1 993a), Feldstein and Stock ( 1 994), Haldane and Salmon ( 1 995), and the individual authors in Bryant et al. ( 1 988, 1 993). In some of these studies it is pretended, for the sake of the issue at hand, that the selected target variables are kept precisely on their target path; the Bean, West, Aizenman-Frenkel, Frankel-Chinn, Ratti, and (in part) Henderson-McKibbin studies are of that type. Others, however, focus on RMS deviations in simulations with policy rules expressed in terms of instrument variables. Proponents of the first approach would argue, presumably, that they prefer to keep the issue of whether a variable can be controlled separate from the evaluation of its effects if well-controlled. Those who disagree would point out that there is little need to know such properties for variables that in fact can be controlled only very poorly. Indeed, they might argue that unless controllability is taken into account, the issue is simply that of specifying an appropriate social objective function; i.e., that "targeting" is not the matter under investigation. In this regard it is worth keeping in mind the point emphasized above, namely, that there is in fact no professional agreement on the appropriate specification of a dynamic macroeconomic model. This implies not only an absence of agreement on the "true" social objective function, but also the absence of agreement on a matter as basic as the listing of relevant macroeconomic shocks. Keynesians and real-business­ cycle analysts, for example, would disagree sharply as to the very nature of the relevant shock processes. For the candidate target variables mentioned above, other than the hybrid variable, an important question is whether it is preferable to specify a growth-rate target or one of the growing-levels type, i.e., whether the target should be specified in a difference­ stationary or trend-stationary manner. This issue is often discussed under the heading of "inflation vs. price-level targeting," but similar considerations would apply if the target variable were nominal GDP, some other measure of nominal spending, or even

2(' These

are the two va1iables that arc most closely related to the utility fimctions of individuals in explicit optimizing models such as those of Ireland ( 1 997) or Rotembcrg and Woodford ( 1 997).

1 498

B. T. McCallum

a money-stock variable 27 . Specifically, the weakness of the growth-rate choice is that it will - by treating past target misses as bygones - introduce a random walk (or more general unit root) component into the time-series processes for all nominal variables, including the price level. Thus there will exist a possibility that the price level would drift arbitrarily far away from any given value (or predetermined path) as time passes, implying considerable uncertainty as to values that will obtain in the distant future. By contrast, the main disadvantage with a levels-type target path is that the target variable will be forced back toward the preset path after any disturbance that has driven it away, even if the effect of the disturbance is itself of a permanent nature. Since any such action entails general macroeconomic stimulus or restraint, this type of targeting procedure would tend to induce extra cyclical variability in demand conditions, which may imply extra variability in real output if price-level stickiness prevails. Furthermore, variability in output and other real aggregative variables is probably more costly in terms of human welfare than is an equal amount of variability in the price level about a constant or slowly-growing path. Also, although it is not entirely clear that fully permanent shocks are predominant, most time-series analysis seems to suggest that the effects of shocks are typically quite long lasting - indeed, are virtually indistinguishable from permanent. Consequently, it would seem desirable not to drive nominal variables back to preset paths - or at least not to do so quickly and frequently. Thus, it seems preferable to adopt a nominal target of the growth-rate type, rather than the growing-levels type 28. One reason for the foregoing conclusion is that very few transactions are based on planning horizons as distant as 50 years. A more representative long-lasting arrangement might be more like 20 years in duration. But price-level uncertainty 20 years into the future might not be very large even if the (log of the) price level included a unit root component. Suppose that the log price level were to behave as a pure random walk relative to a preset target path (say, a zero-inflation path). Then if it is assumed that the random, unpredictable component at the quarterly frequency has a standard deviation of0.0045 (which is approximately the standard deviation of one-step ahead forecast errors for the USA over 1 954-1991) 29, it follows that a 95% confidence interval for the (log) price level 20 years ahead would be only about 8% (plus or minus) 3 0 . This, it seems to the writer, represents a rather small amount of price level

27 Here and below the language will often be stated in terms of nominal variables such as nominal GDP or a price index when it is the natural logarithm of that variable that is actually meant. 28 For alternative arguments that reach this conclusion, which is taken for granted by Feldstein and Stock ( 1 994), see Fischer ( 1 995) and Fillion and Tetlow ( 1994). The opposing position is taken by Hall and Mankiw ( 1994) and Svensson ( 1 996) [but see footnote 8 above]. 29 Thus it is being tentatively assumed that the control error, if inflation targeting were adopted, would have a mean of zero and a variance equal to that of the currently-prevailing one-step-ahead forecast error, which might be taken as an approximation of the minimum feasible control error variance. 30 I am taking the control error to be serially 1mcorrelated. Then the 80-period ahead error would have variance (80) (0.00452 ) = 0.001 62 whose square root is 0.040. Thus two standard deviations equals 0.08

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uncertainty - at least in comparison with the mah'11itudes that prevailed over the 1 960s, 1 970s, and 1980s, because of non-zero and uncertain trend rates. The foregoing argument seems moderately persuasive to the present writer, but it is clearly not compelling and the conclusion is certainly not accepted by all analysts. Furthermore, even if it were accepted, it might be possible to obtain the benefits of trend stationarity by adopting a target that is a weighted average of ones of the growth-rate and growing-level types 3 1 . Accordingly, in the simulations reported below, consideration will be given to growth-rate, growing level, and weighted average types. Now let us consider some points regarding the comparative merits of three leading target-variable possibilities. Because they seem at present to command the most support, we will discuss (i) the inflation rate, (ii) the growth rate of nominal GDP, and (iii) the above-mentioned hybrid variable. As some notation will be useful, henceforth let X t . y1, and p1 denote logs of nominal GDP, real GDP, and the price level (as represented by the deflator so that x1 y1 + p1), with time periods referring to quarter­ years. Then the three contending target variables in their simplest form are 1'1p1, 1'1x1, and h1 = 1'1pr + 0. 25y1, where y1 = y1 - y1 with ji1 denoting the reference value of real GDP. In choosing among these three contenders, a straightforward approach would be to select the target variable that corresponds most closely to the central bank's views about social objectives that are influenced by monetary policy. From that perspective, it would appear that the hybrid variable h1 might be the most appropriate of the three, a point of view taken implicitly by Blinder ( 1 996), with 1'1x1 arguably ranking second 3 2 . But among actual central banks that have adopted formal numerical targets, virtually all have (as of early 1 997) opted for inflation targets. So apparently the straightforward approach is not the only one that needs to be considered. There are undoubtedly several reasons for this tendency for actual central banks to choose 1'1p1 over the others as their formal target, but three of these seem justifiable and in any event deserve to be mentioned. First, it is believed by a large number of policymakers and a large number of scholars that monetary policy has, from a =

�o a 95% confidence interval will have width roughly ±0.08 or ±8 percent. If the control error is serially correlated, then the relative effect of the unit root term will depend on the autocorrelation pattern but is likely to be more serious. 3 1 If used in a rule of form (3. 1), this sort of weighted-average target would be equivalent to a pure growing-levels target with both "proportional" and "derivative" feedback. 32 The case for nominal income targeting is that it should, from a long-tern1 perspective, provide almost as good inflation control as direct inflation targeting, since average real output growth will be virtually independent of monetary policy and reasonably forecastable, while probably providing somewhat better automatic stabilization of real variables. About the latter advantage one cannot be certain, because of the absence of professional understanding mentioned in footnote 1 4 . The basic logic of nominal income targeting applies, moreover, to other aggregative measures of nominal spending, not just to nominal GDP or GNP per se. The sharp criticism of nominal income targeting recently expressed by Ball ( 1 997) is, it is argued below, fundamentally misguided.

1 500

B.T. McCallum

long-run perspective, no substantial effect on y1 y1 - y1 33. In other words, while monetary policy may have significant effects on output relative to capacity, these are only temporary. Therefore, so the argument goes, central banks should concentrate their attention on the 11p1 variable that their policy actions affect strongly on a long­ run basis 34. Second, measurement of y1 and therefore ji1 is difficult and controversial, even in comparison to measurement of 11p1 • We have described y1 as a capacity, trend, or reference value, but that does not define the appropriate variable even in conceptual terms, much less in operationally measurable terms 35. In particular, errors in measuring y1 are likely to be much larger than errors in measuring the long-term average value of 11y1 , which is all that is necessary for correct design of a /1x1 target. Thus the h1 target is more demanding of knowledge concerning the economy than is either of the other contenders under discussion. The third reason is related to the other two, especially the first. It is that communication with the public is thought by practitioners to be much easier when only the inflation variable is involved. Typical citizens have an understanding of the concept of inflation, so the argument goes, but not of the national income accounting concepts x1 and y1, much less the reference value y1 • In addition, it must be mentioned that in practice actual inflation targets are typically based on yearly average inflation rates, and with those values forecasted to prevail 1-2 years into the future 36. Since inflation forecasts are in practice based in part on recent levels or growth of real output, the three target variables under consideration may be fairly closely related to each other. Furthermore, inflation targets are usually accompanied by provisions stating that the occurrence of "supply shocks" - such as crop failures, terms-of-trade changes, or indirect tax-rate changes - will entail temporary modification of the current inflation target measures. Thus, for example, the New Zealand legislation includes several such escape clauses - termed "caveats" ­ that are built into the Reserve Bank's targeting procedures 37. Because of considerations such as these, it would probably be unrealistic (and unreasonable) to expect that a truly compelling argument could be made for any one =

33 This proposition, often termed the "natural rate hypothesis", is subscribed to by a large fraction of macroeconomic researchers. 34 This position is explicitly expressed by McCallum (l 997a) and by Reserve Bank of New Zealand ( 1 993 ). 35 In recent years there has been a tendency, most marked in media discussions but also present in professional literature, to speak as if "natural rate" and "NAIRU" concepts and theories were equivalent. To the present writer that is far from being the case. The strict version of the natural rate hypothesis, due to Lucas ( 1 972), is the proposition that there is no monetary policy that will keep output permanently high in relation to its natural rate (i.e., market clearing) value. By contrast, the NAIRU (non-accelerating­ inflation rate of nnemployment) approach posits a stable relationship between unemployment (or output relative to its reference value) and the "acceleration" magnitude, i.e., the change in the inflation rate. But the latter implies that permanent acceptance of a positive acceleration magnitude (i.e., increasing inflation) will result in a permanent increase in output relative to its reference value, in stark contradiction to the natural rate hypothesis. 36 Of course the same smi of averaging could be applied to the Ax, and h1 variables. 37 On this subject, see Reserve Bank of New Zealand ( 1 993).

Ch. 23:

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E DLXGAP

1 501

------- DLPGAP

-----

J

ZERO

fig. 1 . Gap measures for inflation and nominal GDP targets, 1 960-1995.

of the candidate target measures. Consequently, it should be of interest to compare actual past values of the three leading measures with those values that would have been called for if corresponding targets had been in place. For the purpose of this exercise, it will be assumed that the desired value of f...p1 is 0.005, which amounts to approximately two percent inflation on an annual basis. Also, for simplicity it will be assumed that y1 values are given by deterministic trends obtained by regression ofy1 on time for the sample period under consideration. This last assumption is unsatisfactory, of course - as will be discussed again - but should suffice for the limited purpose at hand of making comparisons. Let us first consider the time period 1 960. 1-1 995 .4, with United States GDP data used for x1 and with y1 based on GDP in 1 992 fixed-weight prices (i.e., using the fixed­ weight rather than the chain-weight deflator). Over this period, the y1 trend variable is given by the expression Yt = 7. 520749 + 0.00688 1 t (with t = 1 in 1 947 . 1). Therefore, f...y = 0.00688 1 is assumed and the target value for f...x 1 is 0.0 1 1 88 1 , with 0.005 being the target value for both f...p1 and h1• For each of the three variables we calculate the gap between actually observed values and these retrospective, hypothetical target values. These gaps are denoted /).p(gap )1 /).Pt 0. 005, f...x(gap )1 = f...x1 - 0. 0 1 1 8 8 1 , and h (gap)1 = 1'1p1 + 0. 25y1 - 0. 005. Their values for the first two variables (over 1 960. 1-1995 .4) are plotted in Figure 1 and those for the second and third are plotted in Figure 2. In Figure 1 we see that the f...p1 and !'u1 targets both suggest that monetary policy was excessively expansive most of the time between 1 965 and 1 989. The f...x(gap) measure is considerably more variable from quarter to quarter than the f...p(gap) measure, basically because /).y1 is more variable than 11p1• Averaging over the whole period, the two measures give the same signals simply because the f...x 1 target value was calculated =

--

1 502

B. T. McCallum -- ----0.06 ,------

0.04

0.02

0.00

-0.02

•)

...

.�: ' ,'.' ,'

/'/:

�: :

1 - DLXGAP

------- HGAP

----·

j

ZERO

Fig. 2. Gap measures for hybrid and nominal GDP targets, 1 96()-.1 995.

so as to yield the desired inflation rate given the realized average growth rate of output over the sample period. Of course, actual policymakers could not know this rate in advance, when choosing their target value for fu1• Thus desired inflation would tend to differ from the average realized value to the extent that average output growth is forecast incorrectly. The magnitude of this error would not be large, however, when averaged over long spans of time. By and large, a striking feature of Figure 1 is that the two target variables do not give greatly different signals when averaged over periods as short as 2-3 years. Nevertheless, there are a few quarters when the l'u1 variable suggests that policy should be loosened whereas the /l..p1 variable suggests the opposite, and this situation prevails for over a year during 1 990-199 1 . Those analysts who favor A\:1 targeting believe, of course, that keeping fu1 values steady would result in smaller fluctuations in ji1 than would a policy of keeping /l..p, values steady. Whether such is the case in fact will depend upon the precise nature of the economy's short-term, dynamic Phillips relation, a point emphasized in McCallum ( 1 988, 1 997a) 38 . Figure 2 compares gap values for h1 and A\:1 targets. In this case there is much more divergence in signals, with the hybrid measure calling for more monetary expansion over lengthy periods during the early 1 960s and 1 990s, and tighter monetary policy during much of the 1 970s, in comparison with the At, measure. (Of course both measures signal that policy was too inflationary from 1 965-1 989, as before.) These features of the plots in Figure 2 are basically a consequence of the fact that a linear trend line for y1 implies negative residuals in the early 1 960s and 1 990s and many

38

Sec footnote 1 4 above.

Ch. 23:

1 5 03

Issues in the Design of Moneta1y Policy Rules 0.06 ,---------,

0.04

0.02

0.00

-0.02

85

86

87

88

89

1 - DLXGAP85

90

n-----

91

92

HGAP85

93 ----·

94

95

ZERO

I

Fig. 3. Gap measures for hybrid and nominal GDP targets, 1 985-1995.

positive residuals during the 1 970s, which it does because of the sustained period of rapid growth in real GDP from 1 960 to 1 973. To emphasize this last point, Figure 3 gives results for the same type of exercise but with the sample period limited to 1 985. 1-1995.4. Here it will be noted that the h(gap)1 values are quite different from those for 1 98 5-1995 in Figure 2, solely because the y1 trend line is estimated differently and yields a significantly different residual pattern 39. Now there are no major discrepancies that persist as long as in Figure 2, although the two measures give quite different policy signals over most of 1 990 and 1 992, the Ax, target calling for a relatively more expansionary monetary stance in the former year and a more restrictive stance in the latter year. The sizable difference between the h(gap)1 figures shown in Figures 2 and 3 illustrates the main weakness of the hybrid target variable, namely, its sensitivity to alternative calculations of y1 reference values. Proponents of the hybrid variable might argue that more sophisticated measures of y1 should be used, and it is certainly true that our linear trends are not conceptually attractive. But neither are, say, Hodrick­ Prescott (HP) filtered series, for reasons emphasized by Cogley and Nason ( 1 995) plus a recognition of what the HP filter would imply about US GNP for the period 1 929- 1 93 9 4 0 . Other measures exist, but have attracted little professional support. In

39

It also has a reduced slope, which changes the definition of fu:(gap) to l'!.x1 - 0.0 1 0336. 40 If the HP filter were applied to US real GNP over a period including 1 929- 1 939, the HP "trend" series would turn down fairly sharply during the early 1 930s. If this series were used as one's measure of trend or capacity output, it would then be concluded that the Great Depression was not very serious i.e., that output was low over 1 932-1938 largely because capacity was low. But measured unemployment figures suggest strongly that this conclusion would be misleading.

1 504

B. T. McCallum 0.06 -r---------,

0.04

0.02

-0.02

65

70

1 -- DLXFGAP

75

80

85

------- DLPFGAP

90 -----

ZERO

95

I

Fig. 4. Gap measures for inflation and nominal GDP values forecast 4 quarters ahead, 1 960-1 995.

sum, there is no widely accepted and conceptually sound measure for j!1 , but use of the hybrid target variable requires such a measure and its value is rather sensitive to the particular measure adopted. One weakness of the indicators presented in Figures 1 -3 is that they pertain to currently-measured values of the target gaps whereas in practice actual central banks focus upon gaps expected to prevail several months in the future. Also, Svensson ( 1 997a) has argued rather convincingly that "inflation forecast targeting" has several attractive features. Consequently, indicators of expected future gaps were obtained by regressing gap values on information variables observed 4 to 7 quarters in the past. The variables used in these regressions are Ax1 , !1p1 , l1bt . and R1 (four lagged values of each), where b1 is the log of the monetary base and R 1 is the 3-month Treasury bill interest rate. Also one lagged value of y1 was included; a second lagged value would create perfect collinearity among the regressors. Values of these forecasted future gaps are presented in Figures 4 and 5, where the measures should be interpreted as giving policy signals one quarter in advance of the dates shown. Clearly, the values are smoothed greatly for Ax1 and !1pt . relative to the previous graphs, but the overall messages remain the same: that there is apparently little basis for choice between Ax1 and !1p1 while the h1 indicator appears to give signals that are quite different. Recently, Ball ( 1 997) has put forth, in rather strong language, some striking propositions regarding target variables 4 1 • Among these are claims to the effect that efficient monetary policy 42 consists of a special case of a Taylor rule that is equivalent 4 1 Some of these have been noted favorably by Svensson ( 1 997a,b).

42 The paper's concept of "efficient monetary policy" is one that focuses on the variances of inflation and output (relative to capacity) while assmning unrealistically that the central bank has full contemporaneous

Ch. 23:

Issues in the Design of Monetary Policy Rules

1 505

0.06 -r------,

0.04

0.02

-�-�7�--------------------J�i�-------�\�-�.�A� '

0.00

-0.02

' "

'

.'

65

70

75

1 - DLXFGAP

80

------- HFGAP

85 ----·

90

ZERO

95

I

Fig. 5. Gap measures for hybrid and nominal GDP values forecast 4 quarters ahead, 1 960-- 1 995.

to a partial-adjustment variant of inflation targeting (even when output variance is important); that efficient monetary policy requires much stronger responses to output fluctuations than is implied by historical practice or Taylor's ( 1 993b) suggested weights; and that nominal income targeting would be "disastrous" as it would give rise to non-trend-stationary behavior of output and inflation processes. These results are shown to hold, however, only in a single theoretical model, with no attempt being made to determine their robustness. In fact, the last one depends sensitively upon details of the utilized model that are not justified either theoretically or empirically. The model's Phil lips curve, in particular, has a superficial similarity in appearance to the Calvo-­ Rotemberg specification as exposited by Roberts ( 1 995), but differs by being backward rather than forward-looking. If a forward-looking version were utilized, the implied coefficient relating inflation to current output would have the opposite sign and Ball's instability result would be overturned, as it would be with several other prominent Phillips curve specifications.

5. Choice of instrument variable

In this section we consider the choice of a variable to serve as the instrument through which a central bank's policy rule will be implemented. It i s well known that, although a substantial number of academic economists have favored use of a monetary base or

knowledge of all variables (on this, see Section 6 below). Thus it simply assumes away the first-order problem of designing an operational rule that will generate the desired mean value for JT1 while avoiding explosions.

1 506

B. T. McCallum

reserve aggregate instrument, almost all actual central banks utilize some short-term interest rate in that capacity. Before turning to a review of their relative desirability, however, it will be appropriate to consider the sheer feasibility of interest rate and monetary base instruments, since there are a few scholars who have contended that one or the other would be infeasible in some sense. In this category the most well-known argument is that of Sargent and Wallace ( 1 975). That paper put forth the claim that, in a model in which all private agents are free of money illusion and form their expectations rationally, the economy's price level would be indeterminate if the central bank were to use an interest rate as its instrument. Specifically, the Sargent-Wallace ( 1 97 5) paper included a result suggesting that if the interest rate R 1 were set each period by means of a policy feedback rule that specifies R1 as a linear function of data from previous periods, then all nominal variables would be formally indeterminate. Sargent ( 1 979, p. 3 62) summarized this conclusion as follows: "There is no interest rate rule that is associated with a determinate price level." 43 Subsequently, however, McCallum ( 1 9 8 1 , 1 986, p. 1 48) showed that the Sargent­ Wallace claim was actually incorrect in such a model; instead, all nominal variables are fully determinate provided that the policy rule utilized for the interest rate instrument involves some nominal variable, as suggested previously by Parkin ( 1 978) and in the classic static discussion of Patinkin ( 1 96 1 ). The problem with the alleged proof of Sargent and Wallace is that it showed that the model at hand imposed no terminal condition on the price level, but did not consider the possibility of an initial condition. In the present context it is important to distinguish between two quite different types of price-level behavior that have been referred to in the literature as involving "indeterminacy". Both involve aberrational price level behavior, but they are never­ theless very different both analytically and economically. Consequently, McCallum ( 1 986, p. 1 37) proposed that they be referred to by terms that would recognize the distinction and thereby add precision to the discussion. The proposed terms are "nominal indeterminacy" and "solution multiplicity (or nonuniqueness)" 44 . The former refers to a situation in which the model at hand fails for all nominal variables (i.e., variables measured in monetary units) to pin down their values. Thus money stock values and values of (say) nominal income, as well as the price level, would not be defined by the model's conditions. Paths of all real variables are nevertheless typically well defined. In terms of real-world behavior, such a situation could conceivably obtain 43 Sargent and Wallace ( 1982) advanced arguments quite different from those of their 1 975 paper, and attJibuted this difference to their use in ( 1 982) of a model with agents who solve explicit dynamic optimization problems, in contrast to the linear IS-LM model with a Lucas supply function in ( 1 975). In fact, however, the main relevant difference is that the 1 982 analysis is based on a model in which monetary and nonmonetary assets cannot be distinguished - and indeterminacy does not actually prevail in any case. On this, see McCallum ( 1 986, pp. 144-154). An impmiant recent contJibution is Benassy ( 1 999). 44 Actually, McCallmn ( 1 986) proposed "indeterminacy" for the former, but the addition of the adjective is clearly desirable.

Ch. 23:

Issues in the Design of Monetary Policy Rules

1 507

if the monetary authority failed entirely to provide a nominal anchor45 . This type of phenomenon has been discussed by Gurley and Shaw ( 1 960), Patinkin ( 1 949, 1 96 1 ), Sargent ( 1 979, pp. 3 60-363), Sargent and Wallace ( 1 975), McCallum ( 1 98 1 , 1 986), and Canzoneri, Henderson and Rogoff ( 1 983), among others. Solution multiplicity, by contrast, refers to aberrational behavior usually described as involving "bubbles" or "sunspots" that affect the price level. In these situations it is typically the case that the path of the money stock - or some other nominal instrument controlled by the monetary authority - is perfectly well specified. Nevertheless, more than one path for the price level - often an infinity of such paths - will satisfy all the conditions of the model. In terms of real world behavior, arbitrary yet self­ justifying expectations is the source of this type of aberration. It has been discussed by a vast number of writers including Taylor ( 1 977), Sargent and Wallace ( 1 973), McCallum ( 1 983), Brock ( 1 975), B lack ( 1 974), Obstfeld and Rogoff ( 1 983), and Flood and Rodrick ( 1 990). Nominal indeterminacy is a static concept that concerns the distinction between real and nominal variables whereas solution multiplicity is an inherently dynamic concept involving expectations. An important application of this distinction is to the "indeterminacy" results of Brock ( 1 975, pp. 1 44-147) and Woodford ( 1 990, pp. 1 1 1 9-1 1 22). These results pertain to cases in which (base) money is manipulated by the central bank and involve non-uniqueness of rational expectations equilibria when the imposed money growth rates are low, close to the Chicago Rule rate that satiates agents with the transaction-facilitating services of money. But since these equilibria involve well­ specified paths of nominal money holdings, the non-uniqueness is clearly not of the nominal indeterminacy type. Instead, it is of the solution multiplicity type, involving price level bubbles or sunspots. Such theoretical multiplicities may or may not be of practical significance 46 , but in any event are not examples of "price level indeterminacy" in the sense of Gurley and Shaw ( 1 960), Patinkin ( 1 949, 1 96 1), Sargent ( 1 979, pp. 3 60-363), or Sargent and Wallace ( 1 975). To some readers, this fact may diminish the force of Woodford's ( 1 990, 1 994) argument in favor of an interest rate instrument. Let us now return to the issue of instrument feasibility, switching to the extreme opposite side of the debate. In a recent article, Goodhart ( 1 994) has argued not just that monetary base control by a modern central bank is undesirable, but that it is essentially infeasible. In particular, Goodhart states that "virtually every [academic?] monetary economist believes that the CB can control the monetary base . . . " so that if the CB does not do so, then "it must be because it has chosen some alternative 45 And the system lacked sufficient inertia or money illusion to make the nominal paths determinate

requirements that are actually almost inconceivable. It is unclear whether there is any compelling evidence in support of the notion that macroeconomic bubbles or sunspots are empirically relevant [Flood and Hodrick ( 1990)]. In any event, it is a plausible hypothesis that, in cases with an infinity of solutions, there is a single bubble-free or fundamentals solution that obtains in practice. 46

1 508

B. T. McCallum

operational guide for its open market operations" (p. 1 424). But, he asserts, "almost all those who have worked in a CB believe that this view is totally mistaken; in particular it ignores the implications of several of the crucial institutional features of a modern commercial banking system, notably the need for unchallengeable convertibility, at par, between currency and deposits, and secondly that commercial bank reserves at the CB receive a zero, or below-market, rate of interest" [Goodhart ( 1 994), p . 1 424] . Then as the discussion proceeds it becomes clear that Goodhart is himself taking a position that is predominantly, if not entirely, supportive of the opinions of those who have worked in a CB. Thus he asserts, on his own account, that "if the CB tried to run a system of monetary base control, it would fail" (p. 1 425). And he goes on to outline the putative flaws in logic or factual knowledge that invalidate the cited views of academic economists (pp. 1 424-1426). In fact, however, although Goodhart's discussion is apparently intended to be concerned with feasibility, the actual argumentation presented pertains to desirability. Specifically, the main analytical points are those made in the first three complete paragraphs of p. 1 425, which argue that tight base control would lead in practice to overnight interest rates that at the end of most days would equal either the CB 's penal rate or a value "near zero" 47 . Having developed that point, Goodhart concludes as follows: "Some economists might prefer such a staccato pattern of interest rates, but it would not seem sensible to practitioners" (p. 1 425). But clearly this is an argument that pertains to the desirability, not the feasibility, of tight base control 48 . Having concluded, then, that neither interest rate nor monetary base instruments are infeasible 49, we turn to the task of considering their relative desirability 50 . In that

47 lf required-reserve averaging is practiced, then the statements referred to pertain only to days near the end of reserve maintenance periods. 48 More extensive but still inconclusive arguments arc presented by Whittaker and Theunissen ( 1987) and Okina ( 1 993). The latter presumes lagged reserve requirements, an arrangement that is inappropriate with a base instrument [McCallum ( 1985)]. 49 A different objection to use of a base instrument is that central banks do not literally control the sum of currency and reserves, since currency is demand determined and only the non-borrowed component of total reserves is directly controlled, since banks can use the discount window to add to or subtract from reserve holdings. But there are three flaws with this position. First, since the base can be read from the CB's own balance sheet, it can observe it frequently and make whatever adjustments are needed to keep the ma!,'llitude closer to its target. Second, the CB could, if it chose, close the discount window. Third, it would be possible to consider the non-borrowed base as the instnunent under discussion. 50 Brief mention should be made of a study by Howitt ( 1992), who finds that an interest rate peg would lead to dynamic instability in a model that includes a sticky-price Phillips curve and a generalized adaptive form of dynamic "learning behavior" rather than rational expectations. Whether or not one finds the latter feature appealing, Howitt's results do not pertain to the issue at hand since the type of "pegging" that he is concerned with involves keeping R1 at some preset value indefinitely, not varying R1 period by period in an instrument capacity. Several writers have shown that, under rational expectations, nominal indeterminacy does not prevail with an interest rate peg. Canzoneri, Henderson and Rogoff ( 1 983) and McCallum ( 1 986) have established this in models of the IS-LM-AS type under the assumption that the peg is a limiting version of a money supply rule designed to reduce interest rate fluctuations.

Ch. 23:

issues in the Design of Monetary Policy Rules

1 509

regard, most proponents of a base instrument do not deny that such a regime would involve substantially more variability of short-term interest rates than is experienced under today's typical procedures, which involve interest-rate instruments and short­ term interest rate smoothing 5 1 . Base proponents would contend, however, that with a base instrument it may be possible to design simple policy rules that are more effective from a macroeconomic perspective than are comparable rules with interest­ rate instruments 5 2 • 53 . In order to illustrate the plausibility of that contention, let us consider some counterfactual historical simulations of the general type used by McCallum ( 1 988, 1 993a, 1 995a) with quarterly US data. In order to keep the model specification from biasing the results, the macroeconometric model in these simulations will be an unconstrained VAR with four lags included for each of the four variables �Yr, �pr , �b1, and R1 54. Here R1 is the three-month treasury bill rate, b1 is the log of the St. Louis Fed adj usted monetary base, and GNP data is utilized for y1 and p1• The estimation and simulation period is 1 954. 1 - 1 99 1 .4. We have seen above that there has not been a large discrepancy, historically, between signals provided by fu1 and �p1 targets, when the target values are gauged so as to imply the same average inflation rate. Accordingly, let us concentrate our attention on rules for �b1 and R1 designed to keep x1 close to three target paths, all of which provide expected fu1 values of 0.01 1 25 (i.e., approximately 4.5 nominal GNP growth per year,

Woodford ( 1 990, 1 994) and Sims ( 1994) extend this type of result to a "pure peg" and conduct their analysis in general equilibrium models with explicit optimization on the part of individual agents. 5 1 The concept of interest rate smoothing that I have in mind is keeping R, close to R,_b but there is no major conflict here with concepts such as a tendency to minimize E(R, � E, 1 R, f [Goodfriend ( 1987)]. 52 The reason why design of a simple interest rate rule may be more difficult stems from the ambiguity of nominal interest rates as indicators of monetary tightness or ease. High interest rates, that is, are associated with tight monetary policy from a short-run or point-in-time perspective, but with loose monetary policy from a long-nm (i.e., maintained) perspective. This means that the interest rate effects of an open market action are in opposite directions from short-term and long-term perspectives. Accordingly, the design of a policy rule for the control of target variables would seem to be more complex and dynamically delicate if an interest rate is the instrument variable than if a nominal quantity variable serves in that capacity. 53 One objection to use of a base instrument for the USA is that much of the currency component of the base which is by far the larger component is believed to be held outside the country. Recently, Jefferson ( 1997) has indicated that use of only that portion held in the country [as estimated by Porter and Judson ( 1996)] alters the estimated relationship between the base and nominal GDP, and yields improved base-rule simulation results for the period 1 984- 1 995. 54 The use of an unconstrained VAR is undesirable because such a model is almost certainly not policy invariant. However, the small "structural models" used in McCallum ( 1 988) are biased in favor of the base instrument because the real monetary base (and no interest rate) appears as an explanatory variable in these models' common aggregate demand relation. In Hess, Small and Brayton ( 1 993), by contras1, the small macro model discussed on pp. 14�21 might be considered to be biased in favor of an interest rate instrument. The author hopes to conduct simulations with a more appropriate model in the near future. �

�

B. T McCallum

1510

designed to yield 2.0 percent inflation). These three paths will be of the growth-rate, growing level, and weighted average types. For the monetary base instrument, the rule to be considered is (5 . 1 ) where A > 0 is a policy adj ustment parameter and the target variable x; can be defined in various ways 55. To yield a growing-levels target, we would have x;1 x�� � + 0. 0 1 125 whereas a growth-rate version would use instead x;3 = x1_ + 0. 0 1 125. Besides these, 1 we will consider x72 0.2x; 1 + 0. 8x�3 , where the weights are chosen semi-arbitrarily but so as to give more importance to the growth-rate target. According to the policy rule (5. 1 ), monetary base growth is set in each quarter so as to equal the target value for nominal GNP growth minus average base velocity growth over the past four years 56, plus a cyclical correction terrn that reacts to past target misses. Note that =

=

x;� l - Xt-1 = (Xt-2

+

0. 0 1 1 25)

��

Xt-1 = 0. 0 1 1 2 5 - fu:t I

and that

X�21 - X1_1 = 0.2(x7 1 1 - Xt-1) + 0. 8(0. 0 1 125 - fu;t- 1) = 0.2(x;� 1 - Xt-1) + 0.8(fu:� 1 - fu:t- I ) so that use of x;2 is equivalent to having a growing-levels target but using derivative as well as proportional feedback, in the terminology of Phillips ( 1 954). So as to obtain some indication of robustrJess to rule specification, a range of A values from 0 to 1 will be examined. For the interest instrument rule, no velocity growth term is needed so the comparable rule can be expressed as (5.2) Thus, the value of the mterest rate instrument is lowered relative to the previous quarter when target spending x; exceeds the actual level in the previous quarter. The - 1 00 factor is inserted so as to make the same range of A values as in Equation ( 5. l )

55

This is the type of rule studied in McCallum ( 1 988, 1 993a, 1 995a).

56 The velocity connection term serves implicitly as a forecast of the average growth rate of base

velocity over the indefinite future, i.e., the long-lasting component of velocity growth that is due to institutional change (not growth due to cyclical effects, which are accounted for in the third te1m). More sophisticated methods of forecasting the pem1anent component of both velocity growth and real output growth would be used in practice by actual central banks.

Ch. 23:

15 1 1

Issues in the Design of Monetary Policy Rules

Table 1 RMS errors with base/interest instruments, rules (5. 1 ) and (5.2), VAR Model, US Data 1 954. 1-199 1 .4 RMS error relative to:

Jc = O.OO

Jc = 0.50

Jc = 0.25

Jc = 1 .00

�-----�·------�--------- - ------------

0.0503 1.153 0.0133 0.24 1 5 0.0097 0.0184

0.0503 1 . 1 53 0.0133 0.2415 0.0097 0.01 84

0.0503 1 . 1 53 0.0133 0.24 1 5 0.0097 0.0184

Panel 0.0235

A:

x;1 target 0.0376

expl "

expl

O.o l l 3

0.0 1 84

expl

expl

0.0 1 1 2

0.0 1 88

expl

expl

Panel B: x;2 target 0.0232 0.0381

0.0284 0.0619 0.0109 0.01 55

0.0100 0.0105

0.0 1 06 0.0123 0.0105 0.0107

Panel C: x;3 target 0.0361 0.0418 0 . 1 825 0.3321 0,0 1 1 7 0.0123 0.0378 0.0680 0.0099 0.0 104

0.0 1 02 0.0 1 00

expl expl expl expl expl expl

0.020 1 0.0254 0.0 1 14 0.0 1 47 0.01 1 8 0.0142

0.0292 0.0959 0.01 1 6 0.02 1 7 0.01 1 1 0.0123 -- ------------

" expl, explosive oscillations.

appropriate again 57 . The same trio of x7 definitions is employed as with the base instrument. Table 1 reports results of counterfactual historical simulations each using rule ( 5 . 1 ) o r (5 .2) with VAR equations for �y1, �pr, and either R 1 or �b1• In these, estimated residuals for �y1, �Ph and either R1 or �b1 are fed into the system as estimates ot shocks that occurred historically, with the simulations beginning with initial conditions

The factor 1 00 is needed because R1 is expressed in tem1s of percentage points whereas [l,h, is in logarithmic (i.e., fractional) units. Comparability is not complete, however, because R, is measured as percentage points on a per annum basis. Use of -400 as the scale factor would, however, result in dynamically unstable behavior for most A values over 0.25. 57

1512

B. T. McCallum

as of 1 954. 1 and running for 1 52 periods 5 8 . The table's entries are RMS errors, i.e., deviations of x1 from target values x7 , with the top figure in each pair pertaining to the t...b1 instrument and the bottom figure to the R1 instrument. The three panels A, B, and C refer to simulations with the three target values (x; 1 , x;2, x;3), and for each simulation the RMS error performance is reported relative to each of the three target paths. Thus, we are able to see if performance relative to alternative criteria is sensitive to the target utilized, for each of the targets. Comparing the three panels we see that when the levels target is used (with only proportional feedback) performance is very bad with the R 1 instrument, explosive fluctuations in x1 resulting with A = 0.25, 0.5, and 1 .0 . Even with the base instrument, the levels target does not perform too well and leads to instability when A = 1 .0. With A = 0 .25, somewhat better performance relative to the x7 1 target path obtains than when x;2 or x;3 is the target, but the difference is not large. Panel C, by contrast, shows that when the pure growth rate target x;3 is adopted, successful stabilization of x1 is achieved for all A values with both instruments. Performance relative to the growing levels path x7 1 is much better in Panel B with the x;2 target, however, and brings about very little deterioration in performance relative to the pure growth rate criterion (i.e., the x;3 path). Accordingly, the weighted average criterion x;2 seems quite attractive, as was noted for Japan in McCallum ( 1 993a). Equivalently, application of a limited amount of proportional as well as derivative feedback is evidently desirable 59. As for the comparison between monetary base and interest rate instruments, the results in Table 1 are distinctly more favorable to the former. In only one of 30 separate comparisons 60 is the RMS error value smaller with the R1 instrument 61 . And, more significantly, the number of cases in which explosive oscillations result is larger with the interest instrument. These cases, should be noted, all involve the growing-levels target, x; 1 . Some proponents of an interest instrument might argue that it is important that R1 be adjusted relative to a reference level, rather than to the previous quarter's value. Following the practice of Taylor ( 1 993b), therefore, let us also consider performance of a rule of the following type: Rt = 1 00[0. 029 + (Pt- 1 -- Pt s )] - 1 00A (x;_ 1 sg

- Xt-1 ) .

(5.3)

Stochastic simulations, with shocks generated randomly, have been conducted by Judd and Motley ( 1 992) in a related study mentioned below in Section 6. 59 Judd and Motley's ( 1 992) findings with regard to the use of some proportional control are less encouraging, evidently because their mixture is more heavily weighted toward proportional control. Also, they do not consider performance relative to the x* 1 1 path when x*2 1 is the target utilized. 60 Note that the first-column cases are the same with the three different targets, since with A = 0 there i s no feedback from target misses. "1 Michael Woodford has emphasized to me that there is no inherent interest in comparing base and interest instruments with equal values of A; that we want to compare entire families. These comments are correct. But Table 1 attempts to do that by scaling the A values - recall that the factor - 100 has bvcn inserted in Equation (5.2) - so that instrument instability occurs for about the same value of (scaled) },.

Ch. 23:

Issues in the Design ofMonetary Policy Rules

1 5 13

Table 2 RM S errors with level-style interest instruments, rule (5.3), VAR Model, US Data 1 954. 1 - 1 99 1 .4 RMS error relative to:

). = 0.00

). = 0.25

). = 0.50

0.3825

0 . 1 54 1

0.09 1 5

0.0809

0.0326

0.0208

0.0169

0.01 1 8

0.0 1 04

0.01 08

0.0143

0.3825

0.2996

0.24 ! 6

0. 1 702

0.0809

0.0630

0.0507

0.0366

0.0 1 1 8

0.01 1 1

0.0 1 1 0

0.01 29

). = 1 .00

Panel A: x;1 target 0.05 5 1

Panel B: x;2 target

Panel C: x;3 target 0.3825

0.3687

0.3559

0.332S

0.0809

0.0780

0.0754

0.07 1 1

0.0 1 1 8

0.0 1 1 8

0.01 20

0.0 1 53

Here the (P1-t - Pr-s) term uses the past year's inflation rate as a forecast of the next quarter's so as to make the rule one that sets a real interest rate in relation to the (annualized) target value of 0.029, which is designed to be consistent with a long-run real interest rate of 2.9 percent. The latter follows Taylor's ( 1 993b, p. 202) suggestion of using the sample average rate of growth of real output. The feedback term is as before. Results are presented in Table 2 for cases using rule (5.3) that are exactly analogous to those in Table 1 . It will be seen that the performance is better than with interest instrument rule (5 .2) for all 1 2 comparisons when x� 1 is the target, i.e., when a levels target is utilized. Among the 1 8 remaining comparisons, however, rule (5.3) outperforms (5.2) in only a single case. So, it is unclear whether the levels form of interest instrument rule is superior to the form that calls for adjustment of R1 relative to the previous quarter's value. In comparison to the base instrument, rule (5.3) avoids the explosive outcome in the case in which A = 1 and the levels target x; 1 is used, and also does better relative to the x�3 path in two more cases (with the levels target). But for all cases in which the growth rate target x;3 or the weighted average target x;2 is used, the RMS error is larger with rule (5.3) than with (5 . 1 ) - and is substantially larger when the criterion path is either x;1 or x;2 . It must be emphasized that the foregoing is just a single illustration, not a study purporting to be concl usive - especially since the model used is of the VA R type

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Nevertheless, the apparent superiority of the base instrument gives rise to the question of why it is that, in actual practice, almost all central banks utilize operating procedures that are akin to use of an interest rate instrument. It is almost certainly the case that use of a base instrument would entail more short-term interest rate variability, but it is unclear that this would have any substantial social costs 62. One hypothesis is that interest rate instruments and interest rate smoothing are practiced because financial communities dislike interest variability and many central banks cater to the wishes of financial institutions with which they have to work in the course of their central-banking duties. The extent of interest-instrument preference by CBs suggests, however, that there are additional reasons. Accordingly, Goodfriend ( 1 99 1 ) and Poole ( 1 99 1 ) have made interesting efforts to understand the Fed's attachment to an interest rate instrument. Despite their contribution of various insights, however, the question remains unanswered 63 . My own thoughts on the subject suggest two intelligible reasons for a CB to prefer a R, instrument, one having to do with beliefs concerning possible instrument instability and the other involving the CB 's role as a lender of last resort. Regarding the former, consider a grossly simplified base money demand function that includes lagged as well as current interest rates: Ot <

0.

(5 .4)

Here the absence of price level and income/transaction variables reflects the presump­ tion that their movements are slow in comparison to those of b, and R1 64 . Now suppose that the CB were to manage b, exogenously 65 . Then R, will behave as

(b,

determinants),

(5.5)

where /3 1 = - a2/ a 1. Thus, i f a2 < 0, there will be oscillations in R1• More importantly, if I a2 l > I a t l , then the system will be explosive. Belief that market demand for the monetary base is such that I a2 1 > I a 1 I represents the actual state of affairs would then lead one to believe that use of a base instrument would be disastrous, as suggested by Goodhart. And, in fact, there is some reason to 62 Between 1 975 and 1 987 the Swiss National Bank used procedures that were akin to use of a base instrument. [See Rich ( 1 987, pp. 1 1-1 3).] Short-term interest rate variability in Switzerland was much greater than in other economies, but macroeconomic performance was excellent. (In 1 987 there were two major institutional changes, involving new required-reserve structures and a new clearing system, that seriously disrupted monetary control and resulted in altered operating procedures.) 63 It is possible that Goodhart's ( 1 994) belief, that a base instrument would be infeasible, is shared by many central bankers. But why? One possible reason is developed in the next two paragraphs. 64 This simplification should not be misleading for the purposes at hand, although it would be fatal for many other issues. In Equation (5.4 ) 1]1 is a stochastic disturbance term. 65 Here I do not literally mean exogenous, but rather that b1 is varied for macroeconomic reasons, not so as to smooth R1 values. ,

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think that such beliefs might b e held by central bankers. In particular, econometric estimates of base money demand functions (direct or indirect) sometimes indicate that l a2 1 > l at l in fact. Central bank analysts would be aware of these estimates. My own belief is that it is not true that I a2 1 > I a 1 1 holds in reality, for time periods of one month or longer, so that the posited CB attitude is unjustified. 66 But it could be prevalent, nevertheless, even if my belief is correct. A second intelligible reason for CB interest instrument preference concerns the lender-of-last-resort (LLR) role. That role is to prevent financial crises that involve sharply increased demands for base money [Schwartz ( 1 986 ), Goodfriend and King ( 1 988)]. To prevent such crises, the CB needs to supply base money abundantly in times of stress [Bagehot ( 1 873)]. This is usually conceived of as occurring by the route of discount-window lending. But Goodfriend and King pointed out that a policy involving interest rate smoothing - i.e., not allowing R1 to change much relative to R1_ 1 - would automatically provide base money in times of high demand 67. Then i f a C B i s going to practice R 1 smoothing i t is quite natural for it to use a R1 instrument 68 . This last discussion leads one to consider the possibility o f using an interest rate instrument - and smoothing its movements at a high frequency (e.g., weekly) so as to keep monetary base values close to target levels implied by a policy rule such as (5. 1) . The motivation, of course, is the notion that quarterly base rules seem to function better macroeconomically than interest rules. The preliminary investigation in McCallum ( 1 995a) attempts to study this question while accounting realistically and in quantitative terms for shock variances and market responses in the US economy. The results suggest that the federal funds rate could be manipulated weekly to approximate monetary base values that are designed to hit desired quarterly-average nominal GNP targets, with considerable smoothing of the funds rate on a weekly basis (only about twice as much weekly variability as now obtains).

6. Issues concerning research procedures

In this section consideration will be given to a number of issues concerning procedures used in investigations of the properties of monetary policy rules. One set of issues has to do with the operationality of various rule specifications while another set focuses In part my belief stems from the fact that for base demand in period t the value of R 1 _1 is an irrelevant bygone, so R1_ 1 does not belong in a properly specified demand function. There are reasons, involving omission of expectational variables, why econometric studies would neve1iheless tend to find strong R,_1 effects. On this, see McCallum ( 1 985, pp. 583-585). 67 As would a practice of keeping R1 from rising above some preset penal rate. 68 Goodfriend ( 1 9 9 1 , p. 1 5) and Poole ( 1 9 9 1 , pp. 37-39) observe, however, that this is not a strict logical necessity. Also, many actual CBs apparently do not accept the Goodfriend-King argument that the LLR role can be fulfilled by R1 smoothing without discount-window lending. 66

1516

B. T McCallum

on the types of simulations used to generate model outcomes. Regarding the latter, a weakness of the simulation results reported above in Section 5, and also those in McCallum ( 1 988, 1 993a, 1 995a), is that they are based on simulation exercises with a single set of shock values, i.e., shocks estimated to have occurred historically. As explained by Taylor ( 1 988) and Bryant et al. ( 1 993), there are several advantages to be obtained by using true stochastic simulations with a large number of shock realizations generated by random selection from (multivariate) distributions that have covariance properties like those of the historical shock estimates. The studies of Judd and Motley ( 1 99 1 , 1 992) for example, improve upon those of McCallum ( 1 98 8) by conducting "experiments" each of which consists of 500 stochastic simulations with a given model, policy rule, and policy parameter values, rather than a single simulation with the historical residuals used as shocks. One obvious advantage of stochastic simulations over historical counterfactuals is that they avoid the possibility that the historical residuals happen to possess some particular quirk that makes performance unrepresentative for the shock moments being utilized. Another advantage is that sample-mean values of shocks may not equal zero, as they must by construction in the case of historical residuals. This feature is especially important in considering the consequences of rules that feature difference stationarity (rather than trend-stationarity) of nominal variables. The residual values used as shocks in the simulations in Tables 1 and 2, for example, sum to zero for each equation's shock term. Thus the extent of a tendency for x1 (say) to drift away from a levels target path such as x; 1 is understated by the results in those tables 69. Bryant et al. ( 1 993, pp. 373-375) suggest that, in addition, stochastic simulations are helpful from a robustness perspective. Perhaps the most ambitious project undertaken to date on the characteristics of alternative monetary policy rules is the Brookings-sponsored study reported in Bryant et al. ( 1 993). In this study, which is a follow-up to Bryant et al. ( 1 988), eight prominent modeling groups (or individuals) reported on policy rule simulation exercises conducted with the following multicountry models: GEM, INTERMOD, MSG, MX3, MULTIMOD, MPS, LIVERPOOL, and TAYLOR. These studies were designed to explore the macroeconomic consequences of adopting different target variables for monetary policy, with contenders including nominal GDP (in levels form) and the hybrid variable discussed above in Section 4, as well as monetary aggregates and the exchange rate. Most impressively, the conference organizers took pains to arrange for the various modeling groups all to consider the same range of policy alternatives, thereby creating the possibility of obtaining results that would gain in credibility as a consequence of being relatively robust to model specification. At the strategic level of research design, therefore, this Brookings project possessed the potential for contributing greatly to knowledge concerning the design of monetary

69

Understated, but not entirely absent; time plots of x1 indicate the absence of any path-restoring behavior except toward the end of the ! 52-quarter simulation (and sample) period.

Ch. 23: issues in the Design of Monetary Policy Rules

1517

and fiscal policy rules (even in the face o f potential weaknesses o f the models' specifications). It is argued in McCallum ( 1 993b, 1 994), however, that this potential was signif­ icantly undermined by the particular generic form of policy rule specified for use by all the modeling groups. The alleged problem is that the rule form permits rule specifications that are not operational and, in addition, suggests performance measures that can be seriously misleading. The rule form in question, which has also been used in several other studies, may be written as (6. 1 ) where R1 is an interest rate instrument and z1 is a target variable such as nominal GDP. Here the "b" superscripts designate baseline reference paths for the variables, baseline paths that may be defined differently by different investigators. Also, the performance of various targets is evaluated by measures such as E[(z1 - z�)2 ], which pertain to target variable(s) for the rule and perhaps also other criterion variables. In terms of operationality there are two problems with this rule form (6. 1 ) 70. The more obvious is that it is unrealistic to pretend that monetary policymakers can respond to the true value of current-period realizations of z1 for several leading specifications of the latter. It is reasonable to assume that contemporaneous observations are available for interest rates, exchange rates, or other asset-market prices. It would be unreasonable, however, to make such an assumption for nominal or real GDP (or GNP) or the price level. One could make arguments pro and con in the case of monetary aggregates such as M l or M2, but in the case of national-income values, data are not produced promptly enough for actual central bankers to respond to movements without an appreciable lag. Ignoring that lag, as is done throughout the Bryant et al. ( 1 993) studies, clearly makes it possible for the simulated performance to be significantly better than could be obtained in reality. Furthennore, simulations that ignore this lag also intend to understate the danger of instrument-induced instability, a bias that is quite important because instrument instability is one of the most serious dangers to be avoided in the design of a policy rule. The second and less obvious way in which rules like (6. 1 ) are not operational involves the baseline values R� and zf. Here the problem is that an actual policymaker could not implement any rule of form (6. 1 ) without knowledge of these reference paths. But by definition these paths may be related to each other by the model being investigated, so the policy rule is model-specific and therefore of reduced interest to a practical policymaker. In terms of misleading performance measures, the problem is that the instrument variable under consideration may be one that can be used to smooth out fiuctua · tions in z1 but not to control the long-term growth of z1 • Then by using fluctuations in z1 70

It should be noted favorably that the instrument variable is operational and realistic.

1518

B.T. McCallum

relative to the baseline path z7 in a performance measure like E[(z1 - z7)2 ], the investigator may conclude that R1 is a desirable instrument when in fact it is highly unsuitable 7 1 . Another type of nonoperationality involves the specification of instrument variables that would, in actual practice, be infeasible in this capacity. Broad monetary aggregates such as M2 or M3 would seem clearly to fall into this category and, under typical current institutional arrangements, probably the same applies to variants of M l . Studies that pretend that such variables are feasible instrument have declined in frequency in recent years, as the practice of specifying an interest instrument has gained in popularity [e.g., Taylor ( 1 993a), Bryant et al. ( 1 993), Fuhrer and Moore ( 1 995)] . Objections based on the operationality criterion have been directed at rules that use nominal GDP or GNP targets, even when these rules refer only to values lagged by at least one quarter. The point is that national income statistics are not produced often enough or quickly enough, and are significantly revised after their first release. But this criticism seems misguided since the essence of nominal income targeting is to utilize some rather comprehensive measure of aggregate (nominal) spending; the variable does not need to be GDP or GNP per se. Other measures could readily be developed on the basis of price and quantity indices that are reported more often and more promptly - in the USA, for example, one could in principle use the product of the CPI and the Fed's industrial production index (both of which are published monthly) . It might even be possible to develop a monthly measure that is more attractive conceptually than GDP, by making the price index more closely tailored to public perceptions of inflation and/or by using a quantity measure that treats government activity more appropriately.

7. Interactions with fiscal policy

The relationship between monetary and fiscal policy has been quite an active topic recently, possibly in part as a response to the magnitude and duration of fiscal deficits experienced in many developed countries and/or to controversies concerning proposed fiscal rules for the planned European monetary union. It is obviously impossible to discuss in this chapter all of the many ramifications of monetary/fiscal policy interactions, but it seems important to recognize some recent arguments which suggest that it is necessary, or at least desirable, for the monetary authority to take account of fiscal policy behavior when designing its monetary policy rule 72 . Such a recommendation is implicitly critical of the policy rules discussed in previous sections and runs counter to the spirit of much current central-bank thinking, as expressed for example in the practice of inflation targeting. Consequently, three strands of literature will be considered. 7 1 Some examples are described in McCallum ( 1 994). 72 Among these contributions are papers by A1esina and Tabellini ( 1 987), Debelle and Fischer ( 1 9 9 5),

Leeper ( 1 99 1 ), Sims ( 1994, 1 995), and Woodford ( 1 994, 1 995).

Ch. 23:

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An early paper on the subject that has received a great deal o f attention i s the Sargent nd a Wallace ( 1 98 1 ) piece entitled "Some Unpleasant Monetarist Arithmetic". As many readers will be aware, that paper's principal contention was that an economy's monetary authority cannot prevent inflation by its own control of base money creation if an uncooperative or irresponsible fiscal authority behaves so as to generate a continuing stream of primary fiscal deficits 73 . Whether the central bank has control over inflation is viewed as depending upon, in the words of Sargent and Wallace ( 1 9 8 1 , p. 7), "which authority moves first, the monetary authority or the fiscal authority. In other words, who imposes discipline on whom?" Having posed the problem in that way, the Sargent-Wallace paper then goes on to suggest that it might well be the fiscal authority that dominates the outcome. In fact, however, the paper's analysis proceeds by simply assuming that the fiscal authority dominates, an assumption that is implicit in the procedure of conducting analysis with an exogenously given path of primary deficits. Proceeding in that fashion, the Sargent-Wallace paper seems to show that even a determined central bank could be forced by a fiscal authority to create base money along a path that is inflationary when a non-inflationary path is intended. It is argued by McCallum ( 1 990a, pp. 984--985), however, that this suggestion is unwarranted. It is of course true that fiscal authorities may be able to bring political pressure to bear on central banks in ways that are difficult to resist. But the Sargent­ Wallace analysis is not developed along political lines; instead it seems to invite the reader to conclude that a politically independent central bank could be dominated in some technical sense by a stubborn fiscal authority. My basis for disputing this is that an independent central bank is technically able to control its own path of base money creation, but fiscal authorities cannot directly control their own primary deficit magnitudes. The reason is that deficits are measures of spending in excess of tax collections, so if a fiscal authority embarks on a tax and spending plan that is inconsistent with the central bank's (perhaps non-inflationary) creation of base money, it is the fiscal authority that will have to yield. Why? Simply because in this circumstance, it will not have the purchasing power to carry out its planned actions 74 . In other words, the fiscal authority does not actually have control over the instrument variable -- the deficit - that it is presumed to control in the Sargent-Wallace experiment. Thus a truly determined and independent monetary authority can always have its way, technically speaking, in monetary versus fiscal conflicts. This simple point is one that seems to the author to be of great importance in the design of central bank institutions. The point is also intimately related to a quite recently developed body of theorizing that takes a strongly "fiscalist" stance, leading examples of which include Woodford 73

The r�sult pertains to primary deficits, i.e., deficits exclusive of interest payments, but not to dcficito, measured in the conventional interest-inclusive way. 74 This is directly implied by the government's budget constraint which limits purchases to revenue raised by taxes, net bond sales, and base money creation. In this regard it should be recognized that the government cannot compel private agents to buy its bonds (i.e., lend to it), since such would represent tax ation.

B. T McCallum

1 520

( 1 994, 1 995), Sims ( 1 994, 1 995), and Leeper ( 1 99 1 ) . Perhaps the most dramatic theme in this literature is the presentation of a "fiscal theory of the price level" [Woodford ( 1 995, pp. 5-1 3), Sims ( 1 994)]. For an introductory exposition and analysis, let us consider the simplest case, which involves a Sidrauski-Brock model with constant output y and utility function u(ct , m1) + f3u(c1+ I , mt+! ) + · · · with u(c, m) = ( 1 - at1 A 1 c1-a + ( 1 - 11t 1 Azm H , where a, 11 > 0 and f3 = 11( 1 + p) with p > 0. Also we assume 11 < 1 , in order to facilitate presentation of the fiscalist theory, not the counter-argument outlined subsequently. In this setup, the households' first­ order conditions include

75

A=

(

A a ____!_X_ Az

)-111}

(7. 1 ) ('1.2)

for all t = 1 , 2, . . . . Here P1 is the money price of output, M1 is nominal money at the start of period t, m1 = M/P1 , c1 is consumption during t, and R1 is the rate of interest on government bonds, the household's budget constraint being

1

t

Pt ( Y - Vt) = Pt ct + Mt+l - M t + ( 1 + R r B t+ l - B � o

(7.3)

where v1 is lump-sum taxes and B1 is the nominal stock of bonds at the end of t. ln per-household terms, the government budget constraint with zero purchases is (7.4) so v1 is the per-household value of the fiscal surplus. If the government chooses time paths for M1 and v1 (or B1 ), then Equations (7. 1 )-(7.4) give equilibrium values for c1, P{ , Rt , and B1 (or v1) provided that two transversality conditions are satisfied, these 1 1 requiring that {3 MtfP1 and {3 B11P1 approach zero as t ----+ oo. Note that Equations (7.3) and (7.4) imply c1 y, the constancy of which is utilized in formulations (7. 1 ) and (7.2). Following the fiscalist argument 76, now suppose that the value of M1 is kept constant at M and that v1 = v > 0 for all t = 1 , 2, . . . Then the price level is determined as follows. The GBR can be written as P1 I I (7.5) b1+ 1 = ( l + RI ) pt+ -! [bI - vt ] = f3 -b/ - ut o f3 ,_-

.

_

_

-

implying that b1 = B/P1 will explode as t --+ oo, since 11f3 > 1 , unless it is the case that B 1 /P 1 = v/( 1 - {3), which would induce b1 to remain constant at the level b1 v/( l {3) =

-

75 That is, a model in which infinite-lived households with time-separable preferences make their

decisions in a optimizing fashion and interact with each other and the government (monetary authority and fiscal authority) on competitive markets. Woodford's ( 1995) version of the model, and ours, does not include capital goods but that feat11re of the setup is not relevant to the issues at hand. 76 I am indebted to Michael Woodford for special efforts to explain the argument to me, bLI1 he i s certainly not responsible for the point of view expressed here.

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thereafter. Therefore, so the theory says, P 1 = B 1 ( 1 - {3)/u i s determined by the fiscal surplus magnitude u and the initial stock of nominal debt B 1 . At the same time, Equations (7. 1 ) and (7.2) imply a difference equation relating Pt+ 1 to P1 in an unambiguously explosive fashion, starting from P 1 , provided that P 1 exceeds a critical value Pc . That explosion i n P 1 makes MIP1 approach zero and so, with b1 constant, both transversality conditions are satisfied although B1 is exploding. Thus the fiscal theory of the price level asserts that with a constant money stock and constant fiscal surplus, the price level explodes as time passes, starting from a level that is directly related to the size of the pre-existing nominal bond stock and to the magnitude of the maintained surplus. No other path could be an equilibrium because it would imply an exploding b1 , which would violate a transversality condition. The foregoing is an ingenious argument but, in the opinion of the writer, is open to a crucial objection. It is that there is another equilibrium - typically ignored by fiscalist writers - that does not rely upon explosive-bubble behavior of the price level. 1 This more fundamental "monetarist" equilibrium features Pt+l = P1 = 11dp 1rlfA, i.e., a constant price level, together with values Bt+ 1 = 0 for all t = 1, 2, . . . . With these paths for P1 and B1 it is clear that Equations (7. 1 )-(7.3) and both transversality conditions are satisfied. It might be objected that this solution does not satisfy the budget constraint (7 .4) for the values of u1 = u specified by the fiscalist writers, but it has been argued above that the fiscal surplus is actually not a variable that can legitimately be specified as exogenous 77 . What the monetarist solution says is that if the fiscal authority tried to keep u1 = u as in the fiscalist solution, then households would refuse to purchase the bonds that are required to be sold by the fiscal authority. It would be necessary to distinguish between bonds supplied in (7.4) and bonds demanded in (7.3), with B1 =0 in the latter. If there were an initial stock of bonds outstanding, B 1 * 0, then they would be retired in period 1 with a resulting real primary surplus of BdP 1 • In sum, a formally correct and arguably more plausible solution than the fiscalisl candidate is one in which the price level remains constant, with a magnitude that is proportional to the money stock. At the same time, the stock of bonds offered for sale by the fiscal authority may be explosive but if so these bonds will not be purchased by optimizing households. The fiscal authority's realized surplus will then be zero after the initial period leaving us with a traditional non-fiscalist result 78 . There are, of course, several other cases and more complex models featured in the recent fiscalist literature, indeed, a rather bewildering variety. But it would appear to the present writer that the striking fiscalist outcomes typically result from emphasizing the possibility of bubble

77 This i� also the basis for the argument in a recent paper by Buiter ( 1 998), which reaches conclusions

predominantly compatible with those presented here. n Note that it is not being claimed that this is the only solution, but merely that it i" a solution (and one that might be thought likely to prevail by analysts who are skeptical of the empirical importance of macroeconomic bubbles),

1 522

B.T. McCallu m

solutions while ignoring the existence of a non-bubble or fundamentals solution that would deliver an entirely traditional policy message. 79 • 80 The third strand of the monetary-fiscal interaction literature to be discussed is represented by papers by Alesina and Tabellini ( 1 987) and Debelle and Fischer ( 1 995) . In the former, the workhorse Barro-Gordon model is extended by assuming that real government purchases are controlled by a fiscal authority (FA) that may have different objectives - concerning the level of these purchases as well as inflation and output than those of the central bank (CB). The FA's revenues come from non-lump-sum (distorting) taxes and money growth, government debt being excluded from the model. In this setting, Alesina and Tabellini derive outcomes pertaining to both discretionary and rule-like behavior by the CB 8 1 • Their most striking result is that when preferences of the CB and the FA are sufficiently different 82 , equilibrium outcomes with monetary policy commitment can be inferior 83 to those obtained under discretion. This result is with independent behavior by the CB and FA, so the message is that monetary-fiscal policy cooperation is needed. In a more recent paper, Debelle and Fischer ( 1 995) have modified the Alesina­ Tabellini framework by also including a social objective function, one that can be different from those of the CB and FA. Only the latter cares, in their setup, about the level of government purchases. In this model, Debelle and Fischer conduct analysis always assuming discretionary behavior by the CB but under different assumptions regarding the Stackelberg leadership positions of the CB and FA. A major aim of the analysis is to determine the optimal value, in terms of society's preferences, of the "conservativeness" of the CB, i.e., the relative importance that it assigns to inflation. It is not optimal, they find, for the CB's preferences to match those of society - i.e., 79 Dotsey ( ! 996) shows that a realistic specification of parameter values gives rise to a more traditional policy message than one promoted in the fiscalist literature, for an issue concerning the responsiveness of the CB to fiscal variables under the assumption that the fiscal authority's policy rule tends to prevent debt explosions. 80 One other feature of the recent fiscalis! literature is its contention that pegging the nominal interest rate at a low value will result in a correspondingly low inflation rate and in no indeterminacy problem, implying that such a policy would be preferable to the maintenance of a low growth rate of the (base) money supply. The analytical key to this argument is that explosive price level (bubble) solutions, which are possible with a low money stock growth rate, would be precluded by a constant interest rate in models with a well-behaved (possibly constant) real rate of interest - see, e.g., Equation (7 .2) above. It has been established above, however, that when money growth is exogenous, the possible aberration reflects multiple (bubble) solutions, not nominal indeterminacy. But the empirical relevance of bubble solutions for macroeconomic variables is dubious, this writer would contend, and if such solutions are not relevant then the theoretical disadvantage for the low money growth policy is itself irrelevant. 8 1 In the absence of debt, the FA has no incentive for dynamic inconsistency, i.e., no commitment problem. 8 2 The CB is assumed to assign at least as much weight to the inflation rate (relative to each of the other goal variables) as does the FA. 83 Inferior in tenns of both authorities' preferences; the private sector is assun1ed to care only about real wages.

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the private sector. And they find that it is undesirable socially for the FA to dominate (in a Stackelberg sense) the CB, requiring the CB bank to finance FA deficits 84. An objection to this last strand of analysis stems from its reliance on the presumption at th an economy's CB and FA will have preferences that differ from each other's and from social (i.e., household) preferences. While such might be the case in some nations, one would expect that in democratic societies, CBs and FAs will be aware of and tend to reflect the basic preferences of the population. That tendency might be combatted by various devices, but it seems likely that (e.g.) attempts to appoint CB governors with tastes more anti-inflationary than society's would often result in ex-post surprises regarding these tastes. Also, one might expect that fiscal or monetary legislation would be overturned fairly promptly if it were to yield results that are truly inconsistent with the preferences of the society's voters. In any event, it would seem that designing institutions under the presumption that CB and/or FA preferences differ from those of the society at large is unlikely to be fruitful. 8. Concluding remarks

This final section will consist of a brief and perhaps opinionated recapitulation of conclusions obtained for the main topics of discussion. First, in actual practice the defining characteristics of rule-like behavior are that the central bank conducts policy in a systematic fashion, and while doing so systematically abstains from attempts to exploit existing expectations for temporary gains in output. Central banks can behave in this committed manner if they choose; there are dynamic-inconsistency pressures on them to act in a more discretionary fashion, but there is nothing tangible to prevent committed behavior. Indeed, the adoption of a monetary policy rule is one technique for overcoming discretionary pressures. In terms of research strategy, the chapter's discussion has promoted the robustness approach - i.e., searching for a rule that works reasonably well in a variety of models ­ rather than the more straightforward approach of deriving an optimal rule relative to a particular model. No strong claims are made in this regard, however, and the value of the optimal design approach is recognized. The importance of operationality of any proposed rule is also emphasized, as well as the merits of stochastic simulations as opposed to simpler historical counterfactual simulations. Regarding the choice of a target variable, the chapter suggests that in practice the difference between an inflation target and one that aims for nominal spending growth, at a rate designed to yield the same target inflation rate on average, is unlikely to be large. More dissimilar is the hybrid target variable that adds together inflation and output relative to capacity. This hybrid variable is probably more closely related to Of course, i t i s m·gued above that the FA will not be able to dominate if the CB has independence (i.e., can choose its own base money creation rates).

g4

1 524

B. T McCallum

actual central bank objectives, but the absence of any reliable and agreed-upon method of measuring capacity or trend output creates a major drawback for this variable. Also, it is argued that the magnitude of future price-level uncertainty, introduced by the unit root component that results from a growth-rate type of target, is probably rather small. Thus growth-rate targets appear somewhat more desirable than growing-level targets as the latter requires stringent actions to drive any nominal target variable back toward its predetermined path after shocks have led to target misses. Turning to the choice of an instrument variable, the chapter presents a small bit of evidence designed to illustrate why it is that a number of academic economists are inclined to prefer quantity instruments, such as the monetary base, rather than short-tenn interest rates. The exposition includes arguments against some literature claims that either short-term nominal interest rates or the monetary base are infeasible as instruments. In this discussion, particular emphasis is given to the distinction between two quite different types of abberational price level behavior, namely, nominal indeterminacy and multiple solutions. The former has to do with the distinction between real and nominal variables while the latter concerns self-fulfilling dynamic expectational phenomena - i.e., bubbles. Also, the former pertains to all nominal variables whereas the latter involves real variables. Finally, with regard to prominent fiscalist positions two points are made. First, the recently developed fiscal theory of price-level determination typically leads to a solution that is not unique; there also exists a less exotic bubble-free solution that has a much more traditional (indeed, monetarist) flavor. This conclusion stems from recognition that central banks can dominate in any conflicts with fiscal authorities. Also, there are some results in the literature that suggest that monetary/fiscal cooperation is important, but these depend upon the assumption that central baPl<:s and fiscal authorities have fundamentally different objective functions. It is doubtful whether such an assumption can play a fruitful role in the design of desirable central bank institutions and behavior patterns.

References

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Chapter 24

INF LATION STABILIZATION AND BOP CRISES IN DEVELOPING COUNTRIES* GUILLERMO A. CALVO University ofMaryland CARLOS A. V EGH * * ucLA

Contents

Abstract Keywords 1 . Introduction 2. Understanding chronic inflation 2. 1 . Inflation a s a n optimal tax 2.2. Shocks and accommodation

2.3. Multiple equilibria

2.4. The "provinces" effect 2.5. Delayed stabilization 2.6. In conclusion

3.

Evidence on the real effects of stabilization in chronic-inflation countries 3 . 1 . Exchange-rate-based stabilization: empirical regularities 3 . 1 . 1 . Stabilization time profil es 3 . 1 .2. Panel regressions 3 . 1 .3 . Do exchange-rate-based stabilizations sow the seeds of their own destruction? 3.2. Money-based stabilization: empirical regularities 3.3. Recession now versus recession later 3 .4. A word of caution

4.

Exchange-rate-based stabilization I: inflation inertia and lack of credibility 4. 1 . Inflation inertia

1 533 1 533 1 534 1536 1 537 1 53 8 1539 1 540 1 540 1 54 1 1 54 1 1 543 1 54 7 I 550 1 553 1 554 1 55'/ 1 559 1 562 1 567

We are grateful to Francesco Daveri, David Gould, Amartya Lahiri, Carmen Reinhart, Sergio Rodriguez, Jorge Roldos, Julio Santaella, John Taylor, Aaron Tornell, Martin Uribe, Sara Wong, Mike Woodford, Carlos Zarazaga, participants at the conference on "Recent Developments in Macroecononomics", organized by the Federal Reserve Bank of New York (February 1 997), and, especially, Ratna Sahay and Miguel Savastano for insightful comments and discussions. " Corresponding author. Department of Economics, UCLA, 405 Hilgard Avenue, Los Angeles, CA 90095-1 477. E-mail: [email protected]. Website: http://vegh.sscnet.ucla.edu. Handbook of Macroeconomics, Volume 1, Edited by JB. Taylor and M. Woodford © 1999 Elsevier Science B. V. All rights reserved 1531

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4.2. Lack of credibility 1 569 5 . Exchange-rate-based stabilization I I : durable goods, credit, and wealth effects 1 573 5 . 1 . Durable goods 1 573 5.2. Credit market segmentation 1 57 5 5.3. Supply-side effects 1 577 5.4. Fiscal policy 1 5 80 5.5. And the winner is . . . 1581 6. Money-based stabilization 1 582 6. 1 . A simple model 1 5 82 1 587 6.2. Extensions to other money-based regimes 6.3. Money anchor versus exchange-rate anchor 1 588 7. Balance-of-payments crises 1 590 7. 1 . Liquidity 1 591 7 . 2 . The Krugman model 1 592 7.3. Krugman model: critique and extensions 1 595 7.3 . 1 . Bonds 1 595 1 595 7.3.2. Sterilization 1 596 7.3.3. Interest rate policy 1 597 7.4. The current account approach 1 599 7.5. Financial considerations 1 599 7.5 . 1 . Volatility of monetary aggregates 1 60 1 7.5.2. Short-maturity debt 7.5.3. Domestic debt and credibility 1 603 1 603 7.5.4. Credibility, the demand for money and fiscal deficits 8. Concluding remarks 1 604 1 607 References

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1 533

Ab stract

High and persistent inflation has been one of the distinguishing macroeconomic characteristics of many developing countries since the end of World War II. Countries afflicted by chronic inflation, however, have not taken their fate lightly and have engaged in repeated stabilization attempts. More often than not, stabilization plans have failed. The end of stabilizations - particularly those which rely on a pegged exchange rate - has often involved dramatic balance-of-payments crises. As stabilization plans come and go, a large literature has developed trying to document the main empirical regularities and to understand the key issues involved. This chapter undertakes a critical review and evaluation of the literature related to inflation stabilization policies and balance-of-payments crises in developing countries. The chapter begins by trying to rationalize the existence of chronic inflation in of rational agents. It then offers an empirical analysis of the main stylized world a facts associated with stopping chronic inflation. It is shown that the real effects of disinflation depend on the nominal anchor which is used. Exchange-rate-based stabilizations lead to an initial output and consumption boom - which is particularly evident in the behavior of durable goods - real exchange rate appreciation, and current account deficits. The contractionary costs typically associated with disinflation emerge only later in the program. In contrast, in money-based stabilizations, the contraction occurs in the beginning of the program. The chapter then proceeds to review several explanations for these puzzling phenomena, emphasizing the real effects of lack of credibility, inflation inertia, and consumption cycles generated by durable goods purchases. The chapter also documents the fact that most exchange-rate-based stabilizations end up in balance-of-payments crises. The Mexican crisis of December 1 994 brought back to life some of the key questions: Do exchange-rate-based stabilizations sow the seeds of their own destruction by unleashing "unsustainable" real exchange rate appreciations and current account deficits? Or are credibility problems and self-fulfilling prophecies at the root of these crises? The remainder of the chapter is devoted to analyzing the main ideas behind this unfolding literature.

Keywords

JEL classification:

E52, E63, F41

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G.A. Calvo and CA. Vegh

1 . Introduction

High and persistent inflation has been one of the distinguishing macroeconomic characteristics of many developing countries - particularly in Latin America - since the end of World War II. Pazos ( 1 972) coined the term "chronic inflation" to refer to this phenomenon. In his view, chronic inflation is quite a different creature from the much more spectacular hyperinflations studied by Cagan ( 1 956). First, unlike hyperinflations whose duration is measured in terms of months, chronic inflation may last for decades. Second, countries learn how to live with high and persistent inflation by creating various indexation mechanisms which, in turn, tend to perpetuate the inflationary process. As a result, inflation does not have an inherent propensity to accelerate and, if it does, soon reaches a new plateau. Countries afflicted by chronic inflation, however, do not take their fate lightly. Quite to the contrary, in the last four decades they have engaged in repeated stabilization attempts which, more often than not, have failed. The end of stabilizations - in particular those which rely on a pegged exchange rate - has often involved dramatic balance-of-payments crises with costly devaluations and losses of international reserves. With increasingly open capital markets, some of these crises now send shock waves throughout the world, as vividly illustrated by the Mexican crisis of December 1 994. In the last ten years, however, countries such as Chile, Israel, and Argentina have succeeded in reducing inflation close to international levels. Still, most developing countries continue to struggle through stabilization attempts, and some former socialist economies have also begun to face similar cycles of inflation and stabilization. The currency crises that hit South East Asia during the second half of 1 997 were also a startling reminder that no region is immune to boom-bust cycles which were once thought as being mainly a Latin American disease. Over the course of the last four decades, a myriad of major stabilization plans went by, leaving behind a rich legacy of issues and puzzles. In retrospect, the stabilization plans implemented in the late 1 970s in the Southern Cone countries - Argentina, Chile, and Uruguay - proved to be a turning point. Designed by US-trained technocrats, these plans were in some sense the first ones to openly recognize the constraints imposed on monetary policy by open financial markets. Trying to make the most of such constraints,_ policymakers decided to abandon the "closed-economy" monetary policies of the past - aimed primarily at controlling the money supply - and switch to "open-economy" policies based on setting a declining rate of devaluation which would quickly bring domestic inflation in line with tradable-goods inflation (given by world inflation plus the rate of devaluation). To the consternation of policymakers, however, the inflation rate failed to converge to tradable-goods inflation, which resulted in a large real appreciation of the domestic currency. More puzzling still, in spite of the real appreciation, real economic activity - particularly private consumption -- expanded in the early years of the programs. Later in the programs, a recession set in, even before the programs collapsed. In the mid-1 980s, major programs in Argentina, Brazil, and Israel brought back to

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life some of the same, and still mostly unresolved, issues. In spite of the use of wage and price controls to supplement an exchange rate peg, real appreciation remained an integral part of the picture. More puzzling, however, was the reemergence of the pattern of an initial boom and a later recession. The Israeli recession was viewed as particularly hard to rationalize because of its occurrence in a fiscally sound and largely successful stabilization program. Based on these new programs - and a reexamination of older programs going back to the 1 960s - Kiguel and Liviatan ( 1 992) and Vegh (1992) argued that the outcome observed in the Southern-Cone stabilizations is a pattern common to most stabilization plans which have relied on the exchange rate as opposed to a monetary aggregate - as the main nominal anchor. Specifically, the beginning of an exchange-rate-based stabilization is characterized by an economic boom and sustained real appreciation. Later in the programs - and often aggravated by the collapse of the program - a contraction takes hold. In contrast, the scanty evidence on money-based stabilization in chronic-inflation countries lends support to the notion that, as in low-inflation countries, the recession takes place at the beginning of the program [Calvo and Vegh ( 1 994b)] . Hence, it would appear that under money-based stabilization, the costs (in terms of output losses) would be paid up-front, whereas, under exchange-rate-based stabilization, these costs would be postponed until a later date. The intriguing idea that choosing between the two nominal anchors may imply choosing not if but when to bear the costs of disinflation has been dubbed the "recession-now-versus-recession-later" hypothesis. The twin puzzles of the boom-recession cycle in exchange-rate-based stabilizations and the recession-now-versus-recession-later hypothesis have been the driving force behind recent developments in the area of inflation stabilization in developing coun­ tJies. An emerging empirical literature has attempted to document these phenomena in a systematic way, while an extensive theoretical literature has advanced various hypotheses - such as inflation inertia and lack of credibility - to explain the real effects of disinflation. A critical review and evaluation of this literature constitutes the core of this chapter 1 A third puzzle is the fact that most exchange-rate-based stabilizations end up in balance-of-payments (BOP) crises. The literature, however, has had precious little to say so far about the possible links between the dynamics of exchange-rate-based stabilizations and BOP crises. The Mexican crisis of December 1 994 - which put an end to an exchange-rate-based stabilization plan initiated seven years earlier - brought back to life some of the key questions: Do exchange-rate-based stabilizations sow the •

1 Not suprisingly, most of the literature has been inspired by the experiences of chronic inflation countries, which constitute a rich laboratory for the discussion of inflation and stabilization in developing countries. To focus the discussion, we follow this tradition and confine our discussion on inflation and stabilization mostly to chronic inflation countries. We will thus ignore some rare episodes of full­ blown hyperinfations (like Bolivia in the mid-1 980s) - which have more in common with Cagan's classic hypetinflations [see Vegh ( 1 992)]. We will also mostly ignore the inflationary experience of the transition economies, as the dramatic transformation from plan to market raises some special issues [see, for example, De Melo, Denizer and Ge1b ( 1 995), and Sahay and Vegh ( 1 996)].

1 536

G.A. Calvo and C.A. Vegh

seeds of their own destruction by unleashing "unsustainable" real appreciations and current account deficits? Or are credibility problems and self-fulfilling prophecies at the root of these crises? The remainder of the chapter is devoted to analyzing the main ideas behind this unfolding literature. Of course, the potential for BOP crises is a more general issue, which goes back to Krugman's ( 1 979) seminal contribution, and applies to any pegged exchange rate system. Hence, while many of the issues to be discussed have broader relevance, we focus on factors which may be of particular importance for developing countries. The chapter proceeds as follows. Section 2 focuses on how to explain the existence of chronic inflation in a world of rational economic agents. Section 3 examines the main empirical regularities of inflation stabilization in chronic-inflation countries. Section 4 begins the theoretical discussion on exchange-rate-based stabilization by focusing on two key factors: inflation inertia and lack of credibility. Section 5 continues the analysis of exchange-rate-based stabilization by highlighting the role of consumer durables, credit market segmentation, supply-side effects, and fiscal policy. Section 6 examines money-based stabilization. Section 7 discusses the causes and mechanics of balance-of-payments crises. Section 8 concludes. 2. Understanding chronic inflation

For the purposes of this chapter, the rate of inflation in period t is defined as the proportional rate of growth of the price level (usually the consumer price index) from period t - 1 to period t. An essential ingredient in the definition of inflation is the "price level", that is to say, the relative price of goods in terms of money. Therefore, one cannot have inflation without money, and one cannot have inflation without goods. During high inflation - unless something very unusual is happening to the demand for money or to the demand tor or supply of goods - the supply of money also grows at a high rate. Hence, although inflation is a phenomenon that results from the interaction of monetary and real phenomena, monetary factors are likely to dominate. The situation, however, is not symmetric: it does not follow from the above observations that real phenomena, like output or domestic absorption, are largely independent of money. This would be true only under very special circumstances, including (i) no nominal rigidities, and (ii) no effects of changes in nominal interest rates on consumption (see below). As the ensuing analysis will reveal, the channel from money to output is particularly relevant during stabilization programs. The empirical evidence is quite clear about the following two points: inflation is closely tracked by money supply, and inflation particularly, changes in the rate of inflation - affects real variables. The latter represents a formidable challenge faced by stabilization programs. As will be argued below, however, the real effects of either inflation or stopping inflation are not necessarily rooted in fundamentals but may, to a large extent, be due to factors - like policy credibility - which suitable institutional/political arrangements may help to modify.

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Under ideal circumstances, stopping inflation may be a socially painless process. Those circumstances, however, require appropriate fiscal adjustment. One serious difficulty in that respect is that there is more than one way to effect a fiscal adjustment, and each of these ways has different implications for various groups in society. Consequently, it is not easy to reach wide consensus on any particular policy. This has two important consequences: (i) delayed stabilization, and (ii) adoption of incomplete stabilization programs. Point (i) rationalizes inflation persistence, while point (ii) explains the prevalence of short-lived stabilization programs. But what sets inflation in motion in the first place? And, in particular, how can the phenomenon of high and persistent inflation be explained in a world of rational economic agents? 2 Although it would seem fair to say that the profession is still struggling to provide an answer to these questions and is far from reaching a consensus, the existing literature provides several useful insights.

2. 1. Inflation as an optimal tax One explanation, due to Phelps (1 973), is that in a world of distorting taxes, governments may find it optimal to depart from Friedman's ( 1 969) celebrated optimum quantity of money rule, which calls for setting the nominal interest rate to zero. Phelps 's ( 1 973) result is quite intuitive. It follows from the observation that at Friedman's optimum quantity of money rule, the marginal cost of the inflation tax (i.e., the nominal interest rate) is, by definition, nil. Thus, at the margin, increasing fiscal revenue through money creation has no cost. In contrast, the marginal benefit of lowering any distorting tax is unambiguously positive. Therefore, starting from a zero nominal interest rate, it is welfare-improving to increase the inflation tax and lower any other distorting tax used to collect revenue. Thus, Phelps's result calls for a positive inflation tax 3 . A key assumption in Phelps ( 1 973) and the ensuing literature is that there is no fundamental difference between the inflation tax and other "conventional" taxes. It has long been recognized, however, that the costs of collection, enforcement, and evasion associated with the inflation tax are negligible compared to those of other taxes. As Keynes ( 1 924, p. 46) put it, inflationary finance "is the form of taxation which the public finds hardest to evade and even the weakest Government can enforce, when it can enforce nothing else". An inefficient tax system may make it optimal to resort to 2 An alternative explanation for the existence of chronic inflation is simply that policymakt:rs in these countries are systematically ignorant or incompetent. We find this explanation both implausible as a description of the real world and uninteresting from a theoretical point of view (given that we do not have good theories of "ignorance" or "incompetence"). Hence, the basic premise of this section is that chronic inflation is a phenomenon in search of a "rational" explanation. 3 A large literature has developed which analyzes the robustness of Phelps' ( 1 973) findings [sec the critical survey by Woodford ( 1990)]. Modeling money as an intermediate input, Kimbrough ( 1 986) shows an interesting case in which Friedman's rule holds even though all available taxes arc distorting. Kimbrough's result, however, holds only under rather restrictive assumptions [see Woodford (1 990).. Guidotti and Vegh (1 993), and Correia and Teles ( 1 996)].

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G.A. Calvo and C.A. Vegh

the inflation tax even in cases in which Friedman's optimum quantity of money rule would otherwise be optimal [see Aizenman ( 1 987) and Vegh ( 1 989)]. The above arguments - valid as they may be as normative propositions - appear rather insufficient to rationalize chronic high inflation in developing countries. First, high inflation is a phenomenon that the society is typically trying to get rid of and, thus, could hardly be expected to be optimal in accord with Phelps's ( 1 973) prescriptions. Second, while the evidence does show a long-run relationship between fiscal deficits and inflation [see, for example, Fischer, Sahay and Vegh ( 1 997)], cross­ country econometric studies for developing countries have not found support for the main empirical implication of Phelps's ( 1 973) hypothesis that there should be a positive correlation between the inflation tax and other conventional taxes [see Edwards and Tabellini ( 1 991)]. In fact, the inflation tax appears to act more as a residual source of government revenue. Third, empirical estimates show that inflation is often larger than the level that maximizes revenue from inflation [see, for example, Easterly and Schmidt-Hebbel ( 1 994)] 4 . This implies that lower inflation and higher revenues from inflation could be simultaneously achieved -- a glaring contradiction of Phelps's ( 1 973) prescription. In sum, although the optimal taxation approach could explain perhaps the persistence of low levels of inflation, it would seem that other factors are needed to explain the actual pattern of inflation observed in chronic inflation countries.

2.2. Shocks and accommodation While fiscal deficits may constitute the original sin that gives rise to inflation, the persistence of inflation may involve policy accommodation which transforms temporary domestic or external shocks into permanent increases in the inflation rate [see, in particular, Bruno and Fischer ( 1 986) and Bruno ( 1 993, Chapter 3)]. For example, consider a shock which calls for a real appreciation of the domestic currency. Authorities may dislike real appreciation because, say, it might be detrimental to exports. Therefore, incipient real appreciation would lead authorities to devalue. Since conditions after the shock require a more appreciated equilibrium real exchange rate, such a policy reaction cannot provide a definitive solution to the authorities' problem. After the first devaluation, domestic prices will rise to regain lost ground and attempt, once again, to climb a little higher (in order to generate the equilibrium real appreciation). Thus, another devaluation will eventually follow - and, of course, prices will continue rising, setting in motion an inflationary process quite unrelated to fiscal revenue considerations a la Phelps 5 . 4 Although measuring the seigniorage-maximizing inflation rate i s not without problems [see Easterly, Mauro and Schmidt-Hebbel ( 1 995)]. 5 Empirical evidence on the inflationary consequences of real exchange rate targeting in Brazil, Chile, and Colombia may be found in Calvo, Reinhart and Vegh ( 1 995). At a theoretical level, the i nflationary consequences of real exchange rate targeting have been analyzed by Adams and Gros ( 1 986), Lizondo

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More generally, monetary accommodation is typically reflected in the fact that key nominal variables - the rate of devaluation, the rate of monetary growth, and nominal wage growth - are linked to past inflation through accommodative policy rules and institutional arrangements such as backward-looking wage indexation. A greater degree of accommodation will be reflected in more inflation inertia. Bruno ( 1 993) shows how nominal variables linked to past inflation may generate an autoregressive process for the inflation rate. Under these circumstances, temporary shocks to the inflation rate lead to permanent increases in the inflation rate. Bruno and Melnick ( 1 994) further show that the higher is the degree of monetary accommodation, the higher is the new inflation plateau. While the process of shocks and accommodation captures some important elements of chronic inflation processes, it is less clear whether it can be argued that inflation is unduly high, in the sense of not being socially optimal. Presumably, policymakers ac· commodate shocks because not doing so would bring about undesirable consequences. In fact, one can show simple examples in which, in response to temporary shocks, it may be optimal to keep constant the real exchange rate by generating higher inflation [see Calvo, Reinhart and Vegh ( 1 995)]. In the same vein, it is often argued that not accommodating expected inflation by printing money could bring about a severe liquidity crunch and thus lower output. Hence, this view leaves umesolved the issue of why society would periodically wish to get rid of inflation. 2.3.

Multiple equilibria

A more clear--cut case of socially suboptimal inflation is multiple equilibria. An example that we find particularly relevant [Calvo ( 1 992)] is one in which there is a stock of public debt denominated in domestic currency, D. Let the one-period nominal interest rate be denoted by i. Then, next period's full service of the debt (i.e., principal plus interest) will be ( 1 + i)D. Let us choose units of measurement so that the present price level equals 1 , and indicate the one-period expected inflation rate by Jre . Thus, if, say, the equilibrium real interest rate is zero, we have that i = Jre. Therefore, if actual inflation is zero, the real burden of servicing domestic debt would be ( 1 + nc) D. This could very well be a large number. On the other hand, if the government fulfills the private sector's expectations and sets actual inflation equal to expected inflation, the real burden of the debt is just D. Thus, the temptation not to stop inflation in its tracks may be irresistible. A numerical example may help bringing the above point home. Suppose that the stock of debt is just 20 percent of GDP, and consider the case of Brazil (in the late 1 980s) where the monthly rate of inflation was about 30 percent. If inflation is stopped but the private sector expected it to continue at previous levels, the nominal interest rate will remain at 30 percent per month. Therefore, just interest on the debt will ( 1 99 1 ), Montiel and Ostry (1991), Calvo, Reinhart and Vegh ( 1 995), Uribe ( 1 995), and Lahiri ( 1997). See also Heymann and Leijonhufvud (1 995) for a more general analysis of these issues.

G.A. Calvo ond C.A. Vegh

1 540

amount to 6 percent of GDP per month. This sizable cost of stopping inflation may, quite plausibly, lead authorities to relent by either keeping inflation at the original high levels, or adopting a very gradual stabilization program.

2.4. The "provinces " ejjixt Another explanation is what one might call the "provinces effect." Provinces, municipalities, state enterprises, etc., are entities that, at best, attempt to maximize social welfare by controlling a small set of levers. In particular, for these institutions, inflation is a public good, generated by total government expenditure, to which their individual expenditure adds an insignificant amount. Therefore, in choosing "provincial" expenditure, each entity will overlook the adverse welfare consequences of inflation on all other entities. Consequently, like with any other public good, too much inflation (i.e., too little price stability) will be generated 6. While this approach provides an attractive rationale for the existence of inflation, it still needs to explain cross-sectional variation in inflation outcomes. In other words, why should this effect be more relevant in, say, Argentina than in the USA?

2.5. Delayed stabilization We now come to a more recent explanation for the persistence of high inflation; namely, the "war of attrition". This is an extremely useful idea formally developed by Alesina and Drazen ( 1 99 1 ) 7. Suppose that inflation is unduly high for any of the reasons discussed above. Thus, policymakers would know that inflation could be brought under control if institutions were changed, or some appropriate transfers were put in place. So, why do they not act upon this knowledge and stop inflation in its tracks? Alesina and Drazen's ( 1 99 1 ) explanation is that, since there is more than one way to get out of the inflation quagmire, and each way has different welfare implications across groups, it may be optimal for each group to wait for another group to give in. Eventually, the most "anxious" group will give in, adjustment will take place, and inflation will stop. In the meantime, inflation will remain high. Note, however, that Alesina and Drazen's ( 1 99 1 ) model per se does not rationalize the advent of high inflation. Thus, Alesina and Drazen's model would need to be appended with some inflation-causing factor, or factors, in order to be able to track empirical evidence. An interesting application of the Alesina-Drazen framework is the formalizatiOn of the idea that, in practice, things must get worse before they get better. In other words, oftentimes societies need to go through a truly devastating hyperinflationary 6

Sec Aizenman ( 1 992), Velasco (1 993), Sanguinetti ( 1994), Mondino, Sturzenegger and Tornmasi ( 1 996), Zarazaga ( 1 996), and Jones, Sanguinetti and Tommasi ( 1 997). 7 Of course, the perception of inflation as the outcome of an unresolved distributive struggle is not new, and goes back to Hirschman (1 963) [see Heymann and Leijonhufvud ( 1 995) for a detailed discussion]. It should also be noted that these last two factors the "provinces" effect and delayed stabilization are part of a large, and growing, literature on the polical economy of reform [see Tommasi and Velasco ( 1 996) for a survey]. �

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outburst before a political consensus for a stabilization emerges. In the war-of-attrition framework just described, Drazen and Grilli ( 1 993) show how a higher rate of inflation may be welfare-improving by bringing forward the expected time of resolution. The earlier resolution of the war of attrition may thus more than offset the short-term costs of higher inflation. 2. 6.

In conclusion

Based on the analysis thus far, we believe there is no single explanation for the phenomenon of chronic inflation. In fact, we would argue that, when taken together and in the proper dynamic sequence, the five factors discussed above probably explain the key features of processes of chronic inflation. At a fundamental level, governments with inefficient tax-systems will always find it optimal to resort to some inflation (inflation as an optimal tax). The "provinces effect" is likely to add another - socially suboptimal - layer to the optimal public finance level of inflation. Once inflation has emerged, the economy as a whole naturally develops various indexation mechanisms (including accommodative policy rules) aimed at minimizing, for a given inflation rate. the real effects of inflation. Heavy indexation of the economy makes relative prices less responsive to various shocks, which sets the stage for temporary shocks to have permanent effects on the rate of inflation (the "shocks and accommodation" view). At this stage, the inflationary process will probably bear little relation to its original cause (the fiscal deficit), fueling the perception that putting the fiscal house in order may, after all, not help in dealing with the inflation problem. By now, the government's incentives to tackle the problem seriously are greatly diminished. After inflation has become entrenched in the public's mind, it may be too costly for the government not to validate the public's expectations (multiplicity of equilibria). In addition, and even if the government finally managed to credibly commit to a low level of inflation, political battles over the distribution of the fiscal adjustment needed to implement a stabilization may prolong chronic inflation (delayed stabilization). In the end, things may indeed need to get worse - by, say, having a hyperinflationary outburst - before they get better.

3. Evidence on the real etlects of stabilization in chronic-inflation countries

It is perhaps fair to say that until recently the dominant opinion in the profession was that stopping inflation would bring about a sharp fall in output and domestic absorption. In fact, the notion that disinflation is contractionary is so entrenched in the literature that the question asked has typically been not ifbut by how much output would fall in response to an anti-inflationary program. The best-known manifestation of this approach is the so-called "sacrifice ratio," or cumulative percent output loss per percentage point reduction in inflation. Okun ( 1 978, p. 348), summarizing the findings of several papers on the USA, argues that "the cost of a 1 point reduction in the basic inflation rate is 1 0 percent of a year's GNP, with a range of 6 percern

1 542

G.A. Calvo and C.A. Vegh

to 1 8 percent." Fischer ( 1 986b) estimates a sacrifice ratio of 5 to 6 - at the lower end of the Okun range - for the USA for the period 1 979-1 986. Based on a review of fourteen episodes in eight countries, Gordon ( 1 982) concludes that, by and large, contractionary policies - especially "cold turkey" policies - aimed at bringing down inflation have entailed large output costs. More recently, Ball ( 1 994) examined 28 disinflation episodes in nine OECD countries using quarterly data and found that, with one exception, disinflation is always costly, with the sacrifice ratio ranging from 2.9 for Germany to 0.8 for France and the United Kingdom. The conventional view about the output costs of disinflation has also been taken to apply to open economies. Indeed, in traditional open-economy models, disinflation is expected to cause an initial recession regardless of the nominal anchor which i s used (the exchange rate or the money supply), as argued by Fischer ( 1 986a). Therefore, the choice of the nominal anchor i s based on a comparison of the sacrifice ratio involved in the two alternative strategies. By examining the sacrifice ratio under different parameter configurations, F ischer ( 1 986a) concludes that the exchange rate should be the preferred nominal anchor. A similar conclusion i s reached by Chadha, Masson and Meredith ( 1 992). Based on simulations using MULTIMOD (a large-scale, multi-region macroeconometric model), they conclude that, for the United Kingdom, the sacrifice ratio is cut almost in half under an exchange-rate anchor compared to a money anchor. The intuition behind the view that "disinflation i s always and everywhere contrac­ tionary" owes much to the unemployment-inflation trade-off, Phillips-curve literature. Particularly influential has been the staggered-contracting approach p ioneered by Fischer ( 1 977) and Taylor ( 1 979, 1 980). In these models, wage contracts are preset for a number of periods. Hence, credibility of the policy is not enough to generate a costless disinflation. Only a fully-credible gradual disinflation, which would take into account the structure of labor contracts, could reduce inflation with no output cost. For the case of the U SA, Taylor ( 1 983) concludes that it would take four years to disinfiate from a rate of wage increase of 1 0 percent per year to 3 percent without creating unemployment. The conventional view has not gone unchallenged. In an influential paper, Sargent ( 1 982) has argued that inflation was stopped virtually overnight with little or no output costs in the hyperinflations which developed in Austria, Germany, Poland, and Hungary in the aftermath of World War I. Based on tlus evidence, he argues that disinflation need not be contractionary i f it is accompanied by a credible change in regime, which drastically alters the public's perceptions about future government policies. However, even i f Sargent's ( 1 982) conclusions regarding the output costs of stopping hyperinflation were accepted, such hyperinflations are seen as extreme episodes whose lessons are not necessarily applicable to much more mundane, garden­ variety inflations 8.

�

Notice that the average monthly rate o f inflation in these four episodes in the twelve months preccdin!; stabilization ranged from a low of33.3% in Hungary to a high of 455. 1 % in Gem1any [see Vegh ( 1 992L

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Perhaps a more fundamental challenge to the conventional view began to emerge in the late 1 970s when maj or stabilization plans were implemented in the Southern­ Cone countries of Latin America (Argentina, Chile, and Uruguay). The cornerstone of these programs was the announcement of a predetermined path for the exchange rate, which involved setting a declining rate of devaluation 9 . Contrary to Phillips-curve based predictions, the resulting decline in inflation was accompanied by a boom in consumption and no signs of higher unemployment. Moreover, the expansion took place in spite of a sharp appreciation of the real exchange rate. The contractionary costs associated with disinflation appeared only later in the programs, often before the programs finally collapsed. As it turned out, the puzzling phenomenon of an initial expansion followed by a later recession observed during the Southern-Cone "tablitas" appears to be a common pattern of exchange-rate-based stabilizations [see Kiguel and Liviatan ( 1 992) and Vegh ( 1 992)]. In sharp contrast, money-based stabilizations - which are much less common in chronic-inflation countries - have typically led to an initial recession, as the conventional view would have it. The remainder of this section takes a detailed look at some of the empirical evidence on these issues. 3. 1.

Exchange-rate-based stabilization: empirical regularities

Table 1 lists twelve major exchange-rate-based stabilizations in chronic inflation countries in the last 35 years. These programs - which took place in Argentina, Brazil, Chile, Israel, Mexico, and Uruguay - have been studied in great detail and constitute the main motivation behind much of the literature in the area 1 0 • 1 1 . Based Table 2]. Garber ( 1 982) and Wicker ( 1986) have both taken issue with Sargent's ( 1 982) conclusions. Sec also Vegh ( 1 992) and Bruno ( 1 993, Chapter 1 ). 9 In popular parlance, the announced schedule would be referred to as the "tablita" (Spanish for "little table"). In Chile, the exchange rate was eventually fixed. 1 0 Case studies include - but are certainly not limited to - the following. On the Argentine plans, see De Pablo ( 1 974), Fernandez ( 1 985), Canavese and Di Tella ( 1 988), Heymann ( 1 99 1 ), and Dornbusch ( 1 995). On the Brazilian plans, see Kafka ( 1 967), Modiano (1 988), and Cardoso ( 1 99 1 ). On Chile, sec Corbo ( 1 985) and Edwards and Cox Edwards ( 1 99 1 ). On the Israeli plan, see Bruno ( 1 993) and Bufman and Leiderman ( 1 995). On Mexico, see Dornbusch and Werner ( 1 994) and Santaella and Vela ( 1 996). On the Uruguayan plans, see Finch (1 979), Hanson and de Me1o ( 1 985), Viana ( 1 990), and Talvi ( 1 995). Sec also Foxlcy ( 1 9 80), Diaz-Aiejandro ( 1 98 1 ), Ramos ( 1986), Corbo, De Melo and Tybout ( 1 986), Kiguel and Liviatan ( 1 989), Edwards ( 1991), and Agenor and Montiel ( 1 996, Chapter 8). 1 1 The literature has often distinguished between "orthodox" programs (which do not rely on prices and/or wages controls) and "heterodox" programs (which do, and thus have "multiple nominal anchors"). Of the programs listed in Table 1, five were "orthodox" plans (the three "tablitas", the Argentine 199 1 Convertibility plan, and the Uruguayan 1 990 plan); the rest were "heterodox" plans. Except for the behavior of inflation and domestic real interest rates (see below), the response of key macroeconomics variables to major stabilization plans has been very similar, regardless of whether the plans were orthodox or heterodox. l-Ienee, for the purposes of our analysis, not much will be made of this distinction. It should be noted, however, that the policy debate over the desirability of price and wage controls has been intense: see, for instance, Dornbusch and Simonsen (1 987), Dornbusch, Sturzencgger and Wolf ( 1990), Bruno ( 1 993), Leiderman ( 1 993), and Meltzer ( 1 994).

V> ""' ""'

Table 1 Major exchange-rate-based inflation stabilization plans a Inflation rate b

Did the program end in crisis?

Begin and end date

Exchange-rate arrangement

Brazil 1 964

March 1 964August 1 968

Fixed exchange rate, with periodic devaluations

93 .6

1 8.9

May 1 968

No. In spite of switching to a regime of minidevaluations after the August 1 968 devaluation, inflation remained stable around 20% per year until 1 974.

Argentina 1 967

March 1 967May 1 970

Fixed exchange rate

26.4

5.7

Feb. 1 969

Yes. The initial 1 4% devaluation was followed by further devaluations and an 82% decline in reserves.

Uruguay 1 968 June 1 968December 1 97 1

Fixed exchange rate

1 82.9

9.5

June 1 969

Yes. The initial 48% devaluation was followed by successive devaluations and an 8 1 % decline i n reserves.

Chilean tablita

February 1 978June 1 982

Feb. 1 978-June 1 979: pre-announced crawling peg June 1 979-June 1 982: fixed exchange rate

52. 1

3.7

May 1 982

Yes. About 65% percent of reserves were lost and by February 1 983 the currency had depreciated by 55%.

Uruguayan tablita

October 1 978November 1 982

Pre-announced crawling

4 1 .2

1 1 .0

Nov. 1 982

Yes. By March 1 983 the central bank had lost 90% of its reserves and the peso had devalued by 70%.

Argentine tablita

December 1 978- Pre-announced crawling peg February 1 9 8 1

1 69.9

8 1 .6

Feb. 1 98 1

Yes. By April 1 982, the currency had depreciated by 4 1 0% and reserves fallen by 7 1 %.

Israel 1 985

July 1 985-present Exchange-rate policy had four stages d

445.4

7.8

Nov. 1 995

No. Inflation has continued to decline gradually.

Austral (Argentina)

June 1 985September 1 986

1 128.9

50.1

June 1 986

Yes. By September 1 987, reserves had fallen by 75% and monthly inflation was above 1 0 percent.

Program

Initial

June 1 985-March 1 986: fixed exchange rate March 1 986-Sept. 1 986: crawling peg

c

Lowest Date achieved

continued on next page

Q ;,..

g

c

c tl ;, "--

0 �

;;;:: �

�

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:"-

Table 1 , continued Program

Cruzado (Brazil)

Begin and end date

Exchange-rate arrangement

February 1 986November 1 986

Fixed exchange rate

Inflation rate b

Did the program end in crisis?

5;::,·

Initial c Lowest Date achieved 286.0

76.2

Nov. 1 986

Yes. By March 1 987, reserves had fallen by 58% and by December 1 987, monthly inflation had reached 2 1%.

Mexico 1 987 December 1 987- Feb. 1 988-Dec. 1 988: fixed exchange December 1 994 rate Jan. 1 989-Nov. 1 99 1 : preannounced crawling peg Nov. 1 99 1-Dec. 1 994: exchange-rate band

1 59.0

6.7

Sept. 1 994

Yes. Between February 1 994 and January 1 995, reserves fell by 85% and, following the December 1 994 devaluation, the peso depreciated by about 1 00 percent in four months.

Uruguay 1 990 December 1 990- Exchange-rate band with a declining rate present of devaluation

1 33.7

24.4

Dec. 1 996

No. Uruguay was not much affected by the Mexican crisis, and inflation has continued to decline gradually.

Convertibility April 1 991(Argentina) present

267.0

-0.3

May 1 996

No. As the Mexican crisis of December 1 994 spilled over, reserves fell by 52% between mid-1 994 and March 1 995, but the fixed parity was maintained.

e

a

Currency board with a one-to-one parity to the US dollar

>-.

%, .,

Source: Reinhart and Vegh ( 1 995b), based on data from International Financial Statistics (IMF) and case studies cited in the text. Unless otherwise noted, all pegs are against the US dollar. The fall in reserves is measured with respect to peak reserves during program. Data end in December 1 996. b Twelve-month inflation rate (in percent). c Twelve-month inflation rate in the month in which the program was implemented. d In July 1 985, the New Israeli Shekel was pegged to the US dollar; in August 1 986 the dollar peg was replaced by a peg to a basket of currencies. The second phase of the program consisted of a sequence of devaluations during 1 987 and 1 989. In January 1 989 a band with a fixed central parity was introduced. In December 1 9 9 1 a crawling band was introduced. The exchange-rate fixing followed some initial devaluations between December 1 5, 1 987 and February 29, 1 988.

� [5· ;::,

§

"'­ bo

� Q c:;· [;; ;:;· b �"'

.[ �·

g §

�·

c

�

u, .jo,. v,

1 546

G.A. Caluo and CA. Vegh

on these episodes, the literature has identified the following main empirical regularities associated with exchange-rate-based stabilization 1 2 : (i) Slow convergence of the inflation rate (measured by the CPI) to the rate of devaluation. In heterodox programs, inflation has typically fallen faster due to temporary price controls 1 3 . (ii) Initial increase in real activity -particularly, real GDP andprivate consumption ­ followed by a later contraction. It is less clear whether the same pattern applies to investment 1 4. (iii) Real appreciation of the domestic currency. (iv) Deterioration of the trade balance and current account balance. (v) Ambiguous impact response of domestic real interest rates. Ex-post domestic real interest rates have generally decreased in the initial stages of orthodox plans. However, they appear to have increased substantially in the early stages of the heterodox programs of the mid- 1 980s. To take a closer look at the main stylized facts, we constructed a panel of annual observations for four countries (Argentina, Chile, Israel, and Uruguay), which covers 1 6 years ( 1 978-1993), for a total of 64 observations 1 5 • The panel includes seven of the twelve exchange-rate-based stabilizations listed in Table 1 (the "tablitas" implemented in 1 978 in Argentina, Chile, and Uruguay, the Israeli 1 985 plan, the Argentine 1 985 Austral plan, the Uruguayan 1 990 plan, and the Argentine 1 99 1 Convertibility plan) and ten macroeconomic variables (devaluation rate, inflation rate, rates of growth of GDP, private consumption, durable goods consumption, fixed investment, and public consumption, all expressed in per capita terms, real exchange rate, current account deficit as a proportion of GDP, and real lending rate) 1 6 . 12 See Kiguel and Liviatan ( 1 992), Vegh ( 1992), Calvo and Vegh (1 994b), Reinhart and Vegh ( 1 994, 1 995b), and De Gregorio, Guidotti and Vegh ( 1 998). 1 3 Although less well-documented, casual empiricism suggests that wholesale price inflation (which captures the behavior of tradable goods inflation) converges quite rapidly. 14 Both Kiguel and Liviatan ( 1 992) and Reinhart and Vegh ( 1 995b) report mixed results for investment. Real estate boom-bust cycles also appear to be a hallmark of many of these programs; see Rebelo and Vegh (1 995) and Guerra ( 1 997b). Some spotty data also suggest that output in the non-tradable sector typically expands more rapidly than in the tradable sector [Rebelo and Vegh ( 1 995)]. 1 5 The numerous caveats that apply to the empirical exercises which follow are discussed at the end of the section. 16 The sample chosen was dictated by data availability. The sources of data are as follows. Data on GDP, private consumption, and durable goods consumption were provided by the Central Banks of Argentina, Israel, Uruguay, and the Chilean Ministry of Finance. For Argentina and Uruguay, durable goods consumption is proxied by car sales. Real exchange rate data for Israel were provided by the Bank of Israel. All other data are from International Finance Statistics (IMF). Fixed investment corresponds to gross fixed capital formation adjusted by the GDP deflator. (Ideally, we would have liked to have private fixed investment, but data are hard to come by.) The real exchange rate is a real effective exchange rate, as computed by the IMF, defined as a nominal effective exchange rate index adj usted for relative movements in national price or cost indicators of the home country and its main trading partners. Following common practice, the index is presented in such a way that an increase reflects

Ch. 24:

Inflation Stabilization and BOP Crises in Developing Countries

1 547

3.1 . 1. Stabilization time profiles As a first pass at the data and to illustrate the dynamic response of the different variables to the implementation of an exchange-rate-based stabilization program, we constructed profiles in "stabilization" time (as opposed to "calendar" time) 1 7 Stabilization time is denoted by T + j, where T is the year in which the stabilization program was implemented and j is the number of years preceding or following the year of stabilization (j = -2, . . . , 4) 1 8. We then computed the average value of each variable in stabilization time. The resulting stabilization time profiles, presented in Figures 1 and 2, thus portray the dynamic behavior of key macroeconomic variables for a "representative" exchange-rate-based stabilization plan. Vertical bars indicate the year before stabilization (time T - 1 ) and, where applicable, dashed lines denote the mean of the corresponding variable for the entire sample (i.e., for all 64 observations) . Panel A in Figure 1 illustrates the behavior of the rates of devaluation and inflation 1 9. The U-shaped profile for the rate o f devaluation (the nominal anchor) reflects the fact that, more often than not, policymakers either switch to a more flexible exchange-rate arrangement (often after a brief period with a fixed exchange rate) or abandon the program altogether. While inflation is highly responsive to the reduction in the rate of devaluation, it remains above the rate of devaluation and then lags it as the rate of devaluation increases. Panel B shows that the real exchange rate (set to 1 00 in the year before the stabilization) appreciates for three consecutive years (falling below 80 in year T + 2) before beginning to depreciate, following the higher rate of devaluation. The current account deteriorates up to year T + 3 - reaching a deficit of 4.8 percent of GDP - and then reverses course (Panel C). While the rate of growth of public consumption falls in the year of stabilization presumably reflecting an initial fiscal adjustment - it shows no systematic behavior

a real depreciation. Real interest rates were computed by deflating nominal rates by the same year's inflation rate. Population series from lntemational Finance Statistics (IMF) were used to compute per capita figures. 1 7 Fischer, Sahay and V egh ( 1 996) have used this approach to analyzing stabilization policies in transition economies. Sec also Easterly ( 1 996). 18 If the program began in the last quarter of a given year, the following year is taken as T. Thus, T is 1 978 for the Chilean tablita, 1 979 for the Argentine and the Uruguayan tablitas, 1 985 for the Austral and Israeli plans, and 1 99 1 for the Convertibility and the Uruguayan 1 990 plans. We should also note that we did not allow for any overlapping (i.e., any given year in calendar time corresponds to at most one point in stabilization time). Hence, in the case of Argentina, the first observation in stabilization time for the Austral plan is 1 984 (which corresponds to T I ) and the last one is 1 988 (T + 3). Finally, note that the number of observations for each year in stabilization time may differ, since some stabilizations episodes do not have observations for all years in stabilization time (i.e., from T - 2 through T + 4). For instance, there are 7 observations for T - 1 , T, and T + 1 , but only 4 for T + 4 and 3 for T - 2. 1 9 Since the mean is essentially the same ( 1 79.3 percent for the devaluation rate and 1 77.9 percent fm the inflation rate), the panel contains only one horizontal line. -

G.A. Calvo and CA. Vegh

1 548 A.

1000

\ \

500

� \ \ \

____ _ _

en

( e

er e

(index number, T-1 =100)

120

1 10

' ,,

____

inflation

_::, -----\ \

100 -

\

T-2

B. Real exchange rate

Inflation and devaluation

ar;_ ) p_ p_...:y rc __ __t;_ ----2000 -- --', ,r1500

T-1

T

\ \ \

----����J���t� _n_ _ _ _ ;-- -I o

//

/1

/

\...... ...... devaluation

T+1

T+2

90 80

T+3

T+4

70

T-2

GOP)

C. Current account ( percent of

T-1

T

T+1

T+2

T+4

T+3

D. Public consumption growth

..,.---...:.____:_...:.__;. . ..________��( percent per year)

-1 4

mean

-

-3

mean ---- --- --- - - - ------ ---- - - - --------

-2 -4

-4

-5 +---+-----.--.,----.-----r-----=:-l T-2

T-1

T

E.

T+1

T+2

T+3

Real lending rate

T+4

,

ent _ e_ (_ ea r)_______ rc_ � y;_ per� _;... ----...:.p 60 ,_--, 50

-6 +---1----,---,--____;:....__, T-2

T-1

T

T+1

T+2

T+4

T+3

F. Real deposit rate

10

r---�-----�(p�e��=•n;_t�pe=r�ye=a��-

5

40

mean

30 20

------ - - - - -- --- - - ----- - -- - --- - ----- - -

-5

mean

-10

10 0 +----+-��--�--�----.----4 T-2

T-1

T

T+1

T+2

T+3

T+4

-1 5 +----l---..----...--�---,---! T+4 T+3 T+2 T-2 T-1 T+1 T

Fig. 1 . Exchange-rate-based stabilization.

afterwards. Panels E and F show the behavior of domestic real interest rates 20 Real interest rates fall in the year the plan is implemented (with the real lending rate falling _

20

Some observations are missing for these two variables. The available sample consisted of 59 observations for the real lending rate and 57 observations for the real deposit rate. Note also the different scales used in Panels E and E

Ch. 24:

Inflation Stabilization and BOP Crises in Developing Countries A.

B.

Real GDP growth (percent per year)

12

1 549

Private consumption growth

�---,----�(p=e=�=en�t�pe=r�y=ea=r)�

·------�

4 ------

--

------- ----------

mean

-------------

4

mean

-2 -4

-4

-6 -1--+---,----.--..---.--J T-2 T-1 T T+3 T+4 T+2 T+1

-8:�:-:---+----.�--.----.---.----1 T+4 T-2 T-1 T T+1 T+2 T+3

C. Durables consumption growth

D. Fixed investment growth

e_ roo per�y_ ) -ar� m� __ �e_ (p 60�---�---� -

10 5

40 20

mean

en� ?_ e_ e y_ ea_ rc_ (p _ r) .. ... . --.-----" . r_

------

0

-

7

·--------------

_

----

�.., - -

20

-10

40 +. ----�---� ----4---��---r1---r T+4 T+3 T+ T+2 T T- 1 r2

-15-1---+---.--�--..---,--1 T+4 T+3 T+1 T+2 T-2 T-1 T

E.

Private consumption to GDP

---.:: (i n percent ) ________ -,----- _::�===�

75 74

F. Fixed investment to GDP

18.0

73

(in percent)

18.5

72

1 7. 5

71

1 7.0

mean

70 69. 68

mean

+----�----�---��+4 j�--��----r---�r T T 1 T+2 T-2 T+3 T-1 T

16.5 16.0 +---1---r-�--,..--· --r---1 T+4 T-2 T T-1 T+2 T+3 T+1

Fig. 2. GDP, consumption, and investment in exchange-rate-based stabilization.

for two consecutive years) and increase sharply afterwards. As indicated earlier, the accepted wisdom is that real interest rates have increased on impact in heterodox plans. This does not show up in annual data, suggesting that the initial rise in real interest

1 550

G.A. Calvo and C.A. Vegh

rates in heterodox plans has manifested itself basically as "spikes" immediately after the implementation of the plans 21 . Figure 2 presents the evidence related to the boom-recession cycle in the growth of per capita GDP, consumption, and fixed investment. Panel A shows that real GDP growth increases above the sample mean in the year of stabilization and peaks in T + 1 . In T + 2, growth is back to its mean and decreases sharply thereafter. The same pattern is observed for private consumption (Panel B) and durables consumption (Panel C). In orders of magnitude, however, the cycle in durables goods is much more pronounced than the one in private consumption, which is in turn more pronounced than the one in real GDP. At the peak, durable goods consumption is rising at 47.7 percent per year, private consumption at 8.9 percent, and real GDP at 4.7 percent. Fixed investment growth follows a similar pattern (Panel D). Finally, Panels E and F show the behavior of private consumption and fixed investment as a proportion of GDP. It can be seen that the boom in private consumption is also quantitatively important even relative to GDP. At its peak (in T + 1), the ratio of private consumption to GDP reaches 74.3 percent (compared to a mean of 68.8 percent). In contrast, Panel F shows that the ratio of fixed investment to GDP falls in T and surpasses its mean level only in T + 3 before falling precipitously. The stabilization time profiles thus point to the presence of a boom-recession cycle associated with exchange-rate-based stabilization. Although it is empirically difficult to distinguish a late recession in both successful and unsuccessful programs from the output collapse that typically accompanies the end of failed programs, Figures 1 and 2 are consistent with the idea that the late recession may take hold before the programs collapse. Notice that real activity (i.e., GDP and consumption in Figure 2, Panels A and B) slows down already at T + 2 and falls below the sample mean at T + 3 , which could reflect the effects of rising real interest rates (Figure 1 , panels E and F) and cumulative real exchange appreciation (Figure 1 , Panel B). The fact that this contraction is taking place while the current account deficit continues to grow (Figure 1 , Panel C) suggests that the contraction is not related to the real effects of an eventual collapse.

3. 1.2. Panel regressions By and large, the profiles in stabilization time presented in Figures 1 and 2 are consistent with the stylized facts that have been emphasized in the recent literature. However, while the raw data presented in this manner is clearly suggestive, these plots cannot answer the key questions of whether the boom-recession cycle in GDP, consumption, and investment has been significant in a statistical sense or whether it may have been caused by factors other than the exchange-rate-based stabilization 21

This idea is supported by the quarterly data presented in Vegh ( 1 992) and the evidence in Karninsky and Leiderman ( 1 998). These "spikes" are partly related to the sudden drop in inflation when wages and price controls are part of the stabilization package.

Ch. 24: Infla tion Stabilization and BOP Crises in Developing Countries

1 55 1

programs themselves. While a definite answer to these questions i s far from trivial and remains a challenge for future research - some simple econometric exercises may shed light on these important issues. Specifically - and following Reinhart and Vegh ( 1 994, 1 995b) - we ran panel regressions on dummy variables intended to capture the early and late stages of a program, and test whether growth in per capita GDP, consumption, and fixed investment during those periods was significantly different [rom trend growth 22 . We also test for the significance of the time pattern of public consumption 23 . The regressions control for common external shocks, as suggested by Echenique and Forteza ( 1 997) 24. The sample for the panel regressions remains the same as that used for the stabilization time profiles: four countries (Argentina, Chile, Israel, and Uruguay) with 1 6 observations each ( 1 978- 1 993) for a total of 64 observations. We define the "early" dummy as taking a value of one in the first three years of the programs 25 . If the program lasted less than three years (as was the case for the Argentine "tablita" and the Austral plan), then the "early" dummy takes a value of one in the first two years of the program. In all cases, the "late" dummy takes a value of one in the two years immediately following the "early" stage 26. Notice that the "late" dummy has been defined for all programs, regardless of whether they actually failed or not. While this makes the criterion more stringent (compared to defining the "late" dummy only for those programs that fail), it is more in accordance with the idea that the late recession takes place in both successful and unsuccessful programs. As control variables, we chose the Libor rate (adjusted by US inflation), average growth in OECD countries - both of which are intended to capture the world business cycle and terms of trade 27.

22

See also De Gregorio, Guidotti and Vegh ( 1 998), Gould ( 1 996), and Echenique and Forteza ( 1 997). 23 As will become clear in Section 5, this evidence is relevant for some theories that have emphasized the effects of fiscal policy in explaining the real effects of exchange rate-based stabilization. 24 Of course, one would like to control also for the effects of domestic reforms, which have accompanied several (although certainly not all) of these programs. To that effect, one could construct a "liberalization index" - which would take into account trade, financial, and structural reforms - along the lines of work by De Mclo, Denizer and Gelb ( 1 995) for transition economies. This remains an issue for future research. 25 The year in which the program was implemented is included as part of the "early" dummy if the program started in the first three quarters. Otherwise, the following year is taken as the first year of the "early" dummy. 26 Specifically, the years in which the "early" and "late" dummies take a value of one are the following: Argentine tablita, early = 1 for 1 979 and 1980, late = 1 for 1 98 1 and 1 982; Austral plan, early = 1 for 1985 and 1986, late = 1 for 1 987 and 1 988; Convertibility plan, early = I for 1 99 1 , 1 992, and 1 993; Chilean tablita, early = 1 for 1 978, 1 979, and 1 980, late = 1 for 1 98 1 and 1 982; Israel l 985, early = 1 for 1985, 1 986, and 1 987, late = 1 for 1 988 and 1 989; Uruguayan tab!ita, early = 1 for 1 979, 1980 and 1 98 1 , late = ! for 1 982 and 1 983; Uruguay 1 990, early = ] for 1 99 1 , 1 992, and 1 993. All data were obtained from the International Monetary Fund. Both Libor and OECD growth arc expressed in percentage terms. The terms of trade index measures the relative price of exports in terms of imports.

27

1 552

G.A. Calvo and C.A. Vegh

Table 2 Exchange-rate-based stabilization: Panel regressions " -

Dependent variables Growth in real GDP

(I)

Growth in real private consumption (2)

Growth in real durables consumption (3)

Growth in real fixed investment (4)

Growth in real public consumption (5)

1 4.74* (7.89)

0.80 (3.76)

-3 .78 (2.58)

-4.46 (4.62)

-5.42* (3. 19)

Early dummy

1 .84** (0.73)

3.33 * ( 1 .57)

Late dummy

-3.49*'* (0.82)

-4.60** (1 .93)

-29.61 *** ( 10.0 1 )

Libor (real)

-0.3 1 ** (0 . 14)

-0.68'* (0. 3 1 )

·-3.3 1 ( 1 .59)

-2. 8 1 *" (0.77)

-·1 . 1 8*'' (0.52)

OECD growth

0.71 *** (0.20)

-0. 2 1 (0.47)

1 .97 (2.44)

0.78 ( 1 . 1 5)

0.76 (0.78)

Terms of trade

-0.03 (0.02)

0.02 (0.03)

-0. 1 8 (0.20)

-0. 1 0 (0. 1 0)

0.04 (0.06)

64

64

64

64

64

No. of obs.

*

,;·

a All dependent variables are expressed in per capita terms. The sample includes Argentina, Chile, Israel, and Mexico for the period 1 978-1993. Standard errors are given in parentheses. The method of estimation was a 2-step GLS procedure which allows for groupwise and cross-group heteroscedasticity and groupwise autocorrelation. The regressions include fixed effects (not reported). Significance at the 1 0, 5, and 1 percent level is indicated by one, two, and three asterisks, respectively.

The summary results of the panel regressions are reported in Table 2. Let us first focus on the first three columns (GDP, private consumption, and durables consumption). The "early" and "late" dummies have the expected signs (positive for "early" and negative for "late") and are significant (at least at the 1 0 percent level) in all three cases. For example, column (2) indicates that growth in private consumption per capita is 3.33 percent higher (relative to trend growth) during the early stages of the program and 4.60 lower in the late stages. The size of the coefficients also tends to support the idea _:: suggested by Figure 2 that the boom-recession cycle is the most pronounced for durable goods and the least pronounced for GDP, with consumption falling somewhere in between. The initial rise in durable goods consumption is more than four times larger than the rise in private consumption, which is in turn almost twice as high as the rise in GDP per capita. Increases in Libor (in real terms) negatively affects all three variables (and are always si6rnificant). This result is consistent with the notion that fluctuations in international interest rates also play a key role in generating boom-bust cycles in developing countries [see, for example, Calvo, Leiderman and Reinhart ( 1 993)]. OECD growth matters only for GDP growth, while the effects of terms of trade are never significant. -

Ch. 24:

Inflation Stabilization and BOP Crises in Developing Countries

1553

In sharp contrast, the cycle in fixed investment is not statistically significant [Table 2, column (4)]. Changes in real world interest rates (i.e., real Libor) fully explain the cycles in fixed investment. In any event, this should perhaps not come as a big surprise since casual evidence for a majority of programs suggests that the main force behind the expansionary phase is the sharp increase in private consumption. It is also consistent with evidence from Bruno and Easterly ( 1 998) and Easterly ( 1 996), who find that growth following inflation crises is not driven by investment. Finally, column (5) in Table 2 indicates that the initial fall in public consumption is not statistically significant. We may thus conclude that the econometric evidence is consistent with the notion that exchange-rate-based stabilization leads to boom-recession cycles in real GDP, private consumption, and consumption of durable goods, even when account is taken of external factors. The evidence is inconclusive with regard to investment.

3. 1.3. Do exchange-rate-based stabilizations sow the seeds of their own destruction? A notable aspect of exchange-rate-based stabilization programs is that, as noted in Table 1 , a vast majority have ended in balance-of-payments crises. In fact, of all the major programs listed in Table 1 , the Argentine 1 99 1 Convertibility plan is so far the only successful plan which has maintained the exchange rate at the level chosen at the inception of the program 2 8 . Eight of the twelve plans ended in full-blown crises with large losses of international reserves. Naturally, the stabilization time profiles in Figures 1 and 2 appear to capture this pattern. In T + 4, the current account sharply reverses course (Figure 1 , Panel C), suggesting that a "crisis" has occurred 29 This "crisis" time coincides with a resumption of high inflation, a real exchange rate depreciation, and a collapse in GDP, consumption, and investment. As argued by Reinhart and Vegh ( 1 995b), the dynamics unleashed by exchange-rate based stabilization plans are likely to be partly responsible for the demise of several programs. Prolonged periods of real exchange-rate appreciation and growing current account deficits are seldom sustainable, especially when domestic and external shocks compound the problems. Corrective devaluations do not always work, particularly in a world of increasing financial globalization, as the example of Mexico in December 1 994 dramatically showed. These regimes are also prone to financial and speculative attacks which may be unrelated to problems of current account sustainability. The evidence thus suggests that understanding the links between the dynamics of exchange� rate-based stabilizations and the eventual collapse of most of these programs should 2k The israeli 1 995 plan was also a successful plan in terms of obtaining a lasting reduction in inflation. However, there were several devaluations along the way and finally an exchange rate band was adopted. 29 Kaminsky and Reinhart ( 1 995) show that BOP crises are associated with a sharp rise in exports . which should lead to a dramatic improvement in both the trade and current account balances.

G.A. Calvo and C.A. Vegh

1 554

be an integral part of the research agenda (an analysis of these issues is carried out in Section 7).

3.2.

Money-based stabilization: empirical regularities

Money-based programs in chronic inflation countries have been much less common than programs based on the exchange rate 30. Table 3 presents the main features of five major money-based programs undertaken in the last 25 years 3 1 . As the table makes clear, monetary regimes vary across episodes and pure money-based programs (i.e., a clean floating regime) are rare 32 . Hence, for the purposes of this chapter, the term "money-based" stabilization should be broadly understood as including assorted dirty floating regimes and dual exchange rate systems with a fixed commercial rate (or equivalent systems). The rationale for lumping these regimes together is that in all cases the monetary authority has, to a lesser or greater extent, control over the money supply. This is, of course, in contrast to an exchange-rate-based regime (under perfect capital mobility) in which the money supply is fully endogenous. As will be discussed in detail in Section 5, one should expect regimes in which the monetary authority has control over the money supply to deliver similar outcomes to those that would obtain under a pure money-based regime. Hence, to contrast stylized facts with theory, it makes sense to adopt such a classification. The following empirical regularities have been identified in money-based programs [see Calvo and Vegh ( 1 994b)] : (i) Slow convergence of infla tion to the rate of growth of the money supply. (ii) Real appreciation of the domestic currency. (iii) No clear-cut response of the trade balance and the current account. If anything, there seems to be a short-run improvement in the external accounts. (iv) Initial contraction in economic activity. A sharp, though short-lived, contraction in real GDP, consumption, and investment seems to follow the implementation of money-based programs. (v) initial increase in domestic real interest rates. These empirical regularities are less surprising in that they seem to broadly conform with available evidence for industrial countries. To illustrate some of these empirical regularities, we constructed a panel with five countries (Argentina, Brazil, Chile, 30 As discussed below, there are good reasons to expect the exchange rate to be the prefened anchor

in chronic inflation countries. 31 For case studies, see Harberger ( 1 982), Corbo ( 1 985), Edwards and Cox Edwards (1991), Medeiros ( 1994), Kiguel and Liviatan ( 1 996), and Favaro ( 1 996). 32 Note that, by definition, a pure money-based program implies a clean floating. The reverse, however, is not necessarily true: a clean floating might be adopted in conjunction with, say, interest rate or inflation targeting [see, for instance, Masson, Savastano and Sharma ( 1 997) and Vegh ( 1 997)]. These monetary regimes, however, have not been observed in any major stabilization effort in high inflation countries.

Table 3 Major money-based inflation stabilization plans Program

Begin and end date

�

"'

a

Monetary/exchange-rate policy Initial

Chile 1 975

April 1 975-December 1 977

Bonex (Argentina)

December 1 989-February 1991

Collor (Brazil)

Control of monetary aggregates was cornerstone. Exchange rate adjusted by past inflation d

c

Inflation rate b Lowest

Date achieved

394.3

63.4

Drastic cut in liquidity through forced rescheduling of domestic debt. Floating exchange rate

4923.3

287.3

Feb. 1 99 1

March 1 990-January 1 99 1

Sharp liquidity squeeze through freeze o f 70% of financial assets. Tight monetary policy. Exchange rate had a passive role and simply accommodated inflation

5747.3

1 1 19.5

Jan. 1991

Dominican Republic 1 990

August 1 990-present

Aug. 1990-Dec. 1 990: Exchange controls/black markets. Jan. 1 991-July 1 99 1 : dual exchange rates. July 1 99 1 : exchange market unification and floating.

60.0

2.5

Nov. 1 993

Peru 1 990

August 1 990-present

Control of monetary aggregates; dirty floating.

12 377.8

1 0.2

Sept. 1 995

a

Dec. 1 977

Sources: International Financial Statistics (IMF), Edwards and Cox Edwards (1991), Medeiros ( 1 994), Kiguel and Liviatan ( 1 996), and Favaro ( 1 996). Data end in December 1 996. b Twelve-month inflation rate (in percent). Twelve-month inflation rate in the month in which the program was implemented. d Significant measures toward lifting capital controls enacted only in June 1 979 [Edwards and Cox Edwards ( 1 99 1 )] .

c

:<:-

::.

]> :::t. a ;:,

� §..

�

�· ;:, "

;:, :;:,_ i:l::J

S6

�B: ;;;·

� "'

.[ �6l :;:: ;,

S. B:

'-" '-" V>

1 556

G.A. Calvo and C.A. Vegh

A. Inflation a n d money growth a_:_ r) e..:. pe..:. -Ye_ r :_ t ::..: .:..n..:. rce
...... ..... ..... .....

1500 1000

500

------

T-2

T

C.

110

T+1

T+2

T+3

2

mean

-2 -4 -6

-8

T+4

Real exchange rate T-1�1 00)

-2

T-1

T

T+1

T+2

T+ 3

T+4

D. Current account ent of_ ( erc_ P)_______ D_; __ G_ -i.Ot ..,----,----'-p__

(index number,

105

-1 . 5

100

-2.0

95

-2.5

90

-3.0

85

mean

-3.5

80 75

(percent per year)

4

,I

I I I I I I I I I I I r mean inflation \ - - - - - - - - - - - - -\ - /�---------------\... ....mone .. y growth

T-1

B . Real G D P growth

6

T-2

T-1

T

T+1

T+2

T+3

T+4

-4.0':i-=--I----,--...,---...,.+---...,---I T-2 T+3 T 2 T-1 T+ 1 T+4 T

Fig. 3. Money-based stabilization.

Dominican Republic, and Peru) with 25 years of annual data ( 1 971 - 1 995), for a total of 1 25 observations 33 ' 34. The stabilization time profiles are illustrated i n Figure 3 . Panel A shows that the inflation rate falls dramatically in the first year after stabilization but begins to rise again soon afterwards 35. Although the inflation rate does remain above the rate of money growth, inflation persistence appears to be much less pronounced that in exchange-rate-based programs (recall Figure 1 , Panel A). Real GDP growth falls in the year of stabilization from -3.8 to 7.3 percent, but recovers soon after and is �

33 Again, data availability dictated the sample size. Since we now focus on a smaller number of variables,

the time series available are longer than before. However, the small number of programs and the rather short duration of some of them calls for ,-�ution in the interpretation of the evidence. 34 For these programs, T is 1 975 for the Chilean plan and 1 990 for the Collor, Bonex, Dominican Republic, and Peruvian plans. To avoid overlapping with other, exchange-rate-based plans - and giving priority to the actual plan which was in effect - the Bonex plan is associated with two dummies (1 989 and 1 990), the Collor plan goes back only until T - 1 , and the Chilean 1 975 plan goes forward only until T + l . 35 The fact that inflation actually rises in the year of stabilization (T) is heavily influenced by the Peruvian program.

Ch. 24:

inflation Stabilization and BOP Crises in Developing Countries

1 557

above the sample mean in T + 3 (Panel B). The evidence is thus consistent with a short-lived but sharp contraction in economic activity. It should be noted, however, that real GDP growth is already below its mean in the year before the program. The real exchange rate appreciates throughout the program (Panel C), while the current account shows no clear pattern (Panel D). Lack of data prevented us from looking at real interest rates. Quarterly data presented in Calvo and V egh ( 1 994b ), however, are consistent with the notion of an initial rise in real interest rates. 3.3.

Recession now versus recession later

A comparison of the real activity in money-based and exchange-rate-based sta­ bilizations raises an important issue. The timing of the recessionary effects of disinflation programs appears to differ across nominal anchors: in money-based plans the contraction occurs early in the program, while in exchange-rate-based programs it seems to occur late in the program (compare Figure 2, Panel A with Figure 3 , Panel B). This phenomenon has been dubbed the "recession-now-versus-recession­ later" hypothesis. To test this hypothesis, we carried out two econometric exercises for the rate of growth of real per capita GDP for as large a sample as possible. The sample includes the period 1971-1 995 for eight countries (Argentina, Brazil, Chile, Dominican Republic, Israel, Mexico, Peru, and Uruguay) for a total of 200 observations. The sample comprises 1 4 stabilization plans: 9 exchange-rate-based stabilizations (all of those described in Table 1 except for the first three) and the five money-based stabilizations listed in Table 3 . Table 4 shows the results o f fixed effects regressions on stabilization dummies, con­ trolling for external factors 3 6 . Three regressions are shown: the first two ("individual regressions") attempt to identify the effects of exchange-rate-based stabilization time dummies and money-based stabilization time dummies separately (i.e., each regression includes only the time dummies corresponding to a particular anchor). The third ("joint regression") includes all stabilization time dummies simultaneously. Let us first focus on exchange-rate-based stabilization. First, regressions ( l ) and (3) indicate that growth in the two years before exchange-rate-based stabilization is not statistically different from trend growth 37. Hence, exchange-rate-based stabilizations appear to have been implemented in "normal" times 3 8. Growth in the first two years of stabilization (T and T + 1 ) is significantly above trend growth in the individual regression. In the joint regression, growth is significantly above trend in T + 1 . In both cases, growth is significantly below trend four years after stabilization (i.e., in T + 4) External factors have the expected signs and are always significant. .

36 For the 12 plans analyzed before, T remains the same. For the two new plans in the sample (Cruzado and Mexican plan), T is 1 986 for the Cruzado plan and 1988 for the Mexican plan. We do not allow for overlapping. 37 Of course, since all regressions include fixed effects, trend growth varies across countries. 3 8 This casts doubts on the idea that the booms associated with exchange-rate-based stabilizations began prior to the implementation of the programs, as has been argued by Kydland and Zarazaga ( 1 997).

1 55 8

G.A. Calvo and C.A. Vegh Table 4 Real GDP per capita growth before and after stabilization a Individual regresssions Exchange-ratebased (1)

Moneybased (2)

Joint regression Exchange-ratebased

-

Money -based (3)

T-2

-0.46 ( 1 .09)

-6.86*** ( 1 .56)

-0.71 ( 1 . 1 8)

-6.96*** (1 .66)

T-1

0.94 (1 .08)

-4. 1 8*** ( 1 .59)

0.47 (1. 13)

-4.45"'"' ( ! .59)

T

2.00* (1 .03)

- 1 0.83*** (1 .60)

1 .42 (1. 1 1)

T+ l

2.91 *** ( 1 .03)

-3.84** ( 1 .55)

2.34** {1 . 1 1)

-3.87" ( 1 .58)

T+2

-0.21 (1 .04)

-3.20* ( 1 .7 1 )

-0.61 (1 . 1 1)

-2.84 ( 1 . 76)

T+3

0.49 ( 1 . 10)

-0.83 ( 1 .7 1 )

-0.26 ( 1 .20)

- 1 . 12 ( 1 .77)

T+4

- 1 .99* (1.1 1)

0.39 ( 1 .64)

-2.33** ( 1 . 1 7)

0.49 ( 1 .7 1 )

Libor (real)

-0.62*** (0. 1 3)

-0.58*** (0. 1 3)

-0.60*** (0. 13)

OECD growth

0.55*** (0. 1 6)

0.57*** (0. 1 7)

0.55**' (0. 17)

Terms of trade

0.012* (0.0069)

0.01 3 * (0.0067)

0.013* (0.0067)

200

200

No. of observations

- 1 o.n····

( 1 . 59)

200 ·-----�- --- ----------

a Dependent variable is real GDP per capita growth. The sample comprises Argentina, Brazil, Chile,

Dominican Republic, Israel, Mexico, Peru, and Uruguay for the period 1971--1 995. Standard errors are given in parentheses. The method of estimation was a 2-step GLS procedure, which allows for groupwise and cross-group heteroscedasticity and groupwisc autocorrelation. All regressions include fixed country effects (not reported). Significance at the I 0, 5, and 1 percent level is indicated by one, two, and three asterisks, respectively.

In money-based stabilizations, growth in the two years before stabilization is significantly below trend growth [regressions (2) and (3)] . Money-based stabilizations thus appear to have been implemented in "bad" times. Growth is sharply below trend in the year of stabilization and continues to be significantly below trend in the first year (in both the individual and joint regressions) and second year after stabilization (in the individual regression). External factors have the expected signs and are always significant. These results are thus consistent with the idea of an early recession in money-based stabilization, and an early boom followed by a contraction in exchange-rate-based

Ch. 24:

Inflation Stabilization and BOP Crises in Developing Countries

1 559

stabilization. A caveat to be noticed is the fact that growth was significantly below trend before the stabilization in money-based programs. This raises the possibility that the initial recession might simply be the continuation of that trend 39. While the regressions reported in Table 4 are certainly revealing, they may be asking too much of the data. The reason is that we are really interested in the behavior of growth in the "early" and "late" stages of stabilization programs, rather than in specific years (i.e., we are interested in "joint significance"). Hence, as before, we ran panel regressions with early and late dummies, and control variables 40 . Table 5 shows the same regression estimated by three different methods: OLS, fixed effects, and a 2-step GLS with fixed effects. The results do not vary much across different method of estimations. In all cases, the early and late dummies for exchange-rate-based stabilization are significant and so is the early dummy for money-based stabilization. In other words, growth in the early stages of an exchange-rate-based stabilization is significantly higher than trend growth and significantly below trend growth in the late stages. In money-based stabilizations, growth is significantly below trend growth in the early stages and not significantly different from trend growth in the late stages. Of the control variables, real Libor and OECD growth are always significant. These results are thus consistent with the recession-now-versus-recession-later hypothesis. 3.4. A

word of caution

A final word of caution is in order. Research on the empirical regularities of stabilization in chronic inflation countries is still very much work in progress. In fact, we would argue that too little empirical work - relative to theoretical work - has been done in the area. Needless to say, this type of analysis faces formidable obstacles, including small samples (in particular of money-based programs), the definition of inflation stabilization episodes, the classification of episodes by type of nominal anchor, the quality of the data, and the need to control for other shocks (both domestic and external). Much work remains to be done and the results presented here should be taken as suggestive and pointing out directions to follow, rather than as conclusive evidence. At a methodological level, we think it is important to distinguish between two alternative approaches. One approach - the one adopted in this section - might be 39 In addition, Gould ( 1996) has argued that the state of the economy before stabilization influences the choice of the nominal anchor, with "bad" times inducing policymakers to choose money as the main anchor. 4° For the seven plans which were already part of the previous sample, the dummies are the same but, since the sample is now longer, the late dummy takes a value of 1 during 1 994 and 1 995 for both the Convertibility plan and the Uruguayan 1 990 plan. For the seven new plans, the years in which "early" and "late" take a value of 1 are the following: Bonex plan: early = 1 for 1 990 (no late dummy); Cruzado plan: early = I for 1 986, late = 1 for 1 987 and 1 988; Chile 1 975, early = 1 for 1 975 and 1 976, late = 1 for 1977; Dominican Republic, early = I for 1 990, 1 9 9 1 and 1 992, late = 1 for 1 993 and 1 994; Mexico, early = 1 for 1 988, 1 989, and 1 990, late = 1 for 1 99 1 and 1 992; Peru, early = 1 for 1 990, 1991, and 1 992, late = I for 1 993 and 1 994.

G.A. Calvo and CA. Vegh

1 560 Table 5 Real GDP per capita growth: Panel estimates" OLS (1)

Fixed effects (2)

2-step GLS (3)

Exchange-rate-based stabilization: Early dummy

2.3 1 ** (0.96)

2.40** ( 1 .03)

1 .73*' (0.75)

Exchange-rate-based stabilization: Late dummy

-2.33** ( 1 . 1 0)

-2. 1 8' (1 . 1 6)

- 1 .64*' (0.80)

Money-based: Early dummy

-4.90*** ( 1 .40)

-5.46''* ( 1 .44)

-6.29*** ( 1 . 30)

Money-based: Late dummy

1 .59 ( 1 .66)

0.72 ( 1 .69)

- 1 .89 ( 1 .22)

Libor (real)

-0.50*'* (0. 1 3 )

-0.61*** (0. 14)

-0.62*'' (0. 1 3)

OECD growth

0.55*** (0. 1 9)

0.45'* (0. 1 9)

0.62*** (0. 1 6)

Terms of trade

0.01* (0.006)

-0.005 (0.01 5)

0.01 (0.007)

Adjusted R2

0. 1 8

0.25

No. of observations

200

200

200

a Dependent variable is expressed in per capita terms. The sample includes Argentina, Brazil, Chile, Dominican Republic, Israel, Mexico, Peru, and Uruguay for the period 1 97 1- 1 995. Standard errors are given in parentheses. The 2-step GLS procedure allows for groupwise and cross-group heteroscedasticity and groupwise autocorrelation. The regressions include fixed effects (not reported). Significance at the I 0, 5, and 1 percent level is indicated by one, two, and three asterisks, respectively.

dubbed the "episodic" approach. This approach involves selecting the best-known stabilization episodes, which have received a great deal of attention. At the other extreme, we have a "mechanical" approach, where stabilization episodes are defined based on the behavior of inflation. For example, Easterly ( 1 996) defines a stabilization as an episode characterized by a switch from a period of two years or more with an annual rate of inflation above 40 percent to a period of two years or more with an annual rate of inflation below 40 percent Both approache s have problems. The "episodic" approach is subjective and will tend to omit lesser-known episodes 4 1 . The "mechanical" approach defines a stabilization by its outcome, which is clearly problematic. Conceptually, an inflation stabilization program involves a drastic reduction in the rate of growth of a policy instrument (the exchange rate or the money supply) and not necessarily the attainment of a 41 It should be noted, though, that omitting smaller programs is not necessarily a bad thing. To isolate better the effects of a given phenomenon, it makes sense to select episodes in which the phenomenon in question - relative to many other factors which are difficult to control for - was of overriding importance.

Ch. 24:

Inflation Stabilization and BOP Crises in Developing Countries

1561

policy objective ( a fall i n the inflation rate). I n fact, both theory and evidence provide numerous examples of stabilizations which involve a rather slow reduction (or even an initial increase) in inflation. Whatever the merits of both approaches, in the second· best world of empirical analyses, there is surely something to be learned from both of them. Within the episodic approach, Echenique and Forteza ( 1 997) argue that the results in Reinhart and Vegh ( 1 994, 1 995b) - in particular, the initial boom under ported re exchange-rate-based stabilization - are not robust to the inclusion of external factors (they do not look at either private consumption or durable goods consumption). The revised estimates reported above do not support such a claim, except for investment. In any event, controlling for other factors - both domestic and external - is clearly an important endeavor as it would imply that, quantitatively speaking, models of exchange-rate-based stabilization should be able to account only for a fraction of the actual booms observed. Gould ( 1 996) argues that, after adjusting for initial conditions which make the choice of the nominal anchor endogenous, growth actually improves in either case. Using the "mechanical approach" described above, Easterly ( 1 996) argues that stabilization from high inflation has been expansionary (in terms of GDP and consumption) regardless of the nominal anchor. In other words, he does not find evidence of money-based stabilization being contractionary. The difference may reflect the very different sample - out of 28 episodes, Easterly ( 1 996) classifies all but 9 as money-based stabilization - and the fact that he considers only successful programs. In accordance with our findings, however, Easterly ( 1 996) also argues that higher investment is absent in the early stages of stabilization. The notion that inflation stabilization may be associated with higher growth also receives support from the transition economies. Using a 25-country sample, Fischer, Sahay and Vegh ( 1 996) conclude that inflation stabilization has been expansionary for the transition economies - regardless of the nominal anchor - but that resorting to a fixed exchange rate has had an additional positive effect on growth. A more general critique is that of Kydland and Zarazaga ( 1 997) who argue . based on a review of the literature on disinflation in chronic-inflation countries and an analysis of business cycles in Argentina - that nominal exchange rate shocks do not seem to have had any noticeable real effects, even during exchange-rate-based stabilizations. More specifically, they argue that business cycles in Argentina could be explained by real shocks. It is worth stressing, however, that the stabilization literature has certainly not claimed that stabilizations are the main source of business fluctuations in high-inflation countries; it has only claimed that stabilization programs have real effects. The latter is, of course, perfectly consistent with the idea that real shocks may be the main source of business cycle fluctuations over long periods of time 42 .

42

A case in point is U ruguay. Hoftinaister and V6g h ( 1 996) find that over the period 19'/5 - 1 990 nominal shocks explain only a small fraction of output movements. For the tablita period ( 1 979-1 983). however, a historical decomposition suggests that nominal shocks played a central role.

1 562

G.A. Calvo and C.A. Vegh

Furthermore, for any given country, major stabilizations are relatively rare events. This small-sample problem has led researchers in this area to work with panels (i.e., cross­ country analysis). It is thus doubtful whether time-series, business-cycle analysis for a particular country might be able to pick up the real effects of stabilization. Even if such effects were there, the "recurrent" sources of business cycle fluctuations - whatever they may be, and this literature certainly takes no position on this - would probably dominate. 4. Exchange-rate-based stabilization I: inflation inertia and lack of credibility

Given the main characteristics of chronic inflation processes - decades of high inflation and a rich history of failed stabilization attempts - it is perhaps not surprising that the two main explanations advanced for the stylized facts discussed in Section 3 rely on inflation inertia and lack of credibility.

4. 1. Inflation inertia Rodriguez ( 1 982) was the first to point out that, under conditions of high capital mobility, a credible decline in the rate of devaluation may provoke an initial expansion. The main motivation behind his model was the fall in real interest rates observed in the initial stages of the Argentine tablita [see also Fernandez ( 1 985)] . In the model, a reduction in the devaluation rate leads, through the interest parity condition, to lower domestic nominal interest rates. If inflationary expectations are sticky (i.e., adaptive expectations a la Cagan), then the real interest rate will fall, stimulating aggregate demand in the short run. The initial expansion, however, will eventually be followed by a contraction, as inflation inertia leads to a sustained real exchange rate appreciation. Rodriguez's ( 1 982) major contribution was thus to show that, even though Phillips-curve type implications will eventually hold, short-run dynamics may push the economy in the opposite direction. Notice, incidentally, that the argument relies on some form of expectational inertia 43 . The above explanation has prima facie high predictive power, as it reproduces quite well the stylized facts documented in the previous section, including the boom­ recession cycle imd the U-shaped path of the real exchange rate. It also provides us with a simple model suggesting the possible traps that one might encounter in a stabilization effort. For example, if the process is not well understood, policymakers may reach the conclusion that stabilization has generated a higher sustainable level of output and economic activity. Since expansion is normally accompanied by higher 43 Dornbusch (1 982), in contrast, assumes that agents display rational expectations (i.e, arc fmward­ looking), but that the inflation rate is predetermined and thus exhibits a large degree of inertia. While Dornbusch (1 982) does not focus on the initial output effects of disinflation, he emphasizes the eventual recession brought about by the cmnulative real appreciation of the domestic currency.

Ch. 24:

Inflation Stabilization and BOP Crises in Developing Countries

1 563

fiscal revenue, policymakers may be induced to slacken their control on government expenditure, enhancing the economy's overheating and further widening the fiscal deficit when recession sets in. Further, as emphasized at the time by Dornbusch ( 1 982) - and more recently by Dornbusch and Werner ( 1 994) - sticky-inflation-based models call attention to the problem of "overvaluation" and the public's expectations that a corrective devaluation would have to take place at some point to restore "equilibrium" relative prices. Rodriguez's ( 1 982) model postulates reduced-form aggregate demand functions which depend on the real interest rate and the real exchange rate. In particular, the model assumes that a higher real interest rate unambiguously lowers aggregate demand. These appear to be highly plausible assumptions. However, Calvo and Vegh (1 994a) show that such assumptions are rather strong and are not necessarily supported by models consistent with optimizing behavior. This can be illustrated by a simple example. Consider a small open economy perfectly integrated with the rest of the world in goods and capital markets. The representative household's instantaneous utility depends (separably) on consumption of tradables, cT, non-tradables (or home goods), eN , and real monetary balances in terms of tradables, m 44 . Thus, lifetime utility as of time 0 can be written as:

.fooc [u(cJ) + u(c� ) +

z(mt)] exp(-[3t) dt,

(4. 1 )

where [3(> 0) is the rate of time preference, and u(-), u(-) and z ( - ) are strictly increasing and strictly concave functions. The individual has a constant endowment flow of tradable goods, y T, while output of nontradables, y� , is demand-determined (i.e., in equilibrium, y� = c� for all t). The law of one price holds for the tradable good. The (constant) world real interest rate is denoted by r. (It will be assumed that there is no foreign inflation, so that r is also the world nominal interest rate.) Therefore, the individual's lifetime constraint is given by:

bo + mo +

roo (yT + er +

Jo

�N

Tt

)

exp( -rt) dt =

r= (c; + .��

Jo

et

)

+ itmt exp( rt) dt,

(4.2) where b0 denotes the individual's initial stock of net foreign assets, e1 denotes the real exchange rate (i.e., the relative price of tradable goods in terms of non-tradable goods), it is the nominal interest rate, and it are government lump-sum transfers. Given perfect capital mobility, the interest parity condition i1 = r + ft holds, where £1 is the rate of devaluation. 44 As will become clear below, the other assumptions in the present example make our key t esults

invariant with respect to the price deflator in the definition of real money balances.

1 564

G.A. Calvo and C.A. Vegh

To abstract from fiscal issues, we assume that the government returns back to the consumer all of its revenues. Hence, the government's lifetime budget constraint indicates that the present value of transfers must equal the initial stock of government­ held foreign assets (i.e., international reserves), denoted by R 0 , and revenues from money creation:

1= T1

exp(-rt) d t

=

Ro +

1= (m1

+ E1 m1 ) exp(--rt) dt.

(4. 3)

Combining (4.2) and (4.3), taking into account non-tradable goods market equilibrium, the interest parity condition, and the transversality condition lirn1 0 m1 exp(-rt) = 0, yields the economy's resource constraint _,

T

ko + J!__r

=

•

oc

/ c/ exp(-rt) dt,

fo k(= b + R)

(4.4)

where is the economy's net stock of foreign assets. Equation (4.4) thus constrains this small economy's lifetime consumption of tradable goods to be equal to tradable goods wealth. Maximization of lifetime utility (4 . 1 ) with respect to the budget constraint (4.2) yields the following first-order conditions 45 :

v'(c"{) = A, A N uI (c1 ) = - , et z' (m1 ) = Ait ,

(4.5 ) (4.6) (4.7)

where A is the time-invariant Lagrange multiplier. Equations (4.5) and (4.6) are the familiar conditions whereby, at an optimum, the household equates the marginal utility of consumption to the shadow value of wealth, A, times the relative price of the good (t:nity in the case of tradables and lie in the case of non-tradables). Similarly, at an optimum, the marginal utility of real money balances is set equal to the shadow value of wealth times the opportunity cost of holding real money balances, i [Equation (4.7)]. Equation (4.5) indicates that optimal consumption of tradable goods is constant along a perfect foresight path. From Equation (4.4), it then follows that cT = rk0 +y1, a constant, for all t ;? 0. Further, notice that unanticipated changes in the devaluation rate will not affect consumption of tradable goods. Consequently, from Equation (4.5),

the Lagrange multiplier, A, is invariant with respect to (unanticipated) changes in the rate ofdevaluation 46. This feature will greatly simplifY the ensuing analysis. Backward-looking indexation is introduced along the lines of Calvo and Vegh ( 1 994a). The horne goods sector operates under sticky prices (i.e., the nominal price 4 ·' As usual, we assume that {3 = r to eliminate inessential dynamics. 46 Of course, the multiplier is always invariant to anticipated changes.

Ch 24:

Inflation Stabilization and BOP Crises in Developing Countries

1 565

of home goods, pN , is a predetermined variable). Let the rate of inflation (of non­ tradables) be indicated by :rr . We assume that Jft = Wt +

8(ctN -y-N) '

e > o,

(4.8)

where jiN stands for full-employment output of non-tradables, and w is a predetermined variable which satisfies y > 0.

(4.9)

The variable w can be interpreted as the rate of growth of nominal wages. Hence, Equation (4.8) says that inflation of home goods is equal to the rate of growth of nominal wages plus excess aggregate demand 47 . In tum, equation (4.9) indicates that wage inflation increases (decreases) as price inflation (in terms of nontradables) exceeds (falls short of) wage inflation. This assumption is meant to capture backward­ looking wage indexation mechanisms, whereby the rate of growth of nominal wages is adjusted whenever the inflation rate exceeds the current level of wage growth. To illustrate the implications of this set-up, integrate backwards Equation (4. 9) and substitute the resulting expression for w1 into Equation (4.8) to obtain (4. 1 0) Equation (4. 1 0) shows that current inflation depends on a weighted average of past inflation rates - with inflation rates in the recent past receiving the greatest weight and current excess aggregate demand, which is what the notion of "inflation inertia" is usually taken to mean [see, for instance, Dornbusch and Simonsen ( 1 987)]. We will now study the implications of a once-and-for-all reduction in the rate of devaluation, which is the central exercise in Rodriguez ( 1 982). Given the invariance of the Lagrange multiplier with respect to changes in E1, it follows from first-order condition (4.6) that we can safely write c� as an increasing function of the real exchange rate, e1 ; that is, c� = ¢(e1), with ¢'(e1) > 0. Hence, by Equations (4.8) and (4.9), we have (4. 1 1 )

Furthermore, by definition, e1 = E1P 1*IP� , where E1 i s the nominal exchange rate (in units of domestic currency per unit of foreign currency, pT* is the (constant) foreign 47 Note that, in this specification, JI is not consumption of home goods does so).

a

predetermined variable (i.e., it could jump on 1mpact

1t

1 566

G.A. Calvo and C.A. Vegh (J)

··

ffi = O I I 7•A !

r L

'-------------::c-------··----·--------+ ess e

Fig. 4. Inflation inertia: dynamic system.

currency price of the tradable good and Pr is the price of home goods 48 . Using this definition and Equation (4.8), it follows that (4. 1 2) Equations (4. 1 1) and (4 . 1 2) constitute a system of differential equations in w1 and Since both w1 and e1 are predetermined variables, this ensures that under perfect foresight - and for a given set of parameters all equilibrium paths conyerge to the steady-state. Suppose that initially (i.e., for t < 0), the devaluation rate is expected to remain constant at the value eH . Hence, in the initial steady state (point A in Figure 4), :rr:,5 t:11 and ¢>(ess) _yN . At time 0, policymakers announce an unanticipated and permanent reduction in the devaluation rate from eH to eL. The new steady state is denoted by point B, where inflation of home goods is eL , while the real exchange rate remains unchanged. The dynamics of the adjustment to the new steady state are illustrated by the arrowed path in Figure 4. The time path of the main variables is illustrated in Figure 5 . Nominal wage growth falls monotonically over time (Panel B). The real exchange rate declines (appreciates)

e1 , which can be shown to be locally stable 49.

=

=

48 Note that the real exchange rate is a predetermined vanable because E is a policy variable and pN

is a

predetermined variable. 49 The trace of the matrix associated with the linear approximation around the steady stale is -e,,8rj/(e,J < 0 (where a subscript "ss" denotes steady-state values) and the determinant is ye,,8 ¢'(e,,) > 0, which implies that both roots have negative real parts. For expositional simplicity. roots wi 11 be assnmed to be real.

Ch. 24: Inflation Stabilization and BOP Crises in Developing Countries

mt

A. Rate of devaluation

1 567

B . Nominal wage growth

H E --L E 1

time

0

time

0

C. Real exchange rate

D. Consumption of home goods

\ --

0

-

time

t1

i

�

E. I nflation rate

1t

--

l

-

r

-

___

0

-

-

�

time

t1

-

F. Domestic real i nterest rate

d

H E L E

i

r

-

-

-

-

0

t1

time

�

-0

t1

-

-

-

-•

time

Fig. 5. Disinflation under inflation inertia.

in the early stages of the program, and then returns to its initial steady-state value (Panel C). Given that consumption of tradables remains constant, consumption of nontradables (Panel D) falls in the early stages (as its relative price, 1/e, increases) and increases later on. Hence, during the initial stages of the stabilization program, consumption of home goods (and thus output of home goods) falls - i.e., it does not rise in line with the stylized facts. At some point in time (denoted by t1 in Figure 5), inflation of home goods must fall below its long-run equilibrium value (Panel E) in order for the real exchange rate to return to its unchanged steady-state value. It is this protracted period of deflation needed to restore equilibrium relative prices which underlies the call for a step devaluation at some point during the adjustment

1 568

G.A. Calvo and CA. Vegh

program [see, for instance, Dornbusch and Werner ( 1 994)]. Indeed, in this model, a devaluation at time t 1 in Figure 5 (which corresponds to point C in Figure 4) would immediately take the economy to its new steady state, provided that workers also agreed to reduce the rate of nominal wage growth, w, to EL . It should be noticed that consumption of non-tradables falls in the early stages of the program in spite of the fact that the domestic real interest rate, rd(::= i JT), decreases on impact (Figure 5, Panel F). The reason is that, in utility-maximization models, the real interest rate determines the slope of the consumption path but not the level of consumption. Hence, the initial fall in rd implies that, as long as rd < r, consumption of non-tradable goods will follow a declining path. Calvo and Vegh ( 1 994a) extend this analysis to the case in which instantaneous utility is represented by a constant-elasticity-of-substitution utility function. They show that the results obtained in the context of Dornbusch-Rodriguez models hold true only if the intertemporal elasticity of substitution exceeds the elasticity of substitution between tradables and nontradables. In that case, consumption of both tradable and non-tradables goods increases on impact, which implies that the current account goes into deficit. The relative magnitude of these parameters is, of course, an empirical issue. Estimates provided by Ostry and Reinhart ( 1 992), however, cast some doubts on the relevance of backward-looking models since they show that, for a number of developing countries, the intertemporal elasticity of substitution is typically smaller than that between tradables and nontradables 50 . An important feature of Calvo and Vegh's ( 1 994a) formulation is that the stabilization does not bring about a wealth effect, in the sense that wealth in terms of tradable goods remains unchanged. This appears as the natural assumption to make when the purpose of the exercise is to isolate the effects of inflation inertia on the outcome of an exchange-rate-based stabilization. However, in a more general model with capital accumulation and endogenous labor supply, the wealth effect associated with a permanent reduction in the rate of devaluation will cause an increase in consumption of tradable goods and, given that the real exchange rate cannot change on impact, a corresponding increase in consumption of non-tradable goods [see Rebelo and Vegh ( 1 995), Figure 1 1 ] . Hence, wealth effects associated with supply-side effects (analyzed in more detail below) could help explain the initial boom under backward­ looking indexation even under the more plausible parameter configuration in which the intertemporal elasticity of substitution is smaller than the elasticity of substitution between tradables and non-tradables goods. �

50 The more common criticism of Rodriguez ( 1982) is the assumption of adaptive expectations an assumption that has fallen out of favor among the profession. This criticism is, however, misplaced since Rodriguez's ( 1 982) results still hold under rational expectations, as shown in Calvo and Vegh ( 1 994a) . In other words, the key assumption in Rodriguez ( 1 982) is not adaptive expectations but rather thal aggregate demand depends negatively on the real interest rate (provided, of course, that there is some other source of inflation inertia).

Ch. 24: Inflation Stabilization and BOP Crises in Developing Countries

1 569

4.2. Lack of credibility A common characteristic of stabilization plans is imperfect credibility. As pointed out in S ection 2, there are fundamental reasons for stabilization programs to be less than fully credible. Since stabilization is costly from a political point of view, why would anybody expect that, as a general rule, stabilization programs have no chance to fail? Implementing a program that succeeds in all states of nature is unlikely to be optimal from the policymaker's point of view. Suppose, for the sake of concreteness, that authorities announce a stabilization plan in which the exchange rate is set at a lower and constant level forever, but the private sector believes that the program may eventually be abandoned. To keep matters simple, let us further assume that everybody believes that the program will be abandoned at time T > 0 (where time 0 represents "today"), and the rate of devaluation will, once again, become high after time T (see Figure 6, Panel A). Assuming perfect capital mobility, the latter implies that the nominal interest rate will be low from time 0 to time T, and expected to be high afterwards 51 . Will this have real effects? The answer is negative in the money-in-the-utility-function framework used in subsection 4. 1 to illustrate the effects of backward-looking indexation. In that model, the nominal interest rate does not affect any goods-markets equilibrium condition. Thus, the real economy (under flexible prices) would be undisturbed by the monetary experiment. However, separability between money and goods in the utility function is a very special, and probably umealistic, assumption. It implies that the marginal utility of money is independent of expenditure, a condition that is likely not to hold if money is used for transactions 52 . Following Calvo ( 1 986), let us assume that transactions require holding cash in advance 53 . Thus, using the same notation as before, we postulate 54 T

m1 = a(c1

CN et

+ ...!_ ),

a > 0.

(4. 1 3)

The consumer's preferences are now given by:

r= [v(cl) + u(c� )l

.fo

exp(-/)t) dt.

( 4. 1 4)

51 Note that, formally, lack of credibility is modeled as a temporary stabilization, which explains the label "temporariness hypothesis", often used in the literature. 52 It should be noted, however, that the basic results of Section 4. 1 hold true even under non-separability of real money balances (say, under the cash-in-advance specification explored below). Since we studied a permanent reduction in the devaluation rate, it would still be the case that consumption of traded goods remains unchanged under a cash-in-advance specification. 53 We adopt a cash-in-advance, fiexible-p1ices specification to illustrate the essential mechanisms behind lack-of-credibility in the simplest possible model. The same results would obtain under a money-in-the­ utility-function specification provided that the cross-derivative between conswnption and real money balances is positive [see Calvo (1 986)]. 54 For the derivation of the cash-in-advance constraint in continuous time, see Feenstra ( 1 985)

1 570

G.A. Calvo and C.A. Vegh

After substituting Equation (4. 1 3) into (4.2), we obtain a lifetime constraint that involves only c� and c'J as c�oice variables (and whose corresponding Lagrange multiplier will be denoted by A). Maximization of Equation (4. 1 4) subject to this lifetime budget constraint yields (4.1 5) (4. 1 6) The term involving the nominal interest rate i, J + ai, has a straightforward interpretation. Under the present assumptions, individuals must hold a stock of cash before making purchases. This means that, in addition to the market price of the good (unity for the tradable good and lie for the non-tradable good), the cost of the good is augmented by the opportunity cost of holding the needed real money balances. The ejj(xtive price of consumption is thus 1 + ai for tradable goods and ( 1 + ai)/e for non-tradables. For the present discussion, we can simplify the supply side even further and assume that the domestic supplies of tradables and nontradables are fixed at yT and yN , respectively. Then, by Equations (4. 1 5) and (4. 1 6), and home goods-market equilibrium (i.e., c� = yN ), it follows that (4. 1 7) Hence, in equilibrium, the real exchange rate and consumption of tradable goods move in opposite direction. In other words, any shock that causes consumption of tradable goods to increase will also entail a real exchange rate appreciation (i.e., a fall in e1 ) Consider now the effects of a non-credible stabilization program as described above (Figure 6). Since the representative individual expects a policy reversal at time T, it implies that he/she will expect the nominal interest rate i to be low from 0 to T, and high afterwards. Thus, by Equation (4. 1 5), consumption of tradables will be high between 0 and T and low afterwards. Given that the present discounted value of cT must satisfy the resource constraint (4.4), the path of consumption of tradable goods must look like that in Panel B of Figure 6. Intuitively, since the consumer expects the good to be cheaper between 0 and T than after T, he/she substitutes consumption away from the future (when consumption is expected to be relatively expensive) and towards the present (when consumption is cheaper). The current account deteriorates on impact and worsens throughout the stabilization as debt service increases (or net interest income falls), as illustrated in Panel C of Figure 6. Unlike tradable goods ­ whose supply is rendered perfectly elastic by the rest of the world - non-tradable goods are in fixed supply. Hence, the excess demand for non-tradable goods between 0 and T will have to be met by a rise in their relative price (i.e., a fall in e1), as follows fi·om Equation (4. 1 7) (Panel D of Figure 6). .

Ch. 24:

Inflation Stabilization and BOP Crises in Developing Countries A. Rate of devaluation

H

£

£

CT

t

1571

B. Consumption of traded goods

r

I L i

_______.,.

____

T

0

time

T

0

C . Current account e

•

time

D. Real exchange rate

0

�---�

- ------·- ·

0

T

time

0

T

time

Fig. 6. Temporary stabilization.

At the beginning of the program there is thus a boom in the consumption of tradables and a real appreciation, which is eventually followed by a contraction in the consumption of tradables and a real depreciation 55. Thus, this model displays two basic stylized facts that have accompanied exchange-rate-based stabilization programs, as argued in Section 3. It is also noteworthy that, unlike the previous explanation based on inflation inertia, this model does not rely on an initial fall in real interest rates. Hence, it could also explain the stylized facts even in programs in which only nominal, but not necessarily real, interest rates fall in the early stages 56. By introducing price stickiness into this model, Calvo and Vegh ( 1 993) have shown that a temporary stabilization may account for other key stylized facts discussed in Section 3 : (i) the joint occurrence of an output boom and a real exchange rate 55 The real effects at time T will occur regardless of whether the program is actually abandoned or not, provided that if it is not abandoned, the program becomes fully credible at T. Formally, it can be shown that permanent changes in the rate of devaluation arc everywhere superneutral. 56 An interesting extension of the basic model is to assume that T is a stochastic variable, as in Calvo and Drazen ( 1998), which leads to richer dynamic patterns for consumption. In particular, they show that in the absence of state-contingent assets, consumption rises on impact and continues to increase as long as the policy is in effect. See also Lahiri ( 1996a,b), Mendoza and Uribe (1 996), and Venegas-Martinez (1997). Further variations of the basic model include Obstfeld (1 985), who studies a gradual, tablita-type stabilization, and Talvi ( 1997), who analyzes the endogenous impact of higher consumption on fiscal revenues.

1572

G.A. Calvo and C.A. Vegh

appreciation in the early stages of the program; (ii) a recession in the non-tradable goods sector (i.e., a fall in output below its full-employment level) which may take place before the program is discontinued; and (iii) inflation remaining above the rate of devaluation until the time at which the program is expected to be discontinued 5 7 . Hence, in this case, inflation persistence is not due to some ad-hoc backward-looking mechanism but rather to lack of policy credibility. The model thus suggests that the fact that inflation remains high is not prima-facie evidence of stickiness in the rate of inflation 58. It should be noted that in the exercise illustrated in Figure 6, lack of credibility is socially costly, because a central planner would set consumption of tradables constant and equal to rko + i', instead of setting a path displaying the boom-bust pattern shown in Panel B of Figure 6. Hence, even though consumption rises as a non­ credible exchange-rate-based stabilization program is put into effect, the stabilization still proves to be a socially costly process. This conclusion, though, depends critically on the fact that, in cash-in-advance models (with no labor-leisure choice), there are no benefits associated with a reduction in inflation (i.e., the real equilibrium is independent of permanent changes in the inflation rate). In contrast, in transaction­ costs models, lower inflation is beneficial because it frees time for productive activities. In such a set-up, a temporary stabilization may be welfare-improving if the benefits (in terms of freed resources) of temporarily lower inflation more than offset the intertemporal distortion caused by a non-constant path of the nominal interest rate [see Reinhart and Vegh ( 1 995a)] . Hence, policymakers may still find it optimal to implement stabilizations plans that may not be fully credible, provided they command a "reasonable" level of credibility. Lack of credibility thus provides a rich framework to explain the main stylized facts observed in exchange-rate-based disinflations. The most common criticism of this type of model is that it relies critically on intertemporal consumption substitution, which is believed to be small or not significantly different from zero. Reinhart and Vcgh ( 1 995a) have examined the empirical relevance of the "temporariness" hypothesis, by estimating the intertemporal elasticity of substitution for five chronic-inflation countries (Argentina, Brazil, Israel, Mexico, and Uruguay). Using these estimates, they compute the predicted increases in consumption for seven major stabilization plans In this model, the domestic real interest rate falls on impact. As discussed in Section 3, however, real interest rates have typically increased on impact in heterodox programs. This often reflects tight credit policy in the early stages of the programs. For instance, the Israeli 1 985 plan had an explicit target for bank credit, which was to be achieved by a combination of higher reserves requirements and a higher discount rate [Barkai ( 1 990)]. The idea is for money to act as an additional nominal anchor in the early stages of the plan. This could be modeled by assuming that the stock of money is predetermined at each point in time due to the presence of capital controls [Calvo and Vegh ( 1 993)]. Agenor (1994) incorporates fiscal considerations into a model with imperfect capital mobility to address this issue. SH Within this framework, Ghezzi ( 1 996) has analyzed the important - but still little understood question of when to abandon an initial peg and switch to a more flexible exchange rate regime (a conunon occurrence in practice, as argued in Section 3). 57

Ch. 24: Inflation Stabilization and BOP Crises in Developing Countries

1573

(the three Southern Cone tablitas, the Argentine 1 985 Austral plan, the Brazilian 1 986 Cruzado plan, the Israeli 1 98 5 plan, and the Mexican 1 987 plan) and compare them to the actual increases. They conclude that, in spite of low (but statistically significant) elasticities of substitution ranging from 0 . 1 9 to 0.53 - this mechanism has a good explanatory power in four out of the seven episodes. It is the case, however, that nominal interest rates must fall substantially for this mechanism to be quantitatively important, which explains why the model appears to perform poorly for the Southern­ Cone tablitas 59. If anything, however, the estimates provided by Reinhart and Vegh ( 1 995a) should probably be viewed as a lower bound for the importance of the "temporariness" hypothesis. The reason is that the model does not incorporate durable goods which, as argued in Section 3 , appear to play a central role in the initial consumption boom. The presence of durable goods is likely to increase the quantitative importance of intertemporal substitution for two reasons. First, the introduction of durable goods might yield higher intertemporal elasticities of substitution, as found by Fauvel and Sampson ( 1 9 9 1 ) for Canada. Second, in addition to intertemporal consumption substitution, durable goods introduce the possibility of intertemporal price substitution because goods can be stored [Calvo ( 1 988)] .

5. Exchange-rate-based stabilization II: durable goods, credit, and wealth effects

The explanations discussed in the previous section rely on what we view as two key characteristics of chronic inflation processes: inflation persistence and lack of credibility. There are other elements, however, which may have played an important role in stabilization plans in chronic inflation countries. We first discuss the role of durable goods consumption and credit market segmentation. We then turn to a discussion of wealth effects, which may result from either supply-side responses or fiscal policy. 5. 1 .

Durable goods

As shown in Section 3, the consumption boom that characterizes exchange-rate-based stabilization programs has been particularly evident in the behavior of durable goods. This pattern of durable goods consumption has inspired an alternative explanation for the boom-bust cycle put forward by De Gregorio, Guidotti and Vegh ( 1 998) (henceforth DGV). This hypothesis, which is unrelated to inflation inertia or lack 59 It is worth pointing out that trying to explain all of the observed consumption booms may lx misleading, as other factors - such as lower international interest rates - may account for part of the boom.

1 574

G.A. Calvo and CA. Vegh

time

Fig. 7. Conslllllption of durable goods.

of credibility, is capable of generating a boom-bust cycle even in a fully credible program. Suppose that there are transactions costs associated with the purchase of durable goods. This implies that individuals buy durable goods only at discrete intervals of time. In the aggregate, however, sales of durable goods are smooth over time since different individuals purchase durable goods at different points in time 60 . This is illustrated in Figure 7. There are four consumers (whose purchases of durable goods are represented by the squares labeled A, B, C, and D) who buy durable goods at different points in time (i.e., every four periods). Hence, before time 0, aggregate sales of durables goods are constant. Consider now a stabilization plan implemented at time 0. Furthermore, suppose that there is a wealth effect associated with the stabilization (more on this below). Then, some consumers will be inclined to anticipate their purchase of durable goods and perhaps buy a more expensive durable good. In other words, next year's new Honda becomes today's new Mercedes. In terms of Figure 7, consumers B and C (who, in the absence of the stabilization plan, would have replaced the durable good at time t = 1 and t = 2, respectively) decide to buy the durable good at t = 0 (the picture abstracts from "size" effects). Consumer D, who just replaced his/her durable good at t = - 1 , also anticipates his/her purchase but to t = 1 . In this simple example, there are no purchases of durables at t = 3 and t = 4, due to the initial bunching of purchases at t = 0 and t = 1 . The initial boom (in period 0) is thus followed by a bust in periods 2 and 3 . Hence, this model is capable of accounting for the boom-bust cycle without resorting to inflation inertia or lack of credibility 6 1 . A key difference between this story and the previous two (inflation inertia and lack of credibility) lies in the policy implications. Under the temporariness (i.e., lack of credibility) hypothesis, the boom-bust cycle is a clear indication that policymakers have not done enough at the outset to convince the public that the program is 60 ln the absence of transaction costs and given that durable goods depreciate over time consumers would find it optimal to buy in each period the amount of durable goods that they are planning to consume during that period. Buying a greater amount would imply a loss for next period. Technically, it is assumed that consumers follow (S,s) rules and choose optimally the trigger points. 61 Furthemore, if idiosyncratic shocks were introduced into the picture, aggregate purchases of durabk goods would eventually return to the pattern prevailing before the plan was implemented.

Ch. 24:

Inflation Stabilization and BOP Crises in Developing Countries

1 575

sustainable over time. Hence, one would expect policymakers to worry when the initial boom emerges, and perhaps consider measures aimed at enhancing the program's credibility. In the same vein, inflation inertia (due to backward-looking indexation) also reflects some unresolved institutional problems which clearly endanger the whole stabilization strategy [as in the Chilean tablita; see Edwards and Cox Edwards ( 1 99 1 )] . In such a case, policymakers should try to cut the link between current and past inflation. In sharp contrast, the boom-bust cycle emphasized by DGV ( 1 998) is a direct consequence of the policymakers' ability to implement a fully credible stabilization plan. The eventual consumption bust is the natural counterpart of the initial "bunching" in consumption, and any policy measures aimed at counteracting it are likely to be suboptimal. In DGV ( 1 998), the wealth effect formally comes about because the fall in inflation leads to an increase in real money balances which, in turn, frees time spent in transacting to be used in productive activities. This channel is consistent with models (to be examined below) that emphasize supply-side effects of disinflation. The durable­ goods consumption cycle described above, however, is independent of how this wealth effect comes about, and would also hold under alternative scenarios which may not involve, strictly speaking, a wealth effect. One such scenario, which we find particularly attractive and examine next, relies on the existence of credit market constraints. 5.2.

Credit market segmentation

A boom in domestic absorption, which lies at the heart of the initial expansion and real exchange rate appreciation, can only happen if domestic residents are able to borrow from the rest of the world, or lower their holdings of foreign assets (i.e., capital repatriation). The examples examined so far rely on the fiction of a representative individual. There is thus no room for some individuals to borrow abroad and lend at home, while the rest engage in higher domestic borrowing and spending. Developing countries, however, are typically characterized by large segments of the population which do not have direct access to international borrowing and lending 62 . A relevant scenario with two types of borrowers is one in which type I, say, has perfect access to international capital markets (like in the above examples), and type II can only borrow at home. In addition, type-II individuals borrow in terms of domestic currency and are constrained to loan contracts displaying a constant nominal interest rate or a constant string of nominal installments. These are, admittedly, very special loans but their simplicity may make them cost-effective for medium-ticket durable consumption loans (i.e., television sets). In this setup, lower inflation/devaluation may induce a consumption boom, even though the program is fully credible. To see this, consider the realistic case in which borrowers pay back their debts in the form of a constant stream of nominal installments. 62 See, for instance, Rojas-Suarez and Weisbrod ( 1 995) prevalent in developing than in developed countries.

who

show that domestic bank lending is more

1 576

G.A. Calvo and C.A. Vegh 60

50 en

c 40 Q)

_§

ro u; 30 c

ro Q)

a:: 20

10

time

Fig. 8. Real installments for various nominal interest rates (percent per y(!ar, r = 0.03).

Thus, abstracting from credibility and country-risk problems, and assLm1ing that the real (and nominal) international interest rate is r, the domestic nominal interest rate, i, will be equal to r + E. We now assume, for simplicity, that loans are given in perpetuity and that the rate of devaluation is expected to be constant. Hence, an individual who borrows a sum S will have to pay an installment equal to iS in perpetuity. Furthermore, normalizing the present price level, P0 , to unity, and assuming a constant real exchange rate, we get that domestic inflation will also be equal to E. The real value of the installments is then given by (r + E) S

-----

PI

(r + e) S exp(et) '

t

;? 0,

where t = 0 is the time at which the loan is granted. Consequently, the higher is the rate of devaluation, the higher will be the nominal interest rate, i, and thus the higher will be the real value of the first few installments. When inflation is high, the real value of the first few installments could be exorbitantly large, deterring credit. Figure 8 illustrates the effects of a lower inflation rate on the time path of real payments. In the three cases depicted, r 0.03 . The rate of devaluation takes three different values: 0, 0. 1 7, and 0.47, so that i = 0.03, 0.20, and 0.50, respectively. The figure shows how the rate of inflation/devaluation can dramatically affect the time path of real payments. When i = 0.03, the path of real installments is fiat. When i = 0. 50, real installments in the early periods are the highest. Naturally, changes in the inflation =

inflation Stabilization and BOP Crises in Developing Countries

Ch. 24:

1 577

(devaluation) rate do not affect the present discounted value of real installments as of time 0, which equals S. Formally, note that

1·oo 0

iS

--

exp(Et)

exp(-rt) dt

=

S,

so that changes in E affect real payments, but not the value of the integral. Therefore, a substantially lower rate of devaluation may make credit affordable to type-II individuals. The ensuing consumption boom puts upward pressure on retailing -­ a highly labor-intensive activity - contributing to further real appreciation of the currency. Notice that the boom so generated may be socially desirable because it signifies an improvement in the credit market. Furthermore, if the newly available credit is directed towards durable goods consumption - as is likely to be the case purchases will fall later on during the program along the lines of DGV ( 1 998), contributing to an eventual downturn in economic activity. Hence, this type of scenario should be quite successful in explaining several stylized facts. Existence of credit segmentation may also help to rationalize these phenomena even in the case in which there are no loan-contract constraints on type-11 individuals. This would be so, for example, if type-I individuals take the implementation of the stabilization plan as a signal that the government is starting to "get its house in order". High inflation reflects the existence of tensions among policy objectives. Hence, until a stabilization program is implemented, foreign investors and type-I individuals may feel that placing their funds in the country in question exposes them to some kind of surprise taxation (particularly, if the funds are placed in highly visible domestic banks) 63 . Thus, by assuaging the investors' fears, a stabilization program - which enjoys some but not necessarily complete credibility - may bring about a lowering of interest rates for type-II individuals, stimulating expenditure 64. -­

5.3. Supply-side effects All the explanations examined so far are based on demand-side considerations. This is perhaps only natural considering that much of the literature was inspired by the Southern-Cone tablitas of the late 1 970s where, to most casual observers, the most striking fact was the increase in consumers' demand for goods (particularly durable goods). In more recent programs - such as Mexico 1 987 and Argentina's 1 99 1 Convertibility plan - it has been argued that monetary stabilization may have played an important role in unleashing supply-side responses in labor and investment [see 63

Domestic banks play a key role in making funds available to type-Il individuals, because then comparative advantage stems from their better knowledge of the local market. rA Again, if some of the higher consumption falls on durable goods, a boom-bust pattern may emerge along the lines of DGV ( 1 998). Moreover, there is, in principle, no reason in this example for social welfare to be negatively affected by the rise in consumption.

1 578

G.A. Calvo and C.A.

Vegh

Rebelo ( 1 993), Roldos ( 1 995, 1 997), Uribe ( 1 997a), and Lahiri ( 1 996a, l 996b)] Gs . While the evidence presented in Section 3 casts some doubts on the general empirical relevance of the investment channel, supply-side effects may well have contributed to the initial boom in some instances and thus deserve attention 66 . The role of capital accumulation i n generating a steady rise i n the relative price o f non-tradables (i.e., a real exchange rate appreciation) is emphasized by Rebelo ( 1 993) in the Portuguese context. If reforms increase the economy's steady-state capital stock, then as the capital-labor ratio rises, the price of the capital-intensive good (the tradable good) falls. Roldos ( 1 995) and Uribe ( 1 997a) present models in which domestic money is needed to buy (or install) capital goods, in the spirit of Stockman ( 1 98 1 ) . As a result, inflation drives a wedge between the real return of foreign assets and that of domestic assets, which implies that the domestic capital stock is a decreasing function of the inflation rate. A reduction in the inflation rate thus leads to a higher desired capital stock, and hence to an expansion in aggregate demand and investment. Since the supply of non-traded goods is assumed to be relatively inelastic in the short-run, the expansion in aggregate demand leads to an increase in the relative price of non-traded goods (i.e., a real appreciation) and a trade account deficit. A somewhat unsatisfactory aspect of some of these models is that they rely on some features - gestation lags, adjustment costs, and particularly the assumption that the investment good be a "cash good" - which do not have a clear economic interpretation . In particular, there is no evidence that would seem to tie investment to the level of cash transactions. From a qualitative point of view, however, this assumption is not necessary for this type of model to generate the effects just described, as made clear by Lahiri ( 1 996a). In his model, the nominal interest rate introduces a distortion between consumption and leisure [as in Roldos ( 1 997)]. When inflation falls, labor supply increases. This, in turn, leads to a rise in the desired capital stock and, hence, in investment. Rebelo and Vegh ( 1 995), however, argue that the assumption that investment be in some way related to cash transactions is critical for the quantitative performance of a broad class of models 67. A more fundamental problem of supply-side based models is that, given that the driving force behind such models are wealth effects, they cannot explain the late (,o

lt should be noted that these programs were also accompanied by important structural reforms. As stressed in Section 3, it would be important - though far trom trivial - to disentangle the effects of these reforms from those of the exchange rate-based stabilization per se. Clearly, we would not want to ascribe to monetary stabilization supply-side effects which may be due to real reforms. 06 There is little systematic evidence on labor supply responses in exchange rate-based stabilization. For some evidence on Mexico and Argentina, see Roldos ( 1 995). 67 Similar results would obtain if money were used as a factor of production [sec Uribe ( 1 997b)]. Thi s channel could be rationalized by assuming - following the credit channel literature - that firms do not have access to capital markets and must resort to bank credit to finance the need for short-term working capital [see Bernanke and Gertler ( 1 995) and, in the context of stabilization policies, the discussion below on Edwards and Vegh (1 997)]. Bank-intermediated capital has been used to improve the quantitative predictions of some monetary models; see, for instance, Chari, Jones and Manuelli ( 1 995).

Ch . 24: Inflation Stabilization and BOP Crises in Developing Countries

1 579

contraction observed in many programs. To this end, supply-side considerations must be supplemented by either lack of credibility or some nominal rigidity 68 . To illustrate how supply-side effects may be combined with temporary stabilization to replicate some of the stylized facts of exchange-rate-based stabilizations, we proceed to analyze a simple model which incorporates a consumption-leisure choice in the same cash-in­ advance specification presented in Section 4. Consider a one-good economy in which the representative household maximizes

j·oo u(c},f!1)exp(-f3t)dt,

(5 . 1 )

()

where £1 denotes leisure, subject to the lifetime constraint (which already i ncorporates the cash-in-advance constraint m1 acf) 69 : =

b0 + mo + J/oo ( 1 - £1 + rt) o

exp(-rt) dt

=

1= ci (l + ait) o

First-order conditions imply that (assuming t3

Ucr(cJ, f!t ) Ucr(c'J, f!t ) ue(cJ, f!t)

--=--�-'----"----'

= =

=

exp(-rt) dt.

(5 .2)

r):

X ( l + ctit),

(5.3)

1 + ctit ,

(5 .4)

where X is the Lagrange multiplier associated with constraint (5 .2). Note how the nominal interest rate introduces a wedge between consumption and leisure, as Equation (5 .4) makes clear. Taking into account the government's intertemporal budget constraint, it is easy to show that

-

k0 + /oc ( 1 £1 )

f

. o

exp(-rt) dt =

1= c} o

exp(-rt) dt.

(5.5)

Two important observations, which illustrate some of the points noted above, follow easily from Equations (5.3), (5 .4) and (5.5). First, a permanent reduction in the rate of devaluation, and thus in i, would cause a once-and-for all increase in consumption and output. Hence, this would explain the initial expansionary effects, but not the eventual contraction, observed in exchange-rate-based stabilizations. Second, if the utility function were separable (i.e., Uc1 eO 0), then a temporary (i.e., non-credible) stabilization of the type studied in Section 4.2 would lead to a consumption cycle similar to that illustrated in Panel B of Figure 6, but to a permanent increase in output =

68

Sec Rebelo and Vegh (1 995), Lahiri ( l 996a,b), Mendoza and Uribe ( 1 996), and Edwards and Vegh ( 1 997). 69 The function u( · ) is assmned to be shictly increasing and strictly concave, and goods are assumed to be normal. The household's time endowment is taken to be one. Production is given by 1 - f.

1 580

G.A. Calvo and C.A. Vegh

(i.e., a permanent fall in leisure). Hence, the output cycle cannot be rationalized with a separable utility function. Suppose now that the cross-derivative is negative; that is, ucrcO < 0. Then it follows from Equations (5.3) and (5 .4) that at time T, consumption falls and leisure increases (i.e., work effort decreases). This piece of information, together with Equation (5.5), implies that at time 0 both consumption and labor effort rise. Hence, such a specification of preferences would lead to a boom-bust cycle in both consumption and output. An extension of this simple model - which would generate the boom-recession cycle in output even with separable preferences - is to introduce a costly banking system and assume that firms need bank credit to pay the wage bill [Edwards and Vegh ( 1 997)]. In such a framework, a fall in consumption at time T leads to a fall in demand deposits and, hence, to a reduction in the supply of bank credit. The resulting "credit crunch" leads to higher lending rates, a lower level of bank credit, and a recession. More generally, the idea that the banking system may amplify both booms and busts through changes in bank credit appears quite attractive to explain the issues at hand, from both a theoretical and a quantitative point of view.

5. 4. Fiscal policy The elimination of large public sector deficits is clearly a necessary condition for a lasting reduction in inflation. It is thus not surprising that programs in which the fiscal adjustment was either absent or short-lived got quickly off track, the best­ known examples being the Argentine 1 978 tab1ita and 1 985 Austral plan, and the Brazilian 1 986 Cruzado plan. In successful plans (like the Israeli 1 985 plan and the Argentine 1 99 1 Convertibility plan), however, the fiscal adjustment has often been quite important. Such adjustment typically involves some combination of tax increases and cuts in government spending. While this is consistent with the initial fall in public consumption shown in the stabilization time profile (Figure 1 , Panel D), the panel regressions reported in column (5) of Table 2 indicate that the coefficient on the "early" dummy is not significant. Still, there is an important branch of the literature which has focused on the expansionary effects of the fiscal policies that often accompany major exchange-rate­ based stabilizations. In Helpman and Razin ( 1 987), the reduction in the inflation tax generates a wealth effect due to the lack of Ricardian equivalence. In Drazen and Helpman ( 1 988), the wealth effect comes through the expectation of a future reduction in government spending. Rebelo ( 1 997) considers a scenario in which, in the absence of reforms, government expenditure increases, thus raising the present value of the resources needed to finance that spending. By bringing the fiscal situation in order, a stabilization leads to a wealth effect that may produce a boom even though taxes increase in the short run 7 0 . 'IO Sec also Giavazzi and Pagano ( 1990) and Bertola and Drazen ( 1 993), who analyze the possibly expansionary role of fiscal policy in the stabilizations of Denmark in 1 982 and Ireland in 1 987.

Ch. 24: inflation Stabilization and BOP Crises in Developing Countries

1581

Rebelo and Vegh ( 1 995) examine the effects of reductions i n public consumption and increases in taxes in a two-sector, general equilibrium model. A fall in government consumption of tradable goods leads to a consumption boom and a real appreciation, but investment falls and the current account improves. A reduction in public consumption of non-tradables leads to a counterfactual real depreciation. Hence, cuts in fiscal expenditures seem to have limited power in explaining the stylized facts of exchange-rate-based stabilization. On the other hand, tax increases are recessionary. Finally, as with supply-side effects, fiscal-based explanations would not be able to generate an eventual recession, unless of course the policy is reversed.

5. 5. And the winner is . . . In the end, we would want to have a sense of whether a "winner" emerges among all the competing theories aimed at explaining the empirical regularities associated with exchange-rate-based stabilization which have been examined in the last two sections. To focus on essentials, the above models have abstracted from features which, while "realistic", would have diverted attention away from the key channels. While this is the logical route to follow, it makes a comparison across models difficult since not all channels are operating simultaneously. To remedy this, Rebelo and Vegh ( 1 995) have evaluated, both qualitatively and quantitatively, all the hypotheses examined in the last two sections (except for the one related to durable goods) in a single, two-sector model with a labor-leisure choice and capital accumulation. They conclude that, qualitatively, the only two hypotheses that may explain a boom--recession cycle are lack of credibility and price or wage stickiness (inflation inertia). (In their model, an initial wealth effect stemming from supply-side effects helps the inflation-inertia hypothesis in generating an initial consumption boom.) This is, of course, consistent with the evaluation that follows from the simpler models analyzed above. Quantitatively, however, Rebelo and Vegh ( 1 995) find that supply-side effects seem critical to account for any sizeable fraction of the observed outcomes. Still, baseline parametrizations fall short of explaining the observed consumption booms and real appreciations. While there are configurations of the technology that are consistent with the data, there is still little information to assess whether these configurations are empirically plausible. Hence, further work on the structure of the supply-side and on the differential response of the tradable and non-tradable goods sector - which would allow us to build more refined quantitative models - would be particularly useful. Finally, it is worth stressing the importance of disentangling the effects of stabilization from other reforms. The reason is that we may be asking models to explain "too much" in quantitative terms. In other words, the poor quantitative performance of a broad class of models found by Rebelo and Vegh ( 1 995) may be due not to a lack of "good" models but rather to the fact that we may be trying to explain all of the observed consumption booms and real appreciation as a result of exchange-rate-based stabilizations.

G.A. Calvo and C.A. Vegh

1 582 6. Money-based stabilization

The use of a money anchor to bring down chronic inflation has been much less common than the use of an exchange-rate anchor. Available evidence, however, suggests that these stabilizations have led to an initial recession, higher real interest rates, and real exchange rate appreciation (Section 3). As discussed earlier, the monetary regimes prevailing in these plans have borne little resemblance to the textbook case of a "pure" money anchor (i.e., a clean floating exchange rate), and have ranged from dirty floating to dual exchange rate systems (with a pegged commercial rate). Nonetheless, a common feature of such regimes is that money has been, albeit to varying degrees, the predominant nominal anchor. Therefore, to fix ideas, we will focus on the textbook case of a pure money anchor. We will then argue that, qualitatively, deviations from this benchmark would not alter the basic results.

6. 1. A simple model From an analytical point of view, the two key elements needed to reproduce the stylized facts illustrated in Section 3 are (i) an interest-rate elastic money demand and (ii) sticky prices. We will introduce these two critical elements in the simplest possible way 7 1 . We generate an interest-rate elastic money demand by introducing money in the utility function. We will therefore keep the utility function postulated in Equation (4. 1 ) but assume that it takes a log-specification 72 : ,

1o·= [

log(cJ ) + log(c� ) + log(m1 )] exp(-f3t) d t.

(6. 1 )

The household maximizes Equation ( 6. 1) subject t o (4.2). The first-order conditions imply that (again, assuming that f3 r) =

eN t

1

mt

=

et cJ,

(6.2)

=

Xit ,

(6.3)

where X is the Lagrangean multiplier associated with lifetime constraint (4.2). On the supply side, we follow Calvo 's ( 1 983) staggered-prices formulation a continuous-time version of the overlapping-contracts models a la Fischer (1 977) and Taylor ( 1 979, 1 980) - whereby the price level is sticky (i.e., it is a predetermined -

71 In the absence of sticky prices, there would be no difference between money-based and exchange rate-based stabilization. The reason is that, under money-based stabilization, the real money supply could change at any point in time through changes in the price level. 72 This model is a simplified version of Calvo and Vegh ( 1994c). See also Dornbusch (1 980) and Fischer ( 1986a, 1 988).

Ch. 24:

Inflation Stabilization and BOP Crises in Developing Countries

1 5 83

variable at each instant in time), output of home goods is demand-determined, and the rate of change in inflation is a negative function of excess aggregate demand: � > 0.

(6.4)

Equation (6.4) can be derived by assuming that firms set prices in a non-synchronous manner taking into account the future path of aggregate demand and the average price level prevailing in the economy [see Calvo ( 1 983)]. At any point in time, only a small subset of firms can change their price. The price level is therefore a predetermined variable. If excess demand develops at some point in time, a small subset of firms will change their price and inflation rises. The subset of firms that will change their price diminishes over time, which implies that inflation of home goods falls over time. Hence, the change in the rate of inflation is negatively related to excess demand in the non-traded goods sector 73 . As in the previous section, the interest parity condition implies that it = r + E1 • Output of non-tradable goods is demand determined so that c� = y� for all t. The resource constraint continues to be given by Equation (4.4). To solve the model, we proceed in two stages. In the first stage, we show that the path of real money balances, m1 (= M/E1PT*), is governed by an unstable differential equation. Note that (6.5) where !J-1(= M/Mt) denotes the rate of growth of the money supply, which is the policy instrument in a money-based stabilization. Substituting into Equation (6.5) the interest parity condition and first-order condition (6.3), we have that (6.6) Around the steady state, Equation ( 6.6) is an unstable differential equation 74. Hence, following an unanticipated and permanent reduction in IJ.�> m1 adjusts instantaneously to its higher steady-state value. Hence, from Equation (6.3), it and thus E1 also adjust instantaneously to their lower steady-state values. 73 Note that in this formulation, the price level of home goods (PN ) is sticky (i.e., it is a predermined variable) but the inflation rate of non-tradable goods (n:) is fully flexible (i.e., it is a forward-looking variable). It is also worth stressing that the formulation embedded in Equation (6.4) is not inconsistent with the one postulated in (4.8), where the level of the inflation rate of home goods depends positively on excess aggregate demand. The reason is that, in equilibrium, the staggered-prices formulation given by Equation (6.4) may still generate a Phillips-curve relation in which inflation is above its steady-state value when excess aggregate demand develops. 74 N otice that, as before, X is invariant to changes in �!1 .

1 584

G.A. Calvo and C.A. high t Jt l

it = O

I

n=o

L , � --

!-!

�----

..

L

n

-------

Fig. 9. Money-based stabilization: dynamic system.

Intuitively, if E1 fell on impact below f.l1 , then m1 would be increasing over time, which necessitates of a lower i (and lower E) to equilibrate the money market, which further increases m1, and so on. Thus, for m1 not to diverge, the rate of depreciation, and thus the nominal interest rate, must adjust instantaneously. In the second stage, we form a dynamic system in real money balances in terms of home goods and the rate of inflation. To that effect, let us define real money balances in terms of home goods; that is, n 1 M/Pf. Then, =

(6.7) The second dynamic equation follows from Equation (6.4), taking into account Equation (6.2) and the fact that, from the definition of m1 and n t ? e1 = n/m1 : (6.8) Equations (6. 7) and ( 6.8) constitute a system of differential equations in n and n, for given cJ, m t , and the policy variable f.l1 • Around the steady state, the system is saddle­ path stable, as it should be since n is the only predetermined variable (Figure 9 depicts the corresponding phase diagram) 75 . 1" The determinant associated with the linear approxnnation around the steady state is -l:;n55ci,Im, which indicates that there is one positive and one negative root.

<

0,

Ch. 24: Inflation Stabilization and BOP Crises in Developing Countries

1585

Suppose that initially (i.e., for t < 0), the public expects the rate of money growth to remain constant forever at fJ,H. This initial steady state is characterized by

CTss c� ess

=

=

rko + yT,

jiN ,

jiN

rko + yT '

(6.9) (6. 1 0) (6. 1 1)

Jiss = fJ,H , iss = r + fJ,H,

(6. 1 2) (6. 1 3)

n ss

(6. 1 4)

jiN

r + flH ' d rss = r,

(6. 1 5)

where, as before, the domestic real interest rate, rd , is defined as i - Ji . In terms of Figure 9, the initial steady state is at point A. Suppose now that, at time 0, policymakers announce a permanent and unanticipated reduction in the money growth rate from fJ,H to fJ,L . The new steady state becomes point B where real money balances in terms of home goods are higher and inflation is lower. On impact, the system jumps from point A to point C and then travels along the saddle path towards its new steady state, point B. The path of the main variables is illustrated in Figure 10. Real money balances (in terms of home goods) increase gradually over time (Panel B). On impact, inflation falls below its new steady-state value and then increases over time (Panel C). The path of the real exchange rate (Panel E) follows from the fact that e/e1 = E1 - JE1 • The real exchange rate must fall (i.e., appreciate) on impact to allow for a subsequent real exchange rate depreciation. The initial fall in the real exchange rate is effected through a fall in the nominal exchange rate, given that the price level of home goods is a predetermined variable. The path of consumption of home goods (Panel D) can be derived from Equation (6.2) and the path of the real exchange rate. Since consumption of traded goods does not change - and continues to be equal to permanent income of traded goods - consumption of home goods falls on impact as the relative price of home goods (i.e., the inverse of the real exchange rate) increases. It then increases as home goods become cheaper over time. The path of the domestic real interest rate (Panel F) follows from the definition r� = it - Jit . The domestic real interest rate increases on impact - as the inflation rate of home goods falls below the nominal interest rate -- and then falls towards its unchanged steady state. What is the driving force behind these results? It is best to think about the equilibrium condition in the money market, which is given by: eN

It

n t = --!-- .

(6. 1 6)

We think of the left-hand side of Equation (6. 16) as the real money supply in terms of non-tradable goods and of the right-hand side as real money demand. Upon the

G.A. Calvo and C.A.

1 586 1-L

j

n

A. Rate of monetary growth

j i

""' 1-

B . Real money balances

/

//-

•

0

t

11: ;

0

time

C. Inflation rate

eN

-

time

0

---

time

�

D. Consumption of home goods

0

time

F. Domestic real interest rate

E . Real exchange rate

r

0

j

Vegh

time

I ;-- �

I�

0

-------1>

·

time

Fig. 10. Money-based stabilization: time paths.

announcement of a lower rate of money growth, expected inflation and thus the nominal interest rate fall. For a given cr, this increases real money demand in terms of home goods. Real money supply, n (= MIPN ), however, cannot change on impact because neither M1 (a policy variable) nor pN (a predetermined variable) change. Hence, the fall in the nominal interest rate generates an incipient excess demand for real money balances. To equilibrate the money market, consumption of home goods (and thus output) needs to fall. For consumption of home goods to fall, home goods must become more expensive (i.e., the real exchange rate must fall). Since consumption of home goods must return to its initial steady-state, the domestic real interest rate must increase to induce a rising path of consumption of home goods.

Ch. 24: Inflation Stabilization and BOP Crises in Developing Countries

1 587

This simple model thus reproduces the main stylized facts associated with money­ based stabilization illustrated in Section 3 : an initial recession, a real exchange rate appreciation, and higher domestic real interest rates. The model does not exhibit, however, inflation persistence. To generate that result, we would need to introduce either inflation inertia or lack of credibility, along the lines of Section 4 [see Calvo and Vegh ( l 994c)]. The model also predicts no change in the trade and current account balances. As a first approximation, unchanged external accounts are not really at odds with the facts, as argued in Section 3 . To generate an alternative prediction, we would need to get rid of the separability between eN and cT , which would considerably complicate the solution method because the system would cease to be block-recursive. 6.2.

Extensions to other money-based regimes

Would the basic results change if we deviated from the extreme case of a pure money anchor (i.e., a clean floating)? The answer is no. Consider first a dirty floating, whereby the monetary authorities intervene in foreign exchange markets to influence the nominal exchange rate. In the example just analyzed, policymakers might want, on impact, to buy foreign exchange (i.e., accumulate international reserves) in exchange for domestic money to prevent the nominal exchange rate from appreciating too much. In terms of the model, the effects of intervention could be captured in a very simple way by assuming that, on impact, policymakers increase the nominal money supply so as to prevent the nominal exchange rate - and thus the real exchange rate - from appreciating (while still reducing the rate of growth to f.J,L) 76. Since m(= M/EP T*) j umps immediately to its higher steady-state value, it follows that a higher Mo implies a higher Eo (relative to the case in which the nominal money supply is not changed on impact). In other words, the larger the initial increase in the level of the money supply, the smaller the initial nominal and real appreciation. In terms of Figure 9, this implies that, depending on how much the money supply increases, the system would jump on impact to a point along the saddle path between points C and B and then proceed towards point B. Qualitatively speaking, then, the impact effects would be the same. Quantitatively, the initial real appreciation and thus the initial recession would be lessened. An extreme case of the "intervention" policy just described is a situation in which the initial level of the money supply is increased as much as needed for the nominal exchange rate not to change on impact. In this case, the system would jump immediately to its new steady state (Point B in Figure 9). Neither the nominal nor the real exchange rate would change and the initial recession would be avoided altogether. This case is typically ruled out as implausible on the basis that, in practice, a large initial increase in the stock of money would likely be interpreted as an increase in the rate of growth of money, which would severely affect the credibility of the whole

76 Of course, this is not, stJictly speaking, intervention since there money is introduced through a "helicopter" drop).

IS

no accwnnlation of reserves (1.e ..

1 588

G.A. Calvo and C.A. Vegh

program. Still, it helps rationalizing the monetary authorities' incentives to intervene in foreign exchange markets. From a theoretical point of view, if policymakers can manipulate at will the initial money stock, then to generate a recession it would be necessary to introduce inflation inertia, along the lines analyzed in Section 3 . Consider now the case in which there are capital controls. From a monetary point of view, capital controls give policymakers the ability to have further control over the money supply (if they did not have it to begin with). In the case of a floating rate (or dirty floating), then it should make little difference. In fact, adding capital controls to the model above - by, say, assuming that the private sector's stock of net foreign assets is given and cannot change - would not change anything since the restriction would not be binding (recall that the current account is zero throughout the adjustment). Mixed regimes - such as dual exchange rates with a predetermined commercial rate - should also lead to an initial recession 77• The key is that the initial nominal money supply will still be a policy instrument (unlike a predetermined exchange rate regime in which the initial nominal money supply adjusts endogenously to satisfy real money demand). Hence, any disinflationary policy which leads to a reduction in expected inflation and thus to an increase in real money demand - will lead to a "liquidity crunch" and an initial recession. In sum, the effects of disinflation in any monetary regime which involves significant capital controls should be qualitatively similar to those of a textbook money-based stabilization 78 . -­

6. 3. Money anchor versus exchange-rate anchor As noted earlier, a money anchor is much less common than an exchange-rate anchor in stabilization programs in chronic-inflation countries. Although far from being a panacea for stopping inflation, policymakers' revealed preference for an exchange-rate anchor may be rationalized on a number of grounds. First, the behavior of money velocity may be quite difficult to predict in the transition from high to low inflation, especially in chronic-inflation countries where the distinction between monies and quasi-monies is particularly blurred. Therefore, as a practical matter, it may be quite difficult to gauge how "tight" a given monetary rule is likely to be, and whether a "stable" relationship will hold in the aftermath of disinflation. In contrast, using the exchange rate has the intrinsic advantage tha·l, given the endogeneity of the money supply, there is no need in principle to have any information about money demand and velocity. 77 Models of dual exchange rates using the same type of framework emphasized throughout this chapter may be found in Obstfeld ( ! 986a), Guidotti and Vegh ( 1 992), and Calvo, Reinhart and Vegh ( 1 995). 78 As noted in Section 3, there may be regimes with a clean floating which do not necessarily have a monetary aggregate as the main nominal anchor [see Masson, Savastano and Sharma ( 1 997) for a taxonomy of monetary regimes]. These regimes, however, have been rare in major stabilization program:;. Still, Vegh ( 1 997) shows an example in which nominal and real interest rate rules are equivalent to a money-based regime.

Ch. 24: Inflation Stabilization and BOP Crises in Developing Countries

1 589

A second, and related, issue is that prolonged periods of high inflation lead to a hi gh degree of dollarization of the economy 79. In such a situation, the "relevant" money supply (i.e., the one which affects inflation and real activity) is likely to include (the domestic-currency value of) foreign currency holdings and deposits. Since this component cannot be controlled by policymakers, a reduction in the domestic component of the money supply may have little effect on total liquidity and, hence, on inflation. In effect, policy simulations of money-based disinflation for the case of Uruguay [Hoffmaister and Vegh ( 1 996)] suggest that reducing the rate of growth of either M l or M2 (which do not include foreign currency deposits) results in an extremely slow disinflation compared to using the exchange rate. In sharp contrast, if policymakers could (which, of course, they cannot) control M3 (M2 plus foreign currency deposits), then the speed of disinflation would be roughly the same as that achieved with an exchange-rate anchor. A third issue is that, by the simple virtue of being a price rather than a quantity, the exchange rate provides a much clearer signal to the public of the government's intentions and actual actions than a money supply target. Thus, if the public's inflationary expectations are influenced to a large extent by the ability to easily track and continuously monitor the nominal anchor, the exchange rate has a natural advantage. Based on the considerations just discussed, it should not come as a surprise that, by and far, disinflation programs in chronic-inflation countries have relied on the exchange rate as the main nominal anchor (with the August 1 990 Peruvian program being the most notable exception). Revealed preferences, therefore, would seem to support the view - with which we would certainly agree - that the exchange rate should be viewed as the more suitable nominal anchor in chronic-inflation countries. This is also consistent with Uribe's ( 1 994) findings on the welfare costs of money-based versus exchange-rate-based stabilization. By performing different simulations of Calvo and v egh 's ( 1 994c) model, he argues that exchange-rate-based stabilization is generally less costly, in terms of welfare, than money-based stabilization. An important caveat against the use of an exchange-rate anchor is in situations of very little credibility. For instance, in a country in which a series of failed exchange­ rate-based stabilizations has led the public to identify the initial boom and current account deficit as a signal of an unsustainable stabilization effort, it would probably be wise to try to switch strategies and opt for a money anchor. The main reason is that theory suggests [see Calvo and Vegh ( 1 994c)] that the effects of imperfect credibility differ drastically under each regime: lack of credibility is more disruptive under an exchange-rate anchor because it reduces the benefits (inflation falls by less) at the same time that it increases the size of the real dislocations (the boom-bust cycle becomes more pronounced). In contrast, in money-based stabilization, lack of credibility reduces

79

See Calvo and Vegh ( 1 992) and Savastano ( 1 996).

1 590

G.A. Calvo and C.A. Vegh

both the benefits (in terms of lower inflation) but also the initial recession. Hence, if the public is perceived as being highly skeptical, a money anchor may be less risky 80 . 7 . Balance-of-payments crises

As argued in Section 3, most exchange-rate-based stabilization programs end in balance-of-payments (BOP) crises (recall Table 1). These programs typically unleash dynamics - consumption booms, sustained real appreciation, current account deficits which call into question their sustainability 81 . This, in turn, fuels speculation of a possible abandonment of the exchange-rate anchor. Once the survival of the program has been called into question, financial factors - such as a large stock of short­ term debt - often aggravate the situation and may induce self-fulfilling crises. Whether balance-of-payment crises are ultimately caused by worsening fundamentals 2 or self-fulfilling elements is a matter of ongoing debate 8 . But even if the ultimate demise of the peg responds to some self-fulfilling event, it is still the case that fundamentals go a long way in determining the potential vulnerability of the system [Obstfeld and Rogoff ( 1 995)]. Naturally, the potential for balance-of-payments crises is a more general issue and applies to any pegged exchange rate system, whether the peg is part of an explicit inflation stabilization program or not (as most recently exemplified by the South East Asian crises of the second half of 1 997). However, even when the peg was not instituted as part of a program, crises tend to occur as the economy enters a recession, following a prolonged boom in economic activity, credit expansions, real exchange rate appreciation, and current account deficits [Kaminsky and Reinhart ( 1 995)] 83 . These are, of course, essentially the same dynamics as those generated by exchange-rate-based stabilizations (recall Figures 1 and 2). We suspect this is no coincidence, since it may be argued that pegged exchange rates keep inflation down (mainly by linking inflation of tradable goods to world inflation) at the expense of an appreciating currency. We would thus suspect that some of the mechanisms discussed in Sections 4 and 5 may help in explaining the dynamics leading to balance-of-payment crises in general. This area has enjoyed a renaissance of sorts in the aftermath of the Mexican crisis. Researchers have gone back to Klugman's ( 1 979) seminal paper on the mechanics of balance-of-payments crises and refined it in several important ways. Hence, after a brief discussion of liquidity considerations, we take Krugman's ( 1 979) model as the starting �0 Another argmnent for a money anchor is given in Tomei! and Velasco ( 1995), who argue that a money anchor might provide more fiscal discipline. 81 Naturally, a fiscal disequilibrimn will only reinforce the sense of m1sustainability. 82 See Krugman ( 1 996) and the comments therein by Kehoe and Obstfeld. 83 See also Bordo and Schwartz ( 1 996), Dornbusch, Goldfajn and Valdes ( 1 995), Eichengreen, Rose and Wyplosz (1 995, 1996), Frankel and Rose ( 1 996), Obstfeld ( 1 995), and Sachs, Torncll and Velasco (1 996). For an early analysis of devaluation c1ises, see Harbcrger (1981).

Ch. 24:

Inflation Stabilization and BOP Crises in Developing Countries

1591

point of this section. We then discuss the notion of current account sustainability. Finally, we examine the role of financial factors and lack of credibility in precipitating balance-of-payment crises. 7. 1.

Liquidity

Balance-of-payments crises take different forms. A common characteristic is that the government finds itself unable to comply with financial obligations. An example is when the government is committed to keeping a fixed exchange rate (against, say, the US dollar), and the public wishes to exchange domestic money for dollars in an amount that exceeds the international reserves available for this operation. As a result, the government has to abandon its exchange-rate policy. However, the loss of reserves may occur for other reasons. For instance, reserves may be lost if the country has short­ term liabilities, bonds, that cannot be rolled over in the capital market, and exceed the level of available international reserves 84. A BOP crisis does not necessarily involve insolvency, i.e., the country's inability to pay. As a general rule, countries undergoing BOP crises have ample resources to meet their financial obligations. In practice, the problem is that the country does not have enough financial assets that can be swiftly activated to meet its financial obligations. Thus, at the core of a BOP crisis, there is typically a mismatch between the "liquidity" of financial obligations and that of government financial assets. This mismatch is associated with another dominant characteristic of BOP crises, namely, they take place within a relatively short period of time (normally within a month), a fact that contributes to dramatize the event 85 . The word "liquidity" in the above paragraph is just a signpost, not a definition. A good definition of liquidity is highly elusive. We will discuss the concept in the context of a special environment. Let p(t, u) be the output price of a given asset at time t, if the asset was placed on the market at time u :::.;; t. We say that the asset is perfectly liquid if p(t, t) = p(t, u) for all t and u (and all states of nature). In other words, an asset is perfectly liquid if there is no advantage to the seller in announcing his/her intention to sell in advance of the actual transaction. Otherwise, if p(t, t) < p(t, u), we say that the asset displays some illiquidity. The asset's degree of liquidity could be measured by

�(t, u) =

p(t, t) . p(t, u)

Some simple models assume only two types of assets, namely (i) perfectly liquid assets, and (ii) assets for which �(t, u) 0 for all v < t; that is, assets that would have no =

g4 This was a key ingredient in the December 1 994 balance of payments crisis in Mexico. See. for instance, Sachs, Tomell and Velasco ( 1 995) and Calvo and Mendoza ( 1 996). Rs This should not be interpreted to mean that the ftmdamental reasons behind a balance of payments crisis are so short-lived - just the symptoms are.

G.A. Calvo and C.A. Vegh

1 592

market value if they had to be liquidated in no time's notice 86 . In this case, a BOP crisis would take place if the liabilities that the government is called upon to service at time t exceed the stock of liquid assets. In the models to be discussed here the liquidity properties of an asset are postulated, not explained. 7.2.

The Krugman model

This is an elegant model that captures the essential features mentioned above. We will present a version along the lines of the utility-based models used in previous sections of this chapter [see, for example, Calvo ( 1 987) and Obstfeld ( 1 986b)]. For present purposes, it is enough to assume that all goods are fully tradable, and that the representative individual is endowed with a constant flow of tradable goods per unit of time. Hence, using the same notation, lifetime utility is given by

(7. 1) A s i n Section 4, let the country b e fully integrated i n goods and capital markets aud thus face a constant international price of the tradable good and a constant world real interest rate, r, which equals the subjective discount rate. The consumer's intertemporal budget constraint is thus given by Equation (4.2) (abstracting from the terms that relate to non-traded goods). The first-order conditions are therefore (4.5) and ( 4. 7). Therefore, as before, Equation (4.5) implies that, along a perfect foresight equilibrium path, consumption is constant. The exchange rate is assumed to be fixed if there are enough reserves to sustain the value of the domestic currency (i.e., if reserves are above or at their "critical" level, which we assume to be zero). The exchange rate is sustained by intervening in the foreign exchange market. Thus, the fixed rate is abandoned once the public wants to turn domestic into foreign currency in an amount that exceeds the stock of liquid assets set aside for this operation. In Krugman ( 1 979), these assets are identified with (international) reserves, R. While the fixed exchange rate regime lasts, perfect capital mobility implies that the domestic nominal interest rate equals the international one; that is, it = r. After the fixed rate is abandoned, the exchange rate is allowed to float, and exchange rate intervention is stopped. Hence, again denoting by Et the rate of devaluation/inflation, perfect capital mobility implies that it r + Et . We assume that the central bank transfers net profits to the fiscal budget, which implies that the central bank's capital is constant. Hence, from the central bank's balance sheet, it follows that =

(7.2 ) 86 Lucas's ( 1 990) cash-in-advance model has this characteristic.

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where M is high-powered money, E is the nominal exchange rate (i.e., the price of foreign exchange in terms of domestic currency), R denotes reserves denominated in foreign exchange, and NDA stands for net domestic assets (i.e., domestic credit) 87. The government's only source o f expenditures are lump-sump transfers to house­ holds. It finances an exogenously given level of transfers, r, with central bank credit and proceeds from international reserves (which we assume earn the international interest rate, r) . Thus, (7.3) Since during the fixed-rate period, i = r and hence, by Equation (4.7), the demand for 1 money is constant (implying M1 = 0), we have: (7 .4) In other words, under fixed exchange rates the loss of international reserves equals the budget deficit (given by government transfers minus interest revenues from international reserves) 88 . After fixed rates are abandoned, R1 R 1 0, and hence, by Equations (7.2) and (7.3), =

=

(7. 5 ) Assuming, for simplicity, that the individual initially holds n o foreign assets or liabilities, it follows from first-order condition (4.5) and the lifetime constraint that cf = rR0 + yT for all t. Hence, combining first-order conditions (4.5) and (4.7) and solving for m1, we get the familiar demand-for-money expression:

L;

<

0,

LrRo+yT > 0.

(7. 6)

For simplicity, we will focus on steady states (i.e., (7 .5) and (7.6), we have that

EL(r � · £, rR0 + y r ) �

m1

0). Thus, by Equations (7 .7)

r.

The left-hand side of Equation (7.7) corresponds to revenue from the creation of money at steady state, while the right-hand side is the amount to be financed by these means. Clearly, Equation (7. 7) will in general display multiple equilibria because the demand for money is negatively sloped with respect to £. However, since equilibrium 87 Equation (7.2) implicitly assumes - with no loss of generality - - that the central bank does not monetize nominal capital gains on international reserves. Typically the central bank creates a fictitious non-monetary liability instead. 8 8 It is assumed that the initial fiscal deficit is positive; i.e., r rR0 > 0. --·

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G.A. Calvo and C.A. Vegh

R

.ilR I

I

0

T

•

T*

time

Fig. 1 1 . Krugman crisis.

multiplicity is not a key theme in Krugman ( 1 979), we will assume that the economy settles down on the lowest rate of devaluation consistent with Equation (7. 7), which will be indicated by £* . Clearly, if r > 0, then after the currency peg is abandoned, the economy jumps to a higher inflation plateau, and stays there forever. It follows from expression (7.6) that at "switch point," i.e., the point in time T at which the currency peg is abandoned, the demand for money collapses. This is a key feature of the model. Figure 1 1 depicts the central characteristics of an equilibrium path for international reserves assuming that the government runs a fiscal deficit (i.e., r rR0 > 0) and that the nominal exchange rate is a continuous function of time (this assumption will be rationalized later). From 0 to T reserves are driven by Equation (7.4). The system is abandoned at time T - and not when reserves reach zero - because, as pointed out above, at switch time the demand for money takes a sudden dip equal to L(r, rR0 + yT) - L(r + E, rR0 + yT) = 11R. Since the exchange rate is assumed not to jump at time T , it follows that the government suffers a loss of reserves equal to iJR at time T . Clearly, switch point T is uniquely determined. Thus, the model is able to capture some of the main characteristics of a BOP crises outlined above. To close we will now briefly discuss the continuity of the exchange rate path E. In the first place, we will constrain E to be piece-wise continuous and everywhere right­ hand differentiable. These are technical assumptions which help to make sure that the problem is well-defined in a mathematical sense, and that irrelevant nonuniqueness situations are ruled out. Notice that jumps in E are not ruled out. Suppose that, contrary to our assumption above, E jumps at t � T, and let M; be the left liminf of M at t. If M1- > 0, then the representative individual suffers a capital loss on account of his/her money holdings at time t. Thus, assuming that the demand for money goes to zero as the nominal interest rate diverges to plus infinity, a plausible regularity condition, it follows that it will never be optimal to undergo that kind of capital loss, which implies that M1- 0. Thus, if t > T , there will be an excess supply of money at t, which is inconsistent with equilibrium. Suppose now that t = T , and, -

=

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1 595

hence, the jump takes place exactly at switch point. Since M1- = 0, then the BOP crisis would have occurred before time T , which is a contradiction. This proves that E is continuous everywhere as assumed above. Finally, it is worth stressing that, since the interest rate on international reserves is equal to the international interest rate, the current account will be zero at all times. Notice, however, that external balance equilibrium does not prevent the occurrence of a BOP crisis. This is worth keeping in mind when we discuss the current account approach below.

7. 3. Krugman model: critique and extensions We now extend the above model in several useful directions.

7.3.1. Bonds Domestic debt (outside the central bank) may be introduced and thus account for an element that has played a prominent role recently. Thus, Equation (7.3) would become: (7.8) where D stands for instant-maturity government debt outside the central bank (in nominal terms). Actually, bond issuance could completely finance the deficit and, thus, NDA1 = 0. Under those circumstances, no reserves would be lost during the fixed rates period. However, domestic debt D would increase without bound and, at some point, no more debt could be placed in the market because, otherwise, the government would not satisfy its intertemporal budget constraint. This is an interesting example because it is not unusual for governments to try to mask the fiscal disequilibrium in this manner. International reserves, which are closely watched by the private sector, would in this fashion be insulated from fiscal disequilibrium (prior to the BOP crisis). 7.3.2.

Sterilization

The Krugman model assumes that the monetary authority makes no attempt at sterilizing the effects of reserve accumulation. Money supply is not a target. Thus, the model assumes that at switch time the monetary authority will not interfere with the run against domestic money and allow money supply to fall. In practice, money is not simply cash but includes bank deposits. Therefore, a fall in the money stock is normally associated with a cut in bank credit. This is a cause of trouble especially if the event is not fully anticipated 8 9 . Of course, if bank credit is easily substitutable x9 Under perfect foresight, everybody knows the exact timing of the BOP crisis. However, the model is easily and realistically extended to the case in which, say, the demand for money has a stochastic component and hence, there is always an element of surprise in the timing of the crisis [see Flood and Garber ( 1984)].

G.A. Calvo and C.A. Vegh

1 596

for other type of credit, the bank credit crunch would cause no major disruption. But in LDCs this is not the case. Consequently, the central bank is induced to intervene through open market operations to provide the bank credit that would disappear as a result of the collapse in money demand at switch time. Flood, Garber and Kramer ( 1 996) argue that there are several important instances in which central banks have attempted to fully sterilize the collapse in money demand. Interestingly, they show that this policy, if anticipated, would lead to a BOP crisis happening immediately, i.e., at time 0. There would be no fixed exchange rate period like the interval [0, T) in the Krugman model. The proof is straightforward. For money to remain constant (i.e., full sterilization) at time T, after-crisis inflation should equal inflation before crisis (which is zero). But this would imply that there is no crisis and the exchange rate is constant forever. However, Equation (7.4) implies that sooner or later international reserves will be driven down to zero, and a crisis will take place, a contradiction. Thus, the only possibility left is for the crisis to take place at t = 0. In other words, the fixed-exchange-rate regime collapses upon the announcement. To have a more vivid picture of this instantaneous crisis, let us assume that at the time of the announcement real monetary balances fall short of total reserves (implying that an attack against domestic currency cannot be successful unless it triggers an expansion of domestic credit). The government's announcement is followed by an immediate attack on the domestic currency. Since authorities try to stabilize the stock of money, they intervene increasing domestic credit. Given that the demand for money has collapsed, the additional liquidity infusion only results in a loss of international reserves. This will continue until reserves are depleted. At that point authorities lose control of the exchange rate. Since there are no reserves, the exchange rate is the adjustment variable. Hence, the currency will devalue (the price level will rise) until real monetary balances are consistent with the equilibrium expected rate of devaluation/inflation. Anticipated sterilizatwn although inconsistent with fixed rates under the above assumptions could, however, be sustained under other set of plausible assumptions. F:ood, Garber and Kramer ( 1 996) and Kumhof ( 1 997) show that fixed-rates-cum­ sterilization is consistent with a situation in which government bonds are imperfect substitute with international bonds. Calvo ( 1 996b) shows that the same holds if it is costly to move in and out of money 7. 3 . 3 . interest rate

policy

Another important aspect of reality which is not captured in Krugman's ( 1 979) model i s the possibility of the central bank actively defending the currency by raising short­ term interest rates. Sweden, for instance, raised short-term interest rates to around 500 percent per year in September 1 992 to stave off a speculative attack [see, for instance, Krugman ( 1 996)]. More recently, both Hong Kong and Brazil sharply raised interest rates to defend their currencies in the aftermath of the South East Asian currency crisi s. While not always successful, higher interest rates often buy time for

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the government to try to uphold the system's credibility by adopting more fundamental measures. Lahiri and Vegh ( 1 997) model interest rate policy by assuming that the government controls the interest rate on highly liquid government debt - along the lines of Calvo and Vegh ( 1 995) - and show that by announcing a policy of higher interest rates in the event of a crisis, the crisis may be postponed until international reserves actually reach zero (i.e., at a point like T* in Figure 1 1). At that point, the central bank is forced to float but there is no run (i..e., the money supply remains constant). This result of "crisis with no run" might also explain situations in which central banks abandon a peg with no dramatic loss of international reserves.

7. 4. The current account approach This approach has become popular after Mexico's 1 994 BOP cns1s since some observers have claimed that the crisis originated in the fact that Mexico was spending "beyond its means". In other words, Mexico's current account deficit was "too large." (It is worth recalling that in Krugman's model a BOP crisis could take place even though the current account deficit is nil to the extent that a payments crisis involves a liquidity shortage, irrespective of the country's overall solvency.) More generally and as shown in Section 3 - exchange-rate-based stabilizations typically lead to large current account deficits. Whether or not such imbalances are sustainable is thus a critical question when it comes to evaluate the reasons behind these programs' collapse. The sustainability literature is based on the budget-constraint equation for the country as a whole 90. To illustrate, let us denote by f and CAD net international debt and current account deficit (both as a share of GDP), respectively. Then,

j; CAD, - rJJ;,

(7.9)

=

where rJ is the rate of growth of output. Sustainability analysis focuses on steady states. Thus, setting j; 0, the steady-state - sustainable - current account deficit satisfies =

(7 . l 0) where, as in earlier sections, the subscript "ss" denotes "steady state". This equation establishes a relationship between steady-state debt and current account deficit. In 0), then the sustainable current account deficit the absence of growth (i.e., rJ is necessarily equal to zero. In contrast, with positive growth a sustainable current account deficit is possible. This analysis is unable to give us a definite answer on CADss until we pin down Iss . Recent experience shows that the capital market is reluctant to keep lending to LDCs exhibiting levels of indebtedness that exceed 80 percent of GDP [Williamson =

9° For an elaboration, see Milesi-Ferretti and Razin ( 1 996)"

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G.A. Calvo and C.A. Vegh

( 1 993)] . Hence, this additional piece of information allows us to write the sustainability condition (7 . 1 0) as follows: CADss :(

0. 8rr

(7 . 1 1)

Thus, a country that can be expected to grow at 4 percent per year cannot sustainably run a current account deficit exceeding 3 .2 percent. Since 4 percent growth was, if anything, an upper bound for Mexico, this analysis would conclude that its 8 to 9 percent current account deficits were grossly unsustainable. Notice that CAD1 = r.ft - TS1 , where TS denotes the trade surplus (including non­ financial transfers) as a share of GDP, and rft denotes debt service (r is the international rate of interest). Therefore, by Equation (7 . 1 0), TSss =

(r

�-

TJ) .fss ·

(7. 1 2)

Thus, if we again set the growth rate to 4 percent (i.e., TJ = 0. 04) and, in addition, we assume the international interest rate to be 1 0 percent per annum (i.e., r = 0. 1 0), then, by Equation (7. 12), at the steady state the economy must run a trade balance surplus of 0.06.f.s as a share of GDP. The trade balance surplus increases with the steady-state debt/GDP ratio, .fs5 • In particular, at the upper bound forf�s (80 percent of GDP) the trade balance surplus would be 4.8 percent of GDP. Presumably, the reason for capital markets to be unwilling to extend credit to LDCs beyond 80 percent of GDP is that it may become tempting for those countries to renege on their debt obligations. Temptation, in turn, is likely to be related to the sacrifice associated with servicing the debt. Gross sacrifice of servicing the debt can be measured by the associated trade balance surplus. The previous computation suggests that the capital market becomes nervous about a country's willingness to repay when debt service represents only about 5 percent of GDP. Notice that the net sacrifice from servicing the debt could be much less once one takes into account international penalties from debt delinquency. Thus, one criticism of current account sustainability computations is that they are highly sensitive to the definition of sustainable debt/GDP ratios. Besides, the above example shows that the implied critical sacrifice levels are low when compared to other capital market transactions. For example, mortgages in the USA are easy for a household to get if total mortgage payments are less than 25 percent of the household's income. Thus, if this ratio were also relevant for countries' debt then, using the above parameters, the critical steady-state debt/GDP ratio would be 4.16 ( = 0.25/(r - TJ), where r - TJ = 0.06). Therefore, recalling Equation (7. 1 0), a country growing ai 4 percent per year could run a sustainable current account deficit of more than 1 6 percent of GDP! Of course, countries are not mere households because they are protected by sovereignty clauses. However, prior to the crisis Mexico had given very clear signals that it wanted to belong to the First World and signed treaties that would have made it very costly to engage in strategic repudiation of international debt (or any debt, for that matter).

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1 599

A more fundamental criticism is that steady-state computations could be very misleading for countries that are undergoing deep economic reforms. The current account deficit could in those instances be a temporary phenomenon associated with reform. Once we move away from the steady-state straightjacket, this approach has precious little to say. Finally, the current account approach does not address the BOP-crises issue as such. If the utility function is separable in money and consumption as in expression (7 . 1 ), the demand for money would be impervious to solvency issues. Thus, if we further assume that the government runs no fiscal deficit and there is no expansion in domestic credit, then the currency will never be under attack and a BOP crisis will never take place.

7.5. Financial considerations Financial factors are likely to play a key role in precipitating balance-of-payment crises. We now review several such factors, which we deem particularly relevant.

7. 5. 1. Volatility of monetary aggregates The Krugman model focuses on fiscal deficits as the key determinant of reserves losses. However, even in the absence of domestic credit expansion, international reserves in a fixed-exchange-rate regime may rise or fall as a consequence of fluctuations in the demand for money. This is not a minor consideration for LDCs since some of them exhibit substantially higher fluctuations in their demand for money than advanced industrial countries. To illustrate the significance of these considerations, let us examine the case in which the (log) demand for money follows a random walk and, to abstract from the effects highlighted in Krugman's model, let us assume that the demand for money is totally inelastic with respect to the nominal interest rate, and that there is fiscal balance. To simplify the exposition, we will continue making the assumption that domestic prices equal the nominal exchange rate, which is kept constant unless there is a BOP crisis. Letting m denote the demand for real monetary balances, then we postulate (in discrete time) that (7. 1 3) where m stands for real monetary balances and t 1 is an i.i.d. random variable. Under these circumstances, the demand for money can fall and create a BOP crisis even though there is no fiscal deficit. If L 1 exhibits a mean-zero normal distribution, then the larger its variance, the larger will be the probability of a BOP crisis given an initial level of international reserves. Estimates of Equation (7. 1 3) show Mexico, for instance, with a relatively high standard deviation (about 4 percent per month), while a country like Austria that has successfully pegged to the Deutsche Mark for about 1 5 years shows a standard deviation which is only about 1 percent per month [see Calvo ( 1 996a)] .

1 600

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In addition, balance-of-payments problems could be exacerbated by external factors. For example, Calvo and Mendoza ( 1 996) show that there is a significant effect from US short-term interest rates on Mexico's demand for money (specifically, M2). This was reflected in a sizable fall in the demand for money during 1 994 and, we suspect, lay at the heart of the Mexican difficulties at the end of the year. Mexico and other Latin American countries experienced sizable capital inflows in the first half of the 1 990s. As argued by Calvo, Leiderman and Reinhart ( 1 993), about 5 0 percent of these flows stem from external factors, among which US interest rates hold a prominent role. Capital inflows gave rise to an expansion in consumption and investment which, in tum, increased monetary aggregates. Thus, the above-mentioned link between domestic monetary aggregates and external rates of interest may stem from direct opportunity-cost or indirect absorption-type considerations. Experience in several countries, and most notably in Mexico, suggests that the fluctuations in monetary aggregates provoked by external factors - and more specifically, by capital flows - could be substantial [see Calvo, Leiderman and Reinhart ( 1 996) and Calvo and Mendoza ( 1 996)] . An equation like (7. 1 3), enhanced by taking explicit account of external factors, would be needed to assess the implication of different reserve levels. To illustrate, consider the simple case in which external factors are fully captured by the random term in Equation (7. 1 3). We proceed as follows. Let v1 = m tfR1, where R stands for international reserves, and m is interpreted as the monetary base. Hence, a BOP crisis in period t + 1 will take place if m1 - m t+ 1 > R1• Or, equivalently, if

mt+l Vt - 1 log -- = t 1 1 1 < log -- . mr

Vr

(7. 14)

Clearly, the probability of a BOP crisis is an increasing function of v . Notice that this "vulnerability" index is totally independent of the popular index given by the ratio of reserves to one-month worth of imports. The latter hails back to periods in which reserves were held to ensure smooth trade, while the index developed here is associated with the probability of a BOP crisis as a result of financial fluctuations. In the above example there exists a direct connection between m and R because we assume m stands for base money (i.e., monetary liabilities of the central bank). If instead m stood for M2, the connection is more indirect and depends on how the central bank reacts to shocks in the larger monetary aggregates. If the central bank is not responsible for banking problems but defends the exchange rate parity by intervening and swapping base money for international reserves, then the same analysis developed above is applicable, except that one would need to derive the demand for base money from Equation (7. 1 3 ) - which would now apply to M2 - minimum reserve requirements, and an equation describing the demand for banks' excess liquidity. In turn, if the central bank is responsible for ensuring adequate banks' liquidity, then the central bank may be led to expand domestic credit whenever M2 falls. In the extreme case in which banks are fully insulated from any liquidity loss as a

Ch. 24:

Inflation Stabilization and BOP Crises in Developing Countries

1 60 1

consequence of a fall in M2, then M2 is equivalent to base money and the above example is fully applicable. It is worth noting, however, that in practice M2 is much larger than money base and, hence, the probability of a BOP crisis, given international reserves, is likely to be even higher (unless the volatility of M2 is substantially lower than that of base money). However, by providing liquidity to offset the fall in M2 the central bank does not prevent M2 from falling. Thus, if a central bank is keen on not letting monetary aggregates fall, then it will increase domestic credit even more and provoke a large loss of reserves after just a small contraction in monetary aggregates. This seems to have been the case in Mexico during 1 994. As noted above, Calvo and Mendoza ( 1 996) show that the demand for M2 fell in 1 994. Since banks held sizable domestic public debt in their portfolios, rolling back private debt could have been prevented simply by an open market operation that lowered domestic public debt in banks' portfolios by an amount equal to the fall in M2. However, the central bank went beyond that and prior to the crisis succeeded in stabilizing the level of M2. This meant a sizable expansion of banks' credit to the private sector (more than 40 percent from January to December 1 994). This is quite remarkable given that these measures were undertaken concurrently with a sizable loss of international reserves. This illustrates how much a central bank may be willing to risk in order to safeguard the financial system. Similar behavior was observed in Thailand and Malaysia during the more recent currency crises in South East Asia. 7. 5.2.

Short-maturity debt

As pointed out above, the BOP crisis literature has on the whole ignored the role of domestic debt, and followed Krugman ( 1 979) in assuming that fiscal deficits are fully monetized. However, the assumption that fiscal deficits are fully monetized is becoming increasingly unrealistic as governments have started to have access to international capital markets. It has thus become increasingly possible to finance fiscal deficits by floating domestic or international public debt. The maturity structure of this debt varies across countries but it is perhaps fair to say that emerging-markets' governments are likely to exhibit a debt maturity structure slanted towards the short end of the spectrum. Mexico again shows an extreme case in this respect: in December 1 994 about US$ 1 0 billion of domestic debt was due to mature in January, and about US$30 billion during 1 995 (these are large numbers compared to the US$6 billion stock of international reserves held by Mexico prior to the crisis). As argued in Calvo ( 1 998) the demand for emerging markets ' assets (including public debt) could be highly volatile for two basic reasons. In the first place, the effective rate of return on these assets depends on policy - like everywhere else but with the added complication that policy in emerging markets is itself highly volatile, reflecting imperfect knowledge of structural parameters and, most importantly, relatively unstable political equilibria. The instability of the latter has likely increased after the breakdown of communism. Therefore, assessing the "state of nature" in an

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emerging market could be quite costly. It is not enough to know the particulars of the investment project since, in general, its profitability will depend on government regulations. Thus, a project could be very lucrative and yet be unattractive to foreign investors if, for instance, profits are expected to be subject to high taxes (either directly or through the imposition of, for example, foreign exchange controls). Consequently, assessing the state of nature in a given emerging market is likely to entail large "fixed" costs. The second basic ingredient for high volatility of demand for emerging markets' assets is the so-called "globalization" phenomenon, which is characterized by the fact that investors diversify their portfolios across a large number of emerging markets. Portfolio diversification, in the absence of Tequila or contagion effects, helps to lower portfolio risk. Interestingly, however, the benefit from portfolio diversification does not depend on specific knowledge about the actual state of nature in these economies. For risk hedging, it is enough that the return on the different assets across countries not be perfectly correlated. Thus, for instance, by the law of large numbers, risk could become very low if the different investment projects were stochastically mutually independent. It is intuitive, and can be rigorously shown in a canonical example [Calvo ( 1 998)], that under the above circumstances (i.e., high information costs and globalization), (i) investors will be very sensitive to "news" about expected returns, and (ii) their incentives to learn about the state of nature in each emerging market will eventually decrease as the number of emerging markets rises. Consequently, in a globalized capital market, investment in emerging markets' assets is likely to be highly sensitive to rumors and relatively unresponsive to "fundamentals." The above-mentioned phenomenon poses no direct threat of a BOP crisis to the extent that it only involves fluctuations in stock market prices. However, if a large share of domestic debt is coming due in the short run, adverse changes in investors' sentiments about a given emerging market may cause a BOP crisis, particularly if the exchange rate is held fixed. The only available policy under those circumstances (short of devaluing) is to raise interest rates on newly-issued domestic debt. Unfortunately, since investors are ill-informed about fundamentals, the interest-rate hike could possibly be taken as a sign of weakness and not of strength, since they may feel that higher interest rates are due to the "market" being aware of serious difficulties. Furthermore, even if investors were better informed, the bonds-attack could lead to socially costly crises. As an illustration, consider a simple two-period example in which all public debt has one-period maturity and the international riskless interest rate is zero. We assume that debt can be repaid in full, independently of the repayment schedule. However, output is a function of the debt-repayment schedule. Suppose that the economy is controlled by a social planner and is subject to the standard intertemporal budget constraint. Under these circumstances, a social planner will choose the optimal debt-repayment schedule by maximizing the social utility function subject to the budget constraint. A social optimum is attained if the country can freely choose the share of total debt that will be repaid each period. However, if bond-holders insist on getting fully repaid

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1 603

in the first period, we assume that the effort to comply with the financial obligation is so counterproductive that output next period would fall to zero. Thus, even though the country is able to fully repay its outstanding debt in period 1 , no rescheduling would now be possible because potential investors (rationally) expect output to be zero in period 2 . Thus, the existence of large short-term maturity debt may give rise to multiple equilibria, and make the country vulnerable to socially costly bond-attacks [see Calvo ( 1 998) and Cole and Kehoe ( 1 996)]. 7. 5. 3.

Domestic debt and credibility

In addition, the existence of domestic-currency denominated public debt can generate BOP difficulties if the exchange rate policy is not fully credible. Suppose the government announces a fixed exchange rate but the public believes that the currency will be devalued next period by E times 1 00 with probability p. Then, if investors are risk neutral (in terms of foreign currency) the nominal interest rate satisfies

1 + it

. l - p) = p + ( l + z,)(

--

1+£

1 + r,

(7. 1 5)

where i and r and are the domestic and international one-period interest rates, respectively. Clearly, if E and p are positive numbers, then the domestic interest rate will exceed the international one. This phenomenon is called the "peso problem" and is a common feature of exchange-rate-based stabilization programs. Suppose the government has a fixed debt level d and that, under full credibility (i.e., E = 0), the fiscal deficit is zero (i.e., T - rR, + rd = 0). Assuming, for simplicity, that fiscal deficits are fully monetized, it follows that, if there is an expectation of a devaluation (but the currency is not devalued), the discrete version of Equation (7.4) would be given by Rt+l

-

R,

=

-( T - rR1 + i, d),

with the fiscal deficit now being positive since i, > r due to the peso problem. Hence, the peso problem may put into motion Krugman's B OP-crisis machinery 9 1 . Thus, lack of credibility may result in an unsustainable balance of payments even though "fundamentals" could be fully in line with a sustainable situation. 7. 5. 4.

Credibility, the demand for money and fiscal deficits

Credibility problems may be reflected through other more subtle, but equally important, phenomena. As argued in Section 3, there is typically a consumption boom in the early stages of an exchange-rate-based stabilization. Therefore, the demand for money �1 A related scenario is discussed by Guidotti and Vegh ( 1 999). In their model, the Krugman machinery is put into motion by the probability of a devaluation associated with a fiscal consolidation.

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will contain a cyclical component associated with the stabilization program. Higher monetization at the start of the program may give the impression to policymakers that the program enjoys a high degree of credibility. An argument one commonly hears from policymakers is that higher monetization reflects the return of flight capital due to the higher confidence inspired by the stabilization plan. While this is partially true, policymakers may wrongly conclude that the higher stock of real monetary balances is a permanent positive shock. However, if monetization is provoked by the expectation that the program will be abandoned in the non-too-distant future, then the real stock of money will eventually collapse, possibly generating a BOP crisis. In a recent study, Talvi ( 1 997) shows that if tax revenue is an increasing function of consumption, then prior to crisis the fiscal deficit could shrink, giving the false impression that the fiscal house is in order. In an example, Talvi ( 1 997) shows that the fiscal deficit is nil before the crisis, only to explode afterwards. This pattern of the fiscal deficit is understandably quite confusing to the average policymaker. It is not unusual for the initial slackening of the fiscal constraint to be read as an indication that tax evasion has fallen and, hence, that the higher fiscal revenue has a significant permanent component. As a result, considerable political pressure is built up for more government spending. Unfortunately, if imperfect credibility is the key reason for the initial consumption boom and policymakers give in to pressures to increase government expenditure, then after-crisis fiscal deficits could reach dangerously high levels - which will become apparent only after a crisis erupts and policymakers have little room to manoeuver. 8. C oncluding remarks

We have concluded our long journey through the fascinating world of inflation stabilization and balance-of-payment crises in developing countries. After examining the possible rationale behind the existence of chronic inflation in many developing countries, we carried out some simple econometric exercises which support the existence of two main puzzles in the area of inflation stabilization. First, exchange­ rate-based stabilization leads to an initial boom in real GDP, private consumption, and durable goods consumption. The recession typically associated with disinflation ' programs appears only later in the programs. Second, money-based stabilization leads to an early recession, suggesting that the timing of the contraction depends on the nominal anchor which is used (the "recession-now-versus-recession-later" hypothesis). We did not, however, find support for the existence of an investment cycle in exchange­ rate-based stabilizations. Nor did we find evidence of a significant fall in public consumption around the time of stabilization. We then reviewed the main theories aimed at explaining these puzzles. We first focused on theories that emphasize expansions in demand: inflation inertia, lack of credibility (temporary policy), and durable goods. The first, inflation inertia, relies on a fall in real interest rates to generate the initial boom. However, within an optimizing

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framework and in the absence of any wealth effect, this theory would require some implausible parameter configurations to rationalize the initial boom. Also, it would have a hard time explaining the boom in programs in which real interest rates rise on impact. The second, lack of credibility, conforms quite well with the stylized facts. Quantitatively, however, it faces the problems of low intertemporal elasticities of substitution. The third, which relies on the timing of purchases of durable goods, may also reproduce the consumption cycle. Its quantitative relevance has not been evaluated yet. We then turned to explanations that rely on wealth effects. The first emphasizes supply-side responses - both in labor supply and investment - to the removal of the inflation distortion. While these theories can explain the boom, they cannot explain the late recession. In addition, the fact that the investment cycle was not found significant casts some doubts on the relevance of this mechanism. A second source of wealth effects - cuts in government spending - faces a similar problem. Quantitatively, however, supply-side effects appear to be a critical component of any story aimed at explaining the empirical regularities associated with exchange-rate­ based stabilization. To explain the stylized facts of money-based stabilization, we resorted to an optimizing version of traditional sticky-prices model a la Taylor-Fischer. A reduction in the rate of money growth decreases expected inflation and thus the nominal interest rate. This induces an incipient excess demand for real money balances. To restore money-market equilibrium, consumption (and thus output) of home goods needs to fall. This is effected through a real appreciation of the domestic currency. It is worth stressing that sticky prices are essential to this type of model. Without this feature, money-based stabilization would yield the same results as exchange-rate-based stabilization. Hence, a model designed to explain both the stylized facts of exchange­ rate-based and money-based stabilization - and, in particular, the recession-now­ versus-recession-later hypothesis - requires sticky prices and an interest-rate elastic money demand [see Calvo and Vegh ( 1 994c)]. Since most exchange-rate-based stabilizations end in full-blown balance-of-payment crises - typically accompanied by banking crises - we took a detailed look at both the mechanics and causes of balance-of-payments crises in the final leg of our journey (Section 7). While the starting point of this section was Krugman's ( 1 979) seminal paper on balance-of-payments crises, most of the issues touched upon have come to light after the December 1 994 Mexican crisis, and represent very much research in progress. It was argued that simple extensions of Krugman's ( 1 979) model may account for some missing links in the original story: (i) bond-financing may mask the fiscal problems by preventing reserve losses; (ii) imperfect substitutability between domestic and foreign assets opens the door for the central bank to sterilize the effects of reserve losses on money supply; and (iii) an active interest rate policy allows the central bank to postpone the abandonment of the peg and avoid a run in the final stages. We then analyzed the current account approach; that is, the view that large current account deficits may be unsustainable and lead to balance-of-payments crises. While

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this channel could provide a concrete link between the dynamics of exchange-rate­ based stabilizations and their demise, it still has precious little to say outside the steady state. In addition, the mechanics through which a BOP crisis would occur are unclear. Finally, we highlighted the role of financial considerations and credibility as contributing factors in unleashing balance-of-payments crises. Under high information costs and globalization, demand for emerging markets' assets is likely to be highly sensitive to rumors and relatively unresponsive to fundamentals. Changes in investors' sentiments could make it difficult for the government to roll-over a large stock of short­ term debt, leading to a bond-led attack. A large stock of short-term debt may also result in self-fulfilling crises. Lack of credibility in the peg - and thus high nominal interest rates - may also put into motion the Krugman-type machinery in the face of a large stock of domestic debt. Where do we go from here? l n the area of inflation stabilization, much work remains to be done on the empirical regularities of disinflation in chronic inflation countries. Numerous problems need to be addressed, including sample selection and small samples for money-based programs. Small samples for successful exchange­ rate-based programs also pose a problem since the econometric finding of a late recession is clearly influenced by events in failed programs. A critical aspect in econometric work is to control for other domestic factors, such as trade and structural reforms. Disentangling the effects of stabilization from other reforms is important not only to make sure that the empirical regularities remain such, but also because we may be asking theoretical models to explain "too much", quantitatively speaking. It would also be important to document in a systematic way the behavior of the home­ goods sector relative to the traded-goods sector. Some available evidence suggests that the initial boom is much more evident in the home-goods sector. The behavior of investment should also be looked at in more detail. The goal of this research agenda would be to establish how much needs to be explained and then build more refined quantitative models to evaluate the alternative hypotheses, along the lines of Rebelo and Vegh ( 1 995). It is clear that we are still far away from a good understanding of the links between the dynamics of exchange-rate-based stabilizations and their ultimate demise. While Krugman's ( 1 979) model and variations thereof provide a good description of the mechanics of BOP crises, they offer in general little insight into the more fundamental causes of such crises - over and above the obvious implication that a deterioration in the fiscal balance during a program will put into motion Krugman-type dynamics. We feel that the notion of current account sustainability needs substantial refinement before it can offer a consistent and complete account of the facts, but is an area definitely worth pursuing. In this respect, a productive area of research would be to focus on the role of the financial and banking sectors in amplifYing the expansionary cycle and possibly contributing to the downturn and eventual crisis. A particularly relevant channel has to do with the real estate market. A sizeable fraction of the lending boom goes to finance real-estate operations [see, for instance, Guerra ( 1 997a)]. These loans are usually made

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using as collateral temporarily high asset prices. In the context of the temporariness hypothesis, Guerra ( 1 997b) shows an example in which the fall in asset prices (i.e., land prices) before the abandonment of the program may trigger a banking crisis. While this does not explain the end of the program, it does provide a link between the dynamics of these programs and banking crises.

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Lahiri, A., and C.A. Vegh ( 1997), "Krugman balance of payments crises: are they for real?", mimeograph (UCLA). Leiderman, L. ( 1 993), Inflation and Disinflation: The Israeli Experiment (University of Chicago Press, Chicago, IL). Lizondo, J.S. ( 1 99 1), "Real exchange rate targets, nominal exchange rate policies, and inflation", Revista de Amilisis Econ6mico 6:5-22. Lucas Jr, R.E. ( 1 990), "Liquidity and interest rates", Journal of Economic Theory 50:237-264. Masson, P.R., M.A. Savastano and S. Sharma ( 1 997), "The scope for inflation targeting in developing countries" Working Paper 97/130 (International Monetary Fund). Medeiros, C. (1 994), "A case of a monetary stabilization program: the Dominican Republic's economic program, 1 990-1993", mimeograph (International Monetary Fund). Meltzer, A.H. (1 994), "Book review: Heterodox policy and economic stabilization", Journal of Monetary Economics 34:581-600. Mendoza, E., and M. Uribe ( 1 996), "The syndrome of exchange rate-based stabilizations and the uncertain duration of currency pegs", International Finance Discussion Papers No. 548 (Board of Governors of the Federal Reserve System). Milesi-FetTetti, G.-M., and A. Razin ( 1 996), Current-Account Sustainability, Princeton Studies in International Finance No. 81. Modiano, E.M. (1 988), "The Cruzado first attempt: the Brazilian stabilization program of February 1 986", in: M. Bruno, G. Di Tella, R. Dornbusch and S. Fischer, eds., Inflation Stabilization: The Experience of israel, Argentina, Brazil, Bolivia, and Mexico (MIT Press, Cambridge, MA) 2 1 5-258. Mondino, G., F. Sturzenegger and M. Tommasi ( 1 996), "Recurrent high inflation and stabilization: a dynamic game", International Economic Review 37:981-996. Montiel, P., and J. Ostry ( 1 99 1 ), "Macroeconomic implications of real exchange rate targeting in developing countries", IMF Staff Papers 38:872-900. Obstfeld, M. (1 985), "The capital inflows problem revisited: a stylized model of Southern-Cone disinflation", Review of Economic Studies 52:605-625. Obstfeld, M. (1986a), "Capital controls, the dual exchange rate and devaluation", Journal of International Economics 20: 1-20. Obstfeld, M. ( 1 986b), "Speculative attack and the external constraint in a maximizing model of the balance of payments", Canadian Journal of Economics 1 9 : 1-22. Obstfeld, M. ( 1 995), "International currency experience: new lessons and lessons relearned", Brooking Papers on Economic Activity I : 1 1 9-220. Obstfeld, M., and K. Rogoff (1 995), "The mirage of fixed exchange rates", Journal of Economic Perspectives 9:73-96. Okun, A.M. ( 1 978), "Efficient disinflationary policies", American Economic Review, Papers and Proceedings 68:348-352. Ostry, J., and C.M. Reinhart ( 1 992), "Private saving and terms of trade shocks", lMF Staff Papers 39:495-5 17. Pazos, F. ( 1 972), Chronic Inflation in Latin America (Prager Publishers, New York). Phelps, E. S. (1 973 ), "Inflation in the theory of public finance", Swedish Journal ofEconomics 7 5:67-82. Ramos, J. ( 1 986), Neoconservative Economics in the Southern Cone of Latin America, 1 973-1983 (Johns Hopkins University Press, Baltimore, MD). Rebelo, S .T. ( 1 993), "Inflation in fixed exchange rate regimes: the recent Portuguese experience", in: F. Torres and F. Giavazzi, eds., Adjustment and Growth in the European Monetary Union (Cambridge University Press, Cambridge) 1 28-149. Rebelo, S.T. ( 1 997), "What happens when countries peg their exchange rates? (The real side of monetary reforms)", Working Paper No. 6 1 68 (NBER). Rebelo, S.T., and C.A. Vegh ( 1 995), "Real effects of exchange rate-based stabilization: an analysis of competing theories", in: B.S. Bernanke and J.J. Rotembcrg, eds., NBER Macroeconomics Annual (MIT Press, Cambridge, MA) 125-1 74.

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Reinhart, C.M., and C.A. Vegh ( 1994), "Inflation stabilization in chronic inflation countries", mimeograph (International Monetary Fund). Reinhart, C.M., and C.A. Vegh ( 1995a), "Nominal interest rates, consumption booms, and lack of credibility: a quantitative examination", Journal of Development Economics 46:357�378. Reinhart, C.M., and C.A. Vegh ( 1 995b), "Do exchange rate-based stabilizations carry the seeds of their own destruction?", mimeograph (International Monetary Fund). Rodriguez, C.A. (1 982), "The Argentine stabilization plan of December 20th", World Development 1 0:801�8 1 1 . Rojas-Suarez, L., and S.R. Weisbrod ( 1 995), "Financial fragilities in Latin America: the 1 980s and 1 990s", Occasional Paper No. 1 32 (International Monetary Fund). Roldos, J. ( 1995), "Supply-side effects of disinflation programs", IMF Staff Papers 42: 1 5 8 - 1 83. Roldos, J. ( 1997), "On gradual disinflation, the real exchange rate, and the current account", Journal of International Money and Finance 1 6:37�54. Sachs, .T., A. Tornell and A. Velasco ( 1 995), "The collapse of the Mexican peso: what have we learned?", Working Paper No. 5 142 (NBER). Sachs, J., A. Tornell and A. Velasco ( 1996), "Financial crises in emerging markets: the lessons fi·om 1 995", Working Paper No. 5576 (NBER). Sahay, R., and C.A. Vegh ( 1 996), "Inflation and stabilization in transition economies: an analytical interpretation of the evidence", Journal of Policy Reform 1 : 75�108. Sanguinetti, P. ( 1994), "Intergovernmental transfers and public sector expenditure: a game theoretic­ approach", Estudios de Economia (Universidad de Chile) 2 1 : 1 8 1�21 2 . Santaella, J., and A . Vela ( 1996), "The 1987 Mexican disinflation program: an exchange rate-based stabilization?", Working Paper 96/24 (International Monetary Fund). Sargent, T.J. (1 982), "The ends of four big inflations", in: R.E. Hall, ed., Inflation: Causes and Effects (University of Chicago Press, Chicago, IL) 4 1-97. Savastano, M.A. ( 1 996), "Dollarization in Latin America: recent evidence and policy issues", in: P. Mizen and E.J. Pentecost, eds., The Macroeconomics oflnternational Currencies: Theory, Policy and Evidence (Edward Elgar, London) 225-255. Stockman, A. ( 1 9 8 1 ), "Anticipated inflation and the capital stock in a cash-in-advance economy", Journal of Monetary Economics 8:387�393. Talvi, E. (I 995), "Fiscal policy and the business cycle associated with exchange rate-based stabilizations: evidence from Uruguay's 1 978 and 1 99 1 programs", Working Paper Series 3 1 3 (Inter-American Development Bank). Talvi, E. ( 1 997), "Exchange rate-based stabilization with endogenous fiscal response", Journal of Development Economics 54:59�75. Taylor, J.B. ( 1 979), "Staggered wage setting in a macro model", American Economic Review, Papers and Proceedings 69: 1 08� 1 1 3. Taylor, .T.B. ( 1 980), "Aggregate dynamics and staggered contracts", Journal of Political Economy 88: l - 23. Taylor, J.B. ( 1 983), "Union wage settlements during a disintlation", American Economic Review '/3: 9 8 1 �993. Tommasi, M., and A. Velasco ( 1 996), "Where are we in the political economy of reform?", Journal of Policy Reform 1 : 1 87�238. Tornell, A., and A. Velasco ( 1995), "Fixed versus flexible exchange rates: which provides more fiscal discipline?", Working Paper No. 5 1 08 (NBER). Uribe, M. ( 1994), "Comparing the welfare costs and the initial dynamics of alternative temporary stabilization policies", mimeograph (Board of Governors of the Federal Reserve System). Uribe, M. ( 1 995), "Real exchange rate targeting and macroeconomic instability", International Finance Discussion Papers No. 505 (Board of Governors of the Federal Reserve System). Uribe, M. ( 1 997a), "Exchange-rate-based inflation stabilization: the initial real effects of credible plans", Journal of Monetary Economics 39: 1 97--221 .

1614

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Uribe, M. ( 1 997b), "A note on the analytics of credible exchange rate-based disinflation when money facilitates firms' transactions", mimeograph (Board of Governors of the Federal Reserve System). Vegh, C.A. ( 1 989), "Government spending and inflationary finance: a public finance approach", IMF Staff Papers 36:657-677. Vegh, C.A. ( 1 992), "Stopping high inflation: an analytical overview", IMF Staff Papers 39:626-695. Vegh, C.A. ( 1 997), "Monetary policy, interest rate rules, and inflation targets", mimeograph (UCLA). Velasco, A. ( 1 993), "A model of endogenous fiscal deficits and delayed fiscal reforms", C.V. Starr Center Report 93-4 (New York University). Vcncgas-Martinez, F. ( 1 997), "Temporary stabilization: a stochastic analysis", mimeograph (CIDE, Mexico). Viana, L. ( 1990), "Uruguay's stabilization plan of 1 968", mimeograph (CERES, Uruguay). Wicker, E. ( 1 986), "Terminating hyperinflation in the dismembered Hapsburg monarchy", American Economic Review 76:350-364. Williamson, J. ( 1 993), "Issues posed by portfolio investment in developing countries", in: S. Claessens and S. Gooptu, eds., Portfolio Investment in Developing Countries, Discussion paper No. 228 (World Bank). Woodford, M. ( 1990), "The optimum quantity of money", in: B.F. Friedman and F.H. Hahn, eds., Handbook of Monetary Economics (North-Holland, Amsterdam) 1 067- 1 1 52. Zarazaga, C.E. ( 1 996), "Recurrent hyperinflations in a dynamic game with imperfect monitoring in the appropriation of seignorage", mimeograph (Federal Reserve Bank of Dallas).

Chapter 25

GOVERNMENT DEBT DOUGLAS

W

ELMENDORF'

Federal Reserve Board N. GREGORY MANKIW

Harvard University and NBER Contents

Abstract Keywords 1 . Introduction 2. The data 2 . 1 . Debt and deficits in the USA and other countries 2.2. Measurement issues 2.2. 1 . Adjusting for economic conditions 2.2.2. Assets and liabilities beyond the official debt 2.2.3. Capital budgeting 2.2.4. Generational accounting 2.3. Future fiscal policy

3 . The conventional view of debt 3 . 1 . How does debt affect the economy? 3 . 1 . 1 . The short run: increased demand for output 3 . 1 .2 . The long run: reduced national saving and its consequences 3 . 1 .3 . Other effects 3.2. How large is the long-run effect of debt on the economy? 3.2. 1 . The parable of the debt fairy 3.2.2. A closer look at the effect of debt on private savings 3 .2.3. A closer look at international capital flows 3.2.4. A closer look at the marginal product of capital 3.2.5. The deadweight loss of servicing the debt 3.2.6. Summary

4. Ricardian equivalence 4. 1 . The idea and its history 4. 1 . 1 . The essence of the Ricardian argument 4. 1 .2. A brief history of the Ricardian idea 4. 1 .3 . Why Ricardian equivalence is so important Handbook of Macroeconomics, Volume 1, Edited by J.B. Taylor and M. Woodford © 1999 Elsevier Science B. V All rights reserved 1615

1616 1616 1617 1617 1618 1 620 1 620 1 62 1 1 623 1 624 1 625 1 627 1 628 1 628 1 628 1 63 0 1 632 1 632 1 634 1 63 6 1 63 8 1 63 9 1 63 9 1 640 1 640 1 640 1 642 1 644

D. W Elmendorf and N.G. Mankiw

1616 4.2. The debate over Ricardian equivalence: theoretical issues 4.2. 1 . Intergenerational redistribution 4.2.2. Capital market imperfections 4.2.3. Permanent postponement of the tax burden 4.2.4. Distortionary taxes 4.2.5. Income uncertainty 4.2.6. Myopia 4.3. The debate over Ricardian equivalence: empirical issues 4.3 . I . Testing assumptions about household behavior

4.3.2. Testing the implications for consumption 4.3. 3 . Testing the implications for interest rates

4.3.4. Testing the implications for international variables

5 . Optimal debt policy 5. 1 . Fiscal policy over the business cycle 5.2. Fiscal policy and national saving 5.2 . 1 . Life-cycle saving 5.2.2. Intergencrational saving 5.3. Tax smoothing

6. Conclusion References

1 645 1 645 1 648 1 649 1 65 1 1 652 1 653 1 654 1 654 1 655 1 657 1 658 1 659 1 659 1 660 1 660 1 66 1 1 662 1 663 1 663

Abstract

This chapter surveys the literature on the macroeconomic effects of government debt. It begins by discussing the data on debt and deficits, including the historical time series, measurement issues, and projections of future fiscal policy. The chapter then presents the conventional theory of government debt, which emphasizes aggregate demand in the short run and crowding out in the long run. It next examines the theoretical and empirical debate over the theory of debt neutrality called Ricardian equivalence. Finally, the chapter considers various normative perspectives about how the government should use its ability to borrow.

Keywords

JEL classification:

E6, H6

Ch. 25:

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1617

1 . Introduction

important economic issue facing policymakers during the last two decades of the twentieth century has been the effects of government debt. The reason is a simple one: the debt of the US federal government rose from 26% of GDP in 1 980 to 50% of GDP in 1 997. Many European countries exhibited a similar pattern during this period. In the past, such large increases in government debt occurred only during wars or depressions. Recently, however, policymakers have had no ready excuse. This episode raises a classic question: how does government debt affect the economy? That is the question that we take up in this paper. It will not surprise the reader to learn that macroeconomists are divided on the answer. Nonetheless, the debates over government debt are fascinating and useful to study. They are fascinating because they raise many fundamental questions about economic behavior. They are useful to study because learning the sources of disagreement can help an impartial observer reach a judgment of his own. Our survey of the effects of government debt is organized as follows. Section l considers some of the data on government debt. These data give some sense of the history of government debt in the USA and elsewhere. This section also discusses some recent projections for the beginning of the twenty-first century. Section 2 then examines the conventional view of the effects of government debt. We call this view "conventional" because it is held by most economists and almost all policymakers. According to this view, the issuance of government debt stimulates aggregate demand and economic growth in the short run but crowds out capital and reduces national income in the long run. Section 3 turns to an alternative view of government debt, called Ricardian equivalence. According to this view, the choice between debt and tax finance of government expenditure is irrelevant. This section discusses the basis of this idea, its history and importance, and the debate over its validity. Section 4 moves from positive to normative analysis. It considers various perspec­ tives on the question of how the government should use its ability to borrow. The discussion highlights the potential significance of cmmtercyclical fiscal policy, optimal national saving, and intertemporal tax smoothing. An

2. The data

In this section we present some basic facts about government debt and deficits in the USA and other countries. We give the official data, and then examine a number of issues regarding the appropriate measurement of fiscal policy. We conclude the section by considering projections of future fiscal policy in a number of countries .

D. W Elmendorfand N G. Mankiw

1618 Panel A

Debt as a Percentage of GNP 1791 - 1996

Percent 120

Panel B

Deficit as a Percentage of GNP 1791 - 1996

Percent 30

25

20

15

1790

1810

1830

1850

1870

1890

1910

1930

1 950

1970

1990

Fig. I .

2. 1 .

Debt and deficits in the USA and other countries

We begin with data from the USA. Panel A of Figure 1 shows US federal debt as a percentage of gross national product over the past 200 years 1 . It is common to exclude the debt of state and local govermnents, as we do, although for many purposes it is more appropriate to consider the consolidated debt of all levels of govermnent. Most 1 We take GNP data from Berry ( 1 978, Table ! B) for 1791 to ! 868, ti-orn Romer (1 989) for 1 869 to 1 928, and from the National Income and Product AccOtmts since 1 929. The end-of-year debt comes from Bureau of the Census ( 1 975, series Y493) for 1791 to 1 939, from Congressional Budget Office (CBO) ( 1 993, Table A-2) for 1 940 to 1 96 1 , and from CBO ( 1 997a, Table F-4) since 1 962. We splice the series multiplicatively at the break points and convert debt from fiscal-year to calendar-year form.

Ch. 25:

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state governments hold positive net assets, because they are prohibited from running deficits in their operating budgets, and because the assets they accumulate to fund employee pensions exceed the debt they issue to finance capital proj ects. The figure shows federal debt "held by the public", which includes debt held by the Federal Reserve System but excludes debt held by other parts of the federal government, such as the Social Security trust fund. The primary cause of increases in the US debt-output ratio has been wars: the War of 1 8 1 2 , the Civil War, World War I, and World War II all produced noticeable upswings in federal indebtedness. The Great Depression and the 1 980s are the only two peacetime intervals when this ratio increased significantly. Between these sharp increases, the debt-output ratio has generally declined fairly steadily. An important factor behind the dramatic drop between 1 945 and 1 97 5 is that the growth rate of GNP exceeded the interest rate on government debt for most of that period. Under such circumstances, the government can collect taxes equal to only its non-interest spending, finance the interest payments on the outstanding debt by issuing more debt, and still watch its debt grow more slowly than the economy. This situation has potentially important implications for the effect of government debt, as we discuss later. Panel B of Figure 1 shows the US federal budget deficit as a share of GNP over the past 200 years 2 . These deficit numbers are for the so-called "unified budget", which includes both "on-budget" items like national defense and "off-budget" items like Social Security, thus capturing essentially all of the fiscal activities of the federal government. Once again, the effect of wars is quite apparent. The small deficits between 1 95 5 and 1 975 were consistent with a declining debt-output ratio for the reason just mentioned: although the debt was growing, output was growing faster. After 1 975, larger deficits and a less favorable relationship between the interest rate and the growth rate caused the debt-output ratio to rise. Government debt and deficits in other industrialized countries span a wide range, as shown in Table 1 . The first column presents general government net financial liabilities as a percentage of GOP. This measure differs in several respects from that shown in panel A of Figure 1 : it includes all levels of government, nets out financial assets where the data are available, and normalizes by GOP rather than GNP. Nevertheless, the US value for 1 996 matches the last point shown in the figure. The second and third columns show the budget surplus and primary budget surplus as percentages of GDP. The primary surplus equals taxes less all non-interest spending. The highest reported debt-income ratios are in Italy and Belgium; their high debt service payments induce substantial budget deficits despite primary budget surpluses. 2

The budget surplus comes from Bureau of the Census ( 1 975, series Y337) for 1791 to 1928, from Bureau of the Census ( 1975, series Y341 ) for 1 929 to 1 96 1 , and rrom Congressional Budget Office ( 1997a, Table F-4) since 1 962. We convert these numbers from a fiscal-year basis to a calendar-year basis. Note that the deficit does not equal the annual change in federal debt. Roughly speaking, the change in debt reflects the government's cash outlays and receipts, while the unified deficit involves a limited amount of capital budgeting. We return to this issue below.

D. W Elmendoif and N.G. Mankiw

1 620

Table 1 Debt and deficits in industrialized countries in 1 996, in percent of GOP

a

Net debt

Budget surplus

USA

49

-2

Japan

14

-4

-4

Germany

48

-4

-1

France

39

-4

-1

1 12

-7

3

Country

Italy

Primary budget surplus

United Kingdom

44

--4

-1

Canada

70

-2

4

Australia

29

-1

0

Austria

51

--4

0

Belgium

1 27

-3

5

Denmark

46

-2

Finland

-8

-3

Greece

n.a.

Iceland

37

-2

Ireland

n.a.

-- 1

3

Korea

-22

4

4

48

-2

2

New Zealand

n.a.

3

4

Norway

-28

6

7

Portugal

n.a.

-4

Spain

53

-5

Sweden

26

-4

-1

TOTAL of these cotmtries

45

-3

0

Netherlands

-

7

-1

4

a

Data are from OECD ( 1 997, pages A33 , A35, and A38) and include all levels of government. "n.a." denotes not available.

2.2. Measurement issues The official US data on federal govermnent debt and deficits obscure a number of interesting and important issues iP assessing fiscal policy. We now discuss some of these measurement issues.

2.2. 1. Adjusting for economic conditions Official data on debt and deficits are often adjusted to reflect three economic variables: the price level, interest rates, and the business cycle. The adjustment for the price level

Ch. 25:

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occurs because the real value of the debt is, for many purposes, more important than the nominal value. For the level of the debt, the price-level adjustment is obvious: if D is the debt and P is the price level, then the real debt is DIP. For the deficit, however, the price-level adjustment is somewhat more subtle. It is natural to define the real deficit to be the change in the real value of the debt. In this case, the real deficit equals the nominal deficit (deflated by the price level) minus the inflation rate times the existing debt. That is, d(DIP)

dD/d t

dP/dt D

� - ---p - ---p -p· The inflation correction, which i s represented by the second term o n the right-hand side of this equation, can be large when inflation is high or the outstanding debt is large. Indeed, it can tum a nominal budget deficit into a real budget surplus. The second adjustment is for the level of interest rates. The adjustment arises because the market value of the debt may be more important than the par value. When interest rates rise, outstanding debt falls in value, and when interest rates fall, the opposite occurs; of course, a given rate change will cause debt with a longer maturity to be revalued more than shorter-term debt. The market value of US debt over time can be calculated using the data and procedures outlined in Seater ( 1 9 8 1 ), Butkiewicz ( 1 983), and Cox and Hirschhorn ( 1 983). The annual change in the market value can differ noticeably from the annual change in the par value, but the series follow the same broad trends. The third common adjustment to the budget deficit is for business cycle conditions. Because the deficit rises automatically when economic activity slows, and vice versa, the budget deficit in a given year may offer a misleading impression of underlying fiscal policy. The "standardized employment deficit" [Congressional Budget Office ( 1 997a)] eliminates the effects of the business cycle on the budget. This deficit is based on estimates of what spending and revenue would be if the economy were operating at normal levels of unemployment and capacity utilization. 2.2.2.

Assets and liabilities beyond the official debt

Debt held by the public is the largest explicit liability of the federal government, but it is not the only liability. Moreover, the federal government also holds significant assets. As emphasized by Eisner and Pieper ( 1 9 84) and Eisner ( 1 986), all of these assets and liabilities should be considered in any overall accounting of the government's financial situation. Unfortunately, it is quite difficult to assess the value of many government assets and liabilities. Some valuation problems are primarily technical. For example, a large share of the government's physical capital is defense-related, and many of these goods are not sold in (legal) markets. As another example, federal insurance of bank deposits may prove to be either very costly to the government or very inexpensive, and it is difficult to assess the probabilities of the alternative outcomes.

D. W Elmend01f and N G. Mankiw

1 622

Table 2 US federal government explicit assets and liabilities Category

a

Estimated value in 1 995 ($ billions)

Liabilities Debt held by the public (excluding the Federal Reserve)

3219

Federal pension liabilities

1513

Insurance liabilities Other

66 498

Assets Financial assets

576

Physical assets

1 737

Net liabilities

2983

a

Data are from Office of Management and Budget ( 1 996).

Other valuation problems are more conceptual. Do the future Social Security benefits specified by current law constitute a govemment liability in the same sense as explicit debt? The answer to this question depends at least partly on how the liability is perceived by households. If households believe that these benefits will be paid with the same probability that the explicit debt will be honored, then it may be sensible to count the present value of the benefits as government debt. In this specific case, the additional debt could be roughly three times the explicit debt, as Feldstein ( 1 996a) estimates the present value of Social Security benefits less taxes for current adults at roughly $ 1 1 trillion in 1 995. Similar questions arise for civil service and military retirement benefits, Medicare, and other entitlement programs. The important general point is that the appropriate measure of government indebtedness largely depends on people's behavior. As a result, deciding what measure of fiscal policy is best requires taking a stand on the correct model of economic behavior. Attempts to measure a range of explicit government assets and liabilities include the presentations of historical federal balance sheets by Eisner ( 1 986), Bohn ( 1 992), and Office of Management and Budget ( 1 996). OMB 's estimates for 1 995 are summarized in Table 2. The largest liabilities are debt held by the public (excluding the Federal Reserve) and expected pension liabilities for federal military and civilian employees. OMB also includes the expected cost of contingent liabilities that arise from loan guarantees and insurance programs. The federal government's financial assets include gold and loans owed to the government; its physical assets include both reproducible plant and equipment (about three-quarters of which relates to national defense) and non-reproducible capital such as land and mineral deposits. OMB does not include in these estimates the cost of future Social Security payments and other "continuing commitments", arguing that the appropriate way "to examine the balance between

Ch. 25:

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1 623

future Government obligations and resources is by projecting . . . total receipts and outlays" (p. 20). As it turns out, OMB estimates the government's assets to be worth roughly as much as its non-debt liabilities in 1 995, so net explicit liabilities are close to the value of debt. Indeed, net liabilities appear to have followed debt fairly closely in recent decades, despite sometimes significant differences in their annual changes. Debt increased by about $2.4 trillion between 1 97 5 and 1 995, while OMB estimates that liabilities rose about $2.6 trillion. Yet, these measures diverged sharply before 1 975. Bohn estimates that the net worth of the federal government was roughly the same share of GNP in 1 975 as in 1 947, as a dramatic decline in the debt share was offset by a drop in military assets and a rise in government employee pension obligations. 2.2.3.

Capital budgeting

One way to incorporate some government assets into the regular budget process is to create separate capital and operating budgets. In this way, current outlays would include not the acquisition of capital goods, but the depreciation of previously purchased capital. One effect of capital budgeting is that it would allow the government to spend money on capital assets without running an explicit deficit. Some observers view this situation as an inducement to profligate spending, particularly because it is difficult to decide exactly what constitutes capital, and many types of spending could acquire that label. For whatever reason, the US federal govermnent (unlike many state govermnents) does not rely on a capital budget as a central element of its budget process. Nevertheless, the principle of capital budgeting does affect budget numbers in two ways. First, the unified budget includes some specific kinds of capital budgeting. Since 1 992, for example, govermnent credit programs have been counted not in terms of their current outlays, but in terms of the present value of their expected future outlays. Thus, the deficit cost of a direct student loan is not the loan amount itself, but the net cost of providing the loan, taking into account the probability of default. Because the govermnent's cash outlays reflect the total amount of the loan, the increase in the debt exceeds the deficit. A similar pattern is repeated for some other fiscal activities where the budget amounts differ from the contemporaneous cash outlays or receipts 3 . Second, the federal budget as recorded in the National Income and Product Accounts does treat govermnent consumption and investment in physical capital differently 4 .

3 Formally, the change in debt equals the deficit less so-called "other means of financing". Much of this category consists of short-term differences between the deficit and borrowing needs, but some other means of financing (such as direct student loans) involve quite long-term divergences. 4 This treatment in the National Income and Product Accounts was introduced in 1 996. There are a number of other discrepancies between unified budget principles and NIPA budget principles. These include geographic differences, timing conventions, and some shifting of items between the revenue and expenditure sides of the budget.

D. W Elmendmj' and N G. Mankiw

1 624

Government consumption includes an estimate of the depreciation of government capital, and government purchases of new capital are tallied separately. The federal government's investment in physical capital is fairly modest, with gross investment less than 1 5% of consumption expenditures in 1 994.

2.2. 4.

Generational accounting

One prominent alternative to standard debt and deficit accounting is "generational accounting", proposed by Auerbach et al. ( 1 99 1 ) and Kotlikoff ( 1 992). These authors argue that the conventional deficit and explicit debt "simply reflect economically arbitrary labeling of government receipts and payments", so that the measured deficit "need bear no relationship to the underlying intergenerational stance of fiscal policy" ( p. 56). Generational accounts measure fiscal policy by its impact on different generations, not by the annual flows of spending and taxes. Generational accounts are constructed by extrapolating current policies through the lifetimes of all people currently alive, and calculating the net taxes they would pay under those policies. The net taxes of future generations are then set at a level which satisfies the government's intertemporal budget constraint. These calculations provide important information about how fiscal policy redistributes resources across generations. For example, most of the transfer from young to old during the postwar period occurred not in the 1 980s when measured deficits were high, but between the 1 95 0s and 1 970s when deficits were low but Social Security benefits were being enhanced. Nevertheless, generational accounts do suffer from some problems, as explored by Cutler ( 1 993) and Congressional Budget Office ( 1 995). One set of problems involves technical issues in constructing the accounts. For example, it is unclear what is the appropriate discount rate for future taxes, and different discount rates produce very different quantitative results. A second issue is whether the labelling of government receipts and payments truly is arbitrary. For instance, the methodology of generational accounting treats Social Security payments and interest payments on government debt as essentially equivalent. Yet it is surely easier for the government to reduce future Social Security benefits than to reduce future coupon payments on existing debt securities. The label "government debt" appears to have some true meaning. A final important problem springs from the fact that generational accounting is inextricably tied to a specific model of individual behavior. In particular, the methodology assumes that people are life-cycle consumers without a bequest motive, so that their behavior and well-being depend on their assessment of government policies over their entire lifetimes and only over their lifetimes. If individuals are liquidity-constrained or myopic, however, then their behavior and well-being may be more sensitive to current taxes than to the present value of the future taxes they expect to pay. Conversely, if individuals have altruistic bequest motives (a possibility we discuss extensively later), then their behavior and well-being will be sensitive to future

Ch. 25:

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1 625

taxes that will be paid by their descendants. In either case, generational accounts fail to provide a good gauge of fiscal policy for either positive or normative purposes. 2.3.

Future fiscal policy

Current patterns of taxes and spending are unsustainable in most indust1ialized countries over the next twenty-five years. The primary causes of this situation are the aging of their populations and the rising relative cost of medical care. Table 3 presents the elderly dependency ratio - defined as the population age 65 and over as a percentage of the population ages 20-64 for a number of countries. Between 1 990 and 2030, longer lifespans and continued low birthrates will sharply increase the ratio of retirees to working adults. The US population is projected to age less dramatically than the population of many other industrialized countries, but the increase in retirees per worker in the USA is still expected to exceed 50%. In most countries, health care has absorbed an increasing share of national income over the past several decades. The cost of producing most specific medical services may not have increased, but the cost of providing medical care that meets the social standard clearly has risen. Predicting future developments in this area is difficult, but most analysts expect the relative cost of medical care to continue to increase for some time. A large share of government outlays involves transfers from working adults to retirees or the financing of health care. (Of course, these categories overlap heavily.) Thus, the aging of the population and the increasing cost of health care will put a significant strain on government finances over the coming decades. Table 4 shows projections for the effect of population aging on various countries' budget surpluses and debts under the assumption that current tax and spending rules remain unchanged. The numbers show only the direct effect of aging, and ignore the problem of paying interest on the accumulating debt. The projections are highly uncertain as well . -

Table 3 Elderly dependency ratios " Country

1 990

2030

Japan

19

49

Gcm1any

24

54 43

France

23

Italy

24

52

United Kingdom

27

43

Canada

19

44

USA

21

36

a Data are from Congressional Budget Office ( l 997b)

.

1 626

D. W Elmendotj'and N. G. Mankiw

Table 4 Projected effect of population aging on fiscal conditions in industrialized countries, in percent of GDP ' Country

Primary budget surplus

Change in debt from 2000 to 2030

1 995

2030

USA

0.4

-3.8

44

Japan

-3.4

-8.7

1 90

Gem1any

-

0. 6

-6.6

45

France

- 1 .6

-4.5

62

3 .4

-5 9

1 09

-2.8

- 1 .4

27

1 .5

-1 .0

39

Italy United Kingdom Canada Australia

.

0.0

- 1 .4

37

Austria

-2.7

-7.7

171

Belgium

4.3

-0.5

42

Demnark Finland Iceland

2.0

-2.3

1 24

-4 .3

-8.8

213

-3.3

41

-

I I .

Ireland

1 .8

Netherlands

14

Norway Portugal

0.0

2

-

6 .0

1 42

3.2

-4. 7

135

0. 6

-

.

56 .

1 10

Spain

-1.1

-4.4

66

Sweden

-5. 1

-2.7

117

a Data are from Roseveare et al. (1 996) and refer only to the direct effect of population aging without incorporating the effect of higher interest payments on the larger outstanding debt. The primary budget surplus equals taxes less non-interest spending.

Nevertheless, they show a marked deterioration in the fiscal situation of almost every country. For the USA, Congressional Budget Office ( 1 997b) (CBO) has performed a careful analysis of the fiscal outlook. The analysis incorporates the need to pay interest on the accumulating debt, as well as the feedback between debt and the economy. Table 5 summarizes CBO 's results. Without economic feedbacks, government debt more than doubles as a share of output by 2030; including feedbacks, this share rises three-fold. A large part of this looming fiscal problem is the expected rise in future payments for Social Security and Medicare. Dealing with this long-term fiscal imbalance will likely be one of the most significant challenges facing policymakers during the next century.

Ch. 25:

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1 627

Table 5 CBO baseline projections for the US budget, in percent of GDP a Variable

1 995

2030

2050

Without economic feedbacks Primary deficit

-1

5

6

Interest payments

3

6

12

Total deficit

2

ll

18

50

1 25

267

·- I

5

n.a.

3

12

n.a.

Debt

With economic feedbacks Primary deficit Interest payments Total deficit Debt

2

17

n.a.

50

159

n.a.

a

Data are from Congressional Budget Office ( 1 997b) and assume that discretionary spending grows with the economy after 2007. "n.a." signifies that the values were too extreme to be reported by CBO.

3. The conventional view of debt

In this section we present what we believe to be the conventional view of the effects of government debt on the economy. We begin with a qualitative description of those effects, focusing on the impact of debt on saving and capital formation, and thereby on output and income, on factor prices and the distribution of income, and on the exchange rate and foreign transactions. We also review some other economic and non-economic consequences of government borrowing. Following our qualitative analysis, we try to quantify some of the long-run effects of debt in a very rough way. Although quantifying these effects precisely is an arduous task, we think it important to have some quantitative sense of what is at stake. Therefore, we present a ballpark estimate of the impact of debt, which is interesting in itself and also illuminates some of the critical assumptions underlying all quantitative analyses of government debt. Our analysis assumes that government spending on goods and services is not affected by debt policy. That is, we examine the effects of issuing a given amount of debt and reducing taxes temporarily by an equal amount. Because the government must satisfy an intertemporal budget constraint, and because debt cannot grow forever as a share of income, this temporary tax reduction will generally be accompanied by a future tax increase. For most of this section, we simply assume that the present value of that tax increase equals the current increase in debt. We defer more careful consideration of the budget constraint to the last part of the section, where we re-examine the effects of debt in a world with uncertainty. The analysis also assumes, except where stated otherwise, that monetary policy is unaffected by debt policy. By

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D. W Elmendorf and N G. Mankiw

excluding possible monetization of the debt, we can couch our discussion in real, rather than nominal, terms. 3. 1 .

How does debt affect the economy?

The government's debt policy has important influence over the economy both in the short run and in the long run. We begin by discussing the short-run effects of budget deficits. We then turn to the long-run effects, of which the most important is a reduction in national wealth. In particular, we explain both how deficits affect national saving and how the change in saving affects many aspects of the economy. We also consider several other long-run effects of government debt.

3. 1 . 1. The short run: increased demandfor output Suppose that the government creates a budget deficit by holding spending constant and reducing tax revenue. This policy raises households' current disposable income and, perhaps, their lifetime wealth as well. Conventional analysis presumes that the increases in income and wealth boost household spending on consumption goods and, thus, the aggregate demand for goods and services. How does this shift in aggregate demand affect the economy? According to conventional analysis, the economy is Keynesian in the short nm, so the increase in aggregate demand raises national income. That is, because of sticky wages, sticky prices, or temporary misperceptions, shifts in aggregate demand affect the utilization of the economy's factors of production. This Keynesian analysis provides a common justification for the policy of cutting taxes or increasing government spending (and thereby running budget deficits) when the economy is faced with a possible recession. Conventional analysis also posits, however, that the economy is classical in the long run . The sticky wages, sticky prices, or temporary misperceptions that make aggregate demand matter in the short run are less important in the long run. As a result, fiscal policy affects national income only by changing the supply ofthe factors of production. The mechanism through which this occurs is our next topic. 3. 1.2.

The long run: reduced national saving and its consequences

To understand the effect of government debt and deficits, it is crucial to keep in mind several national accounting identities. Let Y denote national income, C private consumption, S private saving, and T taxes less government transfer payments. The private sector's budget constraint implies that:

Y = C + S + T. National income also equals national output, which can be divided into four types of spending:

Y = C + i + G + NX,

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where I is domestic investment, G is government purchases of goods and services, and NX is net exports of goods and services. Combining these identities yields:

S + (T - G) = I + NX. This identity states that the sum of private and public saving must equal the sum of investment and net exports. The next important identity is that a nation's current account balance must equal the negative of its capital account balance. The current account balance is defined as net exports NX plus net investment income by domestic residents and net transfers; for the most part, we ignore these last two, smaller pieces. The negative of the capital account balance is called net foreign investment, or NFI, which is investment by domestic residents in other countries less domestic investment undertaken by foreign residents. Thus, the third identity is simply:

NX = NFI, so that international flows of goods and services must be matched by international flows of funds. Substituting this identity into the other two identities yields:

S + ( T - G) I + NFI. =

The left side of this equation shows national saving as the sum of private and public saving, and the right side shows the uses of these saved funds for investment at home and abroad. This identity can be viewed as describing the two sides in the market for loanable funds. Now suppose that the government holds spending constant and reduces tax revenue, thereby creating a budget deficit and decreasing public saving. This identity may continue to be satisfied in several complementary ways: private saving may rise, domestic investment may decline, and net foreign investment may decline. We consider each of these possibilities in turn. To start, an increase in private saving may ensue for a number of reasons that we discuss below. In fact, some economists have argued that private saving will rise exactly as much as public saving falls, and the next section of the paper examines this case at length. For now, we adopt the conventional view that private saving rises by less than public saving falls, so that national saving declines. In this case, total investment - at home and abroad - must decline as well. Reduced domestic investment over a period of time will result in a smaller domestic capital stock, which in turn implies lower output and income. With less capital available, the marginal product of capital will be higher, raising the interest rate and the return earned by each unit of capital. At the same time, labor productivity would be lower, thereby reducing the average real wage and total labor income. Reduced net foreign investment over a period of time means that domestic residents will own less capital abroad (or that foreign residents will own more domestic capital).

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D. W Elmendoif and N. G. Mankiw

In either case, the capital income of domestic residents will fall. Moreover, the decline in net foreign investment must be matched by a decline in net exports, which constitutes an increase in the trade deficit of goods and services. As this connection between the budget deficit and the trade deficit became better known in the USA during the 1 980s, it led to the popular term "twin deficits". Pushing the trade balance into deficit generally requires an appreciation of the currency, which makes domestically­ produced goods relatively more expensive than foreign-produced goods 5 . 3. 1 . 3.

Other effects

Although increasing aggregate demand in the short run and reducing the capital stock in the long run are probably the most important effects of government budget deficits, debt policy also affects the economy in various other ways. We describe several of these effects here. First, government debt can affect monetary policy. A country with a large debt is likely to face high interest rates, and the monetary authority may be pressured to try to reduce those rates through expansionary policy. This strategy may reduce interest rates in the short run, but in the long run will leave real interest rates roughly unchanged and inflation and nominal interest rates higher. In the USA, at least in recent years, monetary policy has apparently not responded to fiscal policy in this way. For example, the US debt-income ratio rose sharply during the 1 980s, and the US inflation rate declined sharply. Nevertheless, successive Chairmen of the Federal Reserve Board have warned of the possible link between the budget deficit and inflation 6. In extreme cases, a country with a large debt may have difficulty financing an ongoing deficit through additional borrowing and, as a result, will be tempted to raise revenue through seigniorage. If the fiscal authority can force the monetary authority to finance ongoing deficits with seigniorage, then, as Sargent and Wallace ( 1 98 1 ) argue, inflation i s ultimately a fiscal phenomenon rather than a monetary one 7 . This

5

For more complete analyses of the international effects of debt, see Frenkel and Razin ( 1 992, drs. 7, 8, 1 0 and 1 1) and Obstfeld and Rogoff ( l 996, ch. 3). 6 Paul Volcker told .Congress in 1 985 that "the aetna! and prospective size of the budget deficit . heightens skepticism about our ability to control the money supply and contain inflation" (p. I 0). Alan Greenspan said in 1 995 that he expected that "a substantial reduction iu the long-term prospective deficit of the United States will significantly lower very long-term inflation expectations vis-a-vis other countries" (p. 141). Woodford ( 1 995) proposes an alternative "fiscal theory of the price level", based on the effect of prices on the real value of government debt and thus on aggregate demand. Woodford considers an economy of infinitely-lived households, and hypothesizes an increase in goverrunent debt with no offsetting change in future taxes or spending. This policy makes households wealthier and increases aggregate demand. If aggregate supply is unchanged, both goods-market equilibrium and the government's budget constraint require that the price level increases enough to reduce real debt to its initial value. The mechanism is quite similar to the Pigou-Patinkin ( 1 965) real-balance effect, except that it allows for households that appear to be Ricardian, and it involves total government liabilities rather than just outside money. In

7

Ch. 25:

Government Debt

1 63 1

monetization of the debt i s the classic explanation for hyperinflation. For example, staggering budget deficits as a share of national income were the root cause of hyperinflations in 1 920s Germany and 1 980s Bolivia. As Sargent ( 1 983) explains, inflation can fall sharply in such a country when government borrowing is reduced and the central bank commits not to finance future deficits. Yet, this line of reasoning is not very important for most developed countries today, as seigniorage represents a very small share of total government revenue 8 . A second effect o f government debt is the deadweight loss o f the taxes needed to service that debt. The debt-service payments themselves are not a cost to a society as a whole, but, leaving aside any payments to foreigners, merely a transfer among members of the society. Yet effecting that transfer in a world without lump-sum taxes will create some distortion of individual behavior that generates a deadweight loss. Thus, a policy of reducing taxes and running a budget deficit means smaller deadweight losses as the debt is being accumulated but larger deadweight losses when the debt is being serviced with higher taxes. A third effect of government debt is to alter the political process that determines fiscal policy. Some economists have argued that the possibility of government borrowing reduces the discipline of the budget process. When additional government spending does not need to be matched by additional tax revenue, policymakers and the public will generally worry less about whether the additional spending is appropriate. This argument dates back at least to Wicksell ( 1 896), and has been echoed over the years by Musgrave ( 1 959), Buchanan and Wagner ( 1 977), and Feldstein ( 1 995) among others. Wicksell claimed that if the benefit of some type of government spending exceeded its cost, it should be possible to finance that spending in a way that would receive unanimous support from the voters; he concluded that the government should only undertake a course of spending and taxes that did receive nearly unanimous approval. In the case of deficit finance, Wicksell was concerned that "the interests [of future taxpayers] are not represented at all or are represented inadequately in the tax-approving assembly" ( p . 1 06). Musgrave noted that when budget balance is altered for stabilization purposes, "the function of taxes as an index of opportunity cost [of government spending] is impaired" (p. 522). Buchanan and Wagner asserted that a balanced-budget rule "will have the effect of bringing the real costs of public outlays to the awareness of decision makers; it will tend to dispel the illusory ' something for nothing' aspects of fiscal choice" ( p . 1 78). And Feldstein wrote that "only the 'hard budget constraint' of having to balance the budget" can force politicians to judge whether spending's "benefits really j ustify its costs" (p. 405). It is also possible that the existence of government debt reduces the fiscal flexibility of the government. If moderate levels of debt have only small negative effects, but contrast to the Sargent-Wallace analysis, Woodford's point does not depend on any particular response by the monetary authority to changes in fiscal policy. 8 For further analysis of the connections between fiscal policy and monetary policy, see Aiyagari and Gertler ( 1985), Leeper ( 1 991), McCallum ( 1984), and Sims ( 1 994).

D. W. Elmendorf and N.G. Mankiw

1 632

larger debts are perceived to be quite costly, then a country with a moderate debt will be constrained from responding to calls for greater spending or lower taxes. This constraint on future policymakers is, in fact, one of the explanations sometimes given for why governments choose to accumulate large debts. A fourth way in which government debt could affect the economy is by making it more vulnerable to a crisis of international confidence. The Economist (4/1195) noted that international investors have worried about high debt levels "since King Edward III of England defaulted on his debt to Italian bankers in 1 33 5" (p. 59). During the early 1 980s, the large US budget deficit induced a significant inflow of foreign capital and greatly increased the value of the dollar. Marris ( 1 985) argued that foreign investors would soon lose confidence in dollar-denominated assets, and the ensuing capital flight would sharply depreciate the dollar and produce severe macroeconomic problems in the USA. As Krugman ( 1 9 9 1 ) described, the dollar did indeed fall sharply in value in the late 1 980s, but the predicted "hard landing" for the US economy did not result. Krugman emphasized, however, that currency crises of this sort have occurred in countries with higher debt-output ratios, particularly when much of that debt is held by foreigners, as in many Latin American countries in the 1 980s. A fifth effect of government debt is the danger of diminished political independence or international leadership. As with the danger of a hard landing, this problem is more likely to arise when government borrowing is large relative to private saving and when the country experiences a large capital inflow from abroad. Friedman ( 1 988) asserted: "World power and influence have historically accrued to creditor countries. It is not coincidental that America emerged as a world power simultaneously with our transition from a debtor nation . . . to a creditor supplying investment capital to the rest of the world" (p. 1 3). 3.2.

How large is the long-run ejjixt of debt on the economy?

So far we have described the effects of government debt in qualitative terms. We now present rough quantitative estimates of some of these effects. We begin with an extremely simple calculation of the effect on national income of a reduced capital stock, and we then explore the sensitivity of our results to three key assumptions. Our ballpark estimate is, in fact, broadly consistent with the few other quantitative analyses in the literature. We also note the magnitude of the deadweight loss caused by the taxes needed to finance the debt service. We calibrate our calculations for the US economy, but the approach is applicable to other countries as well. 3.2. 1.

The parable of the debt fairy

As we have discussed, a primary effect of government debt is the crowding out of capital and the consequences that result from this crowding out. How large are these effects? To answer this question, consider the parable offered by Ball and Mankiw ( 1 995). Imagine that one night a debt fairy (a cousin of the celebrated tooth fairy)

Ch.

25:

Government Debt

1 633

were to travel around the economy and replace every government bond with a piece of capital of equivalent value. How different would the economy be the next morning when everyone woke up? It is straightforward to calculate the effect of this addition to the capital stock. If factors of production earn their marginal product, then the marginal product of capital equals the capital share of income (MPK x KIY) divided by the capital-output ratio (K/Y). In the USA between 1 960 and 1 994, the gross return to capital was roughly one­ third of income, and the capital-output ratio averaged a little over three 9. The implied marginal product of capital is about 9.5%. More precisely, this figure represents the gross marginal product; it shows how much an extra dollar of capital adds to gross output and income. If the country wants to maintain that dollar of capital, however, then it needs to do replacement investment to offset depreciation. Depreciation amounts to roughly 3 . 5% of capital, so the net marginal product of capital is about 6%. In other words, each dollar of capital raises gross national product by 9.5 cents and net national product by 6 cents. When the debt fairy magically reverses the effects of crowding out, the amount of capital increases by the amount of federal government debt, which in the USA is about one-half of gross output. Our estimates of the marginal product of capital imply that gross output would be increased by about 4.75%, and net output by about 3% 1 0 In 1 997, these increases amount to about $400 billion and $250 billion, respectively. The story of the debt fairy is appealing because it offers a simple way to calculate the effects of government debt on national income. But is this calculation realistic? The debt-fairy calculation implicitly makes three assumptions: ( 1) Deficits do not affect private saving, so debt crowds out other forms of private wealth one for one. (2) The economy is closed, so crowding out takes the form of a reduced capital stock. (3) The profit rate measures the marginal product of capital, so it can be used to gauge the effects of a change in the capital stock.

9 These data are drawn from the National Income and Product Accmmts of the Commerce Department's Bureau of Economic Analysis (BEA). Net capital income is the sum of corporate profits, rental income, net interest, and a share of proprietors' income (all with appropriate adjustments for inventory valuation and capital consumption). Gross capital income equals net income plus depreciation. We use national income plus depreciation as the measure of total output and income. The capital stock is BEA's net stock of fixed reproducible tangible wealth excluding consumer durables. Including the value of inventories and land in the measure of capital would depress the estimated return on capital. On the other hand, Feldstein et a!. ( 1983) note that "pre-tax" corporate profits in the national income accounts actually represent profits afier the payment of state and local property taxes; adding these taxes back into profits would raise the estimated rates of return. Finally, some authors measure the benefit of additional saving by the return to nonfinancial corporate capital. Because corporate capital is more heavily taxed than other capital, it cams a higher pre-tax return. Yet, there is no reason to assume that any addition to the capital stock would flow disproportionately to corporations. 10 The actual effect of adding this much capital would be somewhat smaller, because the marginal product would decline as the capital stock increased.

1 634

D. W Elmendorf and N G. Mankiw

Let us consider how relaxing each of these assumptions might alter the conclusion that current US government debt reduces US national income by about 3%. 3.2.2.

A closer look at the ejj(xt of debt on private savings

The debt fairy replaces each dollar of government debt with one dollar of capital. Is this dollar-for-dollar substitution appropriate? More concretely, if the US government had run sufficient surpluses during the past twenty years to reduce its debt to zero, would national wealth now be larger by the amount of the actual current debt? In actuality, an increased flow of government borrowing will affect the flow of private saving through several channels. First, private saving will rise because some households will save part of the tax reduction to consume later in life. Second, forward­ looking consumers will realize that the increasing debt will force higher future interest payments by the government and, thus, higher future taxes. Third, greater government borrowing will affect interest rates and wages, and these general-equilibrium effects in turn will affect private saving. Fourth, the government's debt policy may affect distortionary capital taxes, which in turn affect private saving. For all of these reasons, the size of the budget deficit affects the amount of private saving. Understanding the long-run effect of debt on capital therefore requires a formal, general equilibrium model, with particular attention paid to household saving behavior. Conventional analysis focuses on models with overlapping generations of life-cycle consumers introduced by Samuelson ( 1 958) and Diamond ( 1 965). Because this model incorporates people at different stages of their life-cycle who differ in both their level of wealth and marginal propensity to consume out of wealth, aggregation is often difficult in realistic models with more than two generations. Blanchard ( 1 985) resolves this problem by making assumptions about the aging process that simplify aggregation analytically. Auerbach and Kotlikoff ( 1 987) and other researchers resolve this problem by simulating a more complicated model numerically. Before turning to the results from these well-known analyses, however, it is instructive to examine a simple, stylized example. Consider an economy in which every person lives for a fixed number of periods. Assume that the interest rate is given (either because this is a small open economy or because the technology is linear in capital and labor). Also assume that the consumers choose the same level of consumption in each period of life (either because their rate of time preference happens to equal the interest rate or because they have Leontief preferences). Now consider how an increase in government debt affects the steady state. Higher debt means higher interest payments and higher taxes. If those taxes are distributed equally across people of different ages, then each person 's after-tax income is reduced by the amount of those interest payments ( per capita) in each period. Because consumers still want to smooth consumption, they respond to this higher tax burden by reducing consumption in each period by the same amount. As a result, after-tax income and consumption fall equally, private saving is unchanged, and private wealth is unchanged. Each dollar of debt crowds out exactly one dollar of capital, as assumed by the debt fairy parable.

Ch. 25:

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1 635

To see what happens when various assumptions are relaxed, we turn to the Blanchard and Auerbach-Kotlikoff analyses. Blanchard develops a continuous-time overlapping­ generations model in which people have log utility and face a fixed probability of dying in each period. He examines the effect of accumulating additional government debt and then holding debt at its new level forever. To establish notation, let D denote debt and W denote national wealth (domestic capital plus net foreign assets), so private wealth equals D + W. For a small open economy, Blanchard confirms the result from our simple example: steady-state dW/dD equals - 1 if the rate of time preference equals the world interest rate. If the world interest rate and the rate of time preference differ, crowding out may be larger or smaller than one for one 1 1 . Matters become more complicated in a closed economy. In this case, as capital is crowded out, the interest rate rises, and households are encouraged to save. As a result, the absolute value of dW/dD is smaller in a closed economy than in an open economy 12 . Calculations using the Blanchard model indicate that the difference between open and closed economies is substantial, but this result appears highly sensitive to the assumption of log utility, according to which households are very willing to substitute consumption between periods in response to a higher interest rate. Most research in the consumption literature suggests a much smaller intertemporal elasticity of substitution than unity 1 3 . Auerbach and Kotlikoff ( 1 987) construct a large-scale general equilibrium model, and simulate the model to examine the effects of alternative debt, tax, and Social Security policies. The numerical simulations reveal not only the steady-state changes in capital and other variables, but also the transition path to the new steady state. The model assumes that people have an economic lifetime of 55 years, have perfect foresight about future economic conditions, and make rational choices regarding their consumption and labor supply. The government raises funds through distortionary taxes and satisfies an intertemporal budget constraint. A production function for net output 1

1

Let p be the probability of dying in each period or, as suggested by Blanchard and Summers ( 1 984), a "myopia coefficient" that reflects mortality or myopia. Let r equal the world interest rate and e the rate of time preference. Then Blanchard reports that dW

dD

12

= -__E__ � p + r p + l:i - r

Blanchard and Fischer (1 989, p. 1 3 1) report that, in the steady state, dK

dD

(p

+

p(p + 1:1) r)(p + 8 - r) - f'ii(; •

where K is the capital stock, C is consumption, and F is the aggregate net production ftmction. 13 For attempts to usc variants of the Blanchard model to estimate the cost of various debt policies, see Romer ( 1 988) and Evans (1991).

D. W Elmendmfand N. G. Manldw

1 636

completes the model, which describes a closed economy. Auerbach and Kotlikoff choose values for the key parameters based on the empirical literature. Note, in particular, that they assume that the intertemporal elasticity of substitution is 0.25. Auerbach and Kotlikoff examine the effect of reducing taxes and accumulating debt over a certain number of years, and then boosting taxes to hold the debt at its new per capita level forever. This debt policy reduces saving and capital by transferring resources from younger and future generations, who have a low or zero marginal propensity to consume, to older generations, who have a high marginal propensity to consume. Capital is also diminished by the higher rate of distortionary income taxes in the long run, although the initial reduction in the tax rate can actually crowd-in capital in the short run. Auerbach and Kotlikoff analyze deficits equal to 5% of output that last for one year, 5 years, and 20 years; they do not report the resulting levels of debt, but these can be calculated approximately based on the size of the deficits and the interest rate. For all three experiments, the decline in capital appears to be extremely close to the increase in debt 1 4. We conclude this discussion by emphasizing that the short-run effect o f a budget deficit on consumption and saving is a poor guide to the long-run effect of debt on national wealth. In a model with life-cycle consumers, govemment debt may have only a small short-run effect, as confirmed by Blanchard (who finds that initial saving adjusts by only several percent of a change in debt) and Auerbach and Kotlikoff (who find that at the end of a 20-year tax cut, the capital stock is reduced by only one­ fifth of its eventual decline). Nonetheless, debt has a much larger effect on life-cycle consumers in the long run. Auerbach and Kotlikoff's closed-economy model shows approximately one-for-one crowding out; Blanchard's formulas suggest smaller effects in a closed economy but roughly one-for-one crowding out in an open economy. On balance, the debt fairy's one-for-one substitution of capital for debt may be on the high side of the truth, but it seems a reasonable approximation. 3.2.3.

A closer look at international capital flows

When the debt fairy changes government debt into national wealth, the increment to national wealth is assumed to take the form of domestic capital, with no change in net ownership of foreign assets. This is clearly not a realistic description of an open economy. Yet, altemative assumptions about intemational capital flows would have little effect on the estimated impact of government debt. In actuality, net international capital flows are fairly small. Feldstein and Horioka ( 1 980) examined five-year averages of domestic investment and saving across countries and found these two variables moved almost exactly one for one with each other. More recent estimates suggest that the strength of this relationship declined somewhat in 1 4 The increases in debt fi"om the three alternative policies are roughly 5, 30 and 200% of output. The corresponding declines in the capital stock are 5, 29 and 1 82% of output.

Ch. 25:

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the 1 980s. Nonetheless, these estimates indicate about 75% of a long-term change in national saving adds to domestic investment and only 25% goes to investment abroad 1 5. Because many countries allow capital to move freely across their borders, i t is surprising that net international capital flows are not larger in the long run. The literature has considered many possible explanations 1 6 . For our purposes, though, the key point is that the existence of international capital flows - or the lack of such :flows has little impact on the ultimate cost of government debt. Suppose that the debt fairy transformed each dollar of reduced debt into an extra dollar of net foreign assets, rather than an extra dollar of domestic capital. In this case, which is the extreme opposite of our original assumption, the debt reduction would not raise domestic output at all. Instead, it would raise foreign output, and some of that output would flow back to this country as the return on our additional overseas assets. As long as the return to wealth is the same at home and abroad, the location of the extra wealth does not affect our income. Another way to understand this point is to note the distinction between domestic income and national income. Domestic income is the value of production occurring within a nation's borders; this is identically equal to domestic output or GDP. Tomorrow's domestic output and income depend on today's domestic investment. But the consumption of domestic residents depends on their income, which is the value of production accruing to a nation's residents. This is called national income, and it is identically equal to national output or GNP. Tomorrow's national output and income depend on today's national saving, wherever this saving is ultimately invested. Naturally, this strong statement requires several caveats. First, the statement ignores the tax implications of the location of capital. Governments receive a higher effective tax rate on capital located in their countries than on capital owned by their residents but located abroad. Thus, the social return to domestic investment is higher than the social return to foreign investment, even if the private (after-tax) returns are the same. Second, additional capital accumulation does not reduce the marginal product of capital as quickly if the capital can flow abroad. As we saw in our earlier discussion of the Blanchard model, the effect of debt on the capital stock is reduced if changes in the capital stock affect the interest rate and thereby private saving. Third, the location of nationally-owned capital does affect the distribution of income. If the domestic capital stock increases, so does the wage, while the return to capital and the interest rate fall; domestic workers benefit and owners of domestic capital are

15

.

See Feldstein and Bacchetta ( 1991) and Dornbusch ( 1 991 ) Frankel ( 1 99 1 ), Mussa and Goldstein ( 1 993), and Gordon and Bovenberg ( 1 996) review the evidence regarding international capital mobility and discuss a number of explanations for the observed immobility. For a recent attempt to explain the Fcldstein�Horioka puzzle within the context of neoclassical growth theory, see Barro et al. ( 1 995). 16

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hurt 1 7 . An increase in the ownership of capital located abroad does not have these effects. Fourth, international capital flows change the composition of domestic production. If a smaller deficit raises net foreign investment, then net exports will rise, while if it increases only domestic investment, then of course investment spending will rise. Moreover, the budget deficit affects the exchange rate if there are significant international capital flows, but not otherwise. On balance, it seems that the issuance of government debt has only a small effect on international capital flows in the long run and that those flows have only a small effect on the return to extra saving. Acknowledging the openness of the economy, therefore, does not substantially alter the estimated impact of govemment debt. 3.2. 4. A

closer look at the marginal product of capital

In describing the impact of the debt fairy, we calculated the marginal product of capital using the capital share of national income and the capital-output ratio. This calculation was based on the standard premise that the factors of production, including capital, are paid their marginal product. Now we reconsider whether that calculation was appropriate. In recent years, there has been a wave of research that proposes a new view of capital. As Mankiw ( 1 995) discusses, a variety of empirical problems with the basic neoclassical growth model would be resolved if the true capital share in the production function is much larger than the one-third measured from the national income accounts. One reason that the true capital share might be larger than the raw data suggest is that capital may have significant externalities, as argued by Romer ( 1 986, 1 987). If the social marginal product of capital is well above the private marginal product that we observe, then reducing government debt and raising the capital stock would have much larger effects than the debt fairy parable suggests. Another possible reason for a large capital share is that the correct measure of capital includes human capital, such as education and training, as well as tangible physical capital, like plant and equipment. Mankiw et al. ( 1 992) propose an extension of the basic Solow ( 1 956) model in which there are fixed saving rates for both physical capital and human capital. They show that cross-country data are consistent with this model and an aggregate production function of the form Y K 1 13 H 113L 113 . If the share of income devoted to human-capital accumulation is unchanged by debt policy, then the reduction in income caused by the crowding out of physical capital will also reduce the stock of human capital; in this case, govemment debt reduces income substantially more than our earlier calculation indicated. By contrast, if the stock of human capital remained fixed, then our earlier calculation would be correct. =

17 Because some owners of domestic capital are foreigners, this shift actually raises national income slightly.

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The deadweight loss of servicing the debt

When discussing the qualitative effects of debt, we reviewed a number of issues beyond the impact of debt on the capital stock. The only one of those effects that is readily quantifiable is the deadweight loss of the additional taxes needed to meet the debt service burden 18. Of course, the deadweight loss of taxation was reduced during the period when taxes were lower and the debt was accumulated, and optimal debt policy requires balancing these effects. Our concern here, however, is just with the cost of an ongoing debt. If the government builds up a certain debt, and then decides to hold that debt constant in real terms, the additional debt service per dollar of accumulated debt is r, the real interest rate on debt. If A is the deadweight loss per dollar of tax revenue, then the loss per dollar of debt is Ar. The total real return on intermediate-maturity government debt averaged about 2% between 1 926 and 1 994 (Stocks, Bonds, Bills and Inflation, 1 995). A standard choice for A is Ballard, Shoven and Whalley's ( 1 985) estimate of one-third, although Feldstein ( 1 996b) argues that incorporating distortions to the form of compensation and the demand for deductions - in addition to the usual distortions to labor and capital supply - makes the true A much larger. If A equals one­ half, then Ar = 0.0 1 , and with the US debt-income ratio at one-half, the deadweight loss from servicing the debt is about half a percent of output. 3.2. 6.

Summary

As concern about current and prospective US budget deficits has grown, quantitative estimates of the effect of debt have begun to appear in official US government documents. For example, in the 1 994 Economic Report of the President ( pp. 8587), the Council of Economic Advisers assumed that the President's deficit-reduction plan would boost national saving by 1 % of output each year for 50 years. Then the Report used a simple Solow growth model to show the effect of that extra saving on the economy. It concluded that the additional saving would eventually raise output by 3.75%. More recently, the Congressional Budget Office ( 1 997b) constructed a complex model of the economy and the federal budget and simulated the model through the year 2050. Because current law would produce an explosive rise in the national debt over that period, CBO 's results do not reflect steady-state effects. In the simulation that includes the economic effects of increasing debt, debt rises by 30% of output by 2020, resulting in output that is 2% smaller than it otherwise would be. Over the following decade, debt increases by another 80% of output, and output is diminished by more than 8% relative to the same baseline. Thus, these calculations are similar in spirit to those found in the academic literature. 1 x Auerbach and Kothkoff's ( 1 987) estimates of the welfare effects of debt policy include th.i.s cost, but isolating its significance from their published results is not possible.

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We have now quantified, in a very rough way, some long-run effects of government debt on the economy. The debt fairy parable implied that each dollar of debt reduces net output by about 6 cents each year. More careful consideration of the strong assumptions embodied in that parable suggested that this estimated cost is at least in the right ballpark. The deadweight loss from the taxes needed to service the debt adds about another one cent per dollar of debt. Thus, the US debt of the late 1 990s, which equals about half of annual output, is reducing net output by about 3 .5%. In 1 997, this amounts to around $300 billion per year. Is this cost large? Labor productivity has increased by about one percent per year in the USA since 1 97 5, so reducing output by three to four percent is like giving up three to four years of productivity growth. That is a significant loss, but it does not qualify as a disaster. One final comparison of the cost of the current debt is with the effect of the upcoming demographic transition in the USA. Congressional Budget Office ( 1 997b) projects that, under current law, population aging and rising health care costs will boost non-interest spending of the federal government by five percent of output between 1 996 and 2025. If the current debt were maintained in real terms, it would represent about one-third of real output in 2025 (because of economic growth). Thus, eliminating that debt would add about two percent to national income, or almost half of the extra income needed to cover the additional government spending. 4. Ricardian equivalence

So far our discussion has focused on the conventional analysis of government debt. By "conventional", we mean that this analysis describes the views held by most economists and almost all policymakers. There is, however, another view of government debt that has been influential in the academic debate, even if endorsed by only a minority of economists. That view is called Ricardian equivalence after the great 1 9th century economist David Ricardo, who first noted the theoretical argument. In recent years, the Ricardian view has been closely associated with Robert Barro, whose work has given the view renewed vigor and prominence. 4. 1.

The idea and its history

Ricardian equivalence is a type of neutrality proposition: it states that a certain type of government policy does not have any important effects. In this section we discuss the general idea, its history, and its importance as a theoretical benchmark. In the following sections we examine the various dimensions of the debate over the validity of Ricardian equivalence as a description of the real world. 4. 1. 1.

The essence of the Ricardian argument

S uppose that the government cuts taxes today without any plans to reduce government purchases today or in the future. As we have seen, conventional analysis concludes

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that this policy will stimulate consumption, reduce national saving and capital accumulation, and thereby depress long-term economic growth. By contrast, the theory of Ricardian equivalence asserts that this policy will not alter consumption, capital accumulation, or growth. The situation with the tax cut and budget deficit is equivalent to the situation without it. The Ricardian argument is based on the insight that lower taxes and a budget deficit today require (in the absence of any change in government purchases) higher taxes in the future. Thus, the issuing of government debt to finance a tax cut represents not a reduction in the tax burden but merely a postponement of it. If consumers are sufficiently forward looking, they will look ahead to the future taxes implied by government debt. Understanding that their total tax burden is unchanged, they will not respond to the tax cut by increasing consumption. Instead, they will save the entire tax cut to meet the upcoming tax liability; as a result, the decrease in public saving (the budget deficit) will coincide with an increase in private saving of precisely the same size. National saving will stay the same, as will all other macroeconomic variables. In essence, the Ricardian argument combines two fundamental ideas: the govern­ ment budget constraint and the permanent income hypothesis. The government budget constraint says that lower taxes today imply higher taxes in the future if government purchases are unchanged; the present value of the tax burden is invariant to the path of the tax burden. The permanent income hypothesis says that households base their consumption decisions on permanent income, which depends on the present value of after-tax earnings. Because a debt-financed tax cut alters the path of the tax burden but not its present value, it does not alter permanent income or consumption. Thus, all of the predictions of the conventional analysis of government debt no longer hold. Another way to view the Ricardian argument is suggested by the title of Robert Barra's classic 1 974 paper "Are Government Bonds Net Wealth?" To the owners of government bonds, the bond represents an asset. But to taxpayers, government bonds represents a liability. A debt-financed tax cut is like a gift of government bonds to those getting the tax cut. This gift makes the holder of the bond wealthier, but it makes taxpayers poorer. On net, no wealth has been created. Because households in total are no richer than they were, they should not alter their consumption in response to the tax cut. It is important to emphasize that the Ricardian argument does not render all fiscal policy irrelevant. If the government cuts taxes today and households expect this tax cut to be met with future cuts in government purchases, then households' permanent income does rise, which stimulates consumption and reduces national saving. But note that it is the expected cut in government purchases, rather than the tax cut, that stimulates consumption. The reduction in expected future government purchases would alter permanent income and consumption because they imply lower taxes at some time, even if current taxes are unchanged. Because the Ricardian view renders some fiscal policies irrelevant but allows other fiscal policies to matter, providing a convincing test of this view has proven difficult. For example, in the early 1 980s, a debt-financed tax cut advocated by President Reagan

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in his first administration was followed by a substantial rise in government debt and a fall in national saving. Some observers, such as Benjamin Friedman ( 1 992), see this episode as a natural experiment that decisively rejects Ricardian equivalence. Yet it is possible that consumers expected this tax cut to mean smaller government in the future; smaller government was, in fact, President Reagan's intention, and to some extent it has been the result. Moreover, other developments, such as a booming stock market, occurred at the same time and surely had some effect on household decisions. In this case, higher consumption and lower national saving could coincide with a tax cut without contradicting Ricardian equivalence. Because neither interpretation of history can be ruled out, both the conventional and Ricardian views of government debt continue to have adherents within the economics profession. 4. 1.2.

A brief history of the Ricardian idea

The modern literature on Ricardian equivalence began with Robert Barra's 1 974 paper. Not only did thi s paper clearly set out the Ricardian argument but it also anticipated much of the subsequent literature by discussing many of the reasons why Ricardian equivalence might not hold. What the paper did not do, however, was credit Ricardo with the idea. It was not until James Buchanan's 1 976 comment on Barra's paper that the term Ricardian equivalence was coined. Ricardo was interested in the question of how a war might be funded. In an 1 820 article, he considered an example of a war that cost 20 million pounds. He noted that if the interest rate were 5%, this expense could be financed with a one-time tax of 20 million pounds, a perpetual tax of 1 million pounds, or a tax of 1 .2 million pounds for 45 years. He wrote, In point of economy, there i� no real difference in either of the mode�; for twenty million� iu one payment, one million per annum for ever, or 1 ,200,0000 pounds for 45 years, are precisely of the same value . . .

Ricardo also was aware that the question raises the issue of intergenerational linkages (which we discuss more fully in a later section): It would be difficult to convince a man possessed of 20,000 pounds, or any other sum, that a perpetual payment of 50 pounds per annum was equally burdensome with a single tax of 1 000 pounds. He would have some vague notion that the 50 pounds per annum would be paid by posterity, and would not be paid by him; but if he leaves his fortune to his son, and leaves it charged with this perpetual tax, where is the difference whether he leaves him 20,000 pounds with the tax, or 1 9,000 pounds without it?

Although Ricardo viewed these different methods of government finance as equivalent, he doubted whether other people in fact had the foresight to act in so rational a manner: The people who pay taxes . do not manage their private affairs accordingly. We are apt to think that the war is burdensome only in proportion to what we are at the moment called to pay for i1 in taxes, without reflecting on the probable duration of such taxes.

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And, indeed, Ricardo did not dismiss government debt as an insignificant policy concern. Before the British parliament, he once declared, This would be the happiest country in the world, and its progress in prosperity would go beyond the powers of imagination to conceive, if we got rid of two great evils - the national debt and the corn laws 1 9

Because Ricardo doubted the practical validity of Ricardian equivalence, O'Driscoll ( 1 977) suggested the term Ricardian non-equivalence, although this phrase has never caught on. Whether or not Ricardo was a Ricardian, he now gets credit for first noting the possible irrelevance of government debt. More recently, several sources have suggested the possibility of debt neutrality, as Barro in fact noted in his 1 974 paper. In 1 952, Tobin posed the Ricardian question: How is it possible that society merely by the device of incurring a debt to itself can deceive itself into believing that it is wealthier? Do not the additional taxes which arc necessary to carry the interest charges reduce the value of other components of private wealth?

Tobin viewed this Ricardian logic as raising an intriguing theoretical question, but he never suggested that it might actually hold in practice. The Ricardian argument also appears in Patinkin's ( 1 965, p. 289) classic treatise, Money, Interest, and Prices, which was based on a 1 947 dissertation at the University of Chicago. In considering whether government bonds should be treated as part of household wealth, Patinkin wrote, The difficulty with this approach is that the interest burden on these bonds must presumably be financed by future taxes. Hence if the private sector discounts its future tax liabilities in the same way that it discounts future interest receipts, the existence of government bonds will not generate any net wealth effect.

Patinkin does not claim originality for this idea. In a footnote, he says, "This point is due to Carl Christ, who cites in turn discussions with Milton Friedman". In 1 962, Martin Bailey's textbook explained clearly ( p. 75) the possibility "that households regard deficit financing as equivalent to taxes". Bailey explains: [Government debt] implies future taxes that would not be necessary if the expenditures were financed with current taxation. If a typical household were to save the entire amount that was made available to it by a switch from current taxation to deficit financing, the interest on the saving would meet the future tax charges to pay interest on the government bonds, while the principal saved would be available to meet possible future taxes imposed to repay the principal on the government bonds. If the household has a definite idea of how it wants to allocate its total present and future resources among consumption at different points of time, and if it recognizes that the shift from current taxation to deficit financing does not change its total resources at all from a long-run point of view, then it will indeed put entirely into saving any 'income' made available to it by a government decision to finance by bond issue rather than current taxation.

IY

Quoted in Buchholz ( 1989, p. 73). Ricardo's opposition to the corn laws (which restricted the import of grain from abroad) suggests that he took his theory of comparative advantage more seriously than he did his theory of debt neutrality.

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D. W Elmend01f and N. G. Mankiw That is, the household will consume exactly the same amount, whichever fmm of financing is used.

Bailey even points out in a footnote that "the same argument applies if no repayment [of the debt's principal] is expected, if the typical household plans to leave an estate". Bailey does not cite Ricardo, but in the text's preface he refers to this section and notes, "a claim to original authorship must be shared with at least two other persons, Gary Becker and Reuben Kessel, who independently developed the same material for their respective courses". The idea of Ricardian equivalence, therefore, has had a long and distinguished history. Yet there is no doubt that Robert Barro's 1 974 paper was a turning point in the literature on government debt. Barro stated the conditions for Ricardian equivalence more clearly than the previous literature had, and he laid out explicitly the intergenerational model needed to establish the result. (We discuss this model below.) Perhaps the greater thoroughness in B arro's treatment of the issue is founded in his apparent belief in debt neutrality. Previous authors, including Ricardo, raised the theoretical possibility of neutrality but often doubted its practical applicability. In a way, Barro can be viewed as the Christopher Columbus of Ricardian equivalence. Columbus was not the first European to discover America, for Leif Ericsson and others had come before. Instead, Columbus' great confidence in the importance of his mission ensured that he was the last European to discover America: after Columbus, America stayed discovered. Similarly, Robert Barro was not the first economist to discover Ricardian equivalence, but he was surely the last. Since Barro's work, Ricardian equivalence has maintained its place at the center of the debate over government debt, and no one will be able to discover it again. 4. 1 . 3.

Why Ricardian equivalence is so important

Although most economists today agree with David Ricardo and doubt that Ricardian equivalence describes actual consumer behavior, the idea of Ricardian equivalence has been extraordinarily important within the academic debate over government debt. There are two reasons for this. The first reason is that a small but prominent minority of economists, including Robert Barro, have argued that Ricardian equivalence does in fact describe the world, at least as a first approximation. This small group has provided a useful reminder to the rest of the profession that the conventional view of government debt is far from a scientific certitude. The inability of macroeconomists to perform true experiments makes macroeconomic knowledge open to debate. Although we believe that policymakers are best advised to rely on the conventional view of government debt, we admit that there is room for reasonable disagreement. The second and more significant reason that Ricardian equivalence is important is that it offers a theoretical benchmark for much further analysis. There are many parallels both inside and outside of economics. Mathematicians study Euclidean geometry (even though we now know that we live in a non-Euclidean world);

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physicists study frictionless planes (even though all real planes exhibit some friction); and economists study Arrow-Debreu general-equilibrium models with complete and perfectly competitive markets (even though markets in actual economies are neither complete nor perfectly competitive). The theoretical benchmark in economics that is most similar to Ricardian equiva­ lence is the Modigliani-Miller theorem. Modigliani and Miller established conditions under which a firm's choice between debt and equity finance is irrelevant. Similarly, Ricardian equivalence is the claim that the govermnent's choice between debt and tax finance is irrelevant. Few finance economists believe that the Modigliani-Miller theorem describes actual firms' financing decisions. Nonetheless, the theorem provides a starting point for many discussions in corporate finance. Similarly, even if Ricardian equivalence does not describe the world, it can be viewed as one natural starting point in the theoretical analysis of government debt. As the next section should make clear, trying to explain why Ricardian equivalence is not true can yield a deeper understanding about the effects of government debt on the economy. 4.2.

The debate over Ricardian equivalence: theoretical issues

Although most economists today are skeptical of the Ricardian propositiOn that government debt is irrelevant, there is less consensus about why government debt matters. The conventional view (which we discussed earlier) begins with the premise that a debt-financed tax cut stimulates consumption. There are various reasons why this might be the case. 4.2.1.

Intergenerational redistribution

One reason govermnent debt might matter is that it represents a redistribution of resources across different generations of taxpayers. When the govermnent cuts taxes and issues govermnent debt today, the govermnent budget constraint requires a tax increase in the future, but that tax increase might fall on taxpayers who are not yet living. This redistribution of resources from future to current taxpayers enriches those who are now living; current taxpayers respond to the increase in their resources by consuming more. This intergenerational redistribution is the mechanism that makes government debt matter in basic overlapping-generations models, such as those of Diamond ( 1 965) and Blanchard ( 1 985). Barra's 1 974 paper built on Becker's ( 1 974) theory of the family to provide a clever rej oinder to this argument. Barra argued that because future generations are the children and grandchildren of the current generation, it is a mistake to view them as independent economic actors. Instead, Barro suggested that current generations might behave altruistically toward future generations. In the presence of this intergenerational altruism, it is no longer natural to presume that current generations will take advantage of the opportunity to consume at the expense of future generations.

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Barro proposed the following model of the family. Suppose that the total utility of generation t, denoted V�> depends on consumption during its lifetime C1 and on the utility of its children Vt+ 1 , discounted by some factor {3:

Recursive substitution establishes that

That is, the utility of generation t depends on its own consumption and the consumption of all future generations. In essence, the relevant decisionmaking unit is not the individual, who lives only a finite number of years, but the family, which continues forever. As a result, the family member alive today decides how much to consume based not only on his own income but also on the income of future members of his family. Ricardian equivalence is, therefore, preserved: a debt-financed tax cut may raise the income an individual receives in his lifetime, but it does not raise his family's permanent income. Instead of consuming the extra income from the tax cut, the individual saves it and leaves it as a bequest to his descendants, who will bear the future tax liability. The debate over Ricardian equivalence is, therefore, in part a debate over how different generations are linked to one another. This issue has broad significance for macroeconomics. As Kotlikoff and Summers ( 1 98 1) established, a large fraction of wealth in the US economy is eventually bequeathed rather than consumed by its current 2 owner 0 . It is possible that many bequests are accidental rather than intentional; that is, people might leave bequests because they die unexpectedly before consuming their entire wealth. Yet the fact that annuity markets (even if imperfect) are used so rarely suggests that consumers must have some desire to leave bequests. The altruism model proposed by B arro is one possible model of the bequest motive, but there are others. Another popular model is the "joy of giving" or "warm glow" model, according to which a person's utility depends on the size of his bequest rather than on the utility of his children. That is,

where G(B1 ) represents the utility from giving a bequest of size B 1 . Closely related to this model is the "strategic bequest motive" proposed by Bernheim et al. ( 1 985); according to this model, parents use bequests to induce certain types of behavior from their children, such as visiting home more frequently. These alternative models of the bequest motive do not give individuals any reason to look ahead to their children's

2°

For other discussions of the role of intergenerational transfers in wealth accmnulation, see Gale and Scholz ( 1 994), Kessler and Masson ( 1 989), Kotlikoff ( 1 988), and Modigliani ( 1 988).

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tax liabilities and, therefore, do not yield Ricardian equivalence in the presence of policy-induced intergenerational redistributions. It is sometimes mistakenly claimed that the effects of government debt depend on whether people have finite lives (as is the case in the Diamond overlapping-generations model) or infinite lives (as is effectively the case in the Barro intergenerational-altruism model). The key issue, however, is not the finiteness of life but the introduction over time of new taxpayers without links to the past. [This point was established by Philippe Weil ( 1 989).] To see this, imagine an economy in which consumers die (according to some Poisson process) but no new consumers are ever born. In this economy, all future tax liabilities must fall on people who are currently living, so Ricardian equivalence would hold, despite the finiteness of life. By contrast, consider an economy in which new consumers are born over time but, once born, live forever. In this economy, some of the future tax liabilities implied by government debt would fall on future arrivals, and Ricardian equivalence would fail to hold. The Barro model of intergenerational altruism, which links all future arrivals to those currently living, has attracted a variety of theoretical criticisms. One of the more entertaining is that offered by B ernheim and Bagwell ( 1 988), who build on the well established tenet that human reproduction is sexual and that, as a result, people share common descendants. Indeed, if one looks back and forth among everyone's future family trees, one quickly concludes that the entire world population is connected through a web of familial relationships. This observation, together with intergenerational altruism, yields profound predictions. According to the Barro model, a transfer of a dollar (in present value) between Doug Elmendorf and one of his descendants does not affect anyone's consumption. Similarly, a transfer between Greg Mankiw and one of his descendants does not affect anyone's consumption. But if Elmendorf and Mankiw have common descendants, as surely they must, then a transfer between Elmendorf and Mankiw does not affect anyone's consumption. Indeed, because everyone is connected through common descendants, the entire distribution of income is irrelevant - a prediction that is surely false. B ernheim and Bagwell use this argument as a reductio ad absurdum to conclude that the Barro model cannot describe the relationships among generations. A less intriguing, but ultimately more persuasive, critique of the Barro model of intergenerational altruism arises from the work of Evans ( 1 99 1), Daniel ( 1 993), and Smetters ( 1 996). Suppose that we consider a standard model of intergenerational altruism but add the seemingly innocuous wrinkle that the degree of altruism (as measured above by the parameter /3) differs across families. Even if all consumers have some degree of altruism, it is likely in the presence of heterogeneity that many consumers will not have operative bequest motives. In the steady state of such a model, the interest rate is detennined by the time preference of the most patient family (that is, the family with the highest /3). At this interest rate, other families will choose to hit the corner solution of zero bequests and, therefore, will act like a series of overlapping generations: they will save for life-cycle reasons but will leave no bequests. For these zero-bequest families, transfers of resources across generations will have real effects.

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Despite the failure of Ricardian equivalence in this model, the level of government debt does not matter for aggregate variables in the economy's steady state. Because the time preference of the most patient family pins down the steady-state interest rate, it also pins down the capital stock and the level of output. A debt-financed tax cut, for instance, will stimulate consumption, crowd out capital, and raise the real interest rate for a period of time, but the most patient family will respond by increasing saving until, eventually, the capital stock and real interest rate return to their former levels. This result suggests that Ricardian equivalence may work better as a long-run theory than as a short-run theory. Finally, it is worth noting that, for some purposes , the importance of these intergenerational issues may be overstated. Poterba and Summers ( 1 987) claim that, even without intergenerational altruism, people may have long enough time horizons to make Ricardian equivalence approximately true in the short run for some policy interventions. For example, imagine that the government cuts taxes today, issues government debt with an interest rate of 5%, and then services the interest payments with higher taxes over the infinite futme. In this case, about 77% of the future taxes occur within 30 years, indicating that the redistribution of the tax burden toward future generations, though not zero, is relatively small. Moreover, because the marginal propensity to consume out of wealth for life-cycle consumers is relatively small, the redistribution that does occur has only a small effect on consumption. Thus, the immediate result may be an increase in private saving approximately equal to the budget deficit. Poterba and Summers argue that if Ricardian equivalence fails in a substantial way in the short run, the explanation must lie not in the intergenerational redistribution caused by government debt but in some other mechanism 2 1 . 4.2.2.

Capital market imperfections

The simplest, and perhaps most compelling, explanation for the failure of Ricardian equivalence is the existence of capital market imperfections. For households that discount future utility highly or that expect rapidly rising income, the optimal consumption path may require consuming more than their income when young (and less when old) by borrowing in financial markets. The possibility of default and bankruptcy, however, may prevent these households from borrowing for the purposes of current consumption. In this case, the optimal strategy is to consume all of current income and hold exactly zero assets.

2 1 Even if private saving does rise approximately one-for-one with the budget deficit in the short run, there could be substantial crowding out of capital in the long run. The Auerbach-Kotlikoff simulations discussed earlier suggest that the full effects of government debt take a long time to appear in life-cycle models. Thus, the Poterba-Summers argument raises the possibility · in contrast to the model with heterogeneous altruism just discussed - that Ricardian equivalence may work well as a short-run theory but not as a long-run theory. ·

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In the presence of such a binding borrowing constraint, Ricardian equivalence will no longer hold. A debt-financed tax cut effectively gives the constrained household the loan that it wanted but could not obtain from private lenders. The household will respond by increasing consumption, even with the knowledge that the result is higher taxes and lower consumption in the future. The potential importance of capital market imperfections i s highlighted by the small amount of wealth that many people hold compared to the level of government debt in our economy. In recent years, the federal government debt has been about half of national income. If Ricardian equivalence held, the typical household should be holding additional wealth equal to half of annual income. Yet many households have wealth far below that level. To reconcile Ricardian equivalence with these facts, one would need to believe that in the absence of government debt, most households in the economy would have substantially negative net wealth. This seems implausible: few consumers are able to obtain substantial loans without tangible collateral. Thus, it seems that government debt has allowed many households to consume more than they otherwise would. The literature contains some debate over whether capital market imperfections should cause a failure of Ricardian equivalence. Hayashi ( 1 987) and Yotsuzuka ( 1 987) present examples of endogenous capital market imperfections based on asymmet­ ric information that preserve Ricardian equivalence. In these models, asymmetric information about future income, together with the possibility of default, prevents households from borrowing against future income. Yet because taxes are assumed to be lump sum, there is no information problem about the stream of tax payments; as a result, the borrowing constraint does not affect the ability of households to trade off taxes today and taxes in the future. In this case, a debt-financed tax cut causes the borrowing constraint to adjust in such a way as to leave consumption opportunities unchanged. As Bernheim ( 1 987) points out, however, this result is crucially dependent on the assumption that taxes are lump sum. If taxes rise with income, then the asymmetry in information about future income causes a similar asymmetry in information about future tax liabilities. In this more realistic case, these models yield the more conventional result that a debt-financed tax cut relaxes the borrowing constraint, allowing households to consume more. 4.2.3.

Permanent postponement of the tax burden

When a person first hears the case for Ricardian equivalence, a natural response is, "Yes, that theory might apply if a budget deficit today required higher taxation in the future. But, in fact, the government never has to pay off its debts. When the government cuts taxes and runs a budget deficit, it can postpone the tax burden indefinitely". This s imple argument, it turns out, raises a number of complex questions for economic theory. The first point to make is that Ricardian equivalence does not require that the government ever pay off its debts in the sense of reaching zero indebtedness. Imagine

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that the government cuts taxes for one year by dD, increases the government debt by that amount, and then leaves government debt at the new higher level forever. To service this additional government debt would require additional taxes of r x dD every year, where r is the interest rate on the debt. The present discounted value of these higher taxes is dD, which exactly offsets the value of the tax cut. Hence, if consumers look ahead to all future taxes, Ricardian equivalence holds, even though the government never retires the additional debt it has issued. Matters become more complicated if the government does not raise taxes to finance the interest on this additional debt but, instead, finances these interest payments by issuing even more debt. This policy is sometimes called a "Ponzi scheme" because it resembles investment scams in which old investors are paid off with money from new investors. If the government pursues such a Ponzi scheme, the government debt will grow at rate r, and the initial tax cut and budget deficit do not imply higher taxes in the future. But can the government actually get away with this Ponzi scheme? The literature has explored this question extensively 22 . An important issue is the comparison between the interest rate on government debt r and the growth rate of the economy g. If r is greater than g, then government debt will increase faster than the economy, and the Ponzi scheme will eventually be rendered infeasible: the debt will grow so large that the government will be unable to find buyers for all of it, forcing either default or a tax increase. By contrast, if r is less than g, then government debt will increase more slowly than the economy, and there is nothing to prevent the government from rolling over the debt forever. The comparison between r and g has broader general-equilibrium implications, however, and these implications help explain the effects of government debt. In standard neoclassical growth theory, r reflects the marginal product of capital, and g reflects population growth and technological change. These two variables can be used to gauge whether the economy has reached a dynamically efficient equilibrium. If r is greater than g, then the economy is efficient in the sense of having less capital than at the "Golden Rule" steady state. By contrast, if r is less than g, then the economy is inefficient in the sense of having accumulated too much capital. In this case, a reduction in capital accumulation can potentially increase consumption in all periods of time. A govermnent Ponzi scheme, like the "asset bubbles" studied by Tirole ( 1 985), is both feasible and desirable in such an economy because it helps ameliorate the problem of oversavmg. Dynamic inefficiency and successful, Pareto-improving Ponzi schemes offer an intriguing theoretical possibility, but they are not of great practical relevance for the US economy or other economies around the world. Economists today do not believe that households are saving too much, driving the return to capital below the economy's

22 See, for instance, Ball et al. ( 1 998), Blanchard and Wei! ( 1 992), Bohn { 1 993), and O'Connell and Zeldes ( 1 988).

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growth rate. And, indeed, Abel et al. ( 1 989) present evidence for dynamic efficiency. Hence, Ricardian equivalence cannot be refuted by asserting that the government can roll over the debt forever. Yet one nagging fact remains: in the US economy, the interest rate on government debt has on average been less than the growth rate of the economy. Abel et al. reconcile this fact with their finding of dynamic efficiency by noting that government debt and economic growth have different risk characteristics. They present an example of a dynamically efficient economy in which uncertainty about economic growth drives down the return on risk-free assets, such as government debt, below the average growth rate. Thus, one cannot judge dynamic efficiency (and the feasibility of government Ponzi schemes) simply by comparing the average return on risk-free assets with the average growth rate 23 .

4.2.4. Distortionary taxes The Ricardian equivalence proposition is based on the assumption that taxes are lump sum. If instead taxes are distortionary, then a postponement of the tax burden affects incentives and thereby behavior. These microeconomic distortions could have a large macroeconomic impact, making Ricardian equivalence a poor approximation to reality. To see the potential importance of distortionary taxation, imagine an economy described by the standard Ramsey growth model except that taxes, rather than being lump-sum, are raised with a proportional income tax with rate T. The following equations describe the steady state:

y = f(k),

ry = rD + g,

r =f'(k),

( 1 - T) r = p.

The first equation is the production function. The second equation states that tax revenue ry equals the interest on the debt rD plus government spending g. The third equation states that the interest rate r equals the marginal product of capital. (Both interest income and capital income are assumed to be taxed at the same rate, so the tax does not affect this equation.) The fourth equation states that the after-tax interest rate equals the rate of subjective time preference p; this is the steady-state condition for the Ramsey model. Given these equations, it is straightforward to see how an increase in government debt affects the economy. Higher debt leads to higher debt service; a

23

Ball et al. ( 1 998) build on these ideas and consider policies in dynamically efficient economies called "Ponzi gambles" in which the government cuts taxes and rolls over the resulting debt for as long as is possible. In their model, debt can raise the welfare of all generations in those realizations of history in which taxes do not need to be increased. Yet the policy is a gamble because the government is sometimes forced to raise taxes. Moreover, those tax increases are especially undesirable because they occur in realizations of history in which future generations are already burdened by low economic growth.

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higher debt service requires a higher tax rate; a higher tax rate implies a higher before­ tax interest rate; and a higher interest rate requires a smaller steady-state capital stock. As in the traditional analysis, government debt crowds out capital, even though the mechanism here is quite different. We can easily calibrate the magnitude of this effect for this model. By fully differentiating this system we obtain an expression to show how much debt crowds out capital: dk dD

= {r f

Df"

'

+

1 - T).ff"

( f' )2

}- I

If we specialize the production function to Cobb-Douglas y = k0, then this expression becomes: dk dD

- =

{ r + (l - a)- - (1 - r) a } · I D k

1-

--

a

For the US economy, taxes take about one-third of income ( T = 1 /3), capital earns about one third of income (a = 1 /3 ), and the debt equals about one-seventh of the capital stock (Dik = l /7). For these parameter values, dk/dD = - 1 . 1 1 . That is, an extra dollar of government debt reduces the steady-state capital stock by slightly over one dollar. This example shows that substantial crowding out can occur simply because of distortionary taxation 24. Although this example i s sufficient t o show the potential importance o f distortionary taxation, more realistic analyses of debt policy go beyond this special case. In the steady state of the Ramsey model, national saving is infinitely elastic at the rate of time preference. Other models, such as the life-cycle model of Auerbach and Kotlikoff ( 1 987), would predict a more limited saving response to a change in the after-tax rate of return. In addition, it is important to consider the dynamic effects of tax changes, as in Judd ( 1 987) and Dotsey ( 1 994), and the effects of taxes on labor supply, as in Trostel ( 1 993) and Ludvigson ( 1 996). Perhaps the only certain conclusion is that in a world with distortionary taxation, Ricardian equivalence is unlikely to provide a good first approximation to the true effects of debt policy. 4.2. 5.

Income uncertainty

Another possible reason for the failure of Ricardian equivalence is that government debt may alter consumers' perception of the risks they face. This possibility was 24 The numerical results presented here are, of course, sensitive to a variety of detailed assmnptions. lf we introduce depreciation, so that the production function is .f(k) = ka - Ck, then the degree of crowding as measured by dk/dD falls. If we take a broad view of capital, so that a is larger than 1/3, then the degree of crowding rises.

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explored by Chan ( 1 983), Barsky et al. ( 1 986), Kimball and Mankiw (1989) and Croushore ( 1 996). These authors begin with the axioms that taxes are levied as a function of income and that future income is uncertain. Therefore, when the government cuts taxes today, issues government debt, and raises income taxes in the future to pay off the debt, consumers' expected lifetime income is unchanged, but the uncertainty they face is reduced. If consumers have a precautionary saving motive, this reduction in uncertainty stimulates current consumption. Put differently, consumers discount risky uncertain income and uncertain future taxes at a higher rate than the interest rate on government bonds; a postponement of the tax burden, therefore, encourages current spending. The potential importance of this mechanism is highlighted by the recent interest in buffer-stock theories of saving. [See, for instance, Carroll ( 1 997).] In these models, consumers are impatient (in the sense of having a high subjective discount rate) but are nonetheless prudent (in the sense of having a precautionary saving motive). As a result, consumers maintain a small amount of saving in order to protect themselves against unlikely but very adverse shocks to their income. If consumers do not pay significant taxes when these unlikely, adverse outcomes are realized, then a postponement of the tax burden will stimulate current consumption. 4.2. 6.

Myopia

When non-economists are explained the idea of Ricardian equivalence, they often have trouble taking the idea seriously. The reason for this response goes to the heart of how economists view human behavior. Rational, optimizing, forward-looking homo economicus is a creature of the economist's imagination. Economists are trained in the power of this model, but non-economists are often more skeptical. In particular, non-economists are doubtful about whether people have the foresight to look ahead to the future taxes implied by government debt, as is required for Ricardian equivalence to hold. It is hard to incorporate this sort of myopia into economic theory. Yet there have been some attempts to model short-sightedness. Strotz ( 1 956) and Laibson ( 1 997), for instance, consider preferences according to which consumers give excessive weight to current utility (compared to the benchmark case of exponential discounting). As a result, consumers exhibit time-inconsistent behavior and can be made better off through a binding commitment to increased saving. This model can explain the popular notion that people save too little, but it cannot by itself explain a failure of Ricardian equivalence. In this model, the time-inconsistent consumer faces a standard intertemporal budget constraint, so a postponement of the tax burden does not alter the consumer's opportunities. This consumer saves too little but, without a binding borrowing constraint or other imperfection, is fully Ricardian in response to fiscal policy. Although the Ricardian behavior of Strotz-Laibson consumers shows that myopia by itself need not undermine Ricardian equivalence, this result does not necessarily

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render myopia irrelevant in this debate. The impatience implicit in the Strotz-Laibson preferences can explain the prevalence of liquidity constraints and buffer-stock saving, which in turn highlights the deviations from Ricardian equivalence emphasized earlier. In addition, it is possible that the Strotz-Laibson approach to modelling myopia is not the best one. Developing better models of myopic behavior remains a challenge for future research. 4. 3.

The debate over Ricardian equivalence: empirical issues

The theoretical literature just discussed offers various reasons why government debt may affect consumption and capital accumulation. Yet these deviations from Ricardian equivalence do not prove that the proposition is a bad first approximation of the actual economy. To reach such a judgment, one must assess the quantitative importance of these theoretical deviations from the Ricardian benchmark. Some of the research discussed earlier bears on this issue. As noted above, calculations using the Blanchard model of finite lifetimes imply that debt can crowd out a significant amount of capital, and Auerbach and Kotlikoff's simulations show that the combination of finite lifetimes and distortionary taxes can generate roughly one-for-one crowding out. Moreover, many of the theoretical analyses cited in the previous section include calibrations that illustrate the potential importance of the channels through which debt may affect the economy. Simulations, however, are no substitute for evidence. In this section we review the empirical evidence on the validity of Ricardian equivalence. We begin with tests of the assumptions underlying the proposition and conclude that a substantial fraction of households probably do not behave as the proposition assumes. We next turn to tests of the proposition's implications for various macroeconomic variables. Despite substantial research in this area, we believe that the results are ultimately inconclusive 25 . 4. 3. 1 .

Testing assumptions about household behavior

When testing theories, economists typically focus on the theories' implications rather than their assumptions. Yet, because testing the implications of Ricardian equivalence raises substantial difficulties, examining the underlying assumptions is also worthwhile. The key assumption is consumption smoothing both within lifetimes and across generations. That is, households are assumed to choose consumption and saving based on a rational evaluation of an intertemporal budget constraint that includes both current and future generations. One piece of evidence that many households do not behave in this way is the small amount of wealth that they hold. This situation may arise from a combination of

25

Our review of this literatmc is necessarily brief. For more thorough discussions with additional citations, see Bernheim ( 1 987) and Seater ( 1 993).

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impatience and borrowing constraints, as described earlier, or because some people are not very forward-looking. In either case, a deficit-financed tax cut would spur consumption. Numerous papers also present evidence that people do not smooth consumption fully over time. Campbell and Mankiw ( 1 989) use aggregate data to show that consumption is more sensitive to current income than the basic consumption­ smoothing model predicts. Hall and Mishkin ( 1 982), Zeldes ( 1 989), and Carroll and S ummers ( 1 99 1 ) make the same point using household data. Further confirmation comes from households' responses to changes in taxes and government benefits; for example, see Poterba ( 1 988), Wilcox ( 1 989), and Shapiro and Slemrod ( 1 995). In these studies, deviations from the life-cycle model are economically as well as statistically significant. Some studies, such as Runkle ( 1 99 1), Attanasio and Browning ( 1 995), and Attanasio and Weber ( 1 995), have argued that income and consumption data are in fact consistent with the consumption-smoothing model. But the weight of the evidence from the consumption literature is that consumption smoothing is far from complete. In our view, this conclusion casts serious doubt on the empirical plausibility of Ricardian equivalence.

4.3.2. Testing the implications for consumption A large and contentious literature has focused on the implication of Ricardian equivalence that a reduction in current taxes with no change in current or future government spending should not affect household consumption. The standard approach is to estimate a traditional aggregate consumption function, with consumer spending as the dependent variable and income, wealth, fiscal policy, and various other controls as independent variables. Ricardian equivalence is rejected if the coefficients on taxes and debt are significantly different from zero. Although this approach seems to offer a direct test of the Ricardian view, there are a number of problems with its implementation. The first problem is the treatment of expectations. The behavior of forward-looking households depends on expectations of fiscal policy, not just the measures of current fiscal policy that are included in these regressions. Suppose that the current level of taxation reflects expectations of future government spending. (This is in fact implied by the theory of tax smoothing, which we discuss later.) In this case, a significant negative coefficient on current taxes in the consumption function does not necessarily violate Ricardian equivalence. A second problem is simultaneity. Some of this literature estimates the consumption function with ordinary least squares. This approach is valid only if the shocks to the consumption function do not affect fiscal policy or other right-hand side variables. Other papers attempt to address this problem using instrumental variables, but finding persuasive instruments is close to impossible 26 . 26

For a discussion of the identification problem in the cont<:xt of tests of Ricardian equivalence, see Cardia ( 1 997).

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A third problem in this literature is that the number of observations is small compared with the number of highly correlated explanatory variables. In addition to the basic fiscal variables, some authors include measures of the marginal tax rate, while others separate taxes and spending by the level of government. Still others decompose the income and fiscal variables into permanent and transitory components as a way of capturing expectations. Although there may be good reasons to include these variables as a matter of theory, their addition compounds the problem of multicollinearity. One way to increase the independent variation in the explanatory variables is to use a longer estimation period, but this procedure can introduce spans in which consumption is clearly distorted, such as during wars. A final problem is that these specifications may have little power to distinguish between the Ricardian and conventional views of fiscal policy. As discussed earlier, life-cycle consumers' marginal propensity to consume out of a temporary tax cut may be only a few cents on the dollar. This value may be statistically indistinguishable from the Ricardian benchmark of zero effect. Nonetheless, the difference between a small and a zero marginal propensity to consume is economically important, for a small short-run drop in saving can cumulate to a large long-run decline in the capital stock. Various recent papers have tried to avoid some of these problems by building on the Euler equation approach pioneered by Hall ( 1 978). By looking at the first­ order condition for a representative consumer, rather than an aggregate consumption function, some of the problems in measuring expectations are avoided. Yet the problem of power remains. The first-order condition for a finite-horizon consumer in the Blanchard model is not very different from the first-order condition for an infinite­ horizon consumer. Nonetheless, policy can have substantially different effects in the two cases, especially in the long run. With these problems in mind, it is perhaps not surprising that this literature has failed to reach a consensus on the validity of Ricardian equivalence. Some researchers have concluded that equivalence is a reasonable description of the world; for example, see Kormendi ( 1 983), Aschauer ( 1 985), Seater and Mariano ( 1 985), Evans ( 1 988) and Kormendi and Meguire ( 1 986, 1 990, 1 995). Other researchers have reached the opposite conclusion; for example, see Feldstein ( 1 982), Modigliani and Sterling ( 1 986, 1 990), Feldstein and Elmendorf ( 1 990), Evans ( 1 993), and Graham and Himarios ( 1 99 1 , 1 996). Our view is that this literature considered as a whole is simply inconclusive. Many studies that fail to rej ect Ricardian equivalence are also unable to reject the life-cycle model, as their standard errors are large relative to the difference in coefficient values implied by the alternative hypotheses 2 7. Further, some studies that find insignificant

For example, see Evans ( 1 988 ), Kormendi and Mcguire ( 1 990), and Seater and Mariano ( 1 98 5 ). The latter paper presents an extreme example of lack of power: the authors cannot reject the hypothesis that the coefficient on taxes equals zero, but neither can they reject that it equals minus one.

21

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effects of taxes on consumption also find insignificant effects of government spending, which is inconsistent with both Ricardian and life-cycle models and suggests that this framework does not reflect the true effects of fiscal policy 2 8 . More generally, most results in this literature appear very sensitive to small differences in specification 29 . 4.3.3.

Testing the implications for interest rates

Ricardian equivalence implies that a debt-financed reduction in government revenue should not affect interest rates. The conventional view of debt generally implies the opposite. An important set of papers tests this implication by examining the effect of the budget deficit on interest rates after controlling for government spending and other influences. As with the literature concerning the consumption effects of fiscal policy, research into interest-rate effects appears straightforward, but numerous problems quickly arise. Indeed, some of the problems in the two literatures are quite similar. One problem is that interest rates depend on expectations of fiscal policy and other variables and those expectations are hard to measure. A number of studies use forecasts from vector autoregressions as a proxy for expectations, but the quality of those proxies is unclear. Vector autoregressions assume that variables follow a stable time-series process, and they do not incorporate non-quantitative information. Both of these points are likely to be important, especially for fiscal policy variables, which are the outcome of a political process. Measurement error in the proxies for expectations biases the estimated coefficients toward zero and, thus, toward the null hypothesis of Ricardian equivalence. A second problem with this approach as a test of Ricardian equivalence is that there is no natural metric for gauging the size of interest-rate effects. For the effect of taxes on consumption, there are natural Keynesian and life-cycle benchmarks as well as the Ricardian benchmark. Indeed, this feature was critical in assessing whether tests of Ricardian equivalence had any power against alternative descriptions of the world. But no such alternative benchmarks exist for interest rates, because the size of the movements expected under non-Ricardian views depends on a host of elasticities. In particular, if international capital flows have an important effect on the domestic

28

For example, sec Seater and Mariano (1985). For example, some of the strongest evidence in favor of Ricardian equivalence comes from the especially thorough investigation conducted by Kom1endi ( 1 983) and Kormendi and Meguire (1 986, 1 990, 1 995). Yet, Kormendi and Meguire ( 1 990) show that although their results are robust to a variety of changes in specification (Table 1 ), they are not robust to the seemingly innocuous choice of deflator (Table 2). For further discussion of Kormendi and Meguire's specification, see the exchanges between them and Barth et a!. ( 1 986), Modigliani and Sterling ( 1 986, 1 990), and Graham ( 1 995). As another example of the sensitivity of results, Graham and Himarios ( 1 9 9 1 , 1 996) show that the estimates of Aschauer ( 1 985) and Evans ( 1 988) are not robust to alternative formulations of the Euler equation or measures of consumption. 29

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financial market, interest rates may not respond much to fiscal policy even if Ricardian equivalence is invalid. With these caveats in mind, it is worth noting that this literature has typically supported the Ricardian view that budget deficits have no effect on interest rates. Plosser ( 1 982) pioneered the approach of measuring expected policy using vector autoregressions. Further work in this vein by Plosser ( 1 987), Evans ( 1 987a, 1 987b) and Boothe and Reid ( 1 989) has confirmed Plosser's original conclusion that a zero effect of deficits cannot be rejected 30. Our view is that this literature, like the literature regarding the effect of fiscal policy on consumption, is ultimately not very informative. Examined carefully, the results are simply too hard to swallow, for three reasons. First, the estimated effects of policy variables are often not robust to changes in sample period or specification 3 1 . Second, the measures of expectations included in the regressions generally explain only a small part of the total variation in interest rates. For example, the average R-squared of Plosser's basic monthly regressions [Plosser ( 1 987), Tables 6 and 7] is 0.06, and the corresponding value of Evans' basic quarterly regressions [Evans ( 1 987b), Table 1 ] is 0.09. This poor fit suggests some combination of measurement error in expectations and the omission of other relevant (and possibly correlated) variables. Under either explanation, the estimated coefficients on the policy variables must be viewed with skepticism. Third, Plosser ( 1 987) and Evans ( 1 987b) generally cannot reject the hypothesis that government spending, budget deficits, and monetary policy each have no effect on interest rates. Plosser ( 1 987) also reports that expected inflation has no significant effect on nominal interest rates. These findings suggest that this framework has little power to measure the true effects of policy. 4. 3.4.

Testing the implications for international variables

Ricardian equivalence implies that a debt-financed reduction in government revenue should not affect the exchange rate or the current account. In contrast, the conventional view of debt implies that the exchange rate should appreciate in these circumstances and the trade deficit should increase. Several researchers have tested these implications and reached conflicting conclusions. Evans ( 1 986) applies to exchange rates the methodology used by Plosser and Evans to study the effect of budget deficits on interest rates. He concludes that US budget 30 Different sorts of analyses by Evans ( 1 985 ), Hoelscher ( 1 986), and Wachtel and Young ( 1 987) have reached mixed conclusions. 3 1 For example, Plosser ( 1987, Table 1 0) reports sharply different coefficient estimates during the 1 968 1 976 and 1 977-1985 sample periods and using monthly data as opposed to quarterly data. As another example, Evans ( 1 987a, Tables I and 2) estimates that budget deficits had a small and statistically insignificant effect on nominal interest rates during the 1 950s, 1 960s and 1 970s, but an effect that was large, statistically significant, and surprisingly negative between 1 979 and 1 984. Of course, the effect of budget deficits may well have changed over time, but an estimated shift of this magnitude signals some problem with specification.

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deficits tend to cause a depreciation of the dollar, in contrast to both the Ricardian and conventional views. Evans' analysis is subject to the same problems that plague the interest-rate literature discussed above 3 2 . Moreover, a decline in the dollar should cause a strengthening of the trade balance. Yet Bernheim ( 1 988) and Rosensweig and Tallman ( 1 993) conclude that US trade deficits worsen when the US budget deficit increases. In the end, the empirical literature examining the effects of fiscal policy on consumption, interest rates, and international variables fails to offer clear evidence either for or against the Ricardian hypothesis. If the evidence is so weak, why then do most economists feel confident in rejecting Ricardian equivalence as a description of the world? The answer, we believe, is that most economists are incredulous about the assumptions that are needed to support the Ricardian view of government debt. In this case, the debate over theory is more persuasive than the debate over evidence. 5. Optimal debt policy

Disagreement about the appropriate amount of government debt in the USA is as old as the country itself. Alexander Hamilton ( 1 7 8 1 ) believed that "a national debt, if it is not excessive, will be to us a national blessing", while James Madison ( 1 790) argued that "a public debt is a public curse". Indeed, the location of the nation's capital was chosen as part of a deal in which the federal government assumed the Revolutionary War debts of the states: because the Northern states had larger outstanding debts, the capital was located in the South. Attention to the national debt has waxed and waned over the years, but has been intense during the past two decades. Similarly, government debt and deficits have been a focus of recent public debate in many European countries. The appropriate use of government debt depends on how debt affects the economy. As we have seen in the theoretical debate over Ricardian equivalence, debt could potentially have many different effects. As a result, the literature on optimal debt policy is broad in scope. Here we focus on the three effects that are most often viewed as important: the use of debt policy to reduce the magnitude of economic fluctuations, the use of debt policy to increase national saving, and the use of debt policy to reduce tax distortions by smoothing taxes over time. 5. 1.

Fiscal policy over the business cycle

Although some economists argue that fluctuations in aggregate output represent an optimal response to shifts in preferences or technology, most economists believe that some output variability arises from rigidities or coordination failures. These changes For examp le, fewer than half of the estimated coefficients rcp01tcd by Evans ( 1 986, Tables J and 7) are statistically distinguishable from zero. 32

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in output, and especially shortfalls of output relative to the potential determined by the available factors of production, are socially costly. In this case, timely adjustments to the government deficit and debt may raise social welfare. This notion of "countercyclical fiscal policy" dates at least to Keynes, and Blinder and Solow ( 1 973) present one of the classic analyses. Countercyclical fiscal policy arises automatically from the design of tax and transfer programs. When output and income are high, tax liabilities rise and eligibility for government benefits falls, reducing the budget deficit; when output and income are low, these effects reverse and the deficit widens. These "automatic stabilizers" are important quantitatively. The Congressional Budget Office ( 1 997a) estimates that when real output falls by 1 %, tax revenue declines by about 1 %. Countercyclical fiscal policy may also be implemented on a discretionary basis. For example, during the 1 975 recession, Gerald Ford and Congress agreed to a small cut in personal income taxes. Over time, however, this sort of policy has fallen into disfavor. During the 1 990 recession, for instance, taxpayers received a reduction in tax withholding but not tax liability. Part of this shift in views comes from a realization that an explicitly temporary change in taxes has only a small effect on the consumption of even moderately forward-looking consumers. Moreover, there are generally long lags in enacting discretionary changes in fiscal policy, so any effect on aggregate demand may be poorly timed. Finally, and perhaps most important, there is an increased appreciation for the ability of the Federal Reserve to conduct effective countercyclical monetary policy. 5.2.

Fiscal policy and national saving

The most important long-run effect of government debt under the conventional view is to reduce national wealth. Thus, optimal debt policy in the long run depends primarily on optimal national saving. Current public debate often takes as given the notion that saving should be increased. Proving this point, however, is by no means straightforward. Bernheim ( 1 994), Lazear ( 1 994) and Hubbard and Skinner ( 1 996) provide recent discussions of why more saving might be desirable. Examining this topic in detail is beyond the scope of this paper, but we consider briefly the issues that relate to governinent debt. We consider first whether debt policy should be used to make people save more for their own retirement, and then whether debt policy should be used to make current generations leave more wealth to future ones. 5.2. 1 .

Life-cycle saving

Feldstein ( 1 985) argues that people should do more saving within their lifetimes because the marginal product of capital exceeds their marginal rate of substitution between present and future consumption. This wedge arises, he argues, because of the taxation of capital income. He is surely right that capital taxation distorts households'

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consumption decisions. But does this imply that debt policy should be used to increase national saving? The answer is not obvious. Suppose that people are life-cycle consumers whose consumption is distorted by capital taxation. Eliminating the distortion would be desirable, but this goal cannot be achieved simply through debt policy. For instance, if the government raises lump­ sum taxation today, reduces government debt, and thereby reduces lump-sum taxation later within these consumers' lifetimes, Ricardian equivalence obtains, and national saving does not change. By contrast, Ricardian equivalence fails to hold if the future tax reductions benefit future generations. In this case, national saving rises because the income effect of current taxation reduces current generations' consumption. Nonetheless, the distortion between current and future consumption of any given generation is unchanged. That is, the increase in national saving induced by debt policy does not mitigate the distortionary effects of capital taxation. When considering how policy affects national saving, it is important to distinguish between the allocation of consumption across a person 's lifetime and the allocation of consumption across generations. Capital taxation inefficiently encourages consumption when a person is young compared to consumption when the same person is old. In a life-cycle model, however, debt policy does not affect this comparison. Instead, debt policy affects the consumption of current generations compared to the consumption of future generations. Thus, in a life-cycle model with rational consumers and distortionary capital taxes, life-cycle saving is inefficiently low, but debt policy cannot remedy the problem. 5.2.2.

Intergenerational saving

Debt policy can affect national saving by transferring resources among generations of life-cycle consumers. One approach to intergenerational equity in the context of debt policy is to focus on the appropriate distribution of paying for government services. The "benefit principle" implies that current spending should be financed out of current taxes, but capital spending should be financed over the life of the capital. Musgrave ( 1 959) advocated this approach, terming it "pay-as-you-use finance" ( p. 558) 33 . This principle provides one justification for the practice of financing wars ­ which are expected to benefit future as well as current generations - largely through debt issuance. Another approach to intergenerational concerns about government debt is to consider the overall welfare of different generations using an explicit social welfare function. As Romer ( 1 988) notes, a utilitarian social planner discounts income at the rate (5 = e + gla, where e is the intergenerational discount rate for utility, g is the growth rate of income, and a is the intertemporal elasticity of substitution (which equals 33

Musgrave also argued th at the budget deficit should vary over the business cycle for stabili:
purposes.

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the inverse of the elasticity of marginal utility with respect to consumption). Income growth matters here because it reduces the utility gained from an extra dollar of income. If the net marginal product of capital r exceeds c'5, then deferring consumption to future generations is socially optimal. Applying this criterion is by no means straightforward. Obviously, one must determine how much to discount the utility of future generations. One might argue that zero is the most consistent with people choosing a social welfare function "behind a veil of ignorance" [Rawls ( 1 97 1)] about the generation to which they belong. If 8 = 0, g = O.Ol, and a = 0.33, the social discount rate c'5 is 0.03 . If r = 0.06, which is the value we used earlier, the net gain from deferring consumption (r - 0) is 0.03 . One is thus led to conclude that increased national saving would be desirable. Yet the opposite conclusion arises if a = O . l , so that 0 is 0. 1 . In this case, economic growth together with sharply diminishing marginal utility ensures that the marginal utility of future generations is low, so there is little benefit to saving on their behalf. In the end, therefore, the utilitarian approach to intergenerational saving illuminates the key parameters that determine optimal national saving, but it does not allow us to reach an easy conclusion on whether national saving is in fact too low or too high.

5.3.

Tax smoothing

Another approach to analyzing optimal debt policy, advocated by Barro ( 1 979), emphasizes the distortionary nature of taxation. The deadweight loss from a tax depends roughly on the square of the tax rate. Thus, the distortion-minimizing way to finance a given stream of government spending is to maintain a smooth tax rate over time. If future government spending were known with certainty, the optimal tax rate would be constant. Because future government spending is uncertain, the optimal tax rate sets the present value of revenue equal to the present value of expected spending. As information about spending becomes available, the optimal tax rate changes. Under this view, the budget deficit is simply the difference between government spending and the amount of revenue generated by this tax rate, and the debt will rise and fall accordingly over time. Barro's tax-sJ:!loothing model is fom1ally parallel to Friedman's permanent-income hypothesis. According to the permanent-income hypothesis, households smooth consumption by basing it on their expected permanent income; they save and borrow in response to transitory changes in income. According to the tax-smoothing model, governments smooth tax rates by basing tax rates on expected permanent government spending; they increase or decrease government debt in response to transitory changes in spending or revenue. Barro ( 1 979) finds that the tax-smoothing theory of debt explains fairly well the behavior of US debt since 1 920, and Barro ( 1 987) reaches a similar conclusion for British debt from 1 700 through World War I. Much of the variation in spending that Barro studies is related to wars. Thus, the tax-smoothing logic provides another

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justification (in addition to intergenerational equity) for accumulating government debt during wars and paying off the debt during peacetime.

6. Conclusion

This essay has touched on some of the major issues in the debates over the effects of government debt. Because of the broad scope of this topic, we have had to be selective. We have ignored many important related subjects, such as the management of government debt with instruments of varying maturities, the debate over inflation­ indexed debt, the pros and cons of alternative rules for setting fiscal policy, and the theories of political economy that attempt to explain why and when governments issue debt. We trust that readers who have made it to this conclusion will understand why we avoided these additional fascinating but extensive topics.

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Chapter 26

OPTIMAL F ISCAL AND MONETARY P OLICY* VV CHARI

University of Minnesota and Federal Reserve Bank ofMinneapolis PATRJCK J. KEHOE

University of Pennsylvania, Federal Reserve Bank of Minneapolis, and National Bureau of Economic Research Contents

Abstract Keywords Introduction 1 . The primal approach to optimal taxation 1 . 1 . The Ramsey allocation problem 1 .2. Elasticities and commodity taxation

1 .3. Uniform commodity taxation 1 .4. Intermediate goods

2 . Fiscal policy 2. 1 . General framework 2.2. Capital income laxation 2.2. 1 . In a steady state 2.2.2. In a non-steady state 2.3. Cyclical properties 2 .3 . 1 . Debt taxation as a shock absorber 2.3.2. Tax-smoothing and incomplete markets 2.3.3. A quantitative illustration 2.4. Other environments 2.4. 1 . Endogenous growth models 2.4.2. Open economy models 2.4.3. Overlapping generations models

3. Monetary policy 3 . 1 . Three standard monetary models 3 . 1 . 1 . Cash--credit

1 672 1 672 1 673 1 676 1 676 1 680 1 682 1 684 1 686 1 686 1 693 1 693 1 697 1 699 1 699 1 705 1 708 1 71 1 171 1 1714 1718 1 720 1 72 1 1 72 1

* The views expressed herein are those of the authors and not necessarily those of the Federal Reserve Bank of Minneapolis or the Federal Reserve System.

Handbook ofMacroeconomics, Volume /, Edited by .JB. 1aylor and M. Woodford © 1999 Elsevier Science B. V All rights reserved 1 67 1

V. V. Chari and P.J. Kehoe

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3 . 1 .2 . Money-in-the-utility-function 3 . 1 .3 . Shopping-time

3.2. From monetary to real 3.3. Cyclical properties

4. Conclusion References

1 728 1 732 1 73 3 1 736 1 742 1 743

Abstract

We provide an introduction to optimal fiscal and monetary policy using the primal approach to optimal taxation. We use this approach to address how fiscal and monetary policy should be set over the long run and over the business cycle. We find four substantive lessons for policymaking: Capital income taxes should be high initially and then roughly zero; tax rates on labor and consumption should be roughly constant; state-contingent taxes on assets should be used to provide insurance against adverse shocks; and monetary policy should be conducted so as to keep nominal interest rates close to zero. We begin by studying optimal taxation in a static context. We then develop a general framework to analyze optimal fiscal policy. Finally, we analyze optimal monetary policy in three commonly used models of money: a cash--credit economy, a money­ in-the-utility-function economy, and a shopping-time economy.

Keywords

primal approach, Ramsey problems, capital income taxation, Friedman rule, tax smoothing JEL

classification:

ES, E6, E52, E62, H3, H2 1

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Introduction

A fundamental question in macroeconomics is, How should fiscal and monetary policy be set over the long run and over the business cycle? Answering this question requires integrating tools from public finance into macroeconomics. The purpose of this chapter is to lay out and extend recent developments in the attempts to do that within a framework which combines two distinguished traditions in economics: the public finance tradition and the general equilibrium tradition in macroeconomics. The public finance tradition we follow in this chapter stems from the work of Ramsey ( 1 927), who considers the problem of choosing an optimal tax structure in an economy with a representative agent when only distorting taxes are available. The general equilibrium tradition stems from the work of Cass ( 1 965), Koopmans ( 1 965), Kydland and Prescott ( 1 982), and Lucas and Stokey ( 1 983). Within the public finance tradition, our framework builds on the primal approach to optimal taxation. [See, for example, Atkinson and Stiglitz ( 1 980), Lucas and Stokey ( 1 983), and Chari et al. ( 1 99 1 ). ] This approach characterizes the set of allocations that can be implemented as a competitive equilibrium with distorting taxes by two simple conditions: a resource constraint and an implementability constraint. The implementability constraint is the consumer budget constraint in which the consumer and the firm first-order conditions are used to substitute out for prices and policies. Thus both constraints depend only on allocations. This characterization implies that optimal allocations are solutions to a simple programming problem. We refer to this optimal tax problem as the Ramsey problem and to the solutions and the associated policies as the Ramsey allocations and the Ramsey plan. We study optimal fiscal and monetary policy in variants of neoclassical growth models. This analysis leads to four substantive lessons for policymaking: Capital income taxes should be high initially and then roughly zero. Tax rates on labor and consumption should be roughly constant. State-contingent taxes on assets should be used to provide insurance against adverse shocks. Monetary policy should be conducted so as to keep nominal interest rates close to zero. The basic logic behind these policymaking lessons is that Ramsey policies smooth distortions over time and states of nature. Smoothing tax distortions over time implies that capital tax rates should be roughly zero and labor and consumption taxes should be roughly constant [Lucas and Stokey ( 1 983) and Chari et a!. ( 1 994)]. Ramsey policies also imply that heavily taxing inelastically supplied inputs is optimal. Thus Ramsey policies involve taxing capital income at initially high rates, but then dropping these rates, to zero in the long run. [See Judd ( 1 985) and Charnley ( 1 986).] Since keeping capital, labor, and consumption taxes roughly constant is optimal, the government needs some source of revenue to ensure that taxes need not be sharply changed when the economy is hit by shocks. One way to provide such revenue insurance is to have explicitly state-contingent debt, in the sense that the rate of return •

•

•

•

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VV Chari and P.J. Kehoe

on the debt varies with the shocks. Another way is to have non-state-contingent debt with taxes on interest income which vary with the shocks. Revenue insurance can also be provided by having taxes on capital income that vary with the shocks while still being roughly zero on average. In terms of monetary policy, Friedman ( 1 969) advocates a simple rule: set nominal interest rates to zero. In the models we consider, the Friedman rule is optimal if the consumption elasticity of money demand is one. We think that this rule deserves attention because the weight of the empirical evidence is that the consumption elasticity of money demand is indeed one. [See Stock and Watson ( 1 993).] Throughout the chapter, we emphasize that the primal approach, in essence, involves finding optimal wedges between marginal rates of substitution and marginal rates of transformation. Typically, many tax systems can decentralize the Ramsey allocations. Thus optimal tax theory yields results on optimal wedges, and thus the prescriptions for optimal taxes depend on the details of the particular tax system. For example, in the one-sector growth model, a tax system which includes any two of consumption, labor, and capital income taxes can decentralize the Ramsey allocations. In such a model, it is optimal to set intertemporal marginal rates of substitution equal to intertemporal marginal rates of transformation in the long run. With a tax system that consists of capital and labor taxes, this is accomplished by setting capital income taxes equal to zero. With a tax system that consists of consumption and labor taxes, this is accomplished by making consumption taxes constant. Thus the Ramsey allocations can be implemented either with zero capital income taxes or with constant consumption taxes. Throughout this chapter, we focus on economies in which the government effectively has access to a commitment technology. As is well known, without such a technology, there are time inconsistency problems, so the equilibrium outcomes with commitment are not necessarily sustainable without commitment. Economies with commitment technologies can be interpreted in two ways. One is that the government can simply commit to its future actions by, say, restrictions in its constitution. The other, and the way we prefer, is that the government has no access to a commitment technology, but the commitment outcomes are sustained by reputational mechanisms. [See, for example, Chari et al. ( 1 989), Chari and Kehoe ( 1 990, 1 993), and Stokey ( l 99 1 ) for analyses of optimal policy in environments without commitment.] Throughout this chapter we also restrict attention to proportional tax systems. The results we develop all come from environments with an infinite number of periods and include some combination of uncertainty, capital, debt, and money. Many of the basic principles, however, can be developed in a simple static context in which the ideas are easiest to digest. In Section l , in a static context, we develop two of the three main results in public finance which show up repeatedly in macroeconomic models. First, under appropriate separability and homotheticity conditions on preferences, it is optimal to tax goods at a uniform rate. Second, if all consumption goods, types of labor income, and pure profits can be taxed, then it is optimal not to tax intermediate goods. The uniform commodity tax result shows up

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repeatedly in analyses of fiscal policy, and this result and the intermediate-goods result show up repeatedly in analyses of monetary policy. We defer to the next section the development of the third main result, that it is optimal to set taxes on capital income equal to zero in the long run. In Section 2, we lay out a stochastic neoclassical growth model to analyze fiscal policy. We begin with a deterministic version of this model to highlight the long-run properties of optimal fiscal policy. In this version, we develop the results of Charnley ( 1 980, 1 986) on the optimality of zero capital-income taxation in a steady state, the generalizations by Judd ( 1 985) to environments with heterogeneous agents, and some qualifications by Stiglitz ( 1 987) when there are restrictions on the tax system. Next, we show that for a commonly used class of utility functions, optimal capital taxes are zero not only in a steady state, but also after the first period. Next, we consider a stochastic model without capital to highlight how optimal fiscal policy should respond to shocks. We illustrate how, by using debt as a shock absorber, taxes on labor income are optimally smoothed in response to shocks to government consumption and technology [as in Lucas and Stokey ( 1 983) and Chari et al. ( 1 991)]. We then contrast these results with the assertions in Barro ( 1 979) about tax-smoothing in a reduced-form model. We argue that the work of Marcet et al. ( 1 996) on taxation with incomplete markets partially affinns Barra's assertions. We also consider the quantitative features of optimal fiscal policy in a standard real business cycle model [as in Chari et al. ( 1 994)]. We go on to discuss how the results developed in a closed economy with infinitely lived agents and only exogenous growth extend to other environments. We first show that in an endogenous growth framework along a balanced growth path, all taxes are zero. [See Bull ( 1 992) and Jones et al. ( 1 997).] Essentially, in this framework, capital income taxes distort physical capital accumulation, and labor income taxes distort human capital accumulation. Hence it is optimal to front-load both taxes. We then consider an open economy and show that under both source-based and residence­ based taxation, optimal capital income taxation is identically zero. The intuition for these results is that with capital mobility, each country faces a perfectly elastic supply of capital and therefore optimally chooses to set capital income tax rates to zero. [See Atkeson et al. ( 1 999) and Garriga ( 1 999).] Finally, we consider an overlapping generations model and show that only under special conditions is the tax rate on capital income zero in a steady state. The conditions are that certain homotheticity and separability conditions hold. [See Atkeson et al. ( 1 999) and Garriga ( 1 999).] In Section 3, we lay out a general framework for the analysis of monetary policy. We consider three commonly used models of money: a cash-credit monetary economy, a money-in-the-utility-function monetary economy, and a shopping-time monetary economy. For each model, we provide sufficient conditions for the optimality of the Friedman rule. These conditions for the cash-credit economy and the money-in-the­ utility-function economy are analyzed by Chari et al. ( 1 996), while conditions for the shopping-time economy are analyzed by Kimbrough ( 1 986), Faig ( 1 988), Woodford ( 1 990), Guidotti and Vegh ( 1 993), and Correia and Teles ( 1 996), as well as by

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Chari et al. ( 1 996). The common features of the requirements for optimality are simple homotheticity and separability conditions similar to those in the public finance literature on optimal uniform commodity taxation. There have been conjectures in the literature - by Kimbrough ( 1 986) and Woodford ( 1 990), among others - about the connection between the optimality of the Friedman rule and the intermediate-goods results. For all three monetary economies, we show that when the homotheticity and separability conditions hold, the optimality of the Friedman rule follows from the intermediate-goods result. Finally, we report results for a quantitative monetary business cycle model. We find that if debt has nominal non-state-contingent returns, so that asset markets are incomplete, inflation can be used to make real returns contingent, so that debt can serve as a shock absorber. 1 . The primal approach to optimal taxation

The general approach to characterizing competitive equilibria with distorting taxes described in this section is known in the public finance literature as the primal approach to taxation. [See Atkinson and Stiglitz ( 1 980).] The basic idea is to recast the problem of choosing optimal taxes as a problem of choosing allocations subject to constraints which capture the restrictions on the type of allocations that can be supported as a competitive equilibrium for some choice of taxes. In this section, we lay out the primal approach and use it to establish some basic principles of optimal taxation, together with the results on uniform commodity taxation and intermediate­ goods taxation. The rest of this chapter applies these basic principles of optimal taxation to a variety of environments of interest to macroeconomists. These environments all have an infinite number of periods and include some combination of uncertainty, capital, debt, and money. As such, the derivations of the results look more complicated than the derivations here, but the basic ideas are quite similar. 1 . 1.

The Ramsey allocation problem

Consider a model economy in which n types of consumption goods are produced with labor. The resource constraint is given by

F(c 1 + gJ ,

.

.

.

, ell

+ gil , !) = 0,

(1.1)

where c; and g; denote private and government consumption of good i , l denotes labor, and F denotes a production process that satisfies constant returns to scale. The consumer's problem is to maximize utility: max U(c 1 , subject to

. . .

, ell,

l)

L P; ( 1 + r;)

( 1 .2) C; o=

l'

( 1 .3)

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where p; i.s the price of good i and T; is the ad valorem tax rate on good i. Thus there are n linear commodity taxes. We normalize the wage to 1 . A representative firm operates the constant returns technology F and solves ( 1 .4) subject to where

x;

F(xh . . . , Xn, l) = 0,

denotes output of good

i.

( 1 .5) The government budget constraint is ( 1 .6)

Market clearing requires that

c; + g; = x;

for

i=

1, . . .

, n.

( 1 .7)

Throughout this chapter, we take government expenditures as given. A competitive equilibrium is a policy :rr = ( T;)7= 1 ; allocations c, l, and x; and a price system p that satisfy the following: (i) the allocations c and l maximize Equation ( 1 .2) subject to ( 1 .3), (ii) the allocations x and l solve Equation ( 1 .4), (iii) the government budget constraint ( 1 .6) holds, and (iv) the allocations c and x satisfy condition ( 1 .7). Throughout this chapter, we assume that first-order conditions are necessary and sufficient and that all allocations are interior. The sufficiency of the first-order conditions for firms and consumers holds under appropriate concavity assumptions, and interiority can be assured with appropriate monotonicity and Inada conditions. Proposition 1.

The allocations in a competitive equilibrium satisfY ( 1 .8)

and the implementability constraint ( 1 .9)

Furthermore, given allocations which satisfy Equations (1. 8) and (1.9), we can construct policies and prices which, together with the given allocations, constitute a competitive equilibrium. The literature usually refers to Equation ( 1 .9) as the implementability a constraint on the set of allocations that can be implemented as a competitive equilibrium with distorting taxes. This constraint can be thought of as the consumer budget constraint with both the taxes and the prices substituted out by using first-order conditions. Remark:

constraint because it is

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Proof: We first prove that the allocations in a competitive equilibrium must satisfy Equations ( 1 . 8) and ( 1 .9). Condition ( 1 . 8) follows from substituting the market-clearing condition ( 1 .7) into ( 1 . 5). To derive Equation ( 1 .9), notice that the consumer's first­ order conditions are

U; = ap;(l + r;) for i = 1 , . -U1 = a, L P;(l + r;) c; = l,

.

.

, n,

( 1 . 1 0) (1 . 1 1) ( 1 . 1 2)

where a is the Lagrange multiplier on the budget constraint. Substituting Equations ( 1 . 1 0) and ( 1 . 1 1 ) into ( 1 . 1 2) gives ( 1 .9). Next, we prove that if c and l satisfy ( 1 .8) and ( 1 .9), then a price system p, a policy JT, and an allocation x, together with the given allocations, constitute a competitive equilibrium. We use the first-order conditions for the firm, which are

p; = --F;IF1

for

We construct x, p, and

i=

JT

1, . . .

as follows:

U, F1 l + r, = UI F;

( 1 . 1 3)

, n. x;

= c; + g;, p; is from ( 1 . 1 3), and :rr is from

Given our assumptions on the utility function, the first-order conditions are necessary and sufficient for consumer and firm maximization. With x, p, and JT so defined, (c, l, x, p , n) clearly satisfies firm maximization. When a = -U1, conditions ( 1 . 1 0) and ( 1 . 1 1) clearly are also satisfied. Substituting for U; and U1 in Equation ( 1 .9), we have

L c;ap;(l + r;) - al = 0. Dividing by a and rearranging gives Equation ( 1 . 1 2). The government budget constraint is satisfied by Walras' law. D We can now define a type of optimal tax equilibrium in which the government objective is to maximize the utility of consumers. We think of the government as first choosing policies and of private agents as then choosing their actions. Let II denote the set of policies for which a competitive equilibrium exists. A Ramsey equilibrium is a policy JT = (r;)7�1 in II; allocation rules c(-), l(·), and x(·); and a price function p(-) that satisfy the following: (i) the policy JT solves max Jf'

U(c(n'), l(n')) ( 1 . 1 4)

and (ii) for every n' , the allocations c(n'), l(JC1), x(n'), the price system p(n'), and the policy n' constitute a competitive equilibrium.

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Notice that we require optimality by consumers and firms for all policies that the government might choose. This requirement is analogous to the requirement of subgame perfection in a game. To see why this requirement is important, suppose we had not imposed it. That is, suppose we required optimality by consumers and firms only at the equilibrium policies, but allowed allocation and price rules to be arbitrary elsewhere. Then the set of equilibria is much larger. For example, allocation rules that prescribe zero labor supply for all policies other than some particular policy would satisfy all the equilibrium conditions. Since the government's budget constraint is then satisfied only at the particular policy, the government optimally chooses that policy. We think that such equilibria do not make sense. That is, we think the requirement that consumers and firms behave optimally for all policies is the sensible way to solve the government's problem of forecasting private behavior. If the competitive equilibrium associated with each policy is unique, clearly the Ramsey equilibrium is also unique. If there are multiple competitive equilibria associated with some policies, our definition of a Ramsey equilibrium requires that a selection be made from the set of competitive equilibria. In this case, there may be many Ramsey equilibria, depending on the particular selection made. In this chapter, we focus on the Ramsey equilibrium that yields the highest utility for the government. In such a Ramsey equilibrium, a particular allocation and price system are realized, namely, c, l, and p. We call these the Ramsey allocations and prices. We then have the following proposition as an immediate corollary of Proposition I . Proposition 2. The Ramsey allocations solve the Ramsey problem, which is to choose c and l to maximize U(c, l) subject to conditions (1. 8) and (1.9).

We have studied an economy in which the government uses consumption-goods taxes to raise revenues and have shown how the problem of solving for the Ramsey equilibrium reduces to the simpler problem of solving for the Ramsey allocations. Other tax systems lead to the same Ramsey problem. For example, consider a tax system that includes taxes on the n consumption goods as well as taxes on labor income. It can be shown that the Ramsey allocations can be supported by a tax system that uses any n of the n + 1 instruments. For example, the Ramsey allocations can be supported by taxes on consumption goods 2 through n and labor income or by taxes on consumption goods alone. The fact that the Ramsey allocations can be decentralized in many ways implies that it is more useful to think about optimal taxation in terms of the implied wedges between marginal rates of substitution and marginal rates of transformation rather than in tenns of the particular tax system used to decentralize the Ramsey allocations. The form of the Ramsey allocation problem depends on the assumption that the tax system contains at least n independent instruments. We call such a tax system complete. An example of an incomplete tax system is one in which taxes on the first consumption good and labor are constrained to be zero. For such an incomplete tax

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system, the analog of Proposition 1 is that a set of allocations is part of a competitive equilibrium if and only if the set satisfies conditions ( 1 .8) and ( 1 .9), together with

U1 Ut

=

"!:_!_ Ft

Intuitively, this constraint captures the fact that the government has no tax instruments that drive a wedge between the marginal rate of substitution of the first consumption good and labor and the marginal rate of transformation of the same commodities. The reader will find proving this analog useful, in part, because the proof illustrates that condition ( 1 .9) must hold regardless of the nature of the tax system. That is, when the tax system is incomplete, the implementability constraint is unchanged, and the new constraints that reflect this incompleteness must be added to the Ramsey problem.

1.2. Elasticities and commodity taxation We can use the Ramsey allocation problem to derive some simple results on optimal commodity taxes. We show that with additively separable preferences, tax rates depend on income elasticities, with necessities being taxed more than luxuries. The discussion here closely follows Atkinson and Stiglitz ( 1 980, chap. 1 2). Consider the first-order conditions for the Ramsey problem:

( 1 + A) U; - AU;H; = yF; , ( 1 + A) Ut - A UtHt - YFt, =

( 1 . 15) ( 1 . 1 6)

where A and y are the Lagrange multipliers on the implementability constraint and the resource constraint, respectively; H; = -(L:i �ici + Uul)IU; ; and H1 = -(I:1 Uuc1 + Uul)IU1• Using Equations ( 1 . 1 0), ( 1 . 1 1 ), and ( 1.1 3) in ( 1 . 1 5) and ( 1 . 1 6) and simplifying gives

__!!__ 1 + 'T;

=

A(H; - Ht) 1 + A - AH, ·

Rearranging shows that the relative tax rates for two goods i and) are determined by

r/ ( 1 + T;) Tj/( 1 + ri)

-

---

_

-

H; - H1 Hi - H,

----�-

( 1 . 1 7)

Now, Equation ( 1 . 1 7) is not an explicit formula for optimal tax rates, since the H;, Hj, and H1 terms depend on endogenous variables. Nevertheless, ( 1 . 1 7) shows that if H; > Hi , then T; > 1j. Suppose next that the utility function is additively separable. Then

( 1 . 1 8) Let c(p, m), l(p, rn) denote the solution to the problem of maximizing utility subject to L: P; C; = l + m, where m is nonlabor income, so that c;(p, m) is the demand function

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for good i. Letting a denote the Lagrange multiplier on the budget constraint, we can differentiate the first-order condition U;(c(p, m)) = a(p, m)p; with respect to nonlabor income m to obtain

8c; U; 8a U;; am = p; 8a am = a am or

8c; = - -1 8a H1 -1 c; 8m a 8m

(1 . 1 9)

so that H;

Hj

= !}j_ rh

( 1 .20)

where 17; is the income elasticity of demand for good i. Thus necessities should be taxed more than luxuries. The standard partial equilibrium result is that goods with low price elasticities of demand should be taxed more heavily than goods with high price elasticities. In general equilibrium, this result does not necessarily hold. It does hold if preferences are additively separable and there are no income effects. That is, utility is quasi-linear and is given by ( 1 .2 1 ) For such a utility function, Equation ( 1 .20) is not helpful because the income elasticities for all the consumption goods are zero. It is easy to show that for a utility function of the form ( 1 .2 1), H; = li E;, where E; = -(8c/8p;)p;/c; is the price elasticity of demand. To see this, differentiate the first-order condition with respect to p;,

U;(c(p, m), l(p, m)) = ap;,

( 1 .22)

to obtain

8c; = a U'' 8p; '

( 1 .23)

where a is constant because of quasi-linearity. Substituting Equations ( 1 .22) and ( 1 .23) into ( 1 . 1 8) gives H; = 11 E;. Since T; > r1 when H; > H1 , consumption goods which are relatively more price inelastic (have low f;) should be taxed relatively heavily. To summarize, with additive separability, the general result is that tax rates depend on income elasticities, with necessities taxed more than luxuries . Moreover, the familiar

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intuition from partial equilibrium that goods with low price elasticities should be taxed heavily does not necessarily apply in a general equilibrium setting.

1.3. Uniform commodity taxation Here we set up and prove the classic result on uniform commodity taxation. This result specifies a set of conditions under which taxing all goods at the same rate is optimal. [See Atkinson and Stiglitz ( 1 972).] Consider a utility function of the form

U(c, l) = W(G(c) , l) where

c =

(c l , . . . , c11)

( 1 .24)

and

G

is homothetic.

Proposition 3. !f utility satisfies condition (1.24) - that is, utility is weakly separable across consumption goods and is homothetic in consumption - then U/U; = F;IFJ for i = 1 , . . . , n. That is, optimal commodity taxation is un!form in the sense that the Ramsey taxes satisfy T; = 7j for i = 1 , . . . , n. Proof: Substituting the firm's first-order conditions ( 1 . 1 3) into the consumer's first­ order condition, we have that

Thus T; = 7j if and only if U;IF; U;IFJ. Note that a utility function which satisfies condition ( 1 .24) satisfies =

( 1 .25)

To see this, notice that from homotheticity, it follows that

U;(ac, l) Uk(ac, l) or

_ -

U;(c, l) Uk(c, l)

---

l

U; (c, l) U (ac, l). U; (ac, l) = Uk(c, l) �c

J

Differentiating Equation ( 1 .26) with respect to gives ( 1 .25).

( 1 .26)

a

and evaluating it at

a

=

1

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Consider next the first-order condition for c; from the Ramsey problem, namely,

( I + A) U, 1 A

[�

cpij

1

l

IU,

�

yF, ,

( 1 .27)

where, again, A is the multiplier on the implementability constraint and y is the multiplier on the resource constraint. From Equation ( 1 .25), we have that there is some constant A such that _Li ci Uu = AU; for all i. Using this fact and the form of utility function, we can rewrite Equation ( 1 .27) as ( 1 + A) Wt G; + A [AW1 G; + lW1 2 G;] Since Equation ( 1 .28) holds for all U;

F;

=

Wt G;

F;

=

W1 Gi

Fi

=

=

AF;.

i and ), G;IF;

( 1 .28) =

G/FJ for all

i

and ) and

� Fi

D

Note that the Ramsey allocations can be decentralized in many ways. For example, taxes on goods can all be set to an arbitrary constant, including zero, and remaining revenues raised by taxing labor income. Consider some generalizations of this proposition. Suppose that the utility function is homothetic and separable over a subgroup of goods, in the sense that the utility function can be written as U(c� , . . . , ck , t/J(ck+t , . . . , en ), !)

with tjJ homothetic. Then it is easy to show that the Ramsey taxes Tk + 1 = . . . = Tn . Next, if there is some untaxed income, then we need to modify Proposition 3 . Suppose that we add to the model an endowment of good 1 , y1 , which is not taxed. Then the implementability constraint becomes

2:=: U;c; + U1l = U1Y 1 ·

Then even i f U satisfies U (t/J(c 1 , . . . , c11), l) with tjJ homothetic, it i s not true that optimal taxes are uniform (because of the extra terms UlJYt from the derivatives of U1y1 ). If we add the assumption that U is additively separable across c 1 , . . , C11 , then the Ramsey taxes for goods 2 through n will be uniform, but not equal to the tax on good 1 . Next, suppose that the tax system is incomplete in the sense that the government is restricted to setting the tax on good 1 to some fixed number, say, r1 = 0. Then the Ramsey problem now must include the constraint .

U; U,

=

F1

F1

in addition to the resource constraint and the implementability constraint. Then even if U satisfies condition ( 1 .24), optimal commodity taxes on goods 2 through n are not

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necessarily uniform. Finally, in order to connect this result on uniform commodity taxation to some of the later results, suppose that the utility function is defined over an infinite sequence of consumption and labor goods as U(c� , c2 , . . . , !1 , !2, . . . ). The assumption that the utility is of the form V(f/J(c 1 , , c1 , ), li , l2 , . . . ) with fjJ homothetic and separable between consumption and all labor goods l� , !2, . . . , together with the assumption that the utility function is additively separable across time with constant discount factor /3, restricts the utility function to the form • . •

1 . 4.

• • .

Intermediate goods

Here we establish the classic intermediate--goods result for a simple example. (This example turns out to be useful when we study monetary economies.) Recall the standard result in public finance that under a wide variety of circumstances, an optimal tax system maintains aggregate production efficiency. [See Diamond and Mirrlees ( 1 97 1).] In the context of an economy with multiple production sectors, transactions between firms can be taxed. Taxing such transactions distorts the relations between the marginal rate of transformation in one sector and the marginal rate of transformation in another sector and yields aggregate production inefficiency. In such a setup, the standard result on aggregate production efficiency immediately implies that taxing intermediate goods is not optimal. Consider an economy with three final goods - private consumption x, government consumption g, and labor / - and an intermediate good z. The utility function is U(x, !). The technology set for producing the final consumption good using labor /1 and the intermediate good is described by f(x, z, l l ) ::( 0,

( 1 .29)

where f is a constant returns to scale production function. There is a technology set for producing the intermediate good and government consumption using labor h described by ( 1 .30) where h also is a constant returns to scale production function. The consumer's problem is to maximize U(x, lt + l2) subject to p( l

+ r) x ::::;

w(/1

+ /2 ) ,

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where p and w are the prices of the consumption good and labor and T is the tax on the consumption good. The firm that produces private consumption goods maximizes profits

px - w/ 1 - q( l + 17) z subject to condition ( 1 .29); q is the price of intermediate goods, and 17 is the tax on intermediate goods. The firm that produces intermediate goods and government consumption goods maximizes profits

qz + rg - w/2 , where r is the price of government consumption, subject to condition (1 .30). We can easily show that the Ramsey allocation problem is given by max

U(x, /1 + lz)

subject to conditions

( 1 .29), ( 1 .30),

and

xUx + (!1 + /2 ) Ut = 0.

( 1 .3 1 )

We then have Proposition 4.

The solution to the Ramsey allocation problem satisfies production efficiency; namely, the marginal rates of transformation are equated across technologies. Equivalently, setting the tax on intermediate goods 17 0 is optimal. =

Proof:

For this economy, production efficiency is equivalent to

( 1 .32) Solving the Ramsey allocation problem, we obtain the following first-order conditions for z, h , and /2 , respectively:

ufz

( 1 .33) ( 1 .34) ( 1 .35)

-f.-lhz , U, + A (xUtx + Vt + lUu) + ufi = 0, Ut + J..(xV1x + U, + lUu) + f.-lht = 0, =

where v, f.-l, and A are the multipliers on (1 .29), ( l .30), and ( 1 .3 1). Combining Equations (1 .34) and ( 1 .35) gives vft f.-lh1, which, combined with ( 1 .33), establishes Equation ( 1 .32). The first-order conditions for profit maximization for the firms imply that =

fz_ q(l + 17) .ft

=

w

Thus, if condition

=

_

hz ( l YJ). + h,

( 1 .32)

holds, Equation

( 1 .36) ( 1 .36) implies that

TJ

=

0.

D

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1 686

The intermediate-goods result holds in general settings in which there are (possibly infinitely) many goods and many production technologies. We have assumed that the production technologies satisfy constant returns to scale. If there are increasing returns to scale, then there are standard problems with the existence of a competitive equilibrium. If there are decreasing returns to scale, then the intermediate-goods result continues to hold, provided that pure profits can be fully taxed away. It turns out that the result for uniform commodity taxation follows from the inter­ mediate-goods result. To see this, consider a utility function of the form

U (c, l) = W(G(c), l),

( 1 .37)

where c = (c 1 , . . . , c17 ) and G is homogeneous of degree 1 . We can reinterpret this economy as an economy with a single consumption good x, which is produced using n intermediate-goods inputs (c 1 , . . . , en ) with the constant returns to scale technology x = G(c). The intermediate-goods result requires that in an optimal tax system, the taxes on the intermediate-goods inputs be zero, so that there are taxes only on final goods x and !. This is clearly equivalent to a uniform tax on (c 1 , . . . , c17 ) . 2. Fiscal policy

In this section, we begin by setting out a general framework for analyzing optimal fiscal policy in a stochastic one-sector growth model. We use a deterministic version of this model to develop results on the taxation of capital income, in both the short and long run. We first show that the optimal capital income taxes are zero in a steady state, even if there are heterogeneous consumers. We then show that for a class of utility functions, there is only one period with nonzero capital income taxes, following which capital income taxes are zero along a transition to the steady state. We then turn to the cyclical properties of optimal fiscal policy. In a stochastic model without capital, we illustrate how debt can act as a shock absorber. We briefly discuss how incomplete markets can alter these results. We then illustrate the main features of optimal fiscal policy over a business cycle using a calibrated version of the model with capital. Finally, we discuss how these results are altered in three other environments: an endogenous growth model, an open economy model, and an overlapping generations model. 2. 1.

General framework

Consider a production economy populated by a large number of identical, infinitely lived consumers. In each period t 0, 1 , . . . , the economy experiences one of finitely many events s1 • We denote by s 1 (so, . . . , st) the history of events up to and including period t. The probability, as of period 0, of any particular history s 1 is fl(s 1 ). The initial realization s0 is given. This suggests a natural commodity space in which goods are differentiated by histories. =

=

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In each period t, the economy has two goods: a consumption-capital good and labor. A constant returns to scale technology which satisfies the standard Inada conditions is available to transform capital k(s H ) and labor /(s f) into output via F(k(s t-1 ), l(s t) , s )­ t Notice that the production function incorporates a stochastic shock St . The output can be used for private consumption c(s 1 ), government consumption g(s 1 ), and new capital k(s 1 ). Throughout, we will take government consumption to be exogenously specified. Feasibility requires that

c(s t ) + g(s 1 ) + k(s 1 ) = F(k(s 1- 1 ), l(s 1 ), s1 ) + (1 - 6) k(s H ) ,

(2.1)

L f31 /1(S 1 ) U(c(s 1 ), l(s 1 )),

(2.2)

where 0 is the depreciation rate on capital. The preferences of each consumer are given by t, s 1

where 0 < f-3 < 1 and U is strictly increasing in consumption, is strictly decreasing in labor, is strictly concave, and satisfies the lnada conditions. Government consumption is financed by proportional taxes on the income from labor and capital and by debt. Let r(s1) and 8(s 1) denote the tax rates on the income from labor and capital. Government debt has a one-period maturity and a state-contingent return. Let b(s 1 ) denote the number of units of debt issued at state s 1 and Rb(s t+ 1 ) de­ note the return at any state s t+I = (s 1 , s1+ 1 ). The consumer's budget constraint is

c(s 1 ) + k(s 1 ) + b(s 1 ) :::;;;

[1 - r(s 1)] w(s 1 ) l(s 1) + Rk(s 1 ) k(s 1- 1 ) + Rb(s 1 ) b(s H ),

(2.3)

where Rk(s 1 ) 1 + [ 1 - 8(s 1 )] [r(s 1 ) - 0] is the gross return on capital after taxes and depreciation and r(s 1 ) and w(s 1 ) are the before-tax returns on capital and labor. Con­ sumers' debt holdings are bounded by b(s 1 ) ;? -·M for some large constant M . Com­ petitive pricing ensures that these returns equal their marginal products, namely, that =

(2.4) (2.5)

r(s f) Fk(k(s H ), /(sf), s1 ), w(s 1 ) = Ft(k(s 1- 1 ), l(s t ), s1 ). =

Consumers' purchases of capital are constrained to be nonnegative, and the purchases of government debt are bounded above and below by some arbitrarily large constants. We let x(s 1) = (c(s1), /(s 1 ), k(s 1 ), b(s 1 )) denote an allocation for consumers at s 1 and let x = (x(sf)) denote an allocation for all st . We let (w, r, Rh) (w(s 1 ), r(s t ), Rh(s 1 )) denote a price system. The government sets tax rates on labor and capital income and returns for government debt to finance the exogenous sequence of government consumption. The government's budget constraint is =

b(s 1 ) = Rb(s t ) b(s H ) + g(s 1 ) -- r(s 1 ) w(s 1 ) l(s 1 ) 8(: / )[r(s 1 ) - 6] k(s 1 1 ). (2.6) We let n(s 1) (r(sf), 8(s 1 )) denote the government policy at sf and let n; = (n(s1)) denote the infinite sequence of policies. The initial stock of debt, b_ 1 , and the initial stock of capital, k_ 1 , are given. - ·

=

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VV Chari and P.J. Kehoe

Notice that for notational simplicity, we have not explicitly included markets in private claims, so all borrowing and lending is between consumers and the government. Since all consumers are identical, such claims will not be traded in equilibrium; hence their absence will not affect the equilibrium. Thus we can always interpret the current model as having complete contingent private claims markets. A competitive equilibrium for this economy is a policy JC, an allocation x, and a price system (w, r, Rb) such that given the policy and the price system, the resulting allocation maximizes the representative consumer's utility (2.2) subject to the sequence of budget constraints (2. 3), the price system satisfies (2.4) and (2.5), and the government's budget constraint (2.6) is satisfied. Notice that we do not need to impose the feasibility condition (2. 1 ) in our definition of equilibrium. Given our assumptions on the utility function, constraint (2.3) is satisfied with equality in an equilibrium, and this feature, together with (2.6), implies (2. 1 ) . Consider now the policy problem faced by the goverument. We suppose that there is an institution or a commitment technology through which the government, in period 0, can bind itself to a particular sequence of policies once and for all. We model this by having the government choose a policy JC at the beginning of time and then having consumers choose their allocations. Formally, allocation rules are sequences of functions x(JT) (x(s 1 I n)) that map policies JT into allocations x(n). Price rules are sequences of functions w(JT) = (w(s 1 I n)) and r(n) (r(s 1 I n)) that map policies JT into price systems. Since the government needs to predict how consumer allocations and prices will respond to its policies, consumer allocations and prices must be described by rules that associate government policies with allocations. We will impose a restriction on the set of policies that the government can choose. Since the capital stock in period 0 is inelastically supplied, the government has an incentive to set the initial capital tax rate as high as possible. To make the problem interesting, we will require that the initial capital tax rate, 8(s0), be fixed at some rate. A Ramsey equilibrium is a policy JT, an allocation rule x(-), and price rules w ( - ) and r(-) that satisfy the following: (i) the policy JT maximizes =

=

L fJp(s 1 ) U(c(s 1 I n), l(s 1 I n)) t, s '

subject to constraint (2.6), with allocations and prices given by x(lc), w(n), and r(n); and (ii) for every JT1, the allocation x(n'), the price system w(n'), r(n'), and Rb(n'), and the policy JT1 constitute a competitive equilibrium. We now turn to characterizing the equilibrium policies and allocations. In terms of notation, it will be convenient here and throughout the chapter to let Uc(s1) and Ut(s 1) denote the marginal utilities o f consumption and leisure at state s1 and let Fk (s 1) and F1(s1) denote the marginal products of capital and labor at state s 1 • We will show that a competitive equilibrium is characterized by two fairly simple conditions: the resource constraint (2.7)

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and the implementability constraint

L {31 tJ-(s1) [ Uc(s1) c(s 1 ) + u,(s1) l(s1)] = Uc(so) [Rk (so) L I + Rb(so) b_l ] , (2.8) t,st where Rk(so) = l + [1 - 8(s0 )][Fk(s0 ) - D ] . The implementability constraint should be

thought of as an infinite-horizon version of the budget constraint of either the consumer or the government, where the consumer and firm first-order conditions have been used to substitute out the prices and policies. We have

The consumption, labor, and capital allocations and the capital tax rate and return on debt in period 0 in a competitive equilibrium satisfy conditions (2. 7) and (2.8). Furthermore, given allocations and period 0 policies that sati:;fY (2. 7) and (2.8), we can construct policies, prices, and debt holdings that, together with the given allocations and period-0 policies, constitute a competitive equilibrium. Proposition 5.

We first show that a competitive equilibrium must satisfy (2.7) and (2.8). To see this, note that we can add (2.3) and (2.6) to get (2.7), and thus feasibility is satisfied in equilibrium. Next, consider the allocation rule x(n). The necessary and sufficient conditions for c, l, b, and k to solve the consumer's problem are given as follows. Let p(s 1 ) denote the Lagrange multiplier on constraint (2.3 ) . Then by Weitzman's ( 1 973) and Ekeland and Scheinkman's (1986) theorems, these conditions are constraint (2 . 3), together with first-order conditions for consumption and labor: Proof:

{31 tJ-(s1) Uc(s1) ,::;; p(s 1 ), with equality if c(s 1 ) > 0, {31 tJ-(s1) U1(s1) ,::;; -p(s 1 )( 1 - r(s 1 )) w(s 1 ), with equality if l(s 1 ) > 0;

(2.9) (2. 1 0)

first-order conditions for capital and government debt:

[ [

] ]

p(s1) -- L.:><s t+ 1 ) Rb(s t+ 1 ) b(s 1 ) = 0,

(2. 1 1)

p (s t ) - L P(s t l l ) Rk(s H 1 )

(2. 12)

s t+l

s t+l

k (s t ) = 0 ;

and the two transversality conditions lim

"" p(s 1 ) b(s 1 )

t ---+ oo � s'

=

0,

(2. 13) (2. 14)

We claim that any allocation which satisfies (2.3) and (2.9)-(2. 14) must also satisfy (2.8). To see this, multiply (2.3) by p (s 1), sum over t and s 1 , and use (2. 1 1)-(2.14) to obtain

t,s1

(2. 1 5)

1 690

V.V. Chari and PJ Kehoe

Using (2.9) and (2. 1 0) and noting that interiority follows from the Inada conditions, we can rewrite Equation (2. 1 5) as

(2. 1 6) Thus (2.7) and (2. 8) are necessary conditions that any competitive equilibrium must satisfy. Next, suppose that we are given allocations and period-0 policies that satisfy (2.7) and (2.8). We construct the competitive equilibrium as follows. First, note that for an allocation to be part of a competitive equilibrium, it must satisfy conditions (2.3) and (2.9)-(2 . 1 4). Multiplying (2.3) by p(s 1) and summing over all periods and states following sr and using (2.9)-(2. 1 4), we get (2. 1 7) Thus any competitive equilibrium debt allocation must satisfy (2. 1 7), and hence (2. 1 7) defines the unique debt allocations given consumption, labor, and capital allocations. The wage rate and the rental rate on capital are determined by (2.4) and (2.5) from the capital and labor allocations. The labor tax rate is determined from (2. 5), (2.9), and (2. 1 0) and is given by

UI(st) Uc(s 1 )

- -- =

t

[ 1 - T(s )]h, (s t ) .

(2. 1 8)

We can use Equations (2.3), (2.9), (2. 1 1 ), and (2. 1 2) to construct the capital tax rate and the return on debt. From these conditions, it is clear that given the allocations, the tax rate on capital and the return on debt satisfy (2. 1 9)

8tt l is t

(2.20)

c(sL+ 1 ) + k(s t+ 1 ) + b(s 1+1 ) 1 [ 1 - r(s 1+ )] w(s 1+ 1 ) l(s L+1 ) + Rk (s L+l ) k(s 1 ) + Rh (s tt-1 ) b(s 1 ), =

(2.2 1 )

where Rk(sl+ 1 ) 1 + [ 1 8(s t+ 1 )] [r(s t+ 1 ) - Ci]. l t turns out that these conditions do not uniquely determine the tax rate on capital and the return on debt. To see this, suppose that s1+ t can take on one of N values. Then counting equations and unknowns in Equations (2. 1 9)-(2.2 1 ) gives N + 2 equations and 2N unknowns in each period and state. Actually, however, there is one linear dependency across these equations. To see c�

· ·

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1691

(2.21) by {3f.l(s 1+1) Uc(s1+ 1 ) and sum across states in period t + 1 . Use (2. 17), (2. 1 9), and (2.20) to obtain an equation that does not depend on Rb and 8. Since we can replace any of the N equations from (2.21) with this equation, there are only N + 1 equations left to determine Rb and 8. Thus there are N 1 degrees of

this, multiply

-

indeterminacy in setting the tax rate on capital and determining the return on debt. One particular set of policies supporting a competitive equilibrium has the capital tax rate not contingent on the current state. That is, suppose for each s 1,

(2.22) of (2.21)

We can then use (2. 1 9) to define 8(s 1 ) and use the period-t + 1 version to define R�;(s t+ 1 ). It i s straightforward t o check that the constructed return o n debt satisfies (2.20). Another set of policies supporting the same competitive equilibrium has the return on debt not contingent on the current state. [For details, see Chari et al. (1994), and for a more general discussion of this kind of indeterminacy, see Bohn

(1994). ] 0

If the competitive equilibrium associated with each policy is unique, clearly the Ramsey equilibrium is also unique. If there are multiple competitive equilibria associated with some policies, our definition of a Ramsey equilibrium requires that a selection be made from the set of competitive equilibria. We focus on the Ramsey equilibrium that yields the highest utility for the government. Given our characterization of a competitive equilibrium, the characterization of this Ramsey equilibrium is immediate. We have Proposition 6. The allocations in a Ramsey equilibrium solve the following programming problem:

(2.23)

s'

subject to (2. 7) and (2.8). For convenience, write the Ramsey allocation problem in Lagrangian form:

t, subject to (2.7). The function s1

(2.24)

W simply incorporates the implementability constraint into the maximand and is given by

(2.25) where A is the Lagrange multiplier on the implementability constraint, order conditions for this problem imply that, for t :?: 1 ,

Wt(s1)

·- -- ··

Wc(s 1 )

�

1

Ft(S )

(2.8). The first­ (2.26)

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V.V. Chari and P.J. Kehoe

and

(2.27) A property of the Ramsey allocations which is useful in our analysis of the cyclical properties of optimal fiscal policy is the following. If the stochastic process on s follows a Markov process, then from Equations (2.26) and (2.27) it is clear that the allocations from period 1 onward can be described by time-invariant allocation rules c(k, s; A), l(k, s; A), k'(k, s; A), and b(k, s; A). The period-0 first-order conditions include terms related to the initial stocks of capital and debt and are therefore different from the other first-order conditions. The period-0 allocation rules are thus different from the stationary allocation rules, which govern behavior from period 1 onward. Thus far, we have considered a tax system with capital income taxes and labor income taxes. A wide variety of other tax systems lead to the same Ramsey allocation problem. For example, consider a tax system that includes consumption taxes, denoted rc(s1), as well as labor and capital income taxes. For such a system, the implementability constraint is given by

L f)1 tJ(s 1 ) [ Uc(s 1 ) c(s 1 ) + Ut(s 1 ) l(s 1 )] l,s1

=

� \

(so [Rk(so ) LJ + Rb(so ) b_ I ] , c ( + Teo

(2.28) where Rk(s0) 1 + [ 1 - (;l(s0)][Fk (s0) - b] and Teo is the tax rate on consumption in period 0. The first-order conditions of the competitive equilibrium with such a tax system are given by =

(2.29) and (2.30) where Rk(s t+ 1 ) 1 + [ 1 - {;l(s 1+ 1 )] [Fk(s 1 1 1 ) -- b]. Inspection of these first-order conditions shows that if an allocation satisfies the implementability constraint (2.28) and the resource constraint (2. 1 ) , it can be decentralized as a competitive equilibrium under a variety of tax systems. Examples of such tax systems include those with only consumption taxes and labor income taxes and those with only consumption taxes and capital income taxes. More complicated examples include those in which tax rates on capital and labor income are required to be the same, but are allowed to be different from tax rates on consumption. The message of this analysis is that optimal tax theory implies optimal wedges between marginal rates of substitution and marginal rates of =

Optimal Fiscal and Monetary Policy

Ch. 26:

1 693

transformation and is typically silent on the detailed taxes used to implement these wedges. Recall that with a capital and labor income tax system, we ruled out lump-sum taxes by imposing a constraint on period-0 capital income taxes. In a consumption and labor tax system, an analogous constraint is necessary. Notice that if consumption taxes are constant so that Tc (s 1 ) = Teo for all s and that if labor is subsidized appropriately so that T(s 1 ) = - Teo, then (2.29) and (2.30) become the undistorted first-order conditions. By setting Teo arbitrarily high, it is possible to satisfy (2.28) at the lump-sum tax allocations and thus to achieve the undistorted optimum. One way to rule this out is to impose an upper bound on Tc0- (There seems to be some confusion about this point in the literature.)

1

Capital income taxation 2.2. 1 . In a steady state 2.2.

Here we develop the results on the optimality of zero capital income taxes in a steady state, and we consider various generalizations and qualifications for that result. For simplicity, we consider a nonstochastic version of the model in which the stochastic shock in the production function is constant and government consumption is also constant, so g(s 1 ) = g. Suppose that under the Ramsey plan, the allocations converge to a steady state. In such a steady state, We is constant. Thus, from Equation (2.27), 1 = /3( 1 - D + Fk ) .

(2. 3 1 )

The consumer's intertemporal first-order condition (2. 1 9) in a steady state reduces to 1

=

/3 [ 1 + ( l

- 8)(Fk - l5)].

(2.32)

Comparing (2. 3 1 ) and (2.32), we can see that in a steady state, the optimal tax rate on capital income, e, is zero. This result is due to Charnley ( 1 980, 1 986). A natural conj ecture is that with heterogeneous consumers, a nonzero tax on capital income is optimal to redistribute income from one type of consumer to another. We examine this conjecture in an economy with two types of consumers, indexed i 1 , 2, whose preferences are given by =

OG

L f31Ui (cit , lit), t�O

(2.33)

where cit and /;1 denote the consumption and labor supply of a consumer of type i. Notice that the discount factors are assumed to be the same for both types of consumers. The resource constraint for this economy is given by (2.34) where the production function F has constant returns to scale. Notice that the production function allows for imperfect substitutability between the two types of labor

V. V. Chari and PJ. Kehoe

1 694

and capital. For this economy, the implementability constraints for the two types of consumers i 1 , 2 are given by =

(2.35) where kh and b!1 denote the initial ownership of capital and debt by consumers of type i 1 . If the tax system allows tax rates on capital income and labor income to differ across consumer types, then it is straightforward to establish that the resource constraint and the two implementability constraints completely characterize a competitive equilibrium. For the Ramsey equilibrium, we suppose that the government maximizes a weighted sum of consumers' utilities of the form 00

00

(2.36)

1 . The Ramsey problem where the welfare weights W; E [0, 1 ] satisfy w1 + OJ:2 is to maximize Equation (2.36) subject to the resource constraint (2.34) and the implementability constraints (2.35). Let us define

W(cJt, C2l, llt, l2t, }q , A2 )

=

L [W;Ui (cit, lit) + A;(U�[Cit + uj,lu)]

;�

1,2

(2.37)

for t ? 1 ; and for t = 0, W equals the right-hand side of Equation (2.37) evaluated at t 0 minus 2: A; U�0 (R�cokb + R bO bb ). Here A; is the Lagrange multiplier on the implementability constraint for the consumer of type i. The Ramsey problem is, then, to maximize =

C<J

L {)' W(cu, c21, lu, !2�> }q , A2 ) 1 �0

subject to the resource constraint (2.34). The first-order conditions for this problem imply that for In

a steady state,

Wet

i � l,2

and

t = 0, 1 , 2, . .

(2.38)

is a constant, and thus (2.39)

which as before implies that the steady-state tax on capital income is zero. This result is due to Judd ( 1 985). 1 Notice in (2.35) the initial assets are denoted kb and b0, while in (2.8) they are denoted k 1 and b_ 1 Throughout the chapter in detetministic environments initial assets have a subscript 0, while in stochastic environments initial assets have a subscript 1 . This unfortunate inconsistency stems from the tradition of using kt+ 1 to denote the capital choise in period t. �

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This result also holds when type- 1 consumers are workers who supply labor, cannot save or borrow, and hold no initial capital, while type-2 consumers are capitalists who own all the capital but supply no labor. Then we replace Equation (2.35) for type-1 consumers with (2.40) Notice that in the solution to the Ramsey problem, Equation (2.38) continues to hold for the capitalists, and thus the steady-state tax on capital income is zero. Notice also that this result shows that even if the Ramsey planner puts zero weight on the capitalists, taxing capital in the long run is still not optimal. The reason is that the cumulative distortion of the capital taxes on intertemporal margins makes even the workers prefer the static distortion of marginal rates that comes from labor income taxes. Now suppose that the tax system does not allow tax rates on either capital income or labor income to differ across consumer types. These restrictions on the tax system imply extra constraints on the allocations that can be achieved in a competitive equilibrium. Consider first the restriction that tax rates on capital income do not differ across consumers. To derive the restrictions that this adds to the Ramsey problem, consider the consumers' intertemporal first-order conditions, which can be written as (2.4 1) Since the right-hand side of Equation (2.4 1 ) does not vary with

i,

the restriction (2.42)

holds in any competitive equilibrium. Thus Equation (2.42) is an extra restriction that must be added to the Ramsey problem. Let {.1 denote the Lagrange multiplier on (2.42). 1 Defining

where x1 = (c l t , C2 t, li t , l2 �> }"! , A2 ), we can use the same argument as before, with V replacing W, to conclude that the steady-state tax on capital income is zero. Consider next the restriction that tax rates on labor income do not vary across consumers. Consider the consumers' first-order conditions for labor supply, which can be written as -

U£

1

·. ---

u�� Fw

=

1

-

T1 .

(2.43)

1 696

V.V. Chari and P.J Kehoe

Since the right-hand side of Equation (2.43) does not vary with i, the restriction

u,) u;; Fn t U}t U17 - F121 _

(2.44)

holds in any competitive equilibrium and thus must be added to the Ramsey problem. We proceed as before and, with no confusion, define (2.45) where v1 is the Lagrange multiplier on (2.44). A first-order condition for the Ramsey problem is

-f3 Vkt+ t + Vc tt = {3Vclt+ 1 [Fkt+ t + ( 1 - b)] . In a steady state, this reduces to

Clearly, unless Vk 0, the steady-state tax on capital income is not zero. Inspection 0 if and only if F1 1 /F121 does not depend of Equation (2.45) shows that Vk on k. Recall that the production function is separable between k and (It , 12) if Fn tfF121 does not depend on k . Such separable production functions can be written in the form F(k, 1� , !2) F(k, H(l1 , 12)) for some function H. [For some related discussion, see Stiglitz ( 1 987).] This analysis of fiscal policy with restrictions suggests that other restrictions on tax rates may lead to nonzero taxation of capital income in a steady state even in a representative agent model. Consider an economy with identical consumers, and consider another restriction on the tax system, namely, that tax rates are equal for all periods. Suppose, for example, that taxes on capital income are restricted to being equal for all periods from period 1 onward, while labor tax rates are unrestricted. Using the consumer's first-order conditions, we see that =

=

=

(2.46) together with the restriction that el+l across allocations:

�

el for all t > 1 , implies the following restriction (2.47)

The appropriate Ramsey problem, then, has constraints of the form (2.47), as well as the implemcntability constraint and the resource constraint. We leave it to the reader

Ch.

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1 697

(as a difficult exercise) to show that, under suitable conditions, the optimal tax on capital income is positive, even in the steady state. The intuition is that with no such restrictions, it is optimal to front-load the capital income taxes by initially making them large and positive and eventually setting them to zero. When taxes are constant, it is optimal to try to balance these two opposing forces and make them somewhat positive throughout. The discussion of the extra constraints on the Ramsey problem implied by restrictions on the tax system suggests the following observation. Zero capital income taxation in the steady state is optimal if the extra constraints do not depend on the capital stock and is not optimal if these constraints depend on the capital stock (and, of course, are binding). Another possible restriction is that there is some upper bound on tax rates. Suppose, for example, that capital tax rates are at most 1 00 percent. Then in addition to satisfying the analogs of conditions (2.7) and ( 2 . 8), an allocation must satisfy an extra condition to be part of a competitive equilibrium. Rewrite the analog of Equation (2. 1 9) as (2.48) Then if an allocation satisfies (2.49) and 81+ 1 ::S; 1 , Equation (2.48) implies that (2.50) Thus we can simply impose (2.50) as an extra constraint. With this constraint, for suitable restrictions on the utility function, the optimal policy is to set the tax rate to its upper bound for a finite number of periods. After that, the tax takes on an intermediate value for one period and is zero thereafter. 2.2.2.

in a non-steady state

In the preceding subsection, we showed that in a variety of circumstances, in a steady state, the optimal tax on capital income is zero. Sometimes one can establish a much stronger result, namely, that optimal capital income taxes are close to zero after only a few periods. [See Charnley ( 1 986), for example.] In this subsection, we show that for a commonly used class of utility functions, it is not optimal to distort the capital accumulation decision in period 1 or thereafter. The class of utility functions we consider are of the form

U(c, l)

=

l -o C 1 + - (f

V (l).

(2.5 1 )

One might conjecture that 1 f utility functions o f this form have the property that optimal capital income taxes are exactly zero after period l , then for utility functions that are in

1 698

V.V. Chari and PJ Kehoe

some sense close to these, keeping capital income tax rates close to zero after period 1 is also optimal. To motivate our result, we write the consumer's first-order condition for capital as (2.52) where q1+I f3 Uet+ I/Uct is the Arrow-Debreu price of a unit of consumption in period t + 1 in units of consumption in period t. Now, in an undistorted equilibrium, the consumer's first-order condition has the same left-hand side as (2.52), but the right­ hand side equals zero. Thus the right-hand side of (2.52) measures the size of the wedge between the distorted and undistorted first-order conditions for capital accumulation in period t. We then have =

P roposition 7 . For utility functions of the form (2.51), it is not optimal to distort the capital accumulation decision at period 1 or thereafter. Namely, the optimal tax rate on capital income received in period t is zero for t ;? 2. Equivalently,

(2.53)

Proof:

For

1 =

t ;? 1 , the first-order conditions for the Ramsey problem imply that

{3 Wet+ I 1 - u·' --( + Fkl+ I ), Wet

where W is given in Equation (2.25). For for capital imply that

1

=

[3

ucl+l [1 + (1 Uct

--

-

(2.54)

t ;?

1 , the consumer's first-order conditions

et l d (F"t+l - <:5)] .

(2.55)

Now, for any utility function of the form (2. 5 1 ), we can easily show that

Wc!+l = Uet+ l_ Wet Uct .

(2.56)

Substituting Equation (2.56) into (2. 54) and subtracting the resulting equation from (2.55) gives the result. 0

Proposition 7 implies that the tax rate on capital income received in period t is zero for t ;? 2 and is typically different from zero in period 1 . In period 0, of course, the tax rate is fixed by assumption. This result is much stronger than the standard Charnley result, which refers to steady states, and the logic behind this result is actually more connected to the uniform tax results than to the rest of the Chamley-type results. To see this, suppose that the tax

Ch. 26:

Optimal Fiscal and Monetary Policy

1 699

system allows the government to levy only proportional taxes on consumption and labor income. For this tax system, the analog of the restriction of the initial tax on capital income is that the initial consumption tax is given. Then with a utility function of the form (2. 5 1 ), consumption taxes are constant in all periods except period 0 . In a continuous-time version of the deterministic model with instantaneous preferences given by Equation (2. 5 1 ) , Charnley ( 1 986) shows that the tax rate on capital income is constant for a finite length of time and is zero thereafter. The reason for Charnley's different result is that he imposes an exogenous upper bound on the tax rate on capital income. If we impose such an upper bound, the Ramsey problem must be amended to include an extra constraint to capture the restrictions imposed by this upper bound. (See the example in Subsection 2.2. 1 .) In the deterministic version of the model, with preferences given by Equation (2. 5 1 ) , the tax rate is constant at this upper bound for a finite number of periods, there is one period of transition, and the tax rate is zero thereafter. In the stochastic version of the model, constraints of this kind can also be imposed. One can derive an upper bound endogenously. Consider the following scenario. At the end of each period t, consumers can rent capital to firms for use in period t + 1 and pay taxes on the rental income from capital in period t + 1 . Or consumers can choose to hide the capital, say, in their basements. If they hide it, the capital depreciates and is not available for use in t + 1 . Thus, if they hide it, there is no capital income, and consumers pay zero capital taxes. 2.3.

Cyclical properties

2.3. 1 .

Debt taxation as a shock absorber

In thi s subsection, we illustrate how state-contingent returns on debt can be used as a shock absorber in implementing optimal fiscal policy. One interpretation of state-contingent returns on debt is that the government issues debt with a non-state­ contingent return and uses taxes or partial defaults to make the return state-contingent. We show that under reasonable assumptions, during periods of high government expenditures such as wartime, the government partially defaults on debt, and during periods of low government expenditures such as peacetime, it does not. Many of the insights here are developed in Lucas and Stokey ( 1 983) and Chari et al. ( 199 1). We illustrate this shock-absorber role i n a version of our model of fiscal policy with no capital. Specifically, we assume that F(k, l,z) zl , where z is a technology shock. The resource constraint is =

and the consumer's first-order condition for labor supply is (2.57)

V. V Chari and P.J. Kehoe

1 700

The first-order condition for debt is

(2.58)

s t+l

For convenience, let H(s 1 ) = Uc(s') c(s1) + U1(s 1 ) l(s1). Notice that the resource con­ straint and the consumer's first-order condition imply H(s 1 ) = Uc(s 1 )[r(s 1 )z(s 1 ) l(s 1 ) ­ g(s 1 )]. Thus H(s1) is the value of the (primary) government surplus at s 1 in units of current marginal utility. The implementability constraint reduces to

L f31 !J(s 1 ) H(s 1 ) = Uc(so)Ro b t, s 1

Expression

(2.59)

t·

(2. 17) reduces to 00

b(sr) = L L f3t f-l(s t ) H(s t )lf3r f-l(sr) Uc(s'). t=r+ I

(2.60)

s1

Now imagine that the government promises a non-state-contingent (gross) rate of return on government debt R(s 1- 1 ) and then levies a state-contingent tax v(s 1 ) on the gross return on government debt. That is, R and v satisfy

Consider next detern1ining the tax rate and the return on debt. The after-tax return on debt [1 v(s,.)] R(s'-1) in some period r and state s' is obtained as follows. Multiplying the consumer budget constraint by {31 !J(s1) U,(s 1 ) and summing from period r and over all periods and states from period r + 1 onward, we obtain the familiar requirement that the value of the government's after-tax debt obligation must equal the expectea present value of government surpluses:

t =or +

I

s'

(2.6 1 ) While the after-tax returns are determined by Equation (2.6 1), the gross returns and the tax rates on debt are not separately determined. The reason is that both consumers and the government care only about the after-tax return on debt. Obviously, there are many ways of combining (before-tax) gross returns and tax rates to give the same after-tax

Optimal Fiscal and Monetary Policy

Ch. 26:

1701

returns. More formally, if v and R support a particular set of Ramsey allocations, so do any v and R ' that satisfy [1 -

v(s1)] R'(sr-I ) = [ 1 - v(s')] R(sr-I )

for all

r

d sr.

(2.62)

an

We resolve this indeterminacy by normalizing gross returns R to satisfy

(2.63) where

(2.62),

= (s H , st ). Notice that the normalization in Equation implies that tax rates on debt satisfy

s1

L p,(s 1 I s 1- 1 ) Uc(s 1 )v(s 1 ) = 0 st

for all

t

and

(2.63),

together with

s 1- 1 ,

(2.64)

where p,(s1 I s 1- 1 ) p,(s t+ 1 )/ p,(s 1 ). Next, we derive the first-order conditions for the Ramsey problem. Let A denote the Lagrange multiplier on the implementability constraint. The first-order conditions for t � 1 imply that =

(2.65) where Hc(s 1 ) and H1(s 1 ) denote the derivatives of H(s 1 ). For t 0, the first-order condition is the same as (2.65), except that the right-hand side is replaced by

These first-order conditions can be used to prove the following proposition:

For t � 1, there exist functions c, l, and 'i: such that the Ramsey consumption allocations, labor allocations, and labor tax rates can be written as Proposition 8.

0, then c(so), /(so), and r(so) are given by these same functions. Proof: For t � 1 , substituting from the resource constraint for l(s 1 ) into (2.65) gives one equation of the form F(c, g, z; A) = 0. Solving this gives the Ramsey

Moreover, if b

1

=

consumption allocation as a function of the current levels of government consumption, the technology shock, and the multiplier. From the resource constraint and from Equation (2.57), we know that the labor allocation and the labor tax rate are a function of these same variables. For t = 0, the same procedure gives allocations and the labor tax rate in period 0 as a function of g0, z0 , and A. We can solve for A by substituting

1 702

V.V. Chari and P.J. Kehoe

the allocations into the implementability constraint (2.59). Clearly, for b_ 1 first-order conditions for t 0 are the same as the first-order conditions for t =

=

0, the

;?: 1 . D

Proposition 8 says that the allocations and the labor tax rate depend only on the current realizations of the shocks and not separately on the entire history of realizations. This proposition implies that labor tax rates inherit the stochastic properties of the underlying shocks. For example, if government consumption is i.i.d. and the technology shock is constant, then tax rates are i.i.d. (This result does not hold in general with capital.) If government consumption is persistent, then so are the tax rates. This result of standard neoclassical theory sharply contrasts with claims in the literature that optimal taxation requires labor tax rates to follow a random walk. [See Barro ( 1 979), Mankiw ( 1 987), and our discussion in the following subsection, 2.3.2.] To understand the nature of the Ramsey outcomes, we consider several example�. In all of them, we let technology shocks be constant, so z(s1 ) 1 for all s 1• We begin with a deterministic example that illustrates how Ramsey policies smooth distortion" over time. =

Example 1 .

Consider an economy that alternates between wartime and peacetime. Specifically, let g = G for t even and g = 0 for t odd. Let the initial indebtedness 1 1 R_1 b_ 1 = 0. We will show that the government runs a deficit in wartime and then pays off the debt in the ensuing peacetime. Consider the first-order condition for the Ramsey problem in peacetime. Using the resource constraint, we have that ( 1 + Jc)[Uc(O) + Ut(O)] + Jcc[ Ucc (O) + 2 Uc� (O) + Uu(O)]

=

0,

where the partial derivatives are evaluated at g, 0. By strict concavity, the second bracketed term is negative. Since the multiplier A is positive, the first term is positive. From Equation (2.57), we have that Uc + U1 = r: Uc. Thus r:(O) > 0. When we use Proposition 8, Equation (2.59) implies that H( G) + {3H(O) = 0, which can be rewritten as =

Uc( G) [r(G) l(g) - G] + (3 Uc(O) [T(0) /(0)]

c=

0.

That is, the discounted value of the government surplus is zero over the two-period cycle of government consumption. Since the government runs a surplus in peacetime, it must run a deficit in wartime. Here the government sells debt b( G) G r:( G) l( G) in wartime and retires debt in the next peacetime. The gross return on the debt from wartime to peacetime is R(G) Uc(G)/(3 Uc(O), and with our normalization, the tax rate on debt is always zero. =

=

Example 2.

Consider an economy that has recurrent wars with long periods of peace in between. Specifically let g1 G for t = 0, T 2T, . . , and let g1 0 otherwise. Let =

,

=

Ch. 26:

Optimal Fiscal and Monetary Policy

the initial indebtedness R . 1 b 1 over each T -period cycle, that is, =

0.

1703

8,

Again, by Proposition

the budget is balanced

Uc ( G) [ r( G) /( G) - G] + f3 Uc (O) [ r (O) /(0)] + · · · + f3 r Uc(O) [ r(O) /(0)]

-!

=

0.

Here, as in Example 1 , the government runs a deficit in wartime and a constant surplus in peacetime. The war debt is slowly retired during the following T 1 periods of peace. The government enters the next wartime with zero debt and restarts the cycle. Specifically, the government issues debt of level G - r( G) l (G) in wartime. In the first period of peacetime, the government sells -

Uc(G) [ G - r( G) l( G)] - r(O) /(0) f3Uc(O) �--

units of debt. In the second period, it sells

Uc (G) [G /32 Uc(O)

r( G) /( G)]

--

r(O) l(O)·

73

---

-·

r(O), /(0),

and so on. Clearly, the debt is decreasing during peacetime. Example 3. Here we will illustrate the shock-absorbing nature of optimal debt taxes. Let government spending follow a two-state Markov process with a symmetric transition matrix with positive persistence. The two states are g1 = G and g1 0. Let =

:rc =

Prob {gnl

=

G I gt

=

G}

=

Prob {gt+l

=

0 I gt = 0 }

>

�-

Therefore, the probability o f staying at the same state is greater than the probability of switching states. Let go = G, and let the initial indebtedness R_ 1 b_ 1 be positive. The government's period t budget constraint is

(2.66) From Proposition S , the allocations and the labor tax rates depend only on the current realization g1 for t ;? 1 . Under the Markov assumption, Equations (2.60) and (2.63) imply that the end-of-period debt b(s ') and the interest rate R(s 1 ) depend only on the current realization g1 • From Equation (2.66), we know that the tax rate on debt depends on the current and the previous realizations. Let b(g1 ), R(g1 ), and v(g1_ 1 , g1 ) denote the end-of-period debt, the gross interest rate, and the tax rate on debt. For a large class of economies, we can prove the following proposition: Proposition 9. Suppose that in the solution to the Ramsey problem, H(O) > H(G) > 0; that is, the value of'government surpluses is larger in peacetime than in wartime, the

1 704

V.V. Chari and P.J Kehoe

government 's debt is always positive, the marginal utility of consumption is greater in wartime Uc( G) than in peacetime Uc(O), and both b( G) and b(O) are positive. Then v(O, G) > v(G, G) > 0 > v(O, 0) > v ( G , 0).

(2.67)

That is, the debt tax rates are most extreme in periods of transition: they are highest in transitions from peacetime to wartime and lowest in transitions from wartime to peacetime. Furthermore, debt is taxed in wartime and subsidized in peacetime. l t is possible to show that the assumptions in this proposition are satisfied for a large class of economies if the initial debt is sufficiently large.

Remark:

Let V (G) and V (O) denote the expected present value of government surpluses when the economy is in state G and state 0, respectively. These surpluses are given by the left-hand side of Equation (2 6 1 ) multiplied by the marginal utility of consumption in that state, which can be written recursively as

Proof:

.

V (G) = H(G) + f3[n V(G) + (i - n) V (O)], V (O) = H(O) + f3[n V(O) + (1 - n) V( G)].

(2.68) (2.69)

Solving these, we obtain

; ' {3 G) 1 H( 1 ( ( H(O) n) f3Jt) ; , V (O) = V (G) = {3( 1 - n) H(O) ( 1 - {)n) H(G )

where

D

(2.70) (2 . 7 1 )

= ( 1 - f3nf - (32 ( 1 - n)2 > 0. From Equation (2.60), we obtain

b(G) = b(O) =

{3 [nV (G) + ( 1 - n) V(O) ] ' Uc(G) f3[n V(O) + ( 1 -- n) V ( G)] ' Uc(O)

and from Equation

, = R(G) R(O) =

(2.63), we

(2.n)

(2.73)

obtain

Uc(G)

73fnu�(c)-+(l_:_ Ji) uc (o)] '

Uc(O) f3[nUc(O) + ( l -- n) Uc (G)] "

(2.74) (2.75)

Combining these, we obtain expressions for the before-tax obligations of the government:

n V( G) + ( l - n) V (O) n Uc(G) + ( 1 - n) Uc(O) ' n V(O) + ( 1 - n) V (GL_ n U,. (O) + ( 1 - n) Uc (G)

R(G) h(G) =

(2.76)

R(O) b(O) =

(2.

Ch.

Optimal Fiscal and Monetary Policy

26:

1 705

Since H(G) < H(O), Equations (2.70) and (2.7 1 ) imply that V(G) < V(O). Using this result, n > � and Uc(O) < Uc(G), we can see that Equations (2.76) and (2.77) imply ' that

R(G) b(G)

<

R(O) b(O).

(2.78)

We can rewrite Equation (2.61) as (2.79) The right-hand side of Equation (2.79) depends only on the current state; thus (2.78) implies that v(O, G) > v( G, G) and v(O, 0) > v( G, 0). To establish Equation (2.67), we need only show that v(G, G) > 0 > v(O, 0). But this follows from (2.64) and (2.79), using V(G) < V(O) and Uc(O) < Uc(G). 0 The intuition for these results is as follows. The Ramsey policy smooths labor tax rates across states. This smoothing implies that the government runs a smaller surplus in wartime than in peacetime. With persistence in the shocks, the expected present value of surpluses starting from the next period is smaller if the economy is currently in wartime than if it is in peacetime. The end-of-period debt is, of course, just the expected present value of these surpluses. [See Equation (2. 60).] Thus the end-of· period debt is smaller if the economy is in wartime than if it is in peacetime, so

b(G)

<

b(O).

As was shown in (2.78), R(G) b(G) < R(O) b(O). That is, the obligations of the government if there was war in the preceding period are smaller than if there was peace. Suppose the economy is currently in wartime, so g1 = G. The current deficit and end-of-period debt are the same regardless of the history. Thus, if the inherited debt obligations are larger, the only way to meet the government budget constraint is to tax debt at a higher rate. So a transition from peacetime to wartime results in higher debt taxes than does a continuation of wartime. Similar intuition applies for the comparisons of transitions from wartime to peacetime with continuations of peacetime. 2. 3.2.

Tax-smoothing and incomplete rnurkets

Here we develop Barro 's ( 1 979) result on tax-smoothing and compare it to the work of Marcet et al. ( 1 996) on optimal taxation with incomplete markets. In a wel l · known paper, Barro ( 1 979) analyzes a reduced-form model of optimal taxation. In his theoretical development, there is no uncertainty and the government chooses a sequence of tax rates r1 on income to maximize

1 706

V.V. Chari and PJ. Kehoe

where y1 is income in period t and budget constraints of the form

r is an exogenously given interest rate, subject to

br = (1 + r) br- 1 + gt - TrYr. where g1 is government spending, b_ 1

is given, and an appropriate boundedness condition on debt is imposed. These constraints are equivalent to the present value budget constraint 00

=

g _!0__ � __l_ + b O· � � ( 1 + r)l ( 1 t�O + r)l r�o

�

=

(2.80)

B arro shows that in this deterministic setup, optimal tax rates are constant. Barro goes on to assert that the analog of this result with uncertainty is that optimal taxes are a random walk. In an environment with uncertainty, the properties of optimal policy depend on the structure of asset markets. If asset markets are complete, the analogous present value budget constraint is

"' g(s1 ) b . L r(s1)y(s1) = 1 L T+ r(s t ) + o 1 + r(s ) t,st

(2.8 1 )

l,s'

With this asset structure, optimal tax rates are clearly constant across both time and states of nature. If asset markets are incomplete, then the analysis is much more complicated and depends on precise details of the incompleteness. Suppose, for example, that the only asset available to the government is non-state-contingent debt. The sequence of budget constraints for the government can be written as

b(s1)

=

(1

+ r) b(s1-1 ) + g(s 1 ) - 'C(s 1)y(s 1 )

together with appropriate boundedness conditions on debt. Substituting the first-order conditions to the government's problem into the budget constraints and doing some manipulations yields

[ts:;

t t t L L fJI ' fl(s r I s'') Ur (s )y(s�r ;(s';(s )y(s )] t=r

s1

=

( 1 + r) b(sr- 1 ).

(2.82)

The restriction that debt is not state-contingent is equivalent to the requirement that the left-hand side of Equation (2. 82) is the same for any two states in period r in the sense that for all s'- 1 ,

t

t

L.: r-r 'fl(s r s') Ur (s )y(s ' ) [ g(s ) - r(s t )y(s )] L I Ur (s�')y(s' ) _.

r

t

·- '

s'

(2.83)

where s' (s'- 1 , s,) and s'' (s' 1 , s,,) for all s,.,s,, . Analyzing an economy with incomplete markets requires imposing, in addition to (2. 8 1 ), an infinite number of ='

�

Ch. 26:

Optimal rlscal and Monetary Policy

1 707

constraints of the form (2.83). This problem has not yet been solved. An open question is whether optimal tax rates in such an environment follow a random walk. In our general equilibrium setup, restrictions on government policy also impose extra constraints. Suppose that neither capital tax rates nor the return on debt can be made state-contingent. Then the additional restrictions that the allocation must satisfy so that we can construct a competitive equilibrium are given as follows. Substituting Equations (2. 1 7) and (2. 1 8) into the consumer's budget constraint yields, after some simplification, "'"" '"" (3t-r (s f 11

� � t=r s'

- {1

t ) + U,(s f) !(s f ) I s,. ) Uc(:/ ) c(sUc(s r)

+ [ 1 - O(s' 1 )] [F,Js') - 0]

}

(2. 84)

k(s'-1 ) = Rb(s'- 1 ) b(s' 1 ),

where O(sr 1 ) satisfies Uc(s'" 1 )

=

� f3.u(s' s'

{

I s'- 1 ) Uc(s') 1 -1- [ I

- B(s' 1 )] [Fk (s') --

}

b] .

(2.85)

The requirement that the debt be non-state-contingent is, then, simply the requirement that the left-hand side of Equation (2.84) with 8(sr - I ) substituted from (2.85) be the same for all Sr . Furthermore, we need to impose bounds on the absolute value of the debt to ensure that the problem is well posed. We then have that if an allocation satisfies these requirements, together with the resource constraint (2. 7) and the implementability constraint (2.8), a competitive equilibrium can be constructed which satisfies the restriction that neither the capital tax rate nor the return on debt be state-contingent. Clearly, computing equilibria with non-state-contingent capital taxes and return on debt is a difficult exercise. Marcet et al. ( 1996) analyze an economy with incomplete markets but without capital. When government consumption is serially uncorrelated, they find that the persistence properties of tax rates are a weighted average of a random walk and a serially uncorrelated process. They also find that the allocations are close to the complete markets allocations. They argue that their results partially affirm B arro's (1 979) assertion. In Section 3, we consider a model in which debt is nominal and non-state-contingent. There we show that inflation can be used to make the real returns state-contingent and that the Ramsey allocations are identical to those in an economy with real state­ contingent debt. This result is reminiscent of our result that even if debt returns are not state-contingent, as long as capital tax rates are state-contingent, the Ramsey allocations are identical to those in an economy in which all instruments are state­ contingent. This feature suggests that for actual economies, judging the extent of market incompleteness can be tricky.

V.V. Chari and P.J. Kehoe

1 708

2.3.3. A

quantitative illustration

Here we consider a standard real business cycle model and use it to develop the quantitative features of optimal fiscal policy. We follow the development in Chari et al. ( 1 994). In quantitative stochastic growth models, preferences are usually specified to be of the form

U(c, l) =

[c l -Y (L - l) Y ] lf'

-- , --1/J

where L is the endowment of labor. This class of preferences has been widely used in the literature [Kydland and Prescott ( 1 982), Christiano and Eichenbaum ( 1 992), Backus et al. ( 1 992)]. The production technology is usually given by

F(k, l, z, t) k " (e pt+z /) 1 - a . =

Notice that the production technology has two kinds oflabor-augmenting technological change. The variable p captures deterministic growth in this change. The variable z is a technology shock that follows a symmetric two-state Markov chain with states z1 and Zh and transition probabilities Prob(z1 H z; I z1 z; ) = Jf for i l, h. Government consumption is given by g1 = geP', where again p is the deterministic growth rate and g follows a symmetric two-state Markov chain with states g1 and gh and transition ¢ for i l, h. Notice that without shocks probabilities Prob(g1+ 1 = g; I g1 = g;) to technology or government consumption, the economy has a balanced growth path along which private consumption, capital, and government consumption grow at rate p and labor is constant. Zhu ( 1 992) shows that in economies of this form, setting capital income tax rates to be identically zero is not optimal. We ask whether capital tax rates are quantitatively quite different from zero. Recall from the proof of Proposition 5 that certain policies are uniquely determined by the theory, while others are not. Specifically, the labor tax rate is determined, while the state-by-state capital tax rate and return on debt are not. From Equation (2. 1 9), however, we know that the value of revenues fi·om capital income taxation in period t + 1 in terms of the period-t good is uniquely determined. To turn this variable into a tax rate, consider the ratio of the value of these revenues to the value of capital income, namely, =

=

=

=

=

(2.86) where q(s l-t- 1 ) {3fJ,(s 1 1 1 I s 1 ) Uc(s '+ 1 )1Uc(s 1) is the price of a unit of consumption at state s t+ 1 in units of consumption at s 1 • We refer to ee (s 1 ) as the ex ante tax rate on capital income. =

Ch. 26:

Optimal Fiscal and Monetary Policy

1 709

Table 1 Parameter values for two models " Parameters and values

Model

Baseline model

y = 0. 80

Preferences

a = 0.34

Technology Markov chains for Goverrunent consumption Technology shock

g, = 350 Zt

=

0.04

1/J � O

[3

=

0.97

0 = 0.08

p = 0.0 1 6

gh = 402

¢ = 0. 95

zh = 0.04

L

=

5475

:rr; = 0.9 1

High risk aversion model Preferences

a Source: Chari et al. ( 1994).

VJ �� -8

�---------

Next, in defining the last variable that is uniquely determined by the theory, it is useful to proceed as follows. Imagine that the government promises a non-state­ contingent rate of return on government debt r(s 1 1 ) and levies a state-contingent tax v(s 1 ) on interest payments from government debt. That is, r and v satisfy (2.87) and 2::: q(s 1 )v(s 1 ) 0, where q(s 1 ) is the price of a unit of consumption at state s 1 in units of consumption at state s t- 1 . Thus r(s 1 -- I ) is the equilibrium rate of return on a unit purchased in period t - 1 at s t- l , which yields a non-state-contingent return r(s 1 1 ) at all states s 1 • It is clear from (2.2 1 ) that the theory pins down Rk(s 1 ) k(s 1- 1 ) + R6(s 1 ) b(s 1- 1 ) . Given our definition of v, it is also clear that the theory pins down the sum of the tax revenues from capital income and the interest on debt, which is given by =

(2.88) We transform these revenues into a rate by dividing by the income from capital and debt to obtain the tax rate on private assets, given by

rJ(s 1 ) _-

8(s1)[Fk (s 1 ) - 6] k(s 1 1 ) -1 v(s 1 )r(s 1 1 ) b(s 1 1 ) [Fk (s t ) - o] k(s ' - l ) + r(s t - 1 fb(sl1)-

(2.89)

We consider two parametrizations of this model. (See Table 1 .) Our baseline model has ljJ 0 and thus has logarithmic preferences. Our high risk aversion model has = -8. The remaining parameters of preferences and the parameters for technology 1/J are those used by Chari et al. ( 1 994). We choose the three parameters of the Markov chain for government consumption to match three statistics of the postwar US data: =

V.V. Chari and P.J Kehoe

1710 Table 2 Properties of the fiscal policy models Income tax rates

a

Percentage in models Baseline

High risk aversion

Labor 23.87

20.69

Standard deviation

0. 1 0

0.04

Autocorrelation

0.80

0.85

Mean

0.00

--0.06

Standard deviation

0.00

4.06

Mean

Capital

0.83

Autocorrelation

Private assets Mean

1.10

-0.88

Standard deviation

53.86

78.56

Autocorrelation

-0.01

0.02

All statistics are based on 400 simulated observations. The means and standard deviations are in percentage terms. For the US economy, the tax rates are constructed as described by Chari et al. ( 1 994). For the baseline model, the capital tax rate is zero; thus, its autocorrelation is not defined. a

the average value of the ratio of government consumption to output, the variance of the detrended log of government consumption, and the serial autocorrelation of the detrended log of government consumption. We construct the Markov chain for the technology parameters by setting the mean of the technology shock equal to zero, and we use Prescott's ( 1 986) statistics on the variance and serial correlation of the technology shock to determine the other two parameters. For each setting of the parameter values, we simulate the Ramsey equilibrium for our economy, starting from the steady state of the deterministic versions of our models. In Table 2, we report some of the resulting properties of the fiscal variables in our models. In the baseline model, the tax rate on labor income fluctuates very little. For example, if the labor tax rate were approximately normally distributed, then 95 percent of the time, the tax rate would fluctuate between 23.67 percent and 24.07 percent. The tax on capital income is zero. This is to be expected because with 1jJ = 0, the utility function is separable between consumption and leisure and is homothetic in consumption, and the utility function thus satisfies the conditions discussed in Subsection 2.2.2. In the baseline model, the tax on private assets has a large standard deviation. Intuitively, we know that the tax on private asset income acts as a shock absorber. The optimal tax rate on labor does not respond much to shocks to the economy. The government smooths

Ch.

Optimal Fiscal and Monetary Policy

26:

171 1

labor tax rates by appropriately adjusting the tax on private assets in response to shocks. This variability of the tax on private assets does not distort capital accumulation, since what matters for the capital accumulation decision is the ex ante tax rate on capital income. This can be seen by manipulating the first-order condition for capital accumulation. In Table 2, we also report some properties of the fiscal policy variables for the high risk aversion model. Here, too, the tax rate on labor income :fluctuates very little. The tax rate on capital income has a mean of -0. 06 percent and a standard deviation of 4.06 percent so that the tax rate is close to zero. We find this feature interesting because it suggests that, for the class of utility functions commonly used in the literature, not taxing capital income is optimal. Here, as in the baseline model, we find that the standard deviation of the tax rate on the income from private assets is large. 2. 4.

Other environments

2. 4. 1 .

Endogenous growth models

Thus far, we have considered fiscal policy in models in which the growth rate of the economy is exogenously given. We turn now to models in which this growth rate is determined by the decisions of agents. Our discussion is restricted to a version of the model described in Lucas ( 1 990). Analysis of optimal policy in this model leads to a remarkable result: Along a balanced growth path, all taxes are zero. Bull ( 1 992) and Jones et al. ( 1 997) discuss extensions to a larger class of models. Consider a deterministic, infinite-horizon model in which the technology for producing goods is given by a constant returns to scale production function F(k�> h1 lu), where k, denotes the physical capital stock in period t, h, denotes the human capital stock in period t, and /11 denotes labor input to goods production in period t. Human capital investment in period t is given by h1G(l21 ) , where !21 denotes labor input into human capital accumulation and G is an increasing concave function. The resource constraints for this economy are (2.90) and (2.9 1 ) where c 1 i s private consumption, g i s exogenously given government consumption, and 15k and Dh are depreciation rates on physical and human capital, respectively. The consumer's preferences are given by 00

� (Jf c} 0V(l l t + lzt )l(l - a), t�O where v is a decreasing convex function.

Government consumption is financed by proportional taxes on the income from labor and capital in the goods production sector

V. V. Chari and PJ Kehoe

1712

and by debt. Let r, and 81 denote the tax rates on the income from labor and capital. Government debt has a one-period maturity. Let bt+ 1 denote the number of units of debt issued in period t and Rb1 b1 denote the payoff in period t. The consumer's budget constraint is (2.92) where R1a 1 + ( 1 81 )(r1 is the gross return on capital after taxes and depreci­ ation and r1 and w1 are the before-tax returns on capital and labor. Note that human capital accumulation is a nonmarket activity. The consumer's problem is to choose sequences of consumption, labor, physical and human capital, and debt holdings to maximize utility subject to (2.9 1 ) and (2.92). We assume that consumer debt holdings are bounded above and below by some arbitrarily large constants. Competitive pricin�: ensures that the return:> to factor inputs equal their marginal products, namely, tha' =

-

-b)

r1 = Fk(k1, h,lu), (2.93) (2.94) Wt = Ft (kt, htlu). We let x1 = (c1 , l1 �o !21 , k1 , h 1 , b1 ) denote an allocation for consumers in period t and let x (x1 ) denote an allocation for all t. The government's budget constraint is =

(2.95) We let lft (It, et) denote the government policy at period t and let J[ = (nt) denote the infinite sequence of policies. The initial stock of debt, b . 1 , and the initial stock of capital, /c 1 , are given. A competitive equilibrium is defined in the usual way. We have the following proposition. =

The consumption allocation, the labor aliocation, the physical and human capital allocations, the capital tax rate, and the return on debt in period 0 in a competitive equilibrium satisfy (2.90), (2.91), and Proposition 10.

(X)

L iYcr Uct '� Ao,

(2.96)

t�O

where

b1z + G(l2o� .

J

G' (lzo ) Furthermore, given any allocations and period-0 policies that satisfy (2.90), (2.91), (2.96), and

Ult f3 Ult+! f3Utt+l /lt+l --;;,; ' �(2 .97) 1 : G ( l2 H J )J + -ht G'(lztS h1+ 1 c'az�: �5 [ we can construct policies, prices, and debt holdings which, together wtth the given allocations and period-0 policies, constitute a competitive equilibrium. =

�

· u"

,

-

Ch.

26:

Optimal Fiscal and Monetary Policy

1713

The procedure we use to derive the implementability constraint is to express the consumer budget constraint in period-0 form with the prices substituted out. Recall that in the model with exogenous growth, this procedure implied that the capital stock from period 1 onward did not appear in the implementability constraint. It turns out that when human capital is accumulable, human capital does not appear in the implementability constraint from period 1 onward either. The consumer's first-order conditions imply that Proof:

{Jf U,t = At . -(31 U11 = Jc1 ( 1 -- r,) w,h r, 1 -(3 Utt �Lt htG' U2t ) , -�lt + �t+l [ 1 - (jh i G(£21+1 )] + At+ ] ( 1

(2.98) (2.99) (2. 1 00)

=

ft+d Wt+l / lt+ l

=

(2. 1 0 1 )

0.

Multiplying Equation (2. 1 0 1 ) by h n 1 , substituting for {l1 and � 1 1 from (2.99) and 1 (2. 1 00), and using Equation (2. 9 1 ), we obtain

- A1( 1 - T1 ) w1ht+l G' (l2t)

+

Att t ( l - Tt+J ) Wt+J ht+2 + At+l ( l - 'lt-rl ). Wt+l l l t l l hI l l - 0 . G'(l2t+ J ) _

__

(2. 1 02)

From Equation (2. 1 02) and a standard transversality condition, we know that (2. 1 03) Similarly, we can show that oc

(XJ

t�O

t�l

(2 . 1 04)

Next, we multiply the consumer budget constraint (2.92) by A1 and sum from period 0 onward. When we use (2. 1 03) and (2. 1 04), (2.96) follows. To derive (2.97), we substitute (2.99) into (2. 1 02). We leave it to the reader to prove the converse. D The Ramsey problem is to maximize consumer utility subject to conditions (2.90), (2.9 1 ), (2.96), and (2.97). Recall that human capital accumulation occurs outside the market and cannot be taxed. In any competitive equilibrium, the Euler equation for human capital accumulation is undistorted. Therefore, there is no tax instrument that can be used to make the Euler equation for human capital accumulation hold for arbitrary allocations. In contrast, for arbitrary allocations, the Euler equation for physical capital can be made to hold by choosing the tax on capital income appropriately. This incompleteness of the tax system implies that the undistorted Euler equation for human capital accumulation is a constraint on the set of competitive allocations. We have the following proposition.

V. V. Chari and PJ. Kehoe

1714

Proposition 1 1 . Suppose that the Ramsey allocations converge to a balanced growth path. In such a balanced growth path, all taxes are zero.

We prove that along a balanced growth path, the first-order conditions for the Ramsey problem are the same as those for a planner who has access to lump-sum taxes. (This, of course, does not mean that the government can achieve the lump-sum tax allocations, because there are distortions along the transition path.) Let W(c1 , l i t + l21 ; A) = U(c1 , l1 1 + /21 ) + Ac1 Uc1 , where A is the Lagrange multiplier on (2.96). For our specified utility function,

Proof:

The Ramsey problem is to maximize

subject to (2.90), (2. 9 1 ), and (2.97). Consider a relaxed problem in which we drop condition (2.97). Since the objective function in this rewritten problem from period 1 onward is proportional to that of a social planner who has access to lump-sum taxes, the solutions to the two problems are the same along a balanced growth path. This solution also satisfies condition (2.97). Thus, along a balanced growth path, the Ramsey problem has the same solution as the lump-sum tax problem. The solutions to these last two problems differ along the transition paths only because the two problems imply different allocations for period 0 and therefore for the capital stocks for the beginning of period 1 . 0 The reader may be concerned that this result depends on the ratio of government consumption to output going to zero. To see that this concern is not warranted, consider an extension of the model described above. Consider an environment in which the government chooses the path of government consumption optimally. To see this, suppose that the period utility function is given by U(c�, !1 + !2) + V(g), where V is some increasing function of government consumption. The government problem in this setup is to choose both tax rates and government consumption to maximize the consumer utility. We can solve this problem in two parts. In the first part, government consumption is taken as exogenous and tax rates are chosen optimally. In the second part, government consumption is chosen optimally. The proof described above obviously goes through for extensions of this kind. For V(g) = ag1 -0/(1 - a), it is easy to show that along a balanced growth path, govermnent consumption is a constant fraction of output. 2. 4.2.

Open economy models

So far, we have considered models of a closed economy. We turn now to considering issues that arise in an open economy. The elasticity of capital supply is likely to be

Ch. 26:

Optimal Fiscal and Monetary Policy

1715

much greater in an open economy than i n a closed economy because i n the open economy capital is mobile and can flow to the country with the highest rate of return. We consider a small open economy that takes the rates of return on saving in the rest of the world as given. In so doing, we abstract from the interesting strategic issues that arise when more than one authority sets taxes, and we abstract from general equilibrium linkages between an economy's fiscal policy and world prices. In an open economy, in addition to the standard taxes a government can levy on its citizens, a government can tax foreign owners of factors that are located in its country. To allow this possibility, we allow there to be source-based taxes as well as residence-based taxes. Source-based taxes are taxes that governments levy on income generated in their country at the income's source, regardless of ownership. Residence­ based taxes are taxes that governments levy on the income of their residents regardless of the income's source. We show that source-based taxes on capital income are zero in all periods and that, with a restriction that ensures that the economy has a steady state, residence-based taxes on capital income are zero in all periods as well. This result is much stronger than the corresponding result for closed economies. [See Razin and Sadka ( 1 995) for some closely related work.] Consider a model with both source-based and residence-based taxation. We model source-based taxes as those levied on a firm and residence-based taxes as those levied on consumers. Let rt denote the world rental rate on capital absent any domestically levied taxes. The firm's problem is to solve

maxF(kr, Zt ) - ( 1 + 8ft) r1* kt - ( 1 + Tjt) Wr lr, where f)ft and T_tt are the source-based tax rates on capital and labor.

The first-order

conditions are

8ft r; = Fkr - r1* ,

(2. 1 05)

TjtWt F,t - w,.

(2. 106)

=

Consumers solve 00

max 2�)Y U(c1 , l1 )

(2. 1 07)

t�O

subject to

2.:Pt Ct LPrWr ( l - TctH, t�O t�O where Pt = rr: ( l!Rs ), Rs = 1 + ( l

(2. 1 08)

=

f)c_.)(rs -- 6), Po 1 ()s and I's are the residence� I ' based tax rates on capital and labor, and initial assets are set to zero for convenience. The consumer first-order conditions are summarized by �

=

(2. 1 09) (2. 1 1 0)

VV Chari and PJ. Kehoe

1716

The economy-wide budget constraint (which is simply the sum of the consumer and government budget constraints) is given by ()()

00

(2. 1 1 1 )

where q1 = It� 1 ( 1/R;) and R; = r; + 1 D . Notice that the economy as a whole borrows and lends at the before-tax rate R; , while consumers borrow and lend at the after-tax rate R.,. . Intuitively, we know that any taxes on borrowing or lending levied on consumers are receipts of the government and cancel out in their combined budget constraint. N otice also that in the closed economy models studied in earlier sections, the competitive equilibrium has consumer budget constraints, a government budget constraint, and a resource constraint. In this small open economy, there is no resource constraint, and it is convenient to replace the government budget constraint by the economy-wide budget constraint. To derive the constraints for the Ramsey problem, substitute the consumer first-order conditions into Equation (2. 1 08) to get the implementability constraint -

oc

L f:Jf[ Uct Ct + Ult lt] = 0,

(2. 1 12)

t�O

where we have used the fact that Equation (2. 1 1 0) implies that p1 = fY Ucr!Uco . N ext, notice that the first-order conditions of the firm and the consumer can be summarized by Equations (2. 1 05), (2. 1 1 0), and (2. 1 1 3) Thus, for each marginal condition, there is at least one tax rate so that the tax system is complete and there are no additional constraints on the Ramsey problem. Thus, with both source- and residence-based taxes available, the Ramsey problem is to maximize Equation (2. 1 07) subject to (2. 1 1 1 ) and (2. 1 1 2). With purely source-based taxation, ret 8c1 0, so from Equation (2. 1 1 0) it is clear that for such a tax system, the Ramsey problem has the additional constraint =

=

With purely residence-based taxation, Tti 81 1 0, so from Equation (2. 1 05) it is clear that the Ramsey problem has the additional constraint =

=

Ch. 26:

Optimal Fiscal and Monetary Policy

1717

Consider the Ramsey problem when both source- and residence-based taxes are available. For convenience, write the problem as max

CX)

2.:J31 W(c l , ?c) 1,

t�O

1

subject to (2. 1 1 1), where W(c1, l1, A) condition for capital implies that (2. 1 1 4) while the first-order condition for consumption implies that (2. 1 1 5) From Equation (2. 1 14) it is clear that setting 8ft 0 for all that this small economy will have a steady state only if =

t is optimal.

Next, note

(2. 1 1 6) for all t. Under this parameter restriction, Equation (2. 1 1 5) implies that Wet = Wc11 1 , and thus the Ramsey allocations are constant, so in particular, Uct = Uc� 1 1 • Equations (2. 1 1 0) and (2. 1 1 6) imply that Bet = 0 for all t. Under a system with only source-based taxes, the Ramsey problem is to maximize "£�0 fJI W(c1, lt Jc) subject to conditions (2. 1 1 1) and (2. 1 1 5). If we consider a relaxed version of this problem with the constraint (2. 1 1 5) dropped, the above analysis makes clear that the solution to this relaxed problem satisfies this dropped constraint and hence solves the original problem. The first-order condition for capital then implies (2. 1 1 4); hence, eji = 0 for all t. Similarly, under a system with only residence-based taxes, the Ramsey problem is to maximize "£� 0 f31 W(c1 , l1 , A) subject to conditions (2. 1 1 1 ) and (2. 1 1 4). If we consider a relaxed version of this problem with the constraint (2. 1 1 4) dropped, the above analysis makes clear that the solution to this relaxed problem satisfies this dropped constraint and hence solves the original problem . The first-order condition for consumption in the relaxed problem is (2. 1 1 5). Under the parameter restriction (2. 1 1 6), Wet = Wet+ 1 ' so Ucr = Uct+ I . Hence, equations (2. 1 1 0) and (2. 1 1 6) imply that eel = 0 for all t. In sum: .

Under a system with both source- and residence-based taxes, all t. Under a system with only source-based taxes, eft = 0 for all t. Under a system with only residence-based taxes, with the additional restriction (2. 116), Bet 0 for all t.

Proposition 12.

e1r

=

=

Bet

=

0 for

V. V Chari and PJ Kehoe

1718

Notice that the Ramsey allocations from the problem with both source- and residence-based taxes can be achieved with residence-based taxes alone. With the additional restriction (2. 1 1 6), the allocations from the problem with both types of taxes can be achieved with source-based taxes alone. The intuition for why source­ based taxes are zero is that with capital mobility, each country faces a perfectly elastic supply of capital as a factor input and therefore optimally chooses to set capital income taxes on firms to zero. The intuition for why residence-based taxes are zero is that under (2. 1 1 6) the small economy instantly jumps to a steady state, and so the Chamley­ type logic applies for all t. 2.4. 3.

Overlapping generations models

The discussion thus far has focused on models with infinitely lived agents. There is also an extensive literature on optimal policy in overlapping generations models. [See, for example, Atkinson ( 1 97 1 ), Diamond ( 1 973), Pestieau ( 1 974), and Atkinson and Sandmo ( 1 980); the surveys by Auerbach ( 1 985) and Stiglitz ( 1 987); and the applied work of Auerbach and Kotlikoff ( 1 987) and Escolano ( 1 992).] The results in this literature are much weaker than those in standard models with infinitely lived agents. One reason is that in a life cycle model, agents have very heterogeneous preferences over the infinite stream of consumption goods. For example, in a two­ period overlapping generations model, an agent of generation t values consumption goods only in periods t and t + 1 . In this subsection, we show that tax rates on capital income in a steady state are zero if certain homotheticity and separability conditions are satisfied. This result is well known. For an exposition using the dual approach, see, for example, Atkinson and Stiglitz ( 1 980). Here we follow the primal approach used by Atkeson et al. ( 1 999) and Garriga ( 1 999). In this sense, the proposition we prove is more closely connected to the results on uniform commodity taxation than to the results on zero capital taxation in infinitely lived agent economies. We briefly develop a formulation of optimal fiscal policy in an overlapping generations model. Consider a two-period overlapping generations model with a constant population normalized to 1 . The resource constraint is

cu + Czt + k,+ + g = F(k1, lJt, lzt) + ( 1 - D) k�> (2. 1 17) where c11 and c21 denote the consumption of a represemat1ve young agent and a representative old agent in period t, !11 and /21 denote the corresponding labor inputs, k, denotes the capital stock in t, and g denotes government consumption. Each young 1

agent in

t solves the problem

max U (CJt, lJt) + f3U(czt 1 1 , l2t+t ) subject to

CJt + kt+1 + ht.i and

�

(1

TJt ) W]tflt

c21+J = ( 1 - Tzn J ) W2t+ 1 12t+1 + [ 1 + ( I - 8t+ J )(rt+ 1 D)] kt+l + R,+t bt+l ,

Ch. 26:

1719

Optimal Fiscal and Monetary Policy

where T1 1 and Tz1 are the tax rates on the two types of labor inputs and 81 is the tax rate on capital income. The government budget constraint is

To define an optimal policy, we need to assign weights to the utility of agents in each generation. We assume that the government assigns weight )./ to generation t with A < 1 . Then the Ramsey problem can be written as 00

t [U(clr, llr ) + f3 U(c2t l l , l2r+J )]

max U(czo, lzo)IA + L A

t�O

subject to the resource constraint for each

t

and

R(c lr, llt ) + f3R(czt 1 J , l2t l l ) = 0 for each t, where R(c, l) cUc(c, l) + lU1(c, l) and U(c20 , !20)

(2. 1 1 8)

is the utility of the initial = old. There is also an implementability constraint for the initial old, which plays no role in our steady-state analysis. Constraints (2. 1 1 8) are the implementability constraints associated with each generation. It is straightforward to show that if the solution to the Ramsey problem converges to a steady state with constant allocations (cJ t, lJ1, czt+h l2t+l, kt+1 ) (c 1 , / 1 , c2, /2, k), then the Ramsey allocations satisfy =

1

�

A

= F,." + 1 � b.

(2. 1 1 9)

In a steady state, the first-order condition for capital accumulation is (2. 120) Inspecting these equations, we see that unless

Uc(c� , /J ) A f3Uc(Cz, lz) 1

(2. 1 2 1 )

the tax rate on capital income i s not zero. l n general, we would not expect this condition to hold. Notice the contrast with infinitely lived representative consumer models in which, in a steady state, the marginal utility of the representative consumer Uc(ct . It ) is constant. In an overlapping generations model, we would not expect the marginal utility of a consumer to be constant over the consumer's lifetime. If the utility function is of the form

c i--a V (l) U(c, l) = ----+ 1 -- a then we can show the following:

(2. 1 22)

V. V. Chari and PJ. Kehoe

1 720

the utility function is of the form (2. 122), then in a steady state, the optimal tax on capital income is zero.

Proposition 13. If

Proof: To prove this, consider the first-order conditions for the Ramsey problem for consumption evaluated at a steady state:

Uc 1 + atRcl = �tt,

f)[ Uc2 + arRcz]

=

(2. 123)

A�t ,

(2. 1 24)

where },/ �t1 and A 1 a1 are the multipliers on (2. 1 1 7) and (2. 1 1 8), respectively. We can easily see that a1 and �� are constant in a steady state. With a utility function of the form (2. 1 22), Rc is proportional to Uc so that (2. 1 23) and (2. 1 24) imply (2. 12 1 ). D The key properties used in proving this result are homotheticity of the utility function over consumption and the separability of consumption and leisure. In this sense, this proposition is more closely connected to the results on uniform commodity taxation than to the results on zero capital taxation in infinitely lived agent economies. When A f) and F(k, !1 , !2) = F(k, !1 + !2 ) then one can show that for all strictly concave utility functions the optimal tax on capital income is zero in a steady state. [See Atkeson et al. ( 1 999).] =

3. Monetary policy

In this section, we study the properties of monetary policy in three monetary economies. Friedman ( 1 969) argues that to be optimal, monetary policy should follow a rule: set nominal interest rates to zero. For a deterministic version of our economy, this would imply deflating at the rate of time preference. Phelps ( 1 973) argues that Friedman's rule is unlikely to be optimal in an economy with no lump-sum taxes. Phelps' argument is that optimal taxation generally requires using all available taxes, including the inflation tax. Thus Phelps argues that the optimal inflation rate is higher than the Friedman rule implies. In this section, we set up a general framework that allows us to analyze Phelps' arguments. We analyze them in three standard monetary economies with distorting taxes: a cash-credit model, a money-in-the-utility-function model, and a shopping-time model. The conditions for the optimality of the Friedman rule in the first two economies are analyzed by Chari et al. ( 1 996), while those for the shopping-time model are extensively analyzed in the literature. [Sec Kimbrough ( 1 986), Faig ( 1 988), Woodford ( 1 990), Guidotti and Vegh ( 1 993), and Correia and Teles ( 1 996), as well as Chari et al. ( 1 996).) In this section, we show that the Friedman rule is optimal when simple homotheticity and separability conditions are satisfied. These conditions are similar to the ones developed in the uniform taxation results in Section 1 . We explore the cormection between the optimality of the Friedman rule and the intermediate-goods result. For all three monetary economies, when the homotheticity

Ch. 26:

Optimal Fiscal and Monetary Policy

1721

and separability conditions hold, the optimality of the Friedman rule follows from the intermediate-goods result. To prove this, we show that under such conditions, all three monetary economies can be reinterpreted as real intermediate-goods economies, and the optimality of the Friedman rule in the monetary economies follows directly from the intermediate-goods result in the reinterpreted real economies. In contrast, when these conditions do not hold, there is no such connection. To prove this, we show that when these conditions do not hold, there are two possibilities. First, there are monetary economies in which the Friedman rule holds which cannot be reinterpreted as real intermediate-goods economies. Second, there are monetary economies which can be reinterpreted as real intermediate-goods economies but in which the Friedman result does not hold. Finally, we conduct some numerical exercises designed to develop quantitative featnres of optimal monetary policy. We find that if debt has nominal non-state­ contingent retnrns, inflation can be used to make real returns state-contingent so that debt can serve as a shock absorber. 3. 1 .

Three standard monetary models

3. 1 . 1.

Cash-credit

Consider a simple production economy populated by a large number of identical, infinitely lived consumers. In each period t = 0, 1 , . . . , the economy experiences one of finitely many events s • We denote by s1 = (s0, . . . , s ) the history of events up to 1 1 and including period t. The probability, as of period 0, of any particular history s1 is �J(s1). The initial realization so is given. In each period t, the economy has three goods: labor and two consumption goods, a cash good and a credit good. A constant returns to scale technology is available to transform labor /(s 1 ) into output. The output can be used for private consumption of either the cash good c1 (s1) or the credit good c2(s 1 ) or for government consumption g(s1). The resource constraint in this economy is thus

(3 . 1 ) The preferences of each consumer are given by (3.2) s'

where the utility function U is strictly concave and satisfies the Inada conditions. In period t, consumers trade money, assets, and goods in particular ways. At the start of period t, after observing the current state s�> consumers trade money and assets in a centralized securities market. The assets are one-period, non-state-contingent nominal

1 722

V.V. Chari and P.J Kehoe

claims. Let M(s 1 ) and B(s 1 ) denote the money and the nominal bonds held at the end of the securities market trading. Let R(s 1 ) denote the gross nominal return on these bonds payable in period t + 1 in all states s t+1 (s1 , s1 1 J ). Notice that the nominal return on debt is not state-contingent. After this trading, each consumer splits into a shopper and a worker. The shopper must use the money to purchase cash goods. To purchase credit goods, the shopper issues nominal claims, which are settled in the securities market in the next period. The worker is paid in cash at the end of each period. This environment leads to the following constraint for the securities market: =

M(st) + B(s t) R (s t-1 ) B(s t- l ) + M(s t-1 ) - p(st 1 ) c t (st-l ) -p(s t-l ) c2(5t-l ) +p(s t 1 )[1 r(st- 1 )] /(s t-t ) , =

__

(3.3)

where p is the price of the consumption goods and r is the tax rate on labor income. The real wage rate is 1 in this economy given our specification of technology. The left­ hand side of Equation (3.3) is the nominal value of assets held at the end of securities market trading. The first term on the right-hand side is the value of nominal debt bought in the preceding period. The next two terms are the shopper's unspent cash. The fourth term is the payments for credit goods, and the last term is the after-tax receipts from labor services. We will assume that the holdings of real debt B(s 1 )/p(s 1 ) are bounded above and below by some arbitrarily large constants. Purchases of cash goods must satisfy the following cash-in-aduance constraint: (3.4) We assume throughout that the cash-in-advance constraint holds with equality. We let

x(s 1 ) = (c 1 (s1), c2(s 1), l(s 1 ), M(s1), B(s1)) denote an allocation for consumers at s 1, and we let x = (x(s1)) denote an allocation for all s1• We let q (p(s 1 ) , R(s 1)) denote a price system for this economy. The initial stock of money M and the initial stock of 1 nominal debt B_ are given. 1 =

Money is introduced into and withdrawn from the economy through open market operations in the securities market. The constraint facing the government in this market is

M(:/) M(st-1 ) + B(s t) = R(s t 1 ) B(st- l ) +p(s t- 1 ) g(sr-l ) _ p(s t-1) r(s t-1 ) l(s t-1 ). _

(3.5) The terms on the left-hand side of this equation are the assets sold by the government. The first term on the right is the payments on debt incurred in the preceding period, the second term is the payment for government consumption, and the third term is tax receipts from labor income. Notice that government consumption is bought on credit. We let n = (r(s1)) denote a policy for all s 1• Given this description o f an economy, we now define a competitive equilibrium. A competitive equilibrium is a policy n, an allocation x, and a price system q such

Ch. 26:

Optimal Fiscal and Moneta;y Policy

1723

that given the policy and the price system, the resulting allocation maximizes the representative consumer's utility and satisfies the government's budget constraint. In this equilibrium, the consumer maximizes Equation (3.2) subject to (3.3), (3.4), and the bounds on debt. Money earns a gross nominal return of 1 . If bonds earn a gross nominal return of less than 1 , then the consumer can make profits by buying money and selling bonds. Thus, in any equilibrium, R(s 1) � 1 . The consumer's first-order conditions imply that U1 (s 1 )/U2(s 1 ) R(s 1 ); thus in any equilibrium, the following constraint must hold: =

(3.6) This feature of the competitive equilibrium constrains the set of Ramsey allocations. Consider now the policy problem faced by the government. As before, we assume that there is an institution or a commitment technology through which the government can bind itself to a particular sequence of policies once and for all in period 0, and we model this technology by having the government choose a policy :rr = (r(s 1 )) at the beginning of time and then having consumers choose their allocations. Since the government needs to predict how consumer allocations and prices will respond to its policies, consumer allocations and prices are described by rules that associate allocations with government policies. Formally, allocation rules and price functions are sequences of functions x(:rr) = (x(s 1 I :rr)) and q(:rr) = (p(s 1 I :rr) , R(s 1 I :rr) ) that map policies :rr into allocations and prices. A Ramsey equilibrium is a policy :rr, an allocation rule x(-), and a price system q(-) that satisfy the following: (i) the policy :rr maximizes

L f31fJ-(s1) U (c (s 1 I :rr), c2(s 1 I :rr), l(s 1 I :rr)) i

t, s '

subject to (3. 5), with allocations given by x(:rr), and (ii) for every :rr', the allo­ cation x(:rr' ) and the price system q(:rr' ), together with the policy :rr' , constitute a competitive equilibrium. As is well known, if the initial stock of nominal assets held by consumers is positive, then welfare is maximized in the Ramsey problem by increasing the initial price level to infinity. If the initial stock is negative, then welfare is maximized by setting the initial price level so low that the government raises all the revenue it needs without levying any distorting taxes. To make the problem interesting, we set the initial sum of nominal assets of consumers M 1 + R _1 B_1 to zero. For convenience, let U;(s ' ) for i = 1 , 2, 3 denote the marginal utilities at state s 1 • Using standard techniques [for example, from Lucas and Stokey ( 1 983), Chari et al. ( 1 99 1 ), and Section 1 ], we can establish the implementability constraint: Proposition 14. The consumption and labor allocations in a competitive equilibrium satisfy conditions (3. 1), (3. 6), and the implementability constraint

(3.7) s'

V.V. Chari and P.J. Kehoe

1 724

Furthermore, allocations that satisfy (3. 1), (3. 6), and (3. 7) can be decentralized as a competitive equilibrium. The Ramsey problem is to maximize consumer utility subject to conditions (3. 1), (3 .6), and (3.7). Consider utility functions of the form (3.8) where

w

is homothetic. We then have

Proposition 15. For utility functions of the form (3.8), the Ramsey equilibrium has R(s 1) = 1 for all s t

Consider for a moment the Ramsey allocation problem with constraint (3 .6) dropped. We will show that under (3 . 8), constraint (3.6) is satisfied. Let A denote the Lagrange multiplier on (3 . 7) and /)1 J-l(s 1) y(s 1) denote the Lagrange multiplier on (3 . 1 ) The first-order conditions for ci(s 1) for i = I , 2 in this problem are Proof:

.

(3.9) Recall from Section

I

that a utility function which satisfies (3 . 8) also satisfies (3 . 1 0)

Next, dividing Equation (3.9) by Ui and noting that U3jUi have that

=

V12/V1

for

i

=

I , 2, we

(3. 1 1 ) Using Equation (3 . 1 0), we have that the left-hand side of (3 . 1 1 ) has the same value for i 1 and for i 2. Therefore, U1 (s1)/U2(s ') = 1 . Since the solution to the less-constrained problem satisfies (3 .6), it is also a solution to the Ramsey allocation problem. From the consumer's first-order condition, we have that U1 (s 1)/U2(s 1) R(s 1) and thus that R(s1) = l . D =

=

=

Now let us relate our results to Phelps' ( 1 973) arguments for taxing liquidity services. Phelps ( 1 973, p. 82) argues that "if, as is often maintained, the demand for money is highly interest-inelastic, then liquidity is an attractive candidate for heavy taxation at least from the standpoint of monetary and fiscal efficiency". Our results suggest that the connection between the interest elasticity of money demand and the desirability of taxing liquidity services is, at best, tenuous.

Optimal Fiscal and Monetary Policy

Ch. 26:

1725

To see this, suppose that the utility function is of the form (3 . 1 2) Then the consumer's first-order condition U/U2 = R becomes

m -a = R' (c - m)a

(3 . 1 3)

---

where m is real money balances and c money demand 17 is given by 17

=

1

R llo -------0 1 + R 1 1a-l ·

=

c1 +

c2 . The implied interest elasticity of

(3 . 1 4)

-

Evaluating this elasticity at R gives 17 = 112a, and thus the elasticity of money demand can range from zero to infinity. Nevertheless, all preferences in this class satisfy our homotheticity and separability conditions; hence the Friedman rule is optimal. Phelps ' partial equilibrium intuition does not hold up for reasons we saw in Section 1 . As we noted there, in general equilibrium, it is not necessarily true that inelastically demanded commodities should be taxed heavily. The homotheticity and separability conditions are equivalent to the requirement that the consumption elasticity of money demand is unity. To see this, consider a standard money demand specification: =

log m =

a0 + a 1

log c +f(R),

wheref(R) is some invertible function of the interest rate. If a 1 = 1 , so the consumption elasticity of money demand is unity, this formulation implies that m/c = e ao+f (Rl , or that there is some function h such that h(m/c) = R. The consumer's first-order condition is U1 /U2 R. Thus U1 /U2 must be homogeneous of degree 0 in m and c if the consumption elasticity of money demand is unity. This formulation immediately implies the homotheticity and separability conditions. Note two points about the generality of the result First, restricting w to be homogeneous of degree 1 does not reduce the generality of the result, since we can write w(·) = g(f(-)), where g is monotone and f is homogeneous of degree 1 , and simply reinterpret V accordingly. Second, the proof can be easily extended to economies with more general production technologies, including those with capital accumulation. To see how, consider modifying the resource constraint (3 . 1 ) to =

(3 . 1 5) where k is the capital stock andf is a constant returns to scale function, and modifying the consumer's and the government's budget constraints appropriately. Let capital

V.V. Chari and P.J. Kehoe

1 726

income net of depreciation be taxed at rate 8(s 1), and let capital be a credit good, although the result holds if capital is a cash good. For this economy, combining the consumer's and the firm's first-order conditions gives

U1 (s 1) = fi (s 1 ) R(s 1 ) Uz(s1) f2(s 1) . Thus the optimality o f the Friedman rule requires that U1 (s1)/U2 (s 1 ) = f1 (s 1)/f2 (s1). The constraint requiring that R(s 1 ) ? 1 now implies that

U1 (s 1) .fi (s1) ? Uz(s t) h.(s t) '

(3. 1 6)

and the implementability constraint (3.7) now reads

L L /31 ,u(s 1 ) [ U1 (s 1 ) c1 (s 1 ) + Uz(s 1 ) cz(s 1 ) + U3 (s 1 ) l(s 1 )] =

(3. 1 7)

Uc (so ) {[1 - 8(so )] [.fk (so ) - D)] } k_ l ,

where k_ 1 is the initial capital stock. Since the tax on initial capital 8(s0) acts like a lump-sum tax, setting it as high as possible is optimal. To make the problem interesting, we follow the standard procedure of fixing it exogenously. The Ramsey allocation problem is to choose allocations to maximize utility subject to conditions (3 . 1 5), (3 . 1 6), and (3 . 1 7). For preferences of the form (3 .8), the analog of Equation (3. 1 1) has the right-hand side multiplied by /;(s1) for i = 1 , 2. This analog implies that U1 (s 1)/Uz(s1) fi (s 1 )/fz(s 1), and thus the Friedman rule holds. We now develop the connection between the optimality of the Friedman rule and the uniform taxation result. In this economy, the tax on labor income implicitly taxes consumption of the cash good and the credit good at the same rate. In Section 1 , we showed that if the utility function is separable in leisure and the subutility function over consumption goods is homothetic, then the optimal policy is to tax all consumption goods at the same rate. If R(s 1 ) > 1 , the cash good is effectively taxed at a higher rate than the credit good, since cash goods must be paid for immediately, but credit goods are paid for with a one-period lag. Thus, with such preferences, efficiency requires that R(s1) 1 and therefore that monetary policy follow the Friedman rule. To make this intuition precise, consider a real barter economy with the same preferences (3.2) and resource constraint (3 . 1 ) as the monetary economy and with commodity taxes on the two consumption goods. Consider a period-0 representation of the budget constraints. The consumer's budget constraint is =

=

L L q(s 1 ) { [ 1 + r1 (s 1 )] c1 (s 1 ) + [ 1 s'

+

Tz(s 1 )] c2(s 1 )}

=

L q(s 1 ) l(s 1 ),

(3 . 1 8)

and the government's budget constraint is

L L q(s 1 ) g(s 1 ) = L L q(s 1 ) [rl (s 1 ) c 1 (s 1 ) + r2 (s 1 ) c2 (s 1 )] , s'

s'

(3 . 1 9)

where q(s 1) is the price of goods in period t and at state s 1 • A Ramsey equilibrium for this economy is defined in the obvious fashion. The Ramsey allocation problem for

Ch. 26:

Optimal Fiscal and Monetary Policy

1727

this barter economy is similar to that in the monetary economy, except that the barter economy has no constraint (3 .6). The consumer's first-order conditions imply that

U1 (s1) U2(s 1 )

--

_ -

1 + Tt (s1) . 1 + T2(s 1 )

Thus Ramsey taxes satisfy r1 (s1) r2(s1) if and only if in the Ramsey allocation problem of maximizing Equation (3 .2) subject to (3 . 1) and (3.7), the solution has U1 (s1)/U2(s 1 ) = 1 . Recall from Proposition 3 in Section 1 that for utility functions of the form (3 .8), the Ramsey equilibrium has r 1 (s1) r2(s 1) for all s 1. Thus, with homotheticity and separability i n the period utility function, the optimal taxes on the two consumption goods are equal at each state. Notice that this proposition does not imply that commodity taxes are equal across states. [That is, ri(s 1 ) may not equal ij(sr) for t ;e r and for i,j 1 , 2.] We have shown that if the conditions for uniform commodity taxation are satisfied in the barter economy, then in the associated monetary economy, the Friedman rule is optimal. Of course, since the allocations in the monetary economy must satisfy condition (3 .6) while those in the barter economy need not, there are situations in which uniform commodity taxation is not optimal in the barter economy but in which the Friedman rule is optimal in the monetary economy. To see this, consider the following. =

=

=

Example.

Let preferences have the form (3.20)

The first-order conditions for the Ramsey problem in the barter economy imply that

UJ (s 1 ) U2(s 1)

=

c 1 (s't� c2(s 1}-02

=

l + A(l - o2) 1 + A( l - 01 ) ·

(3.2 1 )

Clearly, U1 (s1) ; U2(s 1) i f and only i f 01 ; 02 . For cases i n which OJ = o2, these preferences satisfY condition (3 .6), and both uniform commodity taxation and the Friedman rule are optimal. If OJ > 02, then neither uniform commodity taxation nor the Friedman rule is optimal. What is optimal is to tax good 1 at a higher rate than good 2. In the barter economy, this higher taxation is accomplished by setting r1 (s 1 ) > r2(s 1 ), while in the monetary economy, it is accomplished by setting R(s 1 ) > 1 . More interestingly, when o1 < o2, uniform commodity taxation i s not optimal, but the Friedman rule is. To see this, note that when OJ < o2, the solution in the monetary economy that ignores the constraint UJ (s 1 ) ; U2(s 1) violates this constraint. Thus this constraint must bind at the optimum, and in the monetary economy, U1 (s ') = U2(s1). Thus, in the barter economy, taxing good 1 at a lower rate than good 2 is optimal, and this is accomplished by setting TJ (s 1) < r2(s1). In the monetary economy, taxing

VV. Chari and PJ. Kehoe

1728

good 1 at a lower rate than good 2 is not feasible, since R(s 1 ) ;? 1 , and the best feasible solution is to set R(s 1 ) 1 . =

In this subsection, we have focused on the Lucas and Stokey ( 1 983) cash-credit version of the cash-in-advance model. It turns out that in the simpler cash-in-advance model without credit goods, the inflation rate and the labor tax rate are indeterminate. The first-order conditions for a deterministic version of that model are the cash-in­ advance constraint, the budget constraint, and

� U1� = RtPr f3 Uzt Pt+l where the period utility function is U (c1 l1 ) and R 1 is the nominal interest rate from period t to period t + 1 . Here, only the products R/(1 -- T1 ) and R1p/pt+ 1 are pinned down by the allocations. Thus the nominal interest rate, the tax rate, and the inflation rate are not separately determined. The Ramsey allocation can be decentralized in a variety of ways. In particular, trivially, both the Friedman rule and arbitrarily high rates of inflation are optimal. ,

3 . 1 . 2.

Money-in-the-utility-junction

In this section, we prove that the Friedman rule is optimal for a money-in-the-utility­ function economy under homotheticity and separability conditions similar to those above. Consider the following monetary economy. In this economy, labor is transformed into consumption goods according to (3.22) (We use the same notation here as in the last subsection.) The preferences of the representative consumer are given by (3.23)

s'

where the utility function has the usual monotonicity and concavity properties and satisfies the Inada conditions. In period t, the consumer's budget constraint is

p(s 1 ) c(s 1 ) + M(s 1 ) + B(s 1 )

=

M (s' 1 ) + R(s 1- 1 ) B(s '-1 ) + p(s ' ) [l - r(s 1 )] l(s 1 ). -

(3 .24) The holdings of real debt B(s')lp(s 1 ) are bounded below by some arbitrarily large constant, and the holdings of money are bounded below by zero. Let M_1 and

Ch. 26:

Optimal Fiscal and Monetary Policy

1 729

R_1 B_1 denote the initial asset holdings of the consumer. The budget constraint of the government is given by

B(s 1 ) = R(s 1- 1 ) B(s 1- 1 ) +p(s 1 ) g(s 1 ) - [M(s 1 ) - M(s 1- 1 )] -p(s 1 )[1 -- r(s 1 )]/(s 1 ).

(3.25) A Ramsey equilibrium for this economy is defined in the obvious fashion. We set the initial stock of assets to zero for reasons similar to those given in the preceding section. Let m(s 1 ) M(s 1)/p(s 1 ) denote the real balances in the Ramsey equilibrium. Using logic similar to that in Proposition 1 4, we can show that the consumption and labor allocations and the real money balances in the Ramsey equilibrium solve the Ramsey allocation problem =

(3.26) subject to the resource constraint (3 .22) and the implementability constraint (3.27) These two constraints, (3 .22) and (3.27), completely characterize the set of competitive equilibrium allocations. We are interested in finding conditions under which the Friedman rule is optimal. Now the consumer's first-order conditions imply that (3.28) Thus, for the Friedman rule to hold, namely, for R(s 1 )

=

1, it must be true that (3 .29)

Since the marginal utility of consumption goods is finite, condition (3.29) will hold only if U1 (s 1 ) 0, that is, if the marginal utility of real money balances is zero. Intuitively, we can say that under the Friedman rule, satiating the economy with real money balances is optimal. We are interested in economies for which preferences are not satiated with any finite level of money balances and for which the marginal utility of real money balances converges to zero as the level of real money balances converges to infinity. That is, for each c and /, limm�oo Ut (m, c, l) = 0 and limm_,= U2(m, c, l) > 0. Intuitively, in such economies, the Friedman rule holds exactly only if the value of real money balances is infinite, and for such economies, the Ramsey allocation problem has no solution. To get around this technicality, we consider an economy in which the level of real money balances is exogenously bounded by a constant. We will say that the =

1 730

V. V. Chari and P.J Kehoe

Friedman rule is optimal if, as this bound on real money balances increases, the associated nominal interest rates in the Ramsey equilibrium converge to one. With this in mind, we modify the Ramsey allocation problem to include the constraint

m(s1)

� m,

(3.30)

where m is a finite bound. Consider preferences of the form

U(m, c, V(w(m, c), l), !)

where

w

(3.3 1 )

=

i s homothetic. We then have

Proposition 16.

optimal.

If

the utility function is of the form (3.31), then the Friedman rule is

The Ramsey allocation problem is to maximize Equation (3 .23) subject to (3 .22), (3.27), and (3 .30). Consider a less-constrained version of this problem in which constraint (3.30) is dropped. Let and A, denote the Lagrange multipliers on constraints (3.22) and (3.27). The first-order conditions for real money balances and consumption are

Proof:

{31fl(s1)y(s1)

(3.32) and (3.33)

) m(s1) U11 (s1) c(s1) Un (s1) m(s1) U12 + c(s1) Un(s1) U1(s 1) U2(s 1) +A)+ A [m(s1) U11 (s1)U1 +(s')c(s1) Un (s1) + l(s r) V21V1 (s(s1)1) ] U22(s1) + l(s1) V21(s1)J y(s1) , (l +A)+A [ m(s1) Ul2(s1)U2(s+ c(s1) V1 (s 1) U2(s') 1) y(s r2_ U2(s 1) m(s 1)

Since the utility function satisfies condition (3 . 3 1

,

it follows (as in Section 1) that

+

(3.34)

Using the form of Equation (3 . 3 1 ), we can rewrite conditions (3.32) and (3 .33) as =

(1

and

_

=

0

(3.35)

(3 .36)

From Equation (3.34), we know that =

0

(3 .37)

in the less-constrained problem. Hence the associated is arbitrarily large, and thus for any finite bound m, the constraint (3.30) binds in the original problem. The result then follows from (3.28). D

Ch. 26:

1731

Optimal Fiscal and Monetary Policy

Again, restricting w to be homogeneous does not reduce the generality of the result. Clearly, the Friedman rule is optimal for some preferences which do not satisfy condition (3.3 1 ). Consider (3.38) Note that for cases in which a1 * a2 , Equation (3 .38) does not satisfy condition (3 .3 1). 1 The first-order condition for the Ramsey problem for money balances m (s ) , when the upper bound on money balances is ignored, is (3.39) 1 Unless the endogenous Lagrange multiplier A just happens to equal (a1 - 1 )- , Equation (3 .38) implies that the Friedman rule is optimal. In related work, Woodford ( 1 990) considers the optimality of the Friedman rule within the restricted class of competitive equilibria with constant allocations and policies. Woodford shows that if consumption and real balances are gross substitutes, then the Friedman rule is not optimal. Of course, there are functions that satisfy our homotheticity and separability assumptions which are gross substitutes, for example, l a c i -a m U (m , c , l) = -- + -- + V (l).

1-a

1-a

The reason for the difference in the results arises from the difference implementability constraints. Woodford's problem is max U (m , c, l)

m

the

(3 .40)

subject to

c + g � l, U1 m + U2 c + U3l = ( 1 - (3) U1 ,

(3 .4 1 ) (3 .42)

where (3 .42) is the implementability constraint associated with a competitive equilib­ rium with constant allocations. The first-order conditions for our problem are similar to those for Woodford's problem, except that his include derivatives of the right-hand side of condition (3.42). Notice that in Woodford's problem, if (3 1 and preferences satisfy our homotheticity and separability conditions, then the Friedman rule is optimal. Notice, too, that if the model had state vmiables, such as capital, then constant policies would not typically imply constant allocations. To analyze the optimal constant monetary policy for such an economy, we would analyze a problem similar to that in Equation (3 .26) with extra constraints on allocations that capture these restrictions. [These restrictions would be similar in spirit to those in (2.47).] =

V.V. Chari and PJ. Kehoe

1 732

Shopping-time

3. 1 . 3.

In this subsection, we prove the optimality of the Friedman rule in a shopping-time monetary economy under appropriate homotheticity and separability conditions. Consider a monetary economy along the lines of Kimbrough ( 1 986). Labor is transformed into consumption goods according to

c(s1) + g(s 1) ::;; l(s 1 ).

(3 .43)

The preferences of the representative consumer are given by

L L f31 f.J(s') U (c(s1), l(s1) + ¢(c(s1), M(s1)/p(s1))) ,

(3 .44)

s'

where U is concave, U1 > 0, U2 < 0, 0, and 0 so that with the same amount of money, more time is needed to obtain more consumption goods. We also assume that ¢2 < 0 so that with more money, less time is needed to obtain the same amount of consumption goods. The budget constraints of the consumer and the government are the same as (3 .24) and (3.25). The Ramsey equilibrium is defined in the obvious fashion. Let m(s1) = M(s 1)/p(s 1) and set the initial nominal assets to zero; we can then show that the consumption and labor allocations and the real money balances in the Ramsey equilibrium solve the problem max

L Lf31 f.J(s1) U (c(s1), l(s 1) + ¢(c(s1), m(s 1))) s'

subject t o condition (3.43) and

L L f31f.J(s1) { c(s 1) [U1 (s 1) + ¢1 (s1) U2(s 1)] + /(s 1) Uz(s 1) + m(s1)
From the consumer's fust-·order conditions, we know that ¢2 = 0. We then have Proposition 17.

is optimal.

0.

(3 .45) 1 if and only if

If ¢ is homogeneous of degree k and k ;;,: l , then the Friedman rule

The first-order conditions for the Ramsey problem with respect to are given by

Proof:

l(s1)

R(s1 ) =

=

m(s 1)

Uz
and

(3 .46)

and (3 .47)

where y is the multiplier on the resource constraint and we have dropped refer­ ence to s 1 •

Ch. 26:

Optimal Fiscal and Monetary Policy

1733

Suppose first that ¢h ;e 0 so that the optimal policy does not follow the Friedman rule. Then, from Equations (3.46) and (3.47), we have that (3.48) Now, under the condition that ¢(c, m) is homogeneous of degree k and k ;?: 1 , we have that ¢2(ac, ym) = ak�1¢2(c, m). Differentiating with respect to a and evaluating at a = 1 , we have that c¢ 1 2 + m¢22 = (k - 1 )¢2, and thus (3 .49) Since .A

;?: 0, U2

<

0, and y > 0, conditions (3.48) and (3 .49) contradict each other.

0

Note that this proof does not go through if ¢(c, m) is homogeneous of degree less than 1 . Using the dual approach, however, Correia and Teles ( 1 996) prove that the Friedman rule is optimal for this shopping-time economy when ¢(c, m) is homogeneous of any degree. 3.2.

From monetary to real

In this subsection, we examine the relationship between the optimality of the Friedman rule and the intermediate-goods result developed in Section 1 . The relationship is the following. First, if the homotheticity and separability conditions hold, then in the three monetary models we have studied, the optimality of the Friedman rule follows from the intermediate-goods result. Second, if these conditions do not hold, then in all three economies, the optimality of the Friedman rule and the intermediate-goods result are not connected. To establish these results, we proceed as follows. We begin by setting up the notation for a simple real intermediate-goods economy and review the intermediate­ goods result for that economy. We then show that when our homotheticity and separability conditions hold, the cash-credit goods and the money-in-the-utility­ function economies can be reinterpreted as real economies with intermediate goods. For these two monetary economies, we establish that the optimality of the Friedman rule in the monetary economy follows from the intermediate-goods result in the reinterpreted real economy. It is easy to establish a similar result for the shopping­ time economy. This proves the first result. Next, we consider monetary economies which do not satisfy our conditions. We establish our second result with a couple of examples. We start with an example in which the monetary economy can be reinterpreted as a real intermediate-goods economy but in which the Friedman rule does not hold in the monetary economy. We then give an example of a monetary economy in which the Friedman rule does hold, but this economy cannot be reinterpreted as a real intermediate-goods economy.

V. V. Chari and P.J. Kehoe

1 734

The cash-credit economy can be reinterpreted as a real production economy with intermediate goods. Under our homotheticity and separability assumptions, the period utility is U (w(cI t , c21 ), 11 ) and the resource constraint is (3.50) Since the gross nominal interest rate cannot be less than unity, the allocations in the monetary economy must satisfy (3 . 5 1 ) The reinterpreted economy i s an infinite sequence o f real static economies. I n each period, the economy has two intermediate goods z 1 1 and z2r. a final private consumption good x1 , labor 11, and government consumption g1 • The intermediate goods zu and z21 in the real economy correspond to the final consumption goods cu and c21 in the monetary economy. The period utility function is U(x1 , !1 ). The technology set for producing the final good x1 is given by

f 1 (Xt , ZJt , Z2t, ft ) f2 (Xt , Z]t , Z2t. ft )

=

=

Xt -- W(ZJt , Z2t) :S: 0, W2(Z!t , Z2t ) - WJ (ZJr , Zzt ) :S: 0,

(3.52 ) (3 .53)

while the technology for producing the intermediate goods and government consump­ tion is given by (3. 54) The real economy and the monetary economy are obviously equivalent. The interme­ diate-goods result for the real economy is that the Ramsey allocations satisfy production efficiency. For this economy, because the marginal rate of transformation between z1 and z2 is 1 in the intermediate-goods technology, production efficiency requires that (3 .55) Recall that in the monetary economy, the Friedman rule is optimal when Equa­ tion (3 .55) holds. Thus the intermediate-goods result in the real economy implies the optimality of the Friedman rule in the monetary economy. Does this implication hold more generally? Whenever the monetary economy can be reinterpreted as an intermediate-goods economy, is the Friedman rule optimal in the monetary economy? No. Suppose that the utility function U (c 1 , c2, /) is of the separable form V(w(c� , c2), l), but that it does not have a representation in which w exhibits constant returns to scale. Suppose that w instead exhibits decreasing returns. For example, suppose that w(c 1 , c2) (c 1 + k)aci- '\ where k is a constant. In the =

Ch. 26:

Optimal Fiscal and Monetary Policy

1735

intermediate-goods reinterpretation, the constant k can be thought of as a scarce factor inelastically supplied by the consumer. The intermediate-goods result holds, provided that the returns to the scarce factor are fully taxed away. If the returns to the scarce factor cannot be taxed, then the intermediate-goods result does not hold. It is easy to show that the Friedman rule is not optimal in the monetary economy. In a sense, the Friedman rule is not optimal because in the monetary economy, there is no sensible interpretation under which the parameter k can be taxed. Next, one might ask, Is it true that whenever the Friedman rule is optimal in the monetary economy, there exists an analogous intermediate-goods economy? Again, no. Consider, for example, Ramsey allocation problems in which the constraint U1 ;? U2 binds, but in which the utility function is not separable in consumption and leisure. The Friedman rule is optimal, but the monetary economy cannot be reinterpreted as an intermediate-goods economy. In this subsection, we have shown that under our homotheticity and separability assumptions, the optimality of the Friedman rule follows from the optimality of uniform commodity taxation. We have also shown that the optimality of the Friedman rule follows from the intermediate-goods result. These findings are not inconsistent because the uniform taxation result actually follows from the intermediate-goods result. (See Section 1 .) The construction of the intermediate-goods economy for the money-in-the-utility­ function economy is straightforward. Recall that in the monetary economy, under our homotheticity and separability conditions, the period utility function is U ( w(m1, c1 ), 11) and the resource constraint is c1 + g1 = 11 • The reinterpreted economy is again an infinite sequence of real static economies. In each period, the economy has two intermediate goods z11 and z21, a final private consumption good x1 , labor /1 , and government consumption g1 . The intermediate goods z1, and z21 correspond to money m1 and the consumption good c1 in the monetary economy, respectively. The technology set for producing the final good x1 is given by

The technology set for producing intermediate goods and consumption is given by

The real and monetary economies are obviously equivalent. Production efficiency in the intermediate-goods economy requires that the marginal rates of transformation between Zt and z2 in the two technologies be equated. Since the marginal rate of transformation between z1 and z2 in the intermediate-goods technology is zero (h2/h3 0), we have w 1 /w2 = 0. Thus production efficiency in the intermediate-goods economy implies optimality of the Friedman rule in the monetary economy. =

V. V. Chari and P.J Kehoe

1 736

3.3. Cyclical properties We turn now to some quantitative exercises which examine the cyclical properties of optimal monetary policy in our cash-credit goods model. For some related work, see Cooley and Hansen ( 1 989, 1 992). In these exercises, we consider preferences of the form

where

L

c=

is the endowment of labor and

[( 1

-

a) cr ac J 1/v r

+

.

The technology shock z and government consumption both follow the same symmetric two-state Markov chains as in the model in Section 2. In the baseline model, for preferences, we set the discount factor f3 = 0.97; we set 'ljJ = 0, which implies logarithmic preferences between the composite consumption good and leisure; and we set y = 0. 80. These values are the same as those in Ch1istiano and Eichenbaum ( 1 992). The parameters and v are not available in the literature, so we estimate them using the consumer's first-order conditions. These conditions For our specification of preferences, this condition can be imply that U1 1/U21 = manipulated to be Czr

cu

=

R1 • (-a-a ) 1/(l -v) Ri/(1 v)

a

1-

(3.56)

With a binding cash-in-advance constraint, c1 is real money balances and c2 is aggregate consumption less real money balances. We measure all the variables with US data: real money balances by the monetary base, R1 by the return on three­ month Treasury bills, and consumption by consumption expenditures. Taking logs in Equation (3 .56) and running a regression using quarterly data for the period 1 959-1 989 gives = 0. 57 and v = 0. 83. Our regression turns out to be similar to those used in the money demand literature. To see this, note that Equation (3 .56) implies that

a

�c u + c2

1

=

[ + (-�)l/(1 v) R;/( 1-v)J -1 1

1

-a

(3 .57)

Taking logs in Equation (3.57) and then taking a Taylor's expansion yields a money demand equation with consumption in the place of output and with the restriction that the coefficient on consumption is 1 . Our estimates imply that the interest elasticity of money demand is 4.94. This estimate is somewhat smaller than estimates obtained when money balances are measured by M l instead of the base.

Ch. 26:

Optimal Fiscal and Monetary Policy

1737

Table 3 Properties of the cash-credit goods monetary models Rates

Percentage in models Baseline

High risk aversion

I.!. D.

20.05

20. 1 8

20.05

Standard deviation

0.1 1

0.06

0. 1 1

Autocorrelation

0.89

0.89

0.00

Labor income tax Mean

Correlation with shocks Government consumption Technology Output

0.93

-0.93

0.93

-0.36

0.35

-0.36

0.03

-0.06

0.02

Inflation Mean

-0.44

4.78

-2.39

Standard deviation

19.93

60.37

9.83

0.02

0.06

-0.41

0.37

0.26

0.43

Technology

-0.21

-0.2 1

-0.70

Output

-0.05

-0.08

-0.48

-2.78

Autocorrelation Correlation with shocks Government consumption

Money growth Mean

-0.70

4.03

Standard deviation

1 8.00

54.43

3.74

0.04

0.07

0.00

Autocorrelation Correlation with shocks Government consumption Technology Output

0.40

0.28

0.92

-0. 1 7

-0.20

-0.36

0.00

-0.07

0.02

We set the initial real claims on the government so that, in the resulting stationary equilibrium, the ratio of debt to output is 44 percent. This is approximately the ratio of US federal government debt to GNP in 1 989. For the second parametrization, we set 1/J -8, which implies a relatively high degree of risk aversion. For the third, we set 1jJ = 0 and make both technology shocks and government consumption i.i.d. In Table 3, we report the properties of the labor tax rate, the inflation rate, and the money growth rate for these three parametrizations of our cash-credit goods model. In =

1 738

V. V Chari and PJ. Kehoe

all three, the labor tax rate inherits the persistence properties of the underlying shocks (as it did in Subsection 2.3 . 1 ). Consider the inflation rate and the money growth rate. Recall that for these cash­ credit goods monetary models, the nominal interest rate is identically zero. Table 3 shows that the average inflation rate and the money growth rate are roughly zero. This result may, at first glance, be puzzling to readers familiar with the implications of the Friedman rule in deterministic economies. If government consumption and the technology shock were constant, then the price level and the money stock would fall at the rate of time preference, which is 3 percent per year. In a stochastic economy, the inflation rate and the money growth rate vary with consumption. Therefore, the mean inflation rate depends not only on the rate of time preference, but also on the covariance of the inflation rate and the intertemporal marginal rate of substitution. Specifically, the consumer's first-order conditions imply that (3.58) where E1 is the expectation conditional on s 1 . Under the Friedman rule, R(s 1) 1 . Using the familiar relationship that the expectation of a product of two random variables is the sum of the product of the expectations of these variables and their covariance in Equation (3 .58) and rearranging, we obtain =

(3 .59) In a stationary deterministic economy, Equation (3 .59) reduces to ptfpt+ 1 11{3 so that following the Friedman rule is equivalent to deflating at the rate of time preference. In our stochastic economy, periods of higher-than-average consumption (and hence lower­ than-average marginal utility) are also periods of lower-than-average inflation (and hence higher-than-average p(s 1 )/p(s t+ 1 )). Thus the covariance term in Equation (3.59) is negative. Taking unconditional expectations on both sides of Equation (3 .59), we have that following the Friedman rule implies that E[p(s 1 )/p(st+1 )] > 11{3. For all three parametrizations, the autocorrelation of the inflation rate is small or negative. Thus, in each, the inflation rate is far from a random walk. The correlations of inflation with government consumption and with the technology shock have the expected signs. Notice that these correlations have opposite signs, and in the baseline and high risk aversion models, this leads to inflation having essentially no correlation with output. The most striking feature of the inflation rates is their volatility. In the baseline model, for example, if the inflation rate were normally distributed, it would be higher than 20 percent or lower than -20 percent approximately a third of the time. The inflation rates for the high risk aversion model are even more volatile. The money growth rate has essentially the same properties as the inflation rate. The inflation rates in these economies serve to make the real ret11rn on debt state-contingent. In this sense, =

Ch. 26:

Optimal Fiscal and Monetary Policy

1739 B: Technology Shock

A: Government Consumption Shock

0,75

0

iU

� 8 2 .i'

Labor tax rate

0.5

0.25

Inflation rate -0.25

-0.5 0.2

0.4

0.6

0.8

Autocorrelation of government consumption shock

0.2

0.4

0.6

0.8

Autocorrelation of technology shock

Fig. I . Persistence plots of inflation rates and labor tax rates versus shocks to govemment consumption and technology: (a) government consumption shock; (b) technology shock.

debt, together with appropriately chosen monetary policy, acts as a shock absorber. The inflation rates are volatile in these economies because we have not allowed for any other shock absorbers. The results for the high risk aversion model are basically similar to those for the baseline model, with two exceptions. First, the correlation of the labor tax rate with the shocks has opposite signs from the baseline model. Changing the risk aversion changes the response of the marginal rate of substitution of consumption and leisure to the shocks. This change in the response alters the sign of the correlation. Second, and more significantly, the inflation rate in the high risk aversion model is substantially more variable and has a higher mean than the inflation rate in the baseline model. The reason for the difference is that the higher variability in the inflation rate increases the covariance term in Equation (3.59) and thus increases the average inflation rate. The results for the i.i.d. model are similar to those for the baseline model, with two exceptions. In the i.i.d. model, the autocorrelation of the labor tax rate and the autocorrelation of the inflation rate are quite different from their values in the baseline model. The labor tax rate has basically the same persistence properties as the underlying shocks - and so does the price level. A standard result is that if a random variable is i.i.d., its first difference has an autocorrelation of -0.5. The inflation rate is approximately the first difference of the log of the price level. Thus, in our i . i .d. model, the autocorrelation of the inflation rate is close to -0.5. We investigated the autocorrelation properties of the labor tax rate and the i nflation rate as we varied the autocorrelation (or persistence) of the underlying shocks. We found that the autocorrelation of both the labor tax rate and the inflation rate increased as we increased the persistence of the underlying shocks. Specifically, we set one shock at its mean value and varied the persistence of the other shock. In Figure IA, we plot the autocorrelations of the labor tax rate and the inflation rate as functions of the autocorrelation of govemment consumption. In Figure 1 B, we plot the autocorrelations

V. V. Chari and PJ Kehoe

1 740 A: Shock to Government Consumption

12

�

10

2

iii

" �

*

10

15

20

period

B: Labor Tax Rate

21

� 2 � X

2

20

0 "'

."l 19 0

10

15

20

period C: Inflation Rate

60

c 2 �

40 20

c 0 z ro

E

-20 -40

0

10

period

15

20

Fig. 2. Responses to government consumption shock: (a) the shock to government consumption; (b) labor tax rate; (c) inflation rate.

of these rates as functions of the autocorrelation of the technology shock. In both of these figures, the autocorrelations of the rates increase as the autocorrelations of the shocks increase. The inflation rate and money growth rate are close to i.i.d. These rates are positively correlated with government consumption and negatively correlated with the technology shock. As with the labor tax rate, these shocks have opposing effects on inflation and similar effects on output, implying that the correlation of inflation and money growth with output is roughly zero. To gain some intuition for the labor tax rates and the inflation rates, we simulated a version of the baseline model in which technology shocks were set equal to their mean levels so that the only source of uncertainty is government consumption. In Figure 2, we report a 20-period segment of our realizations. In Figure 2A, we see the shock to government consumption: this variable is constant at a low level from

Ch. 26:

1 74 1

Optimal Fiscal and Monetary Policy

period 0 t o period 5, is then high from period 6 t o period 12, and returns t o its low level from period 1 3 to period 20. In Figure 2B, we plot the optimal labor tax rates. These tax rates follow the same pattern: they are constant between periods 0 and 5, when government consumption is low; are slightly higher between periods 6 and 12, when government consumption is higher; and return to their low level between periods 1 3 and 20, when government consumption returns to its low level. The striking feature is that labor tax rates hardly fluctuate in response to the shocks. In Figure 2C, we plot the optimal inflation rate. There is a large inflation rate from period 5 to period 6, when government consumption rises to its higher level, and a large deflation rate from period 1 2 to period 1 3 , when government consumption falls. In periods without a change in government consumption, the inflation rate is roughly zero. To gain an appreciation of the magnitude of the shock absorber role of inflation, it is useful to trace through the effects of shocks on government debt, revenues, and expenditures. Using the analog of Proposition 7 for this economy, we can show that the allocations c(s 1 ), l(s 1 ), real money balances m(s 1 ), and real debt B(s 1 )/p(s 1 ) depend only on the current state s1 , while the change in the price level p(s 1 )/p(s 1- 1 ) depends on s1 _1 and s1 • We write these functions as c(s1 ), l(st ), m(s1 ), b(s1 ), and n(st- 1 , st ) · Consider now the government's budget constraint under the assumption that the economy in period t - 1 is at the mean level of government consumption and the mean level of the technology shock. Denote this state by s . Consider two scenarios. Suppose first that the economy in period t stays at s . We can rearrange the government's budget constraint to obtain

b(s)

=

[

m(S) 1 R(s) b(s) c- - + ( - [ g(s) - r(s) z(s) /(s)] - m(s) - ( JT s, s ) JT s, s) JT s, s) _ -

_ -

J.

(3 .60)

Suppose next that the economy in period t switches to state s', where g is higher and the technology shock is at its average level. The government budget constraint can then be written as

b(s' ) =

�

R(s b (s) n(s, s')

+

_(

[

J

1 s -_- [ g(s) -- r(s) z(S) l(s)] - m(s') - __1'11 )_ . n(s, s ') n(s, s')

(3 .61)

In both (3 .60) and (3 . 6 1 ), the term on the left is the new debt. The first term on the right is the inherited debt obligations net of the inflation tax. The second term on the right is the inflation-adjusted government deficit from period t - 1 . The inflation adjustment reflects that both government consumption and tax revenues are credit goods that are paid for with a one-period lag. The last term on the right is the seigniorage. Subtracting Equation (3.60) from (3 .61) gives the accounting identity 11 New

debt =

(-23)

11 Value

(-1 9)

of old debt

+ A Tanzi

(+ 1 )

effect -

11

Seigniorage,

(3 .62)

(+5)

where the Tanzi effect is the difference in the inflation-adjusted deficit. [See Tanzi ( 1 977).] (The numbers in parentheses are discussed below.)

1 742

V.V. Chari and PJ Kehoe

We can use our simulation to calculate the terms in Equation (3 .62). We normalize the economy so that mean output is 1 00 units of the consumption good. We consider an innovation in government consumption of 1 unit of this consumption good. This innovation leads to an increase in the present value of government consumption of 28 units of the consumption good. The numbers in parentheses below the terms in Equation (3 .62) are the changes in the relevant terms in units of the consumption good. The value of the old debt falls by 1 9 units because the sharp rise in inflation acts as a tax on inherited nominal debt. In our economy, the government debt is positive when the shocks are at their mean values. The government runs a surplus to pay the interest on the debt. A rise in the inflation rate erodes the value of the nominal surplus, leading to a Tanzi effect of 1 unit. The large inflation rate is, of course, due to a sharp rise in the money growth rate. The government collects 5 units of additional seigniorage by printing this money. Thus the new debt falls by 23 units. Since the present value of government consumption rises by 28 units, the present value of labor tax revenues needs to rise by only 5 units. This result implies that labor tax rates need to change by only a small amount. In this economy, the volatile inflation rate acts as a shock absorber, allowing the labor tax rate to be smooth. In essence, the government pays for 82 percent (23/28) of the increase in the present value of government spending by increasing the price level sharply, which taxes inherited nominal claims, and for only 1 8 percent (5/28) by increasing the present value of labor taxes. Note that our autocorrelation results are quite different from those of Mankiw ( 1 987). Using a partial equilibrium model, he argues that optimal policy implies that both labor taxes and inflation should follow a random walk. It might be worth investigating whether there are any general equilibrium settings that rationalize Mankiw's argument. In the models considered in this subsection, nominal asset markets are incomplete because returns on nominal debt are not state-contingent. The government, however, can insure itself against adverse shocks by varying the ex post inflation rate appropriately. These variations impose no welfare costs because private agents care only about the expected inflation rate and not about the ex post inflation rate. A useful extension might be to consider models in which ex post inflation imposes welfare costs. An open question is whether optimal inflation rates will be roughly a random walk if the welfare costs are high enough.

4. Conclusion

In this chapter we have analyzed how the primal approach can be used to answer a fundamental question in macroeconomics: How should fiscal and monetary policy be set over the long run and over the business cycle? We use this approach to draw a number of substantive lessons for policymaking. Obviously, these lessons depend on the details of the specific models considered. By and large we have considered

Ch. 26:

Optimal Fiscal and Monetary Policy

1 743

environments without imperfections in private markets, such as externalities and missing markets. In models with such imperfections, optimal policy not only must be responsive to the efficiency considerations we have emphasized, but also must attempt to cure the private market imperfections.

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Cooley, T.F., and G.D. Hansen (1992), "Tax distortions in a neoclassical monetary economy", Journal of Economic Theory 58:290-3 16. Correia, I., and P. Teles ( 1 996), "Is the Friedman rule optimal when money is an inte1mediate good?", Journal of Monetary Economics 38:223-244. Diamond, P.A. ( 1 973), "Taxation and public production in a growth setting", in: J.A. Mirrlees and N.H. Stern, eds., Models of Economic Growth (Wiley, New York) 2 1 5-235. Diamond, P.A., and J.A. Min·lees ( 1 97 1 ), "Optimal taxation and public production I: Production efficiency", American Economic Review 6 1 : 8-27. Ekeland, I., and J. Scheinkman (1 986), "Transversality conditions for some infinite horizon discrete time optimization problems", Mathematics of Operations Research 1 1 :2 1 6-229. Escolano, J. ( 1 992), "Optimal taxation in overlapping generations models", manuscript (University of Minnesota). Faig, M. (1 988), "Characterization of the optimal tax on money when it functions as a medium of exchange", Journal of Monetary Economics 22:1 37-148. Friedman, M. (1 969), "The optimum quantity of money", in: The Optimum Quantity of Money and other Essays (Aidine Publishing Company, Chicago, lL) l-50. Garriga, C. (1 999), "Optimal fiscal policy in overlapping generations models", manuscript (University of Barcelona). Guidotti, P.E., and C. Vegh (1 993), "The optimal inflation tax when money reduces transactions costs: a reconsideration", Journal of Monetary Economics 3 1 : 1 89-205. Jones, L.E., R.E. Manuelli and P.E. Rossi ( 1 997), "On the optimal taxation of capital income", Journal of Economic Theory 73:93-1 17. Judd, K.L. (1 985), "Redistributive taxation in a simple perfect foresight model", Journal of Public Economics 28:59-83. Kimbrough, K.P. (1 986), "The optimum quantity of money rule in the theory of public fin ance", Journal of Monetary Economics 1 8:277-284. Koopmans, T.C. (1 965), "On the concept of optimal growth", in: The Econometric Approach to Development Planning (Rand McNally, Chicago, IL). Kydland, F.E., and E.C. Prescott (1 982), "Time to build and aggregate fluctuations", Econometrica 50: 1 345-1370. Lucas Jr, R.E. (1990), "Supply-side economics: an analytical review", Oxford Economic Papers 42: 293-3 1 6 . Lucas Jr, R.E., and N . L . Stokcy ( 1983), "Optimal fiscal and monetary policy i n an economy without capital", Journal of Monetary Economics 1 2 :55-93. Mankiw, N.G. ( 1 987), "The optimal collection of seigniorage: theory and evidence", Journal of Monetary Economics 20:327-3 4 1 . Marcct, A., T.J. Sargent and J . Seppala ( 1996), "Optimal taxation without state-contingent debt", manuscript (Stanford University). Pestieau, P.M. ( 1 974), "Optimal taxation and discount rate for public investment in a growth setting", Journal of Public Economics 3 : 2 1 7-235. Phelps, E.S. (1 973), "Inflation in the theory ofpublic finance", Swedish Journal of Economics 7 5 : 67-82. Prescott, E.C. (1 986), "Theory ahead of business cycle measurement", Federal Reserve Bank of Minneapolis Quarterly Review 1 O(Fall):9-22. Ramsey, F.P. (1 927), "A contribution to the theory of taxation", Economic Journal 37:47 -61 . Razin, A . , and E . Sadka (1 995), 'The status o f capital income taxation i n the open economy", FinanzArchiv 52:21-32. Stiglitz, J.E. ( 1 987), "Pareto efficient and optimal taxation and the new new welfare economics", in: A.J. Auerbach and M. Feldstein, eds., Handbook of Public Economics, vol. 2 (North-Holland, Amsterdam) 991-1042. Stock, J.H., and M.W. Watson ( 1 993), "A simple estimator of cointegrating vectors in higher order integrated systems", Econometrica 6 1 :783-820.

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AUTHOR INDEX

Abel, A.B. 8 1 8, 83 1 , 834, 835, 994, 1069, 1 237, 125 1 , 1 253, 1 265, 1 266, 1268, 1 27 1 , 1 272, 1 284, 1 285, 1 65 1 Abowd, J. 567, 568, 570, 57 1 , 6 1 6, 759 Abraham, J. I 039 Abraham, K.G. 1 058 Abraham, K.J. 1 1 83, 1 22 1 Abramovitz, M. 208 Abramowitz, M. 865, 887 Acemoglu, D. 852, 1 2 1 5 Adam, M. 500 Adams, C. 1 53 8 Adelman, F.L., see Adelman, 1 . 9 Adelman, L 9 Agenor, P.R. 1 543, 1 572 Aghion, P. 264, 665, 672, 7 1 5, 7 1 9, 1 1 57, 1 208, 1 2 1 0, 1 2 1 3, 1 377, 1 450, 1 454, 1 465 Aiyagari, S.R. 442, 547, 552, 566, 567, 983, 1 140, 1 293, 1 63 1 Aizcnman, J. 1 497, 1538, 1 540 Akaike, H. 2 1 7 Akerlot; G . 1 344 Akerlof, G.A. 1 98, 397, 1 034, 1 035, 1 039, 1 1 57, 1 200 al Nowaihi, A. 1 4 1 5, 1 422, 1 43 7 Alesina, A 1 62, 277-279, 692, 1 404, 1 4 1 6, 1 422-1 426, 1 430, 1 432, 1438, 1 439, 1 446, 1 449, 1 450, 1 454, 1 460, 1 46 1 , 1464-1466, 1469, 1 47 1 , 1 5 1 8, 1 522, 1 540 A1csina, A., see Tabellini, G. 1 456, 1465 Alessie, R. 774, 775 Allais, M. 661 , 1 309 Allen, D.S. 8 7 1 Allen, F. 576 Almeida, A. 1 432, 1 495 Alogoskoufis, G.S. 1 66, 2 1 4, 2 1 5 Altonji, J. 6 1 5 Altonji, J. , see Hayashi, F. 796 Altonji, J.G. 789 Altug, S. 584, 595, 61 1 , 6 12, 785, 786, 792 Alvarez, F. 575, 996 Ambler, S . 944, 1 062, 1 067 American Psychiatric Association 1 325

Amman, H.M . 368, 535 Anderson, E. 564 Anderson, E.W 368, 369 Ando, A., see Modigliani, F 762 Andolfatto, D. 994, 1 1 58, 1 1 73, 1 203, 1 207, 1 22 1 Andres, J., see Blanchard, OJ. 1 2 1 4 Araujo, A . 323 Arellano, M. 787 Arifovic, J. 455, 465, 472, 521-523, 525-527, 53 1 Arrow, K. 664, 1 03 3 , 1 042 Arrow, K.J. 1 2 1 8 Arthur, WB. 454, 476, 534 Ascari, G. 1 04 1 Aschauer, D.A. I 656, 1 657 Asea, P., see Mendoza, E. 1439 Ashenfelter, 0. 6 1 8, 1 03 8 , 1 039 Askildsen, J.E. I 074 Atkcson, A. 575, 6 1 0, 786, 847, 1 298, 1 675, 1 7 1 8, 1 720 Atkinson, A.B. 1 673, 1 676, 1 680, 1 682, 1 7 1 8 Attanasio, O.P. 564, 607, 608, 6 1 0-6 1 3, 752, 753, 756, 759, 769, 777, 779, 781 , 783, 784, 787, 789-794, 796, 797, 802, 1 264, 1 655 Auerbach, A.J. 3 80, 549, 576, 588, 590, 5 9 1 , 5 9 3 , 6 1 6, 82 ! , 1 624, 1 634, 1 63 5, 1 639, 1 652, 1 7 1 8 Auerbach, A.J., see Feldstein, M.S. 904, 906 Auernheimer, L. 1 449 Auster, R. 474 Autor, D. 57'1 Axilrod, S.H. 1 493 Azariadis, C. 262, 264, 271 , 289, 389, 395, 5 1 6, 527, 658, 660, 66 1 , 1 03 5

l-1

Bacchetta, P. 1 344 Bacchetta, P., see Feldstein, M. 1 637 Bachelier, L. 1 3 1 6 Backus, C.K. 549 Backus, D. 1 0 1 7, 1 03 1 , 1 270, 1 405, 1 4 14, 1415 Backus, D.K. 9 , 42, 45, 938, 1 3 1 6, 1708

Author Index

1-2 1432, 1 438 1 55, 1485, 1 5 1 5 Bagwell, K . 1 125 1 647 Bagwell, K., see Bernheim, B.D. Bailey, M.J. 1 643 Bairoch, P 7 1 9, 724 Baker, J. B. 1 1 25 Ba1asko, Y. 427, 506 Balassa, B.A. 705 Balke, N.S. 6, 6 1 , 1 14, 204, 205, 221 Ball, L. 42, 72, 1 99, 1 023, 1 037, 1 039, 1 04 1 , 1 1 27, 1 4 1 5, 1 499, 1 504, 1 542, 1 632, 1 650, 1 65 1 Ball, R . 1 32 1 Ballard, C . 1 639 Baneijee, A., see Aghion, P. 1 377 Bange, M.M., see De Bondt, W.F. 1 32 1 Banks, J. 75 1 , 758, 759, 770, 783, 788, 790-792 756, 759, 793, Banks, J., see Attanasio, O.P. 794 Banneijee, A. V 1 332 Bansal, R. 1 25 5 Barberis, N. 1 294, 1322 Barclays de Zoete Wedel Securities 1 238 Barkai, H. 1 572 Barnett, S. 8 3 1 Barnett, W 538, 540 Barone, E. 702 1 0 1 , 1 57, 1 58, 1 73 , 237, 245, 246, Barro, R.J. 252, 269, 27 1 , 272, 277-28 1 , 284, 643, 65 1 , 657, 659, 67 1 , 675, 68 1 , 683-685, 688, 689, 69 1 -694, 696, 943, 974, 1 023, 1 055, 1 1 55, 1 404, 1 405, 1 4 1 1 , 1412, 1 4 14, 1 4 1 5, 1 425, 1438, 1 439, 1 466, 1 485-1489, 1 637, 1 64 1 , 1 642, 1 645, 1 662, 1 675, 1 702, 1 705, 1 707 Barsky, R. 43, 558, 564, 565 Barsky, R., s e e Solon, G. 579, 1 058, 1 102, 1 1 06 Barsky, R., see Warner, E.J. 1 0 19 Barsky, R.B. 1 82, 2 1 5, 2 1 6, 1 149, 1 237, 1 277, 1 294-1296, 1 653 Barth, J.R. 1 657 Bartle, R.G. 76 Barucci, E. 525 Basar, T. 1 449 Basu, S. 399, 402, 433, 983, 992, 994, 1 069, 1 080-1082, 1 096, 1 097, 1 1 1 7, 1 142 Bates, D.S. 1 3 1 0, 1324 Banrnol, W.J. 252, 269 Bade, R.

Bagehot, W.

9, I I , 1 2, 45, 203, 380, 430, 934, 938, 974, 980, 992, 1 296, 1404 Bayonrni, T. 1 6 1 , 2 1 1 , 2 1 6, 2 1 7, 2 1 9 Bayoumi, T. , see Mussa, M . 208 Bazaraa, M.S. 33 1 1214 Bean, C., see Blanchard, O.J. Bean, C.R. 785, 1 497 Beaudry, P. 99, 395, 4 1 3, 592, 1 264 Beaulieu, .J.J. 801 , 802, 876 Becker, G. 592, 653 Becker, G.S. 3 1 7, 1 645 Becker, G.S., see Ghez, G . 6 15, 752, 759 Becker, R. 369 1 4 1 1 , 1 436, 1438 Beetsma, R. Bekaert, G. 1281 Bell, D.E. 1313 Bellman, R. 336, 340 Belsley, D. 882, 887, 888, 892 Beltratti, A. 524, 525 Ben-David, D. 265, 278 Ben Porath, Y. 577, 582 Benabou, R. 1 0 1 7 , 1 0 1 8, 1 03 1 , 1 128, 1 129, 1 469, 1472, 1 473 Benabou, R. 268 Benartzi, S. 1290, 1 3 1 2 , 1 3 1 3 Benassy, J. 507 Benassy, J.-P. 1 506 Benhabib, J. 283, 395, 399-405, 408, 4 1 2-4 1 4, 4 1 7, 4 1 9, 42 1 , 423-427, 43 1 , 433-435, 437, 442, 505, 550, 847, 1 145, 1 449, 1 465, 1 467, 1 472 1 450 Benigno, P., see Missale, A. Benjamin, D . 161 Bennett, R . 395 Bensaid, B. 1 446, 1 449 Benveniste, A. 476, 5 3 1 Benveniste, L.M. 3 2 1 1 0 1 9, 1 020 Bergen, M . , see Dutta, S. Bergen, M., see Levy, D. 1 0 1 4, 1 0 1 5, 1 0 1 9 Bergen, P.R. 1 04 1 Berger, L.A. 1 330 Bergstrom, V 538 Bcrnanke, B.S. 68, 72, 76, 83, 89, 91-93, 1 14, 1 44, 1 78, 1 82-1 84, 800, 856, 857, 1 036, 1 343, 1 345, 1 346, 1 352, 1 357, 1 3 6 1 , 1 363, 1 365, 1 3 69, 1 3 7 1 , 1 373, 1 376-1 378, 1495, 1 578 Bernard, A.B. 254, 27 1 , 287, 288 Bernard, V.L. 1 32 1 Bernheim, B.D. 1 646, 1 647, 1 649, 1 654, 1 659, 1 660 Baxter, M.

Author Index

Berry, M., see Dreman, D. 1 3 20 Berry, T.S. 1 6 1 8 Bertocchi, G . 474 Bertola, G. 643, 708, 801 , 82 1 , 834, 835, 840,

843, 1 1 87, 1 222, 1 472, 1 580 Bertsekas, D.P. 326 Besley, T. 856 Betts, C.M. 2 1 7 Beveridge, S. 1 062, 1 1 43 Bewley, T. 566, 1 1 55 Bhaskar, V. 1 03 7 Bianchi, M . 290, 292 Bikhchandani, S. 1 332 Bils, M. 694, 9 10, 912, 983, 1 053, 1059, 1 069,

1 070, 1072, 1 075, 1 076, 1 078-1081, 1 085, 1 087, 1 102, 1 1 04, 1 1 1 9, 1 120, 1 130 Bils, M.J. 579 Binder, M. 2 7 1 , 1092 Binmore, K. 462 Binmore, K.G. 1 1 88 Bisin, A. 427 Bismut, C., see Benabou, R . 1 0 1 7, 1 0 1 8, 103 1 Bizer, D. 380 Bjorck, A., see Dahlquist, G. 337 Black, F. 4 1 7, 1 280, 1 3 1 0, 1 3 3 1 , 1 507 Blackwell, D. 320 B1ad, M., see Benassy, l 507 Blanchard, OJ. 40---42 , 2 1 1 , 2 1 6, 2 1 7, 3 9 1 , 4 1 6, 47 1, 504, 643, 660, 8 1 8, 852, 877, 887, 888, 890, 892, 906, 9 1 2, I 0 1 3, 1030, 1 033, 1 034, 1 036, 1 04 1 , 1 1 12, 1 1 30, 1 1 62, 1 173, l l 76, 1 1 83, 1 1 84, 1 1 94, 1 202, 1 2 14, 1 22 1 , 1 266, 149 1 , 1 634, 1 635, 1645, 1 650 Blanchard, OJ., see Missale, A. 1450 Blank, R . 579 Blinder, A. 587, 750, 1 0 1 8--1020, 1038 Blinder, A.S. 41, 876, 8 8 1 , 887, 893, 903, 904, 907, 908, 91 0, 1 0 1 8, 1 085, I l l S, 1344, 1485, 1499, 1 660 Blinder, A.S. , see Bernanke, B.S. 83, 91, 93 Bliss, C. 1461 , 1465 Bliss, R., see Fama, E.E 1 280 Blomstrom, M. 277, 279, 280 Bloomfield, A. 156 Blume, L.E. 321, 322, 474 Blume, L.E., see Bray, M. 474 Blundell, R. 572, 602, 6 1 1 , 6 1 2, 620, 764, 770, 779, 7 8 1 , 783, 788, 790-792, 797 Blundell, R., see Banks, l 758, 759, 770, 783, 788, 790-792

I-3 Boadway, R. 1463 Bodnar, G. 1 3 1 8 Bohm, V 475, 646 Bohn, H . 1 465, 1 622, 1 650, 1691 Boldrin, M. 362, 399, 400, 506, 962, 1 062,

1284, 1 297, 1465 Bolen, D.W 1 325 Bollerslcv, T. 1 236, 1 2 80 Bolton, P., see Aghion, P. 1377, 1450, 1454,

1 465 Bona, J.L 3 1 3 Boothe, PM. 1 658 Bordo, M.D. 1 52, 1 55 - 1 60, 1 62, 1 64-167, 1 82,

1 84, 1 85, 1 94, 202-204, 207-209, 2 1 1 , 2 1 5, 2 1 7-221 , 1404, 1 438, 1 590 Bordo, M.D., see Bayoumi, T. 161 Bordo, M.D., see Betts, C . M . 2 1 7 Borenstein, S . 1 1 24 Boschan, C., see Bry, G. 8 Boschen, J.F. 139 Boskin, M.l 618 Bossaerts, P. 454 Bosworth, B., see Collins, S. 653 Bourguignon, F., see Levy-Leboyer, M. 222 Bovenberg, A.L. , see Gordon, R.H. 1 637 Bovenberg, L., see Beetsma, R. 1 4 1 1 Bowen, W 6 1 9 Bowman, D . 1 3 1 3 Boyd, W H ., see Bolen, D.W 1 325 Boyle, M., see Paulin, G. 751 Boyle, P. 380 Boyle, P.P., see Tan, K.S. 334 Brainard, WC. 8 1 7 Brauch, R., see Paulin, G. 75 1 Braun, R.A. 974 Bratm, S.N., see Krane, S.D. 876, 877 Brav, A. 1 290 Bray, M. 454, 463, 465, 466, 473---4 75, 527 Brayton, F. 1 043, 1 344, 1485 Brayton, F, see Hess, G.D. 1 485, 1 509 Breeden, D. 1 246 Breiman, L. 289 Bresnahan, T.F. 9 1 1 , 9 1 2 Bretton Woods Connnission 208 Broadbent, B. 1 4 1 2 Broadbent, B . , see Barro, R.l 1 4 1 2 Broadie, M., see Boyle, P. 380 Brock, W A . 3 1 9, 407, 455, 528, 532, 547, 552, 556, 942, 9 5 1 , 1 507 Brown, C. 585 Brown, P., see Ball, R. 1 3 2 1

I-4 Brown, S. 1 242 Browning, E. 1463 Browning, M. 598, 606, 607, 6 1 0-6 12, 750, 752, 7 7 1 , 778, 787, 792, 798, 803 Browning, M., see Attanasio, O.P. 607, 608, 6 1 0, 6 1 1 , 6 1 3, 779, 789, 791 , 1 655 Browning, M., see Blundell, R. 6 1 1 , 6 1 2, 779, 7 8 1 , 783, 790, 791 Broze, L . 487, 488 Brugiavini, A. 775 Brugiavini, A., see Banks, J. 770, 788 Brumberg, R., see Modig1iani, F. 761 Brumelle, S.L., see Puterman, M.L. 336, 338 Brunner, A.D. I 04 Brunner, K. 179, 1 83, 1 9 1 , 1 025, 1 491 Bruno, M. 471 , 1 090, 1496, 1 538, 1 539, 1 543, 1 553 Bry, G. 8 Bryant, R.C. 1 043, 149 1 , 1 497, 1 5 1 6 - 1 5 1 8 Bryant, R.R. 1 3 J 3 Buchanan, J.M. 1 63 1 , 1 642 Buchholz, T.G. 1643 Buckle, R.A. 1 0 1 9 Bufman, G. 1 543 Buiter, W. 1 030, 1 52 1 Bulirsch, R., see Stoer, J. 334 Bull, N. 1 675, 1 7 1 1 Bullard, J. 466, 507, 509, 5 1 5, 526 Bullard, J., see Arifovic, J. 527 Bulow, J. 1 448, 1 449 Burdett, K. 1 173, 1 196 Bureau of the Census 1 6 1 8, 1 6 1 9 Burns, A.F. 5, 8 , 93 1 , 934 Burns, A.F., see Mitchell, W.C. 8, 44 Burnside, C. 399, 930, 980-985, 994, 1 078, 1 142, 1 1 62 Burt1ess, G. 6 1 8, 620 Butkiewicz, J.L. 1 621

Caballe, J. 578 Caballero, R.J. 399, 749, 7 7 1 , 794, 801 , 802, 82 1-823, 828, 830, 832, 834-838, 840-842, 844, 846, 847, 852, 855, 856, 994, 1 032, 1 1 57, 1 1 58, 1 1 60, 1 1 87, 1 2 1 0, 1 2 1 1 , 1 2 1 3 , 1 472 Caballero, R.J., see Bertola, G. 801 , 821 , 834, 840, 843, 1 1 87 Cagan, P. 1 57, 1 6 1 , 203, 1 534 Cage, R., see Paulin, G. 75 1 Calmfors, L. 1 2 1 4

Author Index

Calomiris, C.W. 1 69, 1 8 1 , 1 83, 1 87, 1 9 1 , 1 376 Calvo, G .A. 389, 397, 408, 419, 422, 1 030, 1 032, 1 034, 1 1 1 4, 1 346, 1 360, 1 363, 1 389, 1 400, 1415, 1428, 1 445-1447, 1449, 1450, 1 535, 1 538, 1 539, 1 546, 1 552, 1 5 54, 1 557, 1 563, 1 564, 1 568, 1 569, 1 57 1 -1 573, 1 5 82, 1 583, 1 5 87-1589, 1 5 9 1 , 1 592, 1 596, 1 597, 1 599-1603, 1 605 Cameron, S. 589 Campbell, J. 92 Campbell, J.R. 846, 847, 994 Campbell, J.Y. 763, 764, 769, 784, 930, 961, 1 120, 1 140, 1 14 1 , 1 145, 1 1 50, 1235- 1238, 1 25 1 , 1 255, 1 257, 1258, 1 26 1 , 1 264-1266, 1 268, 1 270, 1 272, 1 274, 1 275, 1280, 1 284, 1 286, 1290, 1 320, 1 655 Canavcsc, A.J. 1 543 Canetti, E.D., see Blinder, A.S. I 01 8, 1 1 1 8 Canje1s, E. 55 Canova, F. 283, 376, 377, 379 Cantor, R. 1344 Canzoneri, M.B. 1 59, 1 60, 1405, 1414, 1 4 1 5 , 1 507, 1 508 Capie, F. 1 54, 1 63, 222, 1438 Caplin, A. 849, 850 Caplin, A.S. 801 , 9 1 0, 1 03 1 , 1 032 Card, D. 580, 1 0 1 6, 1 1 48 Card, D., see Abowd, J. 567, 568, 570, 5 7 1 , 6 1 6, 759 Card, D., see Ashenfelter, 0. 1 038, 1 039 Cardia, E. 1 655 Cardia, E., see Ambler, S. 1 062, 1 067 Cardoso, E. 1 543 Carey, K., see Bernankc, B.S. 1 78, 1 82 Carlson, J. 473 Carlson, J.A. 904 Carlson, J.A., see Buckle, R.A. 1 0 1 9 Carlson, J.B. 1 04 Carlstrom, C. 1 348, 1 357, 1 368, 1 378, 1 379 Carlton, D. 1 1 29 Carlton, D.W. 1 0 1 8-1020 Carmichael, H.L. 1 1 55 Carpenter, R.E. 876, 881, 9 1 2, 1 344 Carroll, C.D. 567, 572, 573, 593, 759, 762, 769, 7 7 1 , 785, 788, 793, 1 264, 1 344, 1 653, 1 655 Case, K . E . 1323 Casella, A. 1463, 1 465 Caselli, F. 277-279, 283, 284, 286

Author Index

I-5

244, 246, 247, 295, 389, 5 1 6, 643, 649, 662, 942, 948, 1 673 Cass, D., see Balasko, Y. 427 Castaneda, A. 380 Cazzavilan, G. 426 Cecchetti, S.G. 1 82, 2 1 7, 876, 1 0 1 5, 1 0 1 6, 1 01 8, 1 01 9, 1 25 1 , 1 265, 1 270, 1272, 1 294, 1 296 Cecchetti, S.G., see Ball, L . 1 037 Chadha, B. 1 03 1 , 1 542 Chah, E . Y. 775 Chamberlain, G. 283, 286, 785 Chamberlain, T.W 1334 Charnley, C. 400, 85 1 , 1439, 1 673, 1 675, 1 693, 1 697, 1 699 Champsaur, , P. 53!), 463 Chan, L. 1321 Chan, L.K.C. 1 653 Chandler, L.V 1 76 Chang, C.C.Y., see Chamberlain, T.W. 1 334 Chari, V V 72, 1 24, 397, 422, 672, 697, 698, 700, 7 0 1 , 709, 7 1 5, 720, 722, 723, 974, 1 036, 1 037, 1 040-1 042, 1 37 1 , 1448, 1 449, 1459, 1488, 1489, 1 578, 1 673--1676, 1 69 1 , 1 699, 1 708- 1 7 10, 1 720, 1 723 Chari, VV, see Atkeson, A. 1 675, 1 7 1 8, 1 720 Chatterjee, S. 996, 1 126 Chatterji, S. 475, 507 Chattopadhyay, S.K , see Chatterj i, S. 475, 507 Chen, N. 1281 Chen, X. 476, 532 1 334 Cheung, C . S . , see Chamberlain, T. W. Chevalier, J.A. 1 122, 1 1 23 Chiappori, P.A. 39 1 , 395, 5 1 6 Childs, G.D. 882 Chinn, M., see Frankel, J. 1 497 Chirinko, R.S. 8 1 5 , 8 1 7, 1 058, 1 066, 1 086, 1 344, 1 367 592 Chiswick, B., see Becker, G. Cho, D. 278 Cho, I.-K. 455, 465, 524, 525 Cho, J.O. 974, 976, 1 025, 1 036 Cho, .T.O., see Bils, M. 983, 1 075, 1 079, 1 104 Chou, R.Y. 1 236, 1 280 Chou, R. Y., see Bollerslev, T 1 236, 1280 Choudhri, E.U., see Bordo, M.D. 1 84, 1 94 Chow, C.-S. 326, 334 Chow, G.C. 1 294 Christensen, L.R. 673, 688 Cass, D.

.

L .J. 43, 67-70, 83, 84, 89, 9 1 -94, 99, 1 08, 1 09, 1 14, 1 1 5, 1 24, 1 37, 143, 144, 3 14, 329, 330, 339, 347, 349, 350, 355, 362, 364, 367, 369, 370, 376, 377, 379, 426, 504, 547, 764, 881 , 888, 909, 952, 962, 974, 1 0 1 1 , 1 0 1 7, 1 0 1 8, 1 02 1 , 1 030, 1 038, 1 089, 1 100, 1 296, 1 365, 1 369, 1 708, 1 736 Christiano, L..T., see Aiyagari, S.R. 1 140 Christiano, L.J., see Bo1drin, M. 962, 1 284, 1 297 Christiano, L.J., see Chari, VV 72, 1 449, 1 673, 1 675, 1676, 1 69 1 , 1 699, 1708-17 1 0, 1720, 1 723 Chung, K.L. 299 Clarida, R. 95, 96, 1 36, 422, 1 364, 1 368, 1 486 Clark, D., see Kushner, H. 476 Clark, J.M. 816 Clark, K.B. 602, 1 1 73 Clark, P.B., see Mussa, M. 208 Clark, T.A. 1 73 Clark, T.E . 1 09 1 , 1 485 Cochrane, J. 1 1 20 1 0 1 , 2 1 1 , 796, 1 234, 1 246, Cochrane, J.II. 1 249, 1 296 Cochrane, J.H., see Campbell, J.Y. 1237, 1 25 1 , 1 284, 1 286 Coe, D.T. 265 2 1 1 , 395, 547, 967, 1 142, 1 503 Cogley, T. Cohen, D. 271 Cohen, D . , see Greenspan, A . 798, 844, 847 Cohn, R., see Modigliani, F. 1321 Cole, I-LL. 576, 1 1 63, 1 1 94, 120 1 - 1 203, 1 207, 1446, 1 449, 1 603 Cole, H.L., see Chari, V V 1 459 Coleman, T. 601 Coleman, W.J. 367, 380 Coleman II, W.J. I 14 Coleman II, W. J. , see Bansal, R. 1255 Collins, S. 653 Conference Board 43 Congressional Budget Office 1 6 1 8, 1 6 1 9, 1 62 1 , 1 624-1 627, 1 639, 1 640, 1 660 Conley, J M. , see O'Barr, W.M. 1 332 Conlon, J.R. 1032 Constantinides, G.M. 559, 567, 78 1 , 803, 1 237, 1 284, 1 2 9 1 , 1 293 Constantinides, G.M., see Ferson, W.E. 1 284 Contini, B. 1 177, 1 1 78, 1 1 80, 1 200, 1 222 Cook, T. 1 94, 1 95, 1 493 Christiano,

.

Author Index

I-6 Cooley, T.F. 42, 69, 97, 1 0 1 , 1 1 5, 124, 1 37, 376, 380, 408, 4 1 1 , 549, 847, 954, 962, 974, 1 376, 1463, 1 736 Cooley, T.F., see Cho, J.O. 974, 976, 1 025, 1 036 Cooper, R. 204, 398, 824 Cooper, R., see Azariadis, C. 395 Cooper, R., see Chatterjee, S. 996, 1 1 26 Cootncr, P.H. 1 3 1 6 Corbo, V 1 543, 1 554 Correia, I. 974, 1 537, 1 675, 1 720, 1 733 Cossa, R. 584 Council of Economic Advisers 1 639 Cox, D. 705 Cox, WM. 1 62 1 Cox Edwards, A., see Edwards, S . 1 543, 1 554, 1 555, 1 575 Crawford, VP. 475 Crossley, T., see Browning, M. 6 1 0, 798 Croushore, D. 1485, 1 653 Crucini, M.J. 1 78, 705 Crucini, M.J., see Baxter, M. 1296 Cukiennan, A. 1404, 1 414, 1 4 1 5, 1432, 1 437, 1438, 1450, 1 456, 1 463, 1 465 Cuk:ierman, A., see Alesina, A. 1424, 1 426 Cukierman, A., see Brunner, K. 1 025 Cummings, D., see Christensen, L.R. 673, 688 Cummins, J.G. 822, 856, 1 344 Cunliffe Report 1 6 1 Currie, D . 454, 504 Cuslnnan, D.O. 95, 96 Cutler, D.M. 797, 1 290, 1 320, 1 32 1 , 1 624 Cyrus, T., see Frankel, J.A. 280 Dahlquist, G. 337 Daniel, B.C. 1647 Daniel, K. 1322 Danthine, J.-P. 329, 370, 952, 962, 1 002, 1 157 Darby, M.R. 166 Dasgupta, P. 655, 656 d' Antnmc, A. 487 DaVanzo, J. 6 1 8 Davcri, F. 1 220 Davidson, J. 750 Davies, J.B. 766 Davis, D. 1 033 Davis, P.J. 333 Davis, S.J. 1 1 5 1 , 1 1 52, 1 160, 1 1 6 1 , 1 1 76, 1 1 78, 1 1 80, 1 194, 1 1 99

Davis, S J., see Attanasio, O.P. 796, 797 Davutyan, N. 1 5 6 Dawid, H. 523, 527 De Bond!, WF. 1 307, 1 320, 132 1 , 1 323 de Fontnouvelle, P., see Brock, W.A. 528 De Fraja, G. 1 037 De Gregorio, J. 1 546, 1 55 1 , 1 573, 1 575, 1 577 de Haan, J., see Eijffinger, S. 1404, 1 43 8 d e I a Torre, M . 4 1 De Melo, J., see Corbo, V 1543 de Melo, J., see Hanson, J. 1 543 De Melo, M. 1 535, 1 5 5 1 D e Pablo, J.C. 1 543 de Soto, H. 695 Deaton, A. 752, 756, 764, 771 , 775, 776, 783, 785, 787, 794, 798, 1 344 Deaton, A., see Blinder, A. 750 Deaton, A., see Browning, M. 6 1 1 , 6 1 2, 752, 787, 792 Deaton, AS. 1 264 Deaton, A.S., see Campbell, J.Y. 764 Debelle, G. 1489, 1 5 1 8, 1 522 DeCanio, S. 454, 463 DeCecco, M. 155 Degeorge, F. 1 32 1 DeKock, G . 1 5 8 DeLong, .l.B. 252, 279, 695, 1 042, 1 290, 1 324 DeLong, J.B., see Barsky, R.B. 1 237, 1 277, 1 294-1296 den Haan, W.J. 27 1 , 347, 354, 369, 994, 1 1 66, 1 1 94, 1203, 1 204, 1 206, 1 207 Denardo, E. V 320 Denison, E.F. 237, 653 Denizer, C., see De Melo, M. 1 535, 1 5 5 1 Denson, E.M. 40 Desdoigts, A. 290 DeTray, D.N., see DaVanzo, J. 6 1 8 Devereux, M. 952, 1 466, 1471 Devereux, M., see Alcssie, R. TIS Devereux, M., see Beaudry, P. 395, 4 1 3 Devereux, M.B. 1 126 Devereux, M.B., see Beaudry, P. 99 Devine, T.J. 1 1 66 Dewatripont, M., see Aghion, P. 1 1 57 Dezhbakhsh, H. 1 039 Di Tella, G . , see Canavesc, A.J. 1 543 Diamond, P. 796 Diamond, P., see Shafir, E. 1 3 1 6 Diamond, P .A. 66 1 , 1 157, 1 1 6 1 , 1 1 62, 1 1 73, 1 1 88, 1 634, 1 645, 1 684, 1 7 1 8 .

Author Index

I -7

P.A., see Blanchard, OJ. 4 1 , 42, 1 162, 1 173, 1 183, 1 1 84, 1 194, 1 202, 1221 Diaz-Alejandro, C.F. 1 543 Diaz-Gimenez, J., see Castaneda, A. 380 Dickens, WT., see Akerlof, G.A. 1 98 Dickey, D.A. 53, 54, 2 1 2 Dickinson, J. 6 1 8 1633 Dicks-Mireaux, L . , see Feldstein, M . Diebold, F.X. 6, I I Diehnan, T., see Kallick, M . 1 325 Dixit, A. 824, 829, 844, 1 1 1 5, 1 12 1 , 1 126 835 Dixit, A.K., see Abel, A.B. Dixon, H. 537 Dodd, D.L., see Graham, B. 1 323 Dolado, J. 1437 Dolado, J.J. 1214 Dolde, W 1318 Dolde, W C ., see Tobin, J. 773 Domar, E. 640 Domberger, S. 1019 Dominguez, K. 1 64, 182 Domowitz, I. 1 020, 1 083, 1 093 Doms, M. 823, 838 Diamond,

Donaldson, J.B.,

see

Constantinides, G.M.

1293 J B. , see Danthine, J.-P. 329, 370, 952, 962, 1 002, 1 1 57 Doob, J.L. 299 Dornbusch, R. 1 98, 1 043, 1 543, 1 562, 1 563, 1 565, 1 568, 1 582, 1 590, 1 637 Dotsey, M . 370, 952, 974, 1 032, 1 043, 1 5 22, 1 652 Drazen, A . 1463, 1465, 1 54 1 , 1 580 Drazcn, A., see Alesina, A. 1 62, 1 450, 146 1 , 1 465, 1 540 Drazen, A., see Azariadis, C. 262, 264, 2 7 1 , 289, 527, 658, 660 1 5 80 Drazen, A . , see Bertola, G. 1571 Drazen, A . , see Calvo, G.A. Drcman, D . 1 320, 1 323 Dreze, J. 770 1405, 1 4 1 4 , 1 4 1 5 Driffill, J., see Backus, D. Driskill, R.A. 1 042 Drudi, F. 1 450 Drugeon, J.P. 426 Dueker, M.J. 1485 Duffie, D. 380 Duffie, D., see Constantinides, G.M. 567, 7 8 1 , 1 237, 1 2 9 1 Duffy, J . 257, 439, 473, 500 Duffy, J., see Arifovic, J. 527 Donaldson,

.

J., see Bullard, J. 526 P. 2 1 5 Dumas, B . 561, 564 Dunlop, J.T. 939, 1 059 Dunn, K.B. 800, 1 284 Dwme, T., see Doms, M. 823, 838 Dupor, B . 994 Durkheim, E. 1331 Durlauf, S.N. 254, 262-264, 268, 270, 2 7 1 , 287, 289, 303, 550, 905-907 Dmlauf, S.N., see Bernard, A.B. 254, 27 1 , 287, 288 Dutta, P.K. 3 80 Dutta, S. 1 0 1 9, 1 020 1 0 1 4, 1 01 5, 1 0 1 9 Dutta, S., see Levy, D. Dutton, J . 1 56 Dyl, E.A. 1 334 Dynan, K.E. 770 Duffy,

Duguay,

Easley, D., Easley, D.,

see Blume, L E. 3 2 1 , 322, 474 see Bray, M. 474 .

W. 277-279, 2 8 1 , 675, 703, 1 538, 1 547, 1 553, 1 560, 1 56 1 Easterly, W , see Bruno, M. 1 553 Eaton, .J. 7 1 9 801 , 802, 1 344 Eberly, J.C. Eberly, J.C., see Abel, A.B. 83 1 , 834, 835, 994 Echenique, F. 1551, 1561 Eckstein, 0 . 1 344 Eden, B. 1 0 1 9, 1 023 Edin, D.A. 1457 Edwards, S. 1 538, 1 543, 1 554, 1 555, 1 575, 1 57 8- 1 580 Edwards, S., see Cukierman, A. 1456, 1 465 Edwards, W 1 322 Eichenbaum, M. 83, 94, 96, 99, 1 00, 1 37, 1 84, 549, 550, 785, 799, 800, 803, 885, 888, 905-907, 9 12, 957, 1 084 Eichenbawn, M . , see Aiyagari, S.R. 1 140 Eichenbaum, M . , see Burnside, C. 399, 930, 980-985, 994, 1 078, 1 142, l l 62 Eichenbaum, M., see Chmi, V.V. 72, 1449 Eichenbaum, M., see Christiano, L.J. 43, 6770, 83, 84, 89, 9 1 -94, 99, 108, 1 15, 1 24, 1 37, 1 43, 144, 376, 377, 379, 764, 974, 1 0 1 1 , 1 02 1 , 1 038, 1 089, 1 1 00, 1 365, 1 369, 1 708, 1 736 Eichenbawn, M . S . , see Christiano, L.J. 88 1 , 888 Easterly,

I-8

Author Index

Eichcngreen, B.

1 52, 1 54-- 1 57, 1 60, 1 62-164,

1 68, 1 78, 1 85, 1 87, 1 89, 204, 208, 209,

Evans, M.

1 82

Evans, P.

283, 1 635, 1 647, 1 656-1 659

2 1 1 , 2 1 9, 1 449, 1465, 1 590

see

Eichengreen, B., 2 1 7, 2 1 9

see see

Eichengreen, B., Eichengreen, B.,

Fair, R. 1 62

Bordo, M.D.

1 463, 1465

Casella, A.

Farber,

475, 1 1 24

Elison, R.E.,

see

see

80 1 , 802, 82 1 ,

835-838, 840-842, 994, 1 032, 1 1 5 8

see

Engle, R.F.

1 344

Bollers1ev, T.

1 280

Epstein, L.G.

Chou, R.Y.

1 236, 1280

556, 558, 564, 565, 744, 769,

Erceg, C.

1 04 1

see

Bordo, M.D.

1 208

Ermoliev, Y.M.,

see

see

286 Esteban, J.-M. Estrella, A. Evans, C .

Arthur, W.B.

476

1718

Esquivel, G . ,

Caselli, F.

277-279, 283, 284,

264

1 12 1 69, 2 1 7, 1 4 1 6, 1425, 1437

Fauvel, Y.

1 573

Favaro, E.

1 554, 1 555 1 077, 1 1 03 8 1 8, 1 344

Fazzari, S.M.,

Chirinko, R.S.

Evans,

Christiano, L.J.

Feenstra, R.

1 066, 1 086

15 69

1 76

Feenstra, R.C.,

see

Feiwel, G . R .

535

Feldman, M.

474

Feldstein, M.

44, 1 97, 14!:!5, 1 497, 1 498, 1 622,

Bergen, P.R.

1041

64 1 , 6 57

Fcrcj ohn, J.

1425

see Basu,

Fernald, J.G.,

182 67, 68, 70, 83,

Fernandez, R. Ferris, S . P.

Eichenbaum, M.

83, 94, 96,

Ferson, W. E . Festingcr, L.

425, 426, 453-455, 46 1-465, 468,

S.

399, 402, 433, 994,

1 1 1 7, 1 1 42

1 02 1 , 1038, 1 089, 1 1 00, 1 365, 1 369 1 37

904, 906

1 083, 1 1 22

84, 89, 9 1-94, 99, 1 08, 1 37, 1 43, 1 44, 1 0 1 1 ,

see

8 8 1 , 9 1 2,

1 332

60

Fellner, W. Bordo, M.D.

Evans, G.W.

see

Feenberg, D.

Felli, E.

1 05

Evans, C.L.,

Evans, C.L.,

Carpenter, R.E.

see

Fazzari, S.M.,

Feldstein, M.S.

982

see C . L . , see

395, 399---402,

1 63 1 , 1 633, 1 636, 1 637, 1 639, 1 656, 1 660

43, 1 28 1 , 1485

Evans, C.L.

Faust, J.

Federal Reserve Board

i 82

1 3 14

Escolano, J.

Farrell, J.

Featherstone, M.

Erceg, C.J., Erlich, D.

Benhabib, J.

1 344

1 250, 1 256

Eriksson, C.

see

408 , 4 1 2--4 14, 4 1 7, 425, 427, 4 3 1 , 433--435,

Fazzari, S.M.

9

P.

39 1 , 395, 396, 4 l l -4 1 4, 427--430,

Farmer, R.E.,

Fay, J.A.

50

see

662, 1 002

442, 505

1 14

Balke, N.S.

Caballero, R.J.

Engelhardt, G.

1 200

H.

434, 437, 500, 505

215

see

Emery, K.M.,

855

Farmer, R.E.

see Ball, L. 1 650, 1 6 5 1 see Feldstein, M . 1 65 6

Elmendorf, D.W., Emery, K . M .

1 57

1439

Elmendorf, D.W.,

1 82

1 235, 1 2 80, 1 2 8 1 , 1 307, 1 3 1 6,

Fanner, R.

Bordo, M.D.

Elmendorf, D.W.

Dominguez, K. 326

1 320-1323

835

Ellison, G.

Engllmd,

876, 1 077, 1 49 1

see

Fair, R.C.,

Fama, E .F.

673

Engle, R.F.,

Fair, R . C .

Fallick, B.C.

El Karoui, N.

Engle, R.,

1 675, 1 72 0 1 4 1 6, 1 42 5

8 1 7, 1 3 1 0, 1 62 1 , 1 622 1 689

Elias, VJ.

Faig, M.

Falcone, M.

Ekeland, I.

Engel, E.,

2 1 1 , 2 1 6,

1404, 1 432, 1 43 8

Eijffinger, S. Eisner, R .

Bayomni, T.

Fethke, G.

1 543, 1 562

1314 1 284 1314 1037

see Domberger, see Contini, B .

470, 472--478, 480, 48 1 , 483, 484, 487,

Fiebig, D.G.,

S.

489--492, 495-497, 500, 502, 504--5 07,

Filippi, M . ,

1 1 77, 1 1 78, 1 1 80,

509-5 1 3 , 5 1 6, 5 1 8-52 1 , 526-528, 530-532,

J 025, 1 1 25

1 222 Fillion, J.F.

1 49 8

1019

Author Index

I-9

Finch, M . H .J. Finn, M.

619

W

Frenkel, J. A.

1425

Frenkel, J.A.,

see

Fischer, A.M . , Fischer, S.

Dueker, M.J.

1235, 1 2 8 1 , 1 320,

Fama, E.F.

1 32 3

9 8 1 , 1 091

Fiorina, M .

see

French, K.R.,

1 543

see Bowen,

Finegan, T.A.,

Frcnnberg,

1 485

1 82, 1 97, 202, 2 1 5, 2 1 6, 1025,

2 0 3, 1 63 0

see

Aizenman, J.

1497

1 2 38

P.

Friedman, B.M.

43, 4 4 , 1 632, 1642

1 026, 1 1 5 5 , 1 404, 1405, 1438, 144� 1 489,

Friedman, D.

475

1496, 1498, 1 538, 1 542, 1 547, 1 56 1 , 1 582

Friedman, J.H.,

see Breiman, L.

Friedman, M.

46, 48, 6 1 , 1 37, 1 54, 1 60, 162,

see

Fischer, S.,

Blanchard, OJ.

47 1 , 643, 660,

1 68, 1 72, 1 76, 1 79, 1 80, 1 85, 1 89 , 1 95, 203,

1 0 1 3, 1 03 3 , 1 034, 1036, 1 49 1 , 1 635

see Bruno, M. S., see Debelle, G .

Fischer, S . , Fischer,

Fischhoff, B. Fishe,

222, 275, 376, 572, 7 6 1 , 762, 943, 1 0 1 1 ,

1489, 1 5 1 8, 1 522 S.

1318

173

Froot, K.

1 372, 1 377, 1485 92

464, 474

Fudenberg,

D.

Fuerst, T.

Fisher,

Fuerst,

9 1 0, 1 3 68, 1 375, 1 376, 1 37 8

Fisher, J.D.M.

see

Fisher, J.D.M.,

Campbell, J.R.

see

329-334, 343,

348, 356, 365

see

Flood, R.P. ,

Florovsky, G. Forbes, K.

Garber, P.M.

Gale,

Dickey, D.A.

53, 54, 2 1 2

699

R.

299

155

Fortune, P.

1310

Foufoula-Georgiou, E., 326 Fourgeaud, C.

see

Kitanidis,

1 543 1497

Frankel, J.A.

280, 28 1 , 1 590, 1 637

Franses,

289 1431 577

I016

1280

851

909, 1 086, 1 1 24

395, 405-407, 426, 429, 434, 993, 994,

1 1 1 7 , 1 1 1 9 , l 1 20, 1 1 29 1561

Gali,

67, 69, 2 1 7

J.

P.K.

Gali,

see Benhabib, J. J., see Clarida, R.

424 96, 1 36, 422, 1 3 64,

1 368, 1486 Gallarotti, G.M. Gallego, A.M.

Foxley, A.

R.

Gali, J.

Gali, J.,

454, 465, 473, 475

Frankel, J.

P.H.

Charnley, C. 1 646

Galeotti, M.

326

Fratianni, M .

see

Gale, W.O.

see Roscvearc, D. 1 626 Foresi, S., see Backus, D.K. 1316 Forteza, A., see Echenique, F. 1 5 5 1 ,

1 1 82

389, 475, 849, 8 5 1 , 1 3 76

D.

Gale, D.,

1 326

277, 278

Ford, A.G.

French, K .

769, 785

576, 5 8 8 , 6 1 6

Galbraith, J.K. 1 65

Fore, D . ,

Fregert, K.

see

Fuller, WA., Funkhouser,

Carroll, C.D.

875

1 52, 1 5 8, 202, 408, 1428, 1429,

R.P.

Freeman,

J.C., see

Futia, C.

773

1 438, 1 507, 1 595, 1 596

Fox, B.L.

1348, 1 3 57, 1 368,

454, 905, 908, 1039, 1 040, 1 49 1 ,

Fullerton, D .

572, 749, 763, 784

Flemming, J.S.

Carlstrom, C.

Fukuda, S.-i.

Press, W.H.

475

1518 Fuhrer,

1 54

Flannery, B.P.,

T., see

Fuhrer, J.C.

846

1 55

Flandreau, M.

G.

99, 974, 1 37 8

1 378, 1 3 79

350, 355, 362, 364, 962, 1296

Flood,

455, 475, 1 1 55

see Ellison,

Fudenberg, D.,

see Boldrin, M . 962, 1 284, 1 297 J., see Christiano, L.J. 3 1 4, 347, 349,

Flavin, M .

453, 454, 474, 528, 536, 539

R.

Fuchs, G .

Fisher, J.,

Fishlow, A.

1 266, ! 3 1 6

Frydman,

1 54, 1 57, 203, 1 3 1 6, 1321, 1 343,

Fisher, J.

1 1 7 3, 1 325, 1485, 1 488, 1 496, 1 537, 1 674, 1 720

see Lichtenstein,

R.P.H.

Fisher, I .

1 53 8

1 3 1 9, 1 326

Fischhoff, B. ,

289

Galor, 0.

262, 263, 272, 660

Gandolfi, A.E., Garber, P.M. Garber, P.M.,

Darby, M.R.

see Eichengreen, B. see Flood, R.P. 408,

790

R.

Garibaldi,

see

P.

Garratt, A.

166

1 65 , 1 323, 1 543

Garber, P.M., Garcia,

1 54 3 2 1 , 322

1 1 80, 1 222 504

1 87, 1 89 1 595, 1 596

Author Index

I-10

Garratt, A., see Currie, D. Garriga, C.

454, 504

Gaspar, J.

324, 369

Goff, B.L.

689

Gokhale, J.

Gastil, R.D.

Gatti, R., see Alesina, A. Gavin, W. Gear, C.W.

Goldfajn,

395, 458, 1322

1 535, 1 5 5 1

1 65, 1 428

Geoffard, P. Y. , see Chiappori, P.A. Gerlach, S., see Bacchetta, P.

391

1 344

1376 83, 92-94, 1 040, 1 343, 1348, 1 3 66,

1 373, 1 374, 1376-1378 1 293, 1 63 1

Gertler, M., see Aiyagari, S.R.

92, 144, 1 83,

Gertler, M., see Bernanke, B. S .

856, 8 5 7, 1 03 6 , 1345, 134 6, 1352, 1 357, 1 365, 1 369, 1 3 7 1 , 1 373, 1 376-1378, 1 578 Gertler, M., see Clarida, R.

95, 96, 1 36, 422,

1 364, 1 368, 1486 Geweke, J.

34, 334

Gewcke, J., see Barnett, W. Geweke, J.F.

540 908

167, 203, 1438, 1446, 1449, 1 5 8 0

Gibson, G.R.

1450

1 307

847, 1 344 856, 1 036,

Gilchrist, S., see Bernankc, B.S. 1 345, 1 373, 1 376 Gilchrist, S., see Gertler, M.

83, 92-94, 1 366,

1 373, 1 374, 1 376 Gill, P.E. Gilson, R.J.

1 94-- 1 96, 764, 1 0 1 3 , 1 1 1 7, 1 346, 1 509, 1 5 14, 1 5 1 5 Goodhart, C . , see Capic, Goodhart, C.A.E.

329 1 14

1 1 54

F.

Gizycki, M.C., see Gruen, D.K. Glasserman, P. , see Boyle, P. 1456, 1465

Glomm, G.

7 12, 1472

Glosten, L.

1280

1 432,

1 495 Goodhart, C.E.A.

1 438, 1495, 1 507, 1 508,

1 5 14 Goodman,

797

A.

Goolsbee, A.

839, 843, 848

Gordon, D.B.

128, 1 34 1 5 8, 1 1 5 5 , 1405, 69

1030 1 63 7

Gordon, R.J.

40, 46, 48, 49, 1 8 1 , 1 542

Gordon, RJ., see Balke, N.S.

6, 6 1 , 204, 205,

221 553, 5 5 6 , 782, 803 181

Gottfries, N .

463, 1 12 1 , 1 1 22

Gould, D.M.

1 5 5 1 , 1 559, 1 5 6 1

Gourieroux, C.

487

Gouricroux, C . , see Broze, L

4 8 7 , 488

Gourieroux, C., see Fourgeaud, C.

454, 465,

Goetzmann, W., see Brown, S.

1 67 1316

380

609, 1 344

P.-O.

Graham, B.

1323

Graham, F.C.

156, 1 58, 1 60, 1 66, 1 69, 380

Glazer, A.

1 54

Goodhart, C.A.E., see Almeida, A.

Gourinchas,

Giovannini, A., see Giavazzi,

F.

1 93

473, 475

Gilles, C., see Coleman li, WJ. Giovannini, A.

1 1 57

88, 1 20, 121, 1 56, 173, 1 9 1 ,

Gorton, G., see Calomiris, C.W.

195

Gilchrist, S.

Goodfriend, M.

Gorman, W. M .

1308, 1 3 1 8

Gilbert, R.A.

1 1 73

P., see MacLeod, W.B.

Gordon, R.H.

202, 207, 208

Gigerenzer, G.

962, 1 062

Gomme, P., see Andolfatto, D.

Gordon, R.

Giavazzi, F. , see Missale, A .

208, 1 637

994, 1 1 59

Gomme, P. Gomme,

777

1 590

Gordon, D.B., see Leeper, E.M.

1 572

Giavazzi, F.

R.

1 4 1 1 , 1 4 1 5 , 1438, 1485-1489

6 1 5, 752, 759

Ghosh, A.R.

1 624

O.P.

Gordon, D.B., see Barro, RJ.

89

Ghali, M ., see Surekha, K. Ghezzi, P.

I., see Dornbusch,

Gomes, J.

1 290

Gelb, A., see De Melo, M.

Gersbach, H.

750

Goldstein, M., see Mussa, M.

346

Gertler, M.

159

Goldberg, P.K., see Attanasio,

Geczy, C.C., see Brav, A. Genberg, H .

1 242, 1252, 1 3 14, 1 320,

Gokhale, J., see Auerbach, AJ.

1432

1485

Geanakoplos, J.D.

Ghez, G.

Goetzmam1, W.N. 1 333

1 675, 1 7 1 8

1 656, 1 657

Grandmont, J.-M.

439, 454, 460, 464, 474,

475, 48 1 , 507, 5 14, 526, 661 Granger, C.

34

Granger, C.W.J.

8 8 1 , 903

Granger, C.WJ., see Engle, R.F. Gray, J.A.

Green, D., see MaCurdy, T.E. 1242

Green, E .

50

1025, 1 026, 1 03 8 575

6 1 9, 620

Author Index

I-l l

Green, H . , see Beaudry, P.

592

Haberler, G .

Greenberg, D., see Burtless, G.

618

Greenberg, D.H., see DaVanzo, J .

618

Hahn,

1 85

661

F.

Hahn, T. , see Cook, T.

1 94, 1 493

Greenspan, A.

199, 798, 844, 847, 1630

Greenwald, B.

857, 1 1 22, 1 377

Hairau1t, J.-0.

1 036

Greenwood, J.

380, 550, 576, 664, 692, 962,

Haldane, A.G.

1 432, 1 4 38, 1485, 1495, 1497

980, 995

J.

Greenwood, J., see Gomes,

847 994, 1 1 59

Greenwood, J., see Gomme, P. Gregory, A.W

962, 1 062

376, 377 952

Gregory, A.W, see Devereux, M. 253

Griffiths, M., see Dolado, J. Griliches,

1 430

Grilli, V, see DeKock, G.

158

Grilli, V, see Drazen, A . Grilli, VU.

Gros, D., see Adams, C.

1463, 1465, 1 5 4 1 1 53 8

Gross, D.B., see Goolsbce, A. 1 464

1 58, 1 4 1 5, 1 449

Grossman, S.J.

80 1 , 1 23 7, 1 242, 1 246, 1 268,

1 29 1 , 1 293

Guerra, A .

1 546, 1 606, 1 607 439, 454, 460, 464, 465, 474,

475, 506, 5 1 1 , 5 1 6, 526 Guesnerie, R., see Chiappori, P.A.

391, 395,

516 Guesnerie, R., see Evans, G . W.

464

1 537, 1 5 88, 1 603, 1 675, 1 720

Guidotti, P.E.

Guidotti, P. E. , see Calvo, G.A.

1447, 1450

Guidotti, P.E., see De Gregorio, J.

1 546, 1 5 5 1 ,

1 573 , 1 575, 1 577 Guiso, L. Guiso,

202, 207, 208

1317

Gultekin, N.B., see Gultekin, M . Guo, J.-T., see Farmer,

R.E.

Haltiwanger, J.C., see Davis, S.J. Hamermesh, D. Hamilton, A.

577 1 659

963

Hamilton, J.D.

1 2, 72, 80, 1 82, 1 1 1 8, 1 265

Hammerlin, G.

344

Hammour, M.L., see Caballero, R.J. 1 2 1 0, 1 2 1 1 , 1 2 1 3, 1 472

Hannerz, U.

1 332

Hansen, B.

1 1 94

Hansen, B.E.

3 8 , 39

Hansen, G.D.

547, 5 5 1 , 602, 976, 977, 1 200

Hansen, G.D., see Cooley,

69, 97, 1 0 1 ,

T.F.

1 1 5 , 1 24, 1 37, 3 80, 408, 4 1 1 , 974, 1 736 54 7 , 5 5 5 , 556, 558, 572-574, 768,

1 26 1 , 1 294, 1 295 Hansen, L.P., see Anderson, E.W.

368, 369

Hansen, L.P., see Cochrane, J.H.

1 234, 1 246,

1 249

Hanson,

1 507

1 04 1

Guttman, P., see Erlich, D.

846, 847,

852, 855, 856, 1 1 57, 1 1 58, 1 1 60, 1 1 87,

549, 550,

785, 799, 800, 803

4 1 6, 427

1314

1 05 8

1 1 5 1 , 1 1 52,

Hansen, L.P., see Eichenbaum, M.

Gurley, J.G. Gust, C.

1 3 17

395, 427-430, 434,

505

Guo, J.-T.

824

881

769, 784, 882, 9 1 5, 1 234, 1 246, 1 249, 1 250,

909

Guide, A.M., see Ghosh, A.R. Gultekin, M .

8 2 1 , 837,

Haltiwanger, J.C., see Abraham, K.G.

Hansen, L.P.

772

L., see Galeotti, M.

504

1 460, 1465

Haltiwanger, J., see Caballero, R.J.

Hamilton, J.

1316

Guesnerie, R.

Hallerberg, M.

454, 504

1 1 60, 1 1 6 1 , 1 1 76, 1 1 7 8, 1 1 80, 1 1 94, 1 1 99

Grossman, H.J.

Gruen, D.K.

1 656 Hall, S . , see Currie, D .

Haltiwanger, J.C.

839

852

1 068, 1 070, 1 079, 1 089, 1 092, 1 095, 1 096,

Haltiwanger, J . , see Cooper, R .

264, 639, 672, 7 1 5, 1 2 1 0,

Grout, P.A.

784, 789, 79 1 , 794, 8 1 7, 856, 930, 982,

838, 840-842, 1 1 5 8

8 5 7 , 1 344

Grossman, G.M.

399, 556, 573, 595, 607, 608, 673,

679, 680, 683-686, 702, 765, 767-769,

Hall, S., see Garratt, A .

1 69

Gross, D .

911

Hall, R.E.

1 1 64, 1 200, 1 26 1 , 1 485, 1493, 1 498, 1 655,

95, 1404, 1432, 1 438, 1439, 1465

Grilli, V , see Alesina, A.

Hall, G .

585

1 1 4 1-1 143, 1 1 45, 1 1 5 1-1 1 53, 1 1 57, 1 1 60-

1 437

5 41

Z.

Grilli, V

479

Haley, WJ.

Greenwood, J., see Cooley, T.F.

Grier, K.B.

Hahn, W

J.

1 543

Hansson, B., see Frcnnbcrg, P

Harberger, A . C .

1 554, 1 590

1 23 8

Author Index

1-12

Harden,

I., see

1439, 1460,

von Hagen, J.

Hardouvelis, G.A.

see

Harris, R . ,

Harrison, A.

Estrella, A.

Cox, D .

43, 1 28 1

705

see

Harrison, S.H. Harrod, R.

Christiano, L.J.

426

Hercowitz,

402

Hercowitz,

see Davidson, J. 750 Z. 664 Z., see Sarro, R.J. 1023 Z., see Greenwood, J. 550,

Herrendorf, B.

656

Hess, G.D.

9

Hester, D.A.

Harvey, C.R.

1 236, 1 280

Heston, A.,

1 1 52

Hassler, J.

Fallick, B.C.

822, 856,

see Dezhbakhsh, R.A., see Ferris, S.P

Hause, J.C.

H.

1 039

1 3 14

620

576, 578, 579, 582, 584--5 87,

590, 592, 593, 595, 601-603, 605, 6 1 5-6 1 7, 620-624, 752, 759, 1 1 66 Heckman, J.J.,

Heckman,

1 1 1 9, 1 1 20, 1 1 26

Heinemann, M. Hellwig, M., Helpman, E.

D.

Helpman, Helpman,

Hendershott, P.H.

1333

Henderson, D .W.

1497

51, 412

Hoffmann, K.-H., Holbrook, R.

see

Hammerlin, G .

344

569

Holmstrom, B.

1 376, 1 4 1 7, 1 4 1 8, 1 425

see

Davis, D.

1 033

882, 885, 888, 909, 9 1 0, 9 1 2

see

Bryant, R.C.

1 49 1 , 1 497,

1516 Holtz-Eakin, D.,

see

Hommes, C.H.

529, 532

Honkapohja, S.,

265

see

Blinder, AS. Brock, W.A.

41 455, 528,

464, 481, 507, 535

see

Evans, G.W.

425, 426,

454, 455, 46 1 , 464, 465, 468, 470, 472-478,

1 580 G.M.

1281 1 507

1 5 6 1 , 1 589

Hoffman, D.L.

Honkapohja, S.

203, 1 5 80

672, 7 1 5, 1 2 1 0, 1 464

289

532

1 3 '76

see Coe, D.T. E., see Drazen, A. E., see Grossman,

Helpman, E.,

1 332

1 65 8

Hoffmaister, A.

Hommes, C.H.,

495, 525

see Gale,

Franses, P. H .

see Bekaert, G. see Flood, R.P.

Holtham, G.,

601 , 1 1 48 Heijdra, B.J.

1 62 1

Hodrick, R.J.,

Holt, C.C. 550,

Cox, W.M .

9, 12, 34, 428, 93 1 , 932

Holt, C.A.,

Heckman, J.J.,

Heckman,

see

Hoelscher, G.

1 284, 1 293

1 344

33 1

Hodrick, R. Hodrick, R.J.,

380, 547, 569, 803, 1 242, 1 255,

see Ashenfelter, 0. 6 1 8 see Cameron, S . 589 J.J., see Cossa, R. 584 J.J., see Killingsworth, M.R.

Hobijn, B . ,

1 656, 1 65 7

Gilchrist, S .

see Bikhchandani, S. see Daniel, K. 1 32 2

Hirshleifer, D.,

773, 775, 776, 785, 788, 790, 796,

Heckman, J.J.

see

1 540

Hirshleifer, D.,

see Devereux, M.B. 1 1 26 G., see Dasgupta, P 655, 656 G.M., see Ryder Jr, H.E. 1284

Heaton, J.

Graham, F.C.

see

Hirschman, A .

800, 8 1 8, 1 649 Heal,

535, 537

see

Hirschhorn, E.,

Head, A., Heal,

506, 1 539, 1 540, 1 543

1400, 1 425

Hiriart-Urruti, J.B.

see Burtless, G. 620 C.B., see O'Brien, A.M. 776

Hayashi, F.

Hibbs, D.

Himmelberg, C.P.,

Hausman, J., Hawley,

238, 3 0 1 , 640,

1 80

Heymann, D.

Himarios, D.,

569

Hausman, J.

Summers, R.

Hildenbrand, W.

855

9, 1 23 8

Haug, A.A.,

87 1

see

Hetzel, R.L.

821

1 344

see

1 4 1 5, 1 436, 1 43 8

673-675, 677, 680, 68 1 , 689, 720

8 1 5, 8 1 8, 843, 1 344

see Auerbach, A.J. K.A., see Cummins, J.G.

Hassett, K.A.,

Hassett, K.A.,

664,

9, 1 48 5 , 1 509

Harvey, A.C.

Hassett, K.A.

1 60,

962, 980

852, 1 1 54

Hashimoto, M .

Canzoneri, M.B.

1 507, 1 508 Hercowitz,

640

Hartwick, J.

Haugen,

1 49 1 , 1497,

Hendry, D.,

277, 279, 280

Harrison, S.G.,

Hassett,

Bryant, R.C.

D.W., see

Henderson,

1 28 1

see

Hardouvelis, G.A.,

Hart, 0.

see

Henderson, D.W., 1516

1 465

264, 639,

480, 48 1 , 483, 484, 487, 489-492, 495-497, 502, 504--5 07, 509-5 1 3 , 5 1 6 , 5 1 8-52 1 , 526-528, 530-532, 1025 Hooker, M.A.,

see

Fuhrer, J.C.

454

I 13 -

Author Index

Hooper, P. ,

see

Bryant, R.C.

1 043, 149 1 , 1497,

1 5 1 6-1 5 1 8

Hopenhayn, H . 672, 708, 994 Hopenhayn, H.A. 844 Horioka, C., see Feldstein, M. 1 636 Horn, H. 1 4 1 5 Hornstein, A . 549, 996 Hornstein, A., see Fisher, J.D.M. 9 1 0 Horvath, M. 994 Horvath, M., see Boldrin, M. 962, 1062 Hoshi, T. 1344 Hosios, A.J. 1 1 93, 1224 Hotz, V.J. 792, 803 Houthakkcr, H.S. 803 Howard, R. 336 Howitt, P. 3 89, 399, 455, 506, 507, 5 14, 5 1 5 , 5 1 7 , 5 2 1 , 5 2 7 , 1 1 74, 1 508

Howitt, P., see Aghion, P.

264, 665, 672, 7 1 5 ,

7 1 9, 1 208, 1 2 1 0, 1 2 1 3

Howrey, E.P., see Fair, R.C. 14 91 Hoynes, H.W., see Attanasio, O.P. 753 Hsieh, C.-T. 673, 687 Hubbard, R.G. 567, 569, 572, 573, 593, 77 1 , 776, 794, 797, 856, 1 344, 1 3 76, 1660

Hubbard, R.G., see Cummins, J.G. 822, 1344 Hubbard, R.G., see Domowitz, I. 1 020, 1 083, 1 093

Hubbard, R.G., see Fazzari, S.M. 8 1 8, 1 344 Hubbard, R.G., see Gertler, M. 1 376 Hubbard, R.G., see Hassett, K.A. 8 1 5, 8 1 8, 843, 1 344

Huberman, G., see Kahn, C. 1 1 54 Huffman, G.W. 437 Huffu1an, G.W., see Greenwood, J. 380, 962, 980

Huggett, M. 380, 576, 593 Hulten, C. 664 Hultgren, T. 1 1 00 Humphrey, T.M. 1485 Ihm1phreys, B.R. 909 Hurd, M.D. 780 Hybels, J., see Kallick, M. 1 325 Hyslop, D., see Card, D. 1 0 1 6 Ibbotson, R . 1 3 2 1 Tden, G., see Barth, J.R. 1 657 Ikenberry, G.J. 1 63 Im, K. 28 3 Imrohoroglu, A. 797 Ingberg, M., see 1-lonkapohja, S. Ingram, B. 984

Inman, R., see Bohn, H. 1465 Intriligator, M., see Griliches, Z. 541 Ireland, P.N. 1 29, 1 94, 1 036, 1492, 1 494, 1 497

Irish, M . ,

see

Browning, M.

6 1 1 , 6 1 2, 752,

787, 792

Irons, J., see Faust, J. 1 4 1 6, 1 425 D.A. 1 7 8 Isard, P., see Flood, R . P. 1 58, 1429, 1 4 3 8 Islam, N. 283-285, 287, 653 Ito, T. 1425 Iwata, S., see Hess, G.D. 9 Irwin,

Jackman, R. 1 2 2 1 Jackman, R . , see Layard, R.

1 098, 1 1 76, 1 1 77,

1221

Jackwerth, J.C. 1 3 1 0 Jaeger, A., see Harvey, A.C. 9 Jaffee, D.M. 1 376 Jagannathan, R., see G1osten, L. 1 2 80 Jagannathan, R., see Hansen, L.P. 547, 1 234, 1 246, 1 249

James, H., see Bernanke, B.S. 1 83, 1 84 James, W. 1 330 Janis, I. 1 332 Jappelli, T. 776, 780, 790, 1 344 Jappelli, T. , see Guiso, L. 772 Jeanne, 0. 1 56, 1 04 1 Jeanne, 0., see Bensaid, B. 1446, 1449 Jefferson, P.N . 1 4 85, 1 509 Jegadeesh, N. 1 3 2 1 Jegadeesh, N . , see Chan, L. 1 3 2 1 Jensen, H . 1 4 1 5, 1 427 Jensen, H., see Beetsma, R. 1 436, 1 43 8 Jensen, M. 1 344 Jeon , B.N., see von Furstenberg, G.M. 1 333 Jennann, U.J. 1 296 Jem1ann, U.J., see Alvarez, F. 575 Jermann, U.J., see Baxter, M. 980, 992 Jewitt, I., see Buiter, W. I 030 Jimeno, J.F., see Blanchard, O.J. 1 2 1 4 Jimeno, J.F., see Dolado, J.J. 1 2 1 4 John, A . , see Cooper, R. 398 Johnson, H.G. 702, 704, 705 Johnson, P., see Goodman, A. 797 Johnson, P.A., see Dur1auf, S.N. 254, 263, 264, 270, 2 7 1 , 289, 303

535

Johnson, P.G. , see Banks, J. 75 1 Johnson, S.A. 345, 3 8 1 Jones, C.L 237, 264, 290, 292, 672, 696, 7 1 4--7 1 6, 7 1 8 , 7 1 9

I- 1 4

Author index

673, 679, 680,

Jones, C . ! . , see Hall, R.E. 683-686, 702, 856

245, 257, 26 1 , 380, 672, 709,

Jones, L.E.

7 1 5, 1 57 8

Jonung,

L.

1 59, 1485 1 52, 2 1 5, 2 1 7,

220, 2 2 1 1 0 16

I.,

N.

see E1 Karoui,

Kashyap, A.K., see Cccchetti, S.G.

817

Jorgenson, D. W , see Christensen, L.R.

673,

688

Jorgenson, D.W, see Hall, R.E.

817 1 242, 1 252,

Jorion, P. , see Goetzmann, W N. 1 3 20

Kashyap, A.K., see Hoshi, T.

Kashyap, A.K., see Hubbard, R.G. Katz, L.

Jovanovic, B.

702, 848, 1 200

Jovanovic, B., see Greenwood, J.

1 485, 1487, 1 5 1 2, 1 5 1 6 590, 1 652

Judd, K., see Bizer, D.

Katz, L., see Autor, D.

577

Judd, K.J., see Gaspar, J.

797

324 , 369

354, 1 673, 1 675, 1 694 1 509

549

see Backus, D.K.

9, 42, 45, 938,

1 24, 397, 422, 672,

1 449, 1488, 1489, 1 673-1 676, 1 69 1 , 1 699,

Kaas, L., see Bohm, V.

558, 564, 565

Kehoe, T.J.

646

1446, 1 449, 1 603

Kehrer, K. C., see Moffitt, R.A.

1 1 54

Kahn, C.M., see Blanchard, O.J.

3 9 1 , 504

1 78, 705

Kahn, J., see Crucini; M.J. 897, 9 1 0

9 1 0, 9 1 2, 1 053, 1 078,

Kendtick, D.A., see Amman, H.i\1.

1313

Kahneman, D., see Tversky, A.

1 308, 1 3 1 5,

1 3 1 9, 13 30

Kalaba, R., see Bellman, R.

1 646 1 58, 1 6 1 , 1055, 1 059, 1 53 7

Keynes, J.M.

Kahneman, D., see Thaler, R.H.

Kiefer, J .

476

Kiefer, N.M., see Burdett, K. Kiefer, N.M., see Devine, T.J.

340

237, 238, 240, 640, 941

Kiguel, M.

1 054

Kiley, M.T.

Kallick, M.

1 325

Killian, L.

1 1 73 1 1 66

1 535, 1 543, 1 546, 1 554, 1 55 5

Kihlstrom, R.E.

Kalecki, M.

5 35

1 65 , 1 496

803

Kennan, J. Kessler, D.

1 308, 1 309, 1 3 1 1

1 73

Kemmerer, E. W Kenen, PB.

1 079, 1 085

618

271

Kelly, M.

Kahn, J.A., see Bils, M .

1 449

3 1 4, 380, 389, 3 9 1 , 574, 57 5

Kehoe, T.J., see Cole, H.L.

329, 333

Kahneman, D.

1 70 8- 1 7 1 0, 1 720, 1 723

Kehoe, P.J., see Cole, H.L.

1 543

Kahaner, D.

Kaldor, N.

Kehoe, P.J., see Backus, C.K.

974, 1 036, 1 037 , 1 040-1 042, 1 3 7 1 , 1 448,

777

Juster, T., see Barsky, R .

Kahn, J.A.

847, 1 675, 1 7 1 8,

1 720

697, 698, 700, 70 1 , 709, 720, 722, 723,

474

Kahn, C.

1 466, 1 4 7 1

Kehoe, P.J., see Chari, V.V.

569, 6 1 9

Kafka, A.

608, 609, 786, 790

1 708

Judson, R., see Porter, R.

Juster, F.T.

Keane, M.P.

Kehoe, PJ.,

663

Judson, R.

1 1 76

1 344

Kaufman, H .

Kehoe, PJ., see Atkeson, A.

3 1 4, 324, 340, 343, 347, 348, 350,

Judd, K.L.

1 1 83 , 1 22 1

Katz, L.F., see Abraham, K.J.

Keefer, P., see Knack, S . 380

1 344

577, 578

Katz, L. W, see Blanchard, O..J. 664, 692

876

1 344

Katz, L.F., see Cutler, D.M.

Judd, J.P

217

9 1 2 , 1 0 1 8, 1 344, 1 374, 1 376 664

Jorgenson, D.W

Judd, K.

835

1 37, 877, 8 8 1 , 886, 903, 906,

Kashyap, A.K.

881

Jorgenson, D .

Jun, B .

Karatzas,

476

856, 1 344

Karras, G., see Cecchetti, S.G.

Jonung, L . , see Fregert, K .

Juhn, C.

1 236, 1 280

Kaniovski, Y.M., see Arthur, W.B. Kaplan, S.N.

Jonung, L., see Bordo, M.D.

Jorda, 0.

475

Kane, A., see Chou, R.Y.

1 404, 1 4 1 1 , 1 4 1 5, 1 426, 1 43 8

Jonsson, G.

1 550, 1 553, 1 590

1 235, 1 252, 1 253, 1 265, 1 270,

Kandel, S. Kandori, M.

1 540

Jones, M.

428

1 272

7 1 1 -7 1 3 , 720, 1 675, 1 7 1 1

Jones, L.E., see Chari, V.V.

Kamihigashi, T. Kaminsky, G.L.

563

422, 423, 1 04 1 , 1 1 1 7, 1 1 2 9 87

1- 1 5

Author Index

550, 60 1 , 1 148

Killingsworth, M.R. Kim, J.

129, 1 036

Kim, M.,

see

Kim, K. Kim, S.

Kim, S.-J.

Kocherlakota, N.R.

377, 379

see

see

Kimball, M.S.

558, 564, 565

Barsky, R .

762, 771

Carroll, C.D.

556, 770, 1 036, 1 04 1 , 1 056,

1 1 1 4, 1 1 1 7 , 1 1 27, 1 65 3 see

Kimball, M.S.,

1 73 2

983, 992, 994,

Basu, S .

1 537, 1 675, 1 676, 1 720, 1018

Stigler, G.

Koopmans, T.

278-28 1 , 67 1 , 1 656, 1 657

703

Kornai, J.

see

Kot1ikoff, L.J.,

974

King, R.G.,

see

Dotsey, M.

see

King, R.G.,

974, 1 032, 1 043

Kramer, C.,

Goodfriend, M.

1 0 1 3 , 1 1 1 7,

326

1 378, 1 379

Kiyotaki, N . , Kiyotaki, N.,

see

Blanchard, OJ.

1033, 1 034

399

Boldrin, M.

see

see

Easterly, W

see see

Kreps, D.M.,

Krishnamurthy, A. see

Kroner, K . F.,

1 3 76, 1 378

Bollerslev, T.

94 1

Kmeger, J.T.

702, 705, 707

Klenow, P.J., Klenow, P.J.,

Klock, M., Knack, S .

see

see

see

Kneese, A . Knowles, S.

694

Heckman, J.J.

Silberman, .J.

578 1316

Krusell, P.,

see

Kurz, M.

1281

Meyer, J.R.

576

1 596

474

Kushner, H. Cole, H.L.

Greenwood, J.

476

Kumhof, M .

574, 954, 985, 1 234, 1 25 1 , see

see

Kuan, C.-M. Kuh, E . ,

277, 278

Kocherlakota, N.,

380, 547, 566, 567, 9Y4, 1 2<)3,

Kugler, P.

656

1 25 3

1 2 1 5 , 1 53 6, 1 5YO, l )Y2, l ) 'J4,

1 596, 1 60 1 , 1 605, 1 606, 1 632 1 445, 1 473

1 466, 1 47 1

Kocherlakota, N.

1 04, 1 05

Kmgman, P. Krusell, P.

Bils, M.

1 236, 1 280

577

673, 679, 699

Krueger, A.O.

1 121

475

380, 843, 847

202, 2 1 5 , 2 1 6

663, 673, 679, 680, 683-686, 694,

474

Bray, M.

Fudcnberg, D.

Klein, L .

Klenow, P.J.

852

277, 278, 2 8 1 ,

540, 557, 1 256

Kreps, D.M.

Klein, B.

K1emperer, P.D.

1 596

Flood, R.P.

Krueger, A., se e Autor, D.

1 320

K1eidon, A.W

750

Gokha1e, J.

Kremer, M., se e B lanchard, O.J.

K1ieger, S.

see

380, 549,

876, 877

Kreps, D.M.,

524, 852, 857, 1 3 53, 1 356, 1 3 76,

Kiyotaki, N.

Auerbach, A.J.

816

see

Krane, S.D.

675

475, 528, 536, 539-541

Kitanidis, P.K.

see

Koyck, L.M.

Kremer, M.,

1 320

Kirby, C .

796

1 63 5 , 1 639, 1 652, 1 7 1 8

Kotlikoff, L.J.,

101

Kirman, A.P.

Hayashi, F.

780, 1 624, 1 646

9, I I , 1 2, 430, 934,

1 346, 1 5 1 5

King, S .

340

Bellman, R.

576, 588, 590, 5 9 1 , 593, 6 1 6, 1 624, 1 634, 974

Barro, R.J. Baxter, M.

941

1 448, 1 449, 1 465

see

954, 97 1 , 995, 1 036, 1 04 1 , 1 043, 1 062,

719

Klein, L.

618

see

Kotlikoff, L.

Kotlikoff, L.,

1 1 40, 1 364, 1 367, 1 4 9 1

Eaton, J.

see

Kot1ikoff, L.J.

see

244, 246, 247, 295, 643, 649, 9

429, 435, 545, 549, 649, 672, 689, 692,

see

1 1 80, 1 222

93 1 , 942, 948

Koopmans, T.J.

7 1 1 -7 1 3 , 929, 93 1 , 932, 939, 941 , 945, 953,

King, R . G . ,

1316

Garibaldi, P.

Kormendi, R.C.

Kotkin, B . ,

9, 46, 54, 69, 1 0 1 , 278, 369, 3 9 1 ,

King, R.G.,

161

Shiller, R.J.

Koopmans, T.C.

Kosters, M.H.

1 99, 1 333, 1485, 1 489

King, R.G.

see

Kosobud, R . ,

1 62

Kindleberger, C.P. King, M.

see

Kortnm, S.,

see

Kindah1, J.,

Konings, J.,

D.

Benjamin, 904--9 07

1 673

1 069, 1 080, 1 08 1 , 1 1 1 7

Kimbrough, K.P.

Kon-Ya, F.,

984

Ingram, B.

2 7 1 , 673, 694

1 085

Kollman, R.

672, 7 1 1-7 1 4

Kimball, M.,

see

Kochin, L.,

Kollintzas, T.

1 320

Nelson, C.R.

95

Kimball, M.,

see

Kocherlakota, N.,

Kushner, H.J.

476 476

817

664

1- 1 6

Author Index

Kusko, A.L.

1 327

941

Kuznets, S.

572

Layard,

R., see

929, 953, 956, 957, 962, 980, 98 1 , 1 058,

Leahy, J. Leahy,

1 5 6 1 , 1 673, 1 708

Kydland, F.E . ,

549

Kydland,

1 708

see Backus, C.K. F.E., see Backus, D.K. F. E., see Bordo, M.D.

1 58 , 1 60, 1 8 5 ,

see Hotz, V J . see Campbell, J. Y.

Kyle, A.S.,

792, 803

see Giovam1ini, A. 380 see Coleman II, W.J.

Labadie, P. ,

Ladron de Guevara, A .

Laffont,

317

Leeper,

538

Leeper, Lefort,

876

Lai, K.S.

see

Lakonishok, J.,

see

1321

Cecchetti, S.G.

Leiderman,

1 25 1 , 1 265,

290

see

Kashyap, A.K.

L., see Barucci, E .

Lane, P.

88 1 , 9 1 2,

525

1 472

Lemarechal, C., LeRoy, S.F.

Lau, L.

see Grossman,

664

801

33 1

1450, 1 465

see Brayton, F. 1 043, 1 344, 1 485 see Fudenberg, D. 455, 475 D.K., see Kehoe, T.J. 380, 389, 3 9 1 ,

Levine,

574, 575

Levine, J. S.J.

J.B.

283, 1 0 1 7, 1 03 1 , 1035, 1 036, 1 03 8

Levin, A.,

475, 48 1 , 507

Hiriart-Urruti,

470, 472, 524, 527, 1 293, 1 297

Levine, D.K., 474,

see

271

Levin, A.

see Guo, J.-T. 4 1 6 see Devereux, M.B. 1 126 G., see Fuchs, G . 464, 474 G., see Grandmont, J.-M. 464,

Laroque, G . ,

1 539,

Leung, C.

Lapham, B.J., Laroque,

Heymann, D.

Lettau, M .

Lansing, K., Laroque,

1 52, 202, 2 1 5

see

1 23 5 , 1 3 1 9

Levhari, D .

1 329

Langer, E . J.

1 2 8 , 1 34

277-279, 283, 284,

1 540

1 344, 1 3 74

Landi,

69, 2 1 7

D.B .

1 32 1

Leijonhufvud, A . ,

1 457, 1 465

Lamont, O.A.,

8 8 1 , 903 1 0 1 , 1 28, 1 32,

see Roseveare, D . 1 62 6 L. 1 432 , 1 4 3 8 , 1 495, 1 543 L., see Bufman, G. 1 54 3 L., see Calvo, G.A. 1 552 , 1 600 L., see Kaminsky, G.L. 1 550

Leijonhufvud, A. 346

Lambertini, L. Lamo, A . R.

Leiderman, Leiderman,

802

Lambert, J.D.

E.M., see Faust, J. E.M., see Gordon, F., see Caselli, F.

Leiderman,

Chan, L.

1 270, 1 272, 1 294, 1 296

Lam, P.S.

see Granger, C.WJ. E.M. 69, 74, 83, 93,

Leibfritz, W ,

1 323

Lakonishok, J. Lam, P.-S.,

703 395

Lehma11.11, B.N.

1 485

Laidler, D.

277-2 8 1 , 67 1 , 6 8 1 ,

2 86

1 653

Laibson, D.

R.J.

1 520, 1 63 1

1 539, 1 5 7 1 , 1 578, 1 579, 1 597

Lahiri, A.

1 0 1 8, 1 1 1 8

1 34, 137, 4 1 8 , 420, 1 036, 1 089, 1 369, 1 5 1 8,

see Gourieroux, C . 487 J.J., see Kih1strom, R.E. 563

Laffont, J.-J.

Barro,

Lee, T.H . , Leeper,

Laffont, J.,

282

284

Lee, K. 1 14

1019

Lach, S.

849, 850

2 1 5, 1 0 1 6

see

Lee, J.-W Lee, J.Y.

Labadie, P.A.,

Caplin, A.

683-685, 688, 689, 691-694

1 240, 1 320

R.

La Porta,

8 2 3 , 828, 8 3 0

Caballero, R.J.

1 324

Lee, J.-W,

1 290

1 1 52

R.E.

1 62

Lebow, D .E . , see Blinder, A.S. Lee, C.

Kydland, F. E . ,

57 8

844, 1 33 2

J., see Leahy, J., see Leamer, E .E .

Lebow, D.E.

2 1 5, 1 43 8

Heckman, J.J.

Hall,

Leag11e of Nations

1 059, 1 1 40, 1 14 1 , 1 1 45, 1 1 67, 1 1 95, 1 400,

Kydland,

see

1 59

see

Lazear, E.P.,

1 405, 1 4 1 5, 1 449, 1 485, 1 486, 1488, 1 557,

1 22 1

Jackman, R.

1 660

Lazear, E . P.

9 , 42, 1 58, 428, 547, 549, 578,

Kydland, F. E .

1 098, 1 1 76, 1 1 77, 1 2 2 1

Layard, R.

Lazaretou, S.

212

Kwiatkowski, D.

607-609

Lawrance, E .

Layne-Farrar, A.,

see Friedman, M.

Kuznets, S.,

1 037

Lau, S.H.P.

see Evans, C.L. 1 05 Kuttner, K.N., see Friedman, B.M. 43, 44 Kuttner, K.N., see Krueger, J.T. 1 04, 1 05 Kuttner, K.,

Levine,

1 332

P., see

1 43 7

a1 Nowaihi, II..

1 4 1 5, 1 422,

I- 1 7

Author Index

Levine, R.

269, 277-282, 390, 423, 67 1 , 694, 278, 689, 692

Levine, R., see King, R.G.

1 0 1 4, 1 0 1 5, 1 0 1 9

Levy, D.

876

Lucas, R.

1425

Lewis-Beck, M.

345, 3 8 1

346, 95 1 , 998, 999

1318

Lichtenstein, S.

1 1 60, 1 1 83 , 1 22 1

559, 5 6 1 , 575, 578, 582, 583, 6 1 5 , 6 1 6,

569, 572

1 1 95, 1 268, 1 489, 1 490, 1 495, 1 500, 1 592,

F. , see Przeworski, A.

Lin, C., see Levin, A.

293, 454, 457, 463, 474, 545, 547, 554, 672, 7 1 0-7 1 5, 720, 797, 1 022-1 024, 1 043,

1 1 53

Lilien, D.M., see Hall, R.E.

1 673, 1 675, 1 699, 1 7 1 1 , 1 723, 1 728

1466

283

1 098, 1425, 1465

Lindbeck, A.

1 56

Lucas Jr, R . E. , see Atkeson, A.

575

Lucas Jr, R.E., see Stokey, N.L.

2 7 1 , 299

1 1 77, 1 1 78, 1 1 80,

1 22 2

Lundvik, P., see Hassler, J. Lusardi, A.

1 432

9, 1238

608, 790, 791 606, 7 7 1

Lusardi, A., see Browning, M.

Lippi, F. , see Cukierman, A.

Lusardi, A., see Garcia, R .

1438

Lipsey, R.E., see Blomstrom, M .

277, 279,

790

575

Luttrner, E.G.J.

217

Lippi, M .

785, 788, 1 344, 1 652

Ludvigson, S.

Lioni, G., see Contini, B. Lippi, F.

67, 88, 1 5 8, 238, 245, 264, 265,

Lucas Jr, R.E.

1 3 19

Lichtenstein, S., see Fischhoff, B.

Lindert, P.

3 14, 3 1 8-32 1 ,

Lucas, R.E., see Stokey, N.L.

Li, Y., see Jolmson, S.A.

Lillard, L .

46, 50, 380, 1 1 58, 1446, 1449

Lucas, R.E.

326

Lilien, D.M.

398, 424, 425, 64 1 , 65 1 , 929, 932,

953

133 1

Levy-Strauss, C.

380, 547, 569, 1 255,

1 293

222

Levy-Leboyer, M .

1 343

1 03 5 , 1 036, 1 042

Lucas, D.J., see Heaton, J .

1 0 1 9 , 1 020

Levy, D., see Dutta, S.

Limongi,

881, 893, 908, 9 1 0

Lown, C . , see Bernanke, B . S . Lucas, D.J.

Levy, D., see Carpenter, R.E.

Li, J.X.

299

Loury, G.C. Lovell, M.C.

1 3 76

399

Lyons, R.K., see Caballero, R.J.

280 1 032

Liu, C.Y., see Conlon, J.R.

Maberly, E.D., see Dyl, E.A.

1 437

Liviatan, N., see Cukierman, A.

1 535, 1 543, 1 546,

Liviatan, N., see Kiguel, M.

Maccini, L.J., see Blinder, A.S. Maccini, L.J., see Durlauf, S.N.

1214

Ljungqvist, L .

1 255, 1 257, 1 258,

Lo, A.W., see Campbell, J.Y.

708

Lochner, L., see Cossa, R.

Mace, B.J. Mackay, D.

584 576, 578, 582,

Lochner, L., see Heckman, J.J.

141 1 , 1415

Long, J.

1436, 1 438

1 4 16-1 4 1 8, 1 425, 143 1 , 1438

Londregan, J., see Alesina, A.

1 425

1 255,

MaCurdy, T.E.

1321

1 1 57, 1 1 86 5 5 1 , 567-569, 572, 592, 595,

1 148, 1 1 49

344

Lothian, J.R., see Darby, M.R.

MacLeod, WB.

MaCurdy, T.E., see Attanasio, O.P.

1313

Lopez-de-Silanes, F., see L a Porta, R. Lorentz, A.L.

1 307

MacK.inlay, A.C., see Campbell, J.Y.

6 1 5, 6 1 6, 6 1 9-62 1 , 752, 759, 767, 792, 975,

929, 952, 953, 994

Loomes, G .

796

MacKinlay, A.C., see Lo, A.W

Lockwood, B . , see Herrcndorf, B .

909 156

1 257, 1 258, 1 26 1 , 1 266, 1 270, 1 320

584, 586, 587, 590, 592, 593

Lohman, S.

881

Maccini, L.J., see Humphreys, B.R. MacDonald, R., see Bordo, M.D.

1 26 1 , 1 266, 1 270, 1 320

Lockwood, B.

905-907

Maccini, L..T., see Haltiwanger, J.C.

1321

Loayza, N.V

887, 904, 9 1 0,

1 344

474, 476, 4 8 1 , 482

Lo, A.W

88 1 , 893, 894, 903, 907

Maccini, L.J.

1 538 1 459

Lizzeri, A. Ljung, L .

699

MacAvoy, P. W. , see Funkhouser, R.

1 554, 1 555 Lizondo, J.S.

1 334

173

Macaulay, FR.

1 240

MaCurdy, T.E., see B lundell, R. MaCurdy, T.E., see Heckman, J.J.

166

Maddala, G.S.

275

792 602, 620 615

1-18

Author Index

Maddison, A.

288, 673-675, 677, 678, 720,

721

Marshall, D.A., see Marcet, A .

326, 348, 3 5 1 ,

455

Madison, J. 1 659 Mailath, G.J., see Kandori, M. 475 Makhija, A.K., see Ferris, S.P. 1 3 1 4 Malcomson, J.M., see MacLeod, W B.

1 1 57,

1 1 86

Ma1invaud, E., see Blanchard, 0.1. 1 2 1 4 Malkiel, B . 1 3 1 6 Mankiw, N.G. 1 3 5 , 1 5 8 , 1 59, 1 73 , 2 1 6, 244246, 252�255, 269�2 7 1 , 277�279, 289, 397, 567, 653, 655, 660, 673, 679-· 686, 694, 749, 785, 790, 800, 961 , 1 2 8 1 , 1 290, 1 292, 1 638, 1 702, 1 742

Mankiw, N.G., see Abel, A.B. 1 266, 1 65 1 Mankiw, N.G., see Ball, L. 4 2 , 1 023, 1 632, 1 650, 1 65 1

Mankiw, N.G., see Barro, R.J. 1 637 Mankiw, N.G., see Barsky, R.B. 1 653 Mankiw, N G . , see Campbell, J.Y. 769, 784, .

1 26 1 , 1 264, 1 290, 1 655

Mankiw, N.G., see Elmendorf, D. W 1 439 Mankiw, N.G., see Hall, R.E. 1485, 1 493, 1 498

Marston, R., see Bodnar, G. 1 3 1 8 Marston, R.C. 1 64 Martin, J.P. 1 1 8 1 Mas-Co1ell, A., see Kehoe, T.J. 380 Masciandaro, D., see Grilli, V 1404, 1 432, 1 43 8 , 1439, 1 465

Masson, A., see Kessler, D. 1 646 Masson, P., see Chadha, B. 1 542 Masson, P.R. 1 554, 1 5 88 Matheny, K.J. 395, 441 Matsukawa, S. 1 03 7 Matsuyama, K. 3 9 5 , 3 9 9 Matthieson, D., see Mussa, M. 208 Mauro, P. 277 Mauro, P., see Easterly, W 1 538 Maussner, A. 528 Mayhew, S. 1 3 1 0 McAfee, R.P, see Howitt, P 389, 399, 506, 5 1 7, 5 2 1

McCallum, B.T.

8 3 , 1 73, 1 84, 1 98, 2 0 3 , 408,

487, 488, 496, 503, 1 022, 1 026, 1 043, 1 4 1 1 , 1426, 1 432, 1 437, 1 438, 1 485, 1 487,

Mankiw, N.G., see Kimball, M. S . 1 653 Mann, C.L., see Bryant, R.C. 1 043, 1 49 1 , 1 497, 1 5 16�1 5 1 8

Manuelli, R.E., see Chari, V. V. 7 1 5, 1 578 Manuelli, R.E., see Jones, L.E. 245, 257, 26 1 , 380, 672, 709, 7 1 1 �7 1 3 , 720, 1 675, 1 7 1 1

Mao, C.S., see Dotsey, M. 370, 952 Marcet, A. 3 14, 326, 348, 3 5 1 , 454, 455, 464, 465, 468, 473--476, 480, 494, 499, 525, 528�530, 532, 1 675, 1 705, 1 707

Marcet, A., see Canova, F. 283 Marcet, A., see den Haan, W.J. 347, 354, 369 Margarita, S., see Beltratti, A. 524, 525 Margaritis, D. 474 Mariano, R.S., see Seater, J.J. 1 656, 1 65 7 Mariger, R.P ! 344 Marirnon, R. 455, 464, 472, 475, 523, 53 1 , ·

1214

Marimon, R . , see Evans, G.W.

483, 509, 527,

528, 5 3 1

Marion, N . , see Flood, R . P. 1429, 1438 Mark, N.C. , see Cecchetti, S.G. 1 2 5 1 , 1 265, 1 270, 1 272, 1 294, 1 296

Marris, S. 1 632 Marschak, J. 582, 1 043 Marshall, A. 203 Marshall, D.A ., see Bckaert, G.

1281

1 488, 1 490, 1 4 9 1 , 1 493, 1 495, 1 500, 1 502, 1 506� 1 5 1 0, 1 5 1 2 , 1 5 1 5�1 5 1 9, 1 63 1

McCulloch, J.H., see Dezhbakhsh, H . McElroy, M. 6 1 9 McFadden, D . 1 3 14, 1 3 1 6, 1328 McGrattan, E.R. 348, 974 McGrattan, E.R., see Anderson, E. W.

l 039

368,

369

McGrattan, E. R . , see Chari, V V

1 24, 397, 422,

672, 697, 698, 700, 70 1 , 709, 720, 722, 723, 974, 1 036, 1 037, 1 040�1 042, 1 37 1

McGrattan, E.R., see Marimon, R .

455, 475,

523

McGuire, W.J. 1 33 2 Mcintire, J.M., see Carlson, J.B. 1 04 McKelvey, R.D. 3 8 0 McKibbin, W.J., see Henderson, D.W. 1497 McKinnon, R. 1 496 McKinnon, R.I. 1 66, 207 McLaughlin, K.J. 1 0 1 6, 1 1 52 McLean, I., see Eichengreen, B. 1 57 McLennan, A. 474 McLennan, A., see McKelvey, R.D. 380 McManus, D.A. 908 Means, G.C. 1 082 Meckling, W , see Jensen, M . 1 344 Medeiros, C. 1 554, 1 555

1- 1 9

Author Index

1 077, 1 103 1319 Meghir, C . 6 1 1 , 6 1 3 , 775, 804 Meghir, C., see Arellano, M. 787 Meghir, C., see Attanasio, O.P. 793, 794 Meghir, C., see Blundell, R. 6 1 1 , 6 1 2, 779, 78 1 , 783, 790-792 Meghir, C . , see Browning, M. 607, 6 1 1 , 778 Meguire, P., see Konnendi, R.C. 278-28 1 , 671 , 1 656, 1 657 Mehra, R. 547, 961 , 1 234, 1 236, 1 249, 1 25 1 , 1 264, 1 268, 1 270, 1 272, 1 289, 1 3 1 2 Mehra, R., see Constantinides, G.M. 1 293 Mehra, R., see Danthine, J.-P. 329, 370, 952 Meigs, A.J. 191 Melenberg, B., see Alessie, R. 774 Melino, A., see Blanchard, O.J. 9 1 2 Melino, A., see Epstein, L.G. 558, 565 Melino, A., see Grossman, S.J. 1242 Melnick, R., see Bruno, M. 1 539 Meltzer, A.H. 1 62, 1 69, 1 74-176, 1 78, 1 79, 1 85 , 204, 2 1 5-21 7 , 222, 1466, 1 485, 1 543 Meltzer, A.H ., see Bmnner, K. 1 79, 1 83, 1 9 1 , 1 025 Meltzer, A.H., see Cukicnnan, A. 1 41 4, 1 450, 1463 1 439, 1 5 7 1 , 1 579 Mendoza, E. Mendoza, E., see Calvo, G.A. 1 5 9 1 , 1 600, 1 60 1 1 542 Meredith, G., see Chadha, B. Metton, R. 1 275 Merton, R.K. 3 89, 1 333 Merz, M. 994, 1 1 58, 1 173, 1 203, 1207 Metivier, M., see Benveniste, A. 476, 53 1 Metzler, L.A. 867 Meyer, J.R. 8 1 7 Mihov, I., see Bernanke, B . S . 72, 76, 83, 89, 1 14, 1 365, 1 3 69 Milesi-Ferretti, G.-M., see Mendo:;:a, E. 1439 Milesi-Ferretti, G.-M. 1 425, 1 426, 1 597 Milgrom, P. 475, 1 322 Millard, S.P. 1 2 1 7, 1 220 Miller, B L 566 141 1, 1415 Mi ller, M . , see Lockwood, B. 1 343 Miller, M . , see Modigliani, F. 584, 595, 6 1 1 , 6 1 2, Miller, R.A., see Altug, S. 785, 786, 792 Mills, F. 1 082 1314 Mills, J., see Erlich, D. Mills, L.O., see Boschen, J.E 139 Mills, T.C. 204 Medoff, J.L., see Fay, J.A.

Meehl, P.

.

.

Mills, T.C., see Capie, F.

Mincer, J.

1 63, 1 438

58 1 , 592, 684

1313 1 450, 1 465 Mirman, L.J., see Brock, W.A. 3 1 9, 547, 552, 556, 942, 95 1 Miron, J.A. 1 73, 2 1 6, 876, 907, 1 242 Miron, J.A., see Barsky, R.B. 1 149 Miron, J.A., see Beaulieu, J..T. 876 Miron, J.A., see Feenbcrg, D. 60 Miron, J.A., see Mank.iw, N.G. 1 73, 2 1 6, 1 28 1 Mirrlees, J.A. 1 1 54 Mirrlees, J.A., see Diamond, P.A. 1 684 Mishkin, F.S . 1 0 1 , 1 83, 2 1 6, 1 023, 1 380, 1432, 1 438 Mishkin, F.S., see Bernanke, B.S. 1 495 Mishkin., F. S . , see Estrella, A. 1 485 Mishkin, F. S . , see Hall, R.E. 607, 608, 789, 1 655 Mishra, D . 1 4 1 6, 1 425 Missale, A. 1450 Mitchell, B.R. 222 Mitchell, W.C. 8, 44, 1 053 Mitchell, W.C., see Burns, A.F. 5, 8, 93 1 , 934 Mitra, K. 530, 532 Mnookin, R.H., see Gilson, R.J. 1 1 54 Modiano, E.M. 1 543 Modig1iani, F. 7 6 1 , 762, 780, 1 3 2 1 , 1 343, 1 646, 1 656, 1 657 Modigliani, F., see Dreze, J. 770 Modigliani, F., see Holt, C.C. 882, 885, 888, 909, 9 1 0, 9 1 2 Modigliani, F., see J appelli, T. 7 80 Modigliani, F., see Samuelson, P.A. 643 Moffitt, R. 752, 787 Moffitt, R.A. 6 1 8 Moler, C., see Kahaner, D. 329, 333 Mondino, G. 1 540 Monfort, A., see Gourieroux, C. 487 Monro, S . , see Robbins, H . 476, 478 Montgomery, E. 1 01 7, 1 0 1 8 Montiel, P. 1 539 Montiel, P. , see Agenor, P.R. 1 543 Montrucchio, L. 330 Montrucchio, L . , see Boldtin, M . 362 Moore, B.J. 455, 475, 496 Moore, G.H. 1 059 Moore, G.H., see Zarnowitz, V. 40 Moore, G . R . , see Fuhrer, J.C. 905, 908, 1 039, 1 040, 1 5 1 8 Minehati, D., see Bowman, D.

Minnan, L., see Levhari, D.

I-20

Author index

852, 857, 1 353, 1 3 56, 1 376, 1 378, 1379 Moreno, D. 48 1 Morgan, D. 1 374 Morrison, C.J. 1 086 Mortensen, D.T. 1 1 57, 1 1 58, 1 1 62, 1 1 63, 1 1 73, 1 1 82, 1 1 83, 1 1 87, 1 1 88, 1 1 94, 1 1 98, 1 203. 1 208, 1 2 1 7 , 1 220, 1 222 Mortensen, D.T., see Burdett, K. 1 1 73 , 1 1 96 Mortensen, D.T., see Millard, S.P. 1 2 1 7 , 1 220 Morton, T.E. 338 Mosser, P.C. 9 1 0 Motley, B . , see Judd, J.P . 1 485, 1 487, 1 5 1 2 , 1516 Mroz, T.A. 6 1 8 Mroz, T.A., see MaCurdy, T.E. 592, 752 Muellbauer, J., see Deaton, A. 783 Mueller, D. 1464 Mulligan, C.B. 346, 1 1 50 Mundell, R.A. 1496 Murphy, K. 5 8 1 Murphy, K . , see Juhn, C. 569, 6 1 9 Murphy, K . , see Katz, L. 577, 578 Murphy, K.M. 262, 278, 1 082 Murray, C.J., see Nelson, C.R. 1 1 Murray, W , see Gill, P.E. 329 Musgrave, R.A. 1 63 1 , 1 66 1 Mussa, M. 208, 1404, 1 637 Mussa, M., see Flood, R.P. 1 52, 202, 1 428 Mussa, M.L., s ee Frenkel, J.A. 203 Muth, J.F. 457, 473, 484 Muth, J.F., see Holt, C.C. 882, 885, 888, 909, 9 1 0, 9 1 2 Myerson, R . 1459

Moore, J., see Kiyotaki, N.

Nakamura, A. 6 1 8 Nakamura, M . , see Nakamura, A . 6 1 8 Nalebuff, B . , see Bliss, C . 1 46 1 , 1 465 Nance, D.R. 1 3 1 8 Nankervis, J.C., see McManus, D.A. 908 Nash, S., see Kahaner, D. 329, 333 Nason, J.M., see Cogley, T. 395, 547, 967, 1 142, 1 503

Natanson, I.P 342 NBER 8 Neale, M.A., see Northcraft, G.B. 1 3 1 5 Negishi, T. 559 Nelson, C.R. 1 1 , 2 1 1 , 2 1 3 , 264, 969, 1264, 1 320

Nelson, C.R., see Beveridge, S. Nelson, D.B. 1 82

1 062, 1 143

Nelson, E. 1 03 5 Nerlove, M. 2 8 3 , 284 Neumann, G.R., see Burdett, K. 1 1 73 Neusser, K. 941 Neves, J., see Correia, I . 974 Neves, P., see Blundell, R. 792 Ng, S., see Garcia, R. 790 Nickell, S . , see Layard, R. 1098, 1 1 76, 1 1 77 , 1221

Nickell, S.J. 823 Nicolini, J.P., see Marcct, A. 455, 530, 532 Niederreiter, H. 334 Nilsen, 0.A., see Askildsen, J.E. 1 074 Nishimura, K., see Benhabib, 1. 403-405, 425, 435

Nordhaus, W. 1 400, 1 425 North, D. 1 449 Northcraft, G.B. 1 3 1 5 Novales, A . 803 Nurkse, R. 1 63 , 203 Nyarko, Y. 465, 474 O'Barr, W.M. 1 332 O'Brien, A.M. 776 O'Brien, A.P. 1 8 1 Obstfcld, M. 1 59, 1 64, 1 65, 407, 1 4 1 1 , 1 4 1 5 , 1 429, 1 438, 1 449, 1 507, 1 5 7 1 , 1 588, 1 590, 1 5 92, 1 630 Obstfeld, M . , see Froot, K. 1 266 O 'Connell, S.A. 1 650 Odean, T. 1 3 14, 1 323 O'Driscoll, G.P. 1 643 OECD 1 1 8 1 , 1 1 82, 1 2 1 5 , 1 620 Office of Management and Budget 1 622 Officer, L . 15 5 Ogaki, M., see Atkeson, A. 6 1 0, 786 Ohanian, L.E. 1 03 6 Ohanian, L.E., see Cooley, T.F. 42, 962, 974 O'Hara, M., see Blume, L.E. 32 1 , 322 Ohlsson, H., see Edin, D.A. 1 457 Okina, K. 1 508 Okun, A.M. 1 0 1 4, 1 54 1 Oliner, S.D. 1 37, 820, 1 374, 1 376 Oliner, S.D., see Cummins, J.G. 856 Olsdcr, G., see Basar, T. 1 449 Olshen, R.A., see Breiman, L. 289 Oppers, S. 1 54 Orphanides, A. 1 98, 1 485 Ortega, E., see Canova, F. 376, 377, 379 Ortigucira, S., see Ladron de Guevara, A. 3 1 7 Ostry, J . 1 568

1-21

Author Index

Ostry, J., see Montiel, P. 1 539 Ostry, J.D., see Ghosh, A.R. 202, 207, 208 Owen, P.D., see Knowles, S. 277, 278 Ozier, S . 1 457, 1 465 Ozier, S., see Alesina, A. 277-279, 1460, 1 466, 1471

1 456, 1 459, 1460, 1 465, 1466, 1469, 1470, 1 490 Persson, T. , see Englund, P. 9 Persson, T., see Hassler, J. 9, 1238 Persson, T. , see Hom, H. 1 4 1 5 Persson, T. , see Kotlikoff, L . 1 448, 1 449, 1 465

Paarsch, H . , see MaCurdy, T.E. 6 1 9, 620 Pacelli, L., see Contini, B. 1 1 77, 1 1 78, 1 1 80, 1 222

Packalen, M. 525 Padilla, J., see Dolado, J. 1 437 Pagan, A., see Kim, K. 377, 379 Pagan, A.R. 9, 69, 1 08 Pagano, M., see Giavazzi, F. 203, 1438, 1 446, 1 449, 1 5 80

Pagano, M., see Jappelli, T. 776 Papageorgiou, A. 334 Papageorgiou, C., see Duffy, J. 257 Paquet, A., see Ambler, S . 944 Parekh, G. 87, 1 09 Parente, S.L. 672, 674, 702, 708 Parke, WR., see Davutyan, N. 1 5 6 Parker, J., see Barsky, R . 43 Parker, J., see Gourinchas, P.-O. 609, 1 344 Parker, J.A. 1 120 Parker, J .A., see Solon, G. 579, 1 058, 1 1 02, 1 1 06

Parkin, M. 1 037, 1 4 1 2 , 1 4 1 5 , 1 506 Parkin, M., see Bade, R. 1 432, 1438 Pashardes, P., see Blundell, R. 7 8 1 Paskov, S.H. 334 Patel, J., see Degeorge, F. 1 3 2 1 Patinkin, D . 407, 1 506, 1 507, 1 630, 1 643 Paulin, G. 75 1 Paxson, C., see Deaton, A. 798 Paxson, C., see Ludvigson, S. 788 Pazos, F. 1 534 Pclcs, N., see Goctzmann, W.N. 1 3 1 4 Pencavel, .T. 550, 60 1 , 605, 975, 1 1 48 Peralta-Alva, A. 374 Perli, R. 402, 43 1 , 435 Perli, R., see Benhabib, J. 425, 426, 437 Perotti, R. 1466, 1 469, 1 472 Perotti, R., see A1esina, A. 1 439, 1 464, 1 465 Perron, P 264 Perry, G.L., see Akerlof, G.A. 1 98 Persson, M. 1 447, 1 449 Persson, T. 278, 692, 1 400, 1403, 1 4 1 3, 1 4 1 5- 14 1 8, 1 420, 1 42 1 , 1425, 1433, 1435, 1437- 1 440, 1 442, 1 445, 1 448-1450, 1454,

Persson, T. , see Persson, M. 1447, 1449 Pesaran, H. 487 Pesaran, M.H., see Binder, M. 271 Pesaran, M.H., see lm, K. 283 Pesaran, M.H., see Lee, K. 284 Pestieau, P.M. 1 7 1 8 Petersen, B.C., see Carpenter, R.E. 88 1 , 9 12, 1 344

Petersen, B.C., see Domowitz, I .

1 020, 1 083,

1 093

Petersen, B.C., see Fazzari, S.M. 8 1 8, 1 344 Petterson, P. 1 457 Pflug, G., see Ljung, L. 476 Phaneuf, L. 1 028, 1 039, 1 04 1 Phelan, C. 380, 575, 796 Phelan, C., see Atkeson, A. 1 298 Phelps, E. 944, 1 025, 1 026, 1 039 Phelps, E.E., see Frydman, R. 453, 454, 474,

528, 536, 539 46, 1 68, 1 059, 1098, l l 2 1 , l l 22, 1 1 57, 1 1 73 , 1 1 76, 1 1 92, 1 220, 1 537, 1 538, 1 720, 1 724 Philippopoulus, A., see Lockwood, B. 1 4 1 5 Phillips, A.W. 1 5 1 0 Phillips, A .W.H. 46 Phillips, L.D., see Lichtenstein, S. 1 3 1 8 Phillips, P. C.B. , see Kwiatkowski, D. 2 1 2 Picard, P. 1 1 57 Pieper, P. J., see Eisner, R. 1 6 2 1 Pierce, J.L. 1 95 Piketty, T., see Aghion, P. 1 377 Pindyck, R. 1 072 Pindyck, R.S. 835, 9 1 0, 9 1 2 Pindyck, R.S., see Abel, A.B. 835 Pindyck, R.S., see Caballero, R.J. 844 Pippenger, J. 1 56 Pischke, J.-S., see Jappelli, T. 790 Pischke, J.-S. 764 Pissarides, C.A. 774, 1 1 63, 1 1 73, 1 1 83, 1 1 84, 1 1 8 8, 1 1 93, 1 1 94, 1 200, 1 203, 1207, 1 209, 1 220 Pissarides, C.A., see Garibaldi, P. 1 1 80, 1 222 Pissarides, C.A., see J ackman, R. 1 22 1

Phelps, E.S.

1-22

Author Index

1 1 58, 1 1 82, 1 1 83, 1 1 94, 1 1 98, 1 203, 1 208 Plosser, C.l. 952, 954, 958, 96 1 , 963, 1 094, 1 65 8 Plosser, C . I . , see King, R.G. 9 , 5 4 , 369, 3 9 1 , 429, 4 3 5 , 549, 929, 93 1 , 941 , 945, 954, 995 Plosser, C.I., see Long, J. 929, 952, 953, 994 Plosser, C.l., see Nelson, C.R. 1 1, 2 1 1, 213, 264, 969 Plutarchos, S., see Bcnhabib, J. 437 Pissarides, C.A., see Mortensen, D.T.

Polemarchakis, H.M., see Geanakoplos, J.D.

395, 458 1 037

Policano, A., see Fethke, G.

803 Pollard, S. 161 1 92, 1 5 14, 1 5 1 5 Poole, W. Pollak, R. A.

1 039

Poonia, G.S., see Dczhbakhsh, H. Popper, K . Porter, R.

376 1 509

Porter, R.D., see LeRoy, S.F. Porteus, E.L., see Kreps, D.M. Portier, F.

1 235, 1 3 1 9 557, 1 256

Portier, F., see Hairault, J.-0.

1 036

A. 1 404, 1426, 1432, 1 43 8 Posen, A., see Mishkin, F.S. 1432, 1 4 3 8 Posen,

1 59, 1235, 1 3 20, 1 465, 1 648,

1 65 5 Poterba, J.M., see Cutler, D.M.

1 290, 1 320,

1 32 1 Poterba, J.M., see Feldstein, M. Potcrba, J.M., see Kusko,

A.L.

1 633 1 327

L., see Cooper, R. 824 Pradel, J., see Fourgeaud, C. 454, 465, 473, Power,

475 Prasclmik, J., see Hornstein,

V, see Cooley, T.F. 1 376 V , see Krusell, P. 1445, 1473

254, 263, 268, 272, 275, 283, 287, 288, 290-292, 294, 299 Quah, D., see Leung, C. 27 1 Quah, D.T., see Blanchard, O.J. 2 1 1 , 2 1 6, 2 1 7 Quah, D.T., see Durlauf, S.N. 550 Quandt, R.E. 34 Quattrone, G.A. 1 329 Quah, D.

Rabin, M.

549

A. 1 62 Prati, A., see Alesina, A. 1446, 1449 Prati, A., see Drudi, F. 1 450

1 78, 365, 545, 675, 700, 702, 930, 934, 952, 954, 956, 957, 96 1 , 963, 982, 1 033, 1 29� 1 488, 1 489, 1 7 1 0 Prescott, E.C., see Chari, V V 1 488, 1 489, 1 674 Prescott, E . C . , see Cooley, T.F. 376, 549, 954 Prescott, E.C., see Hansen, G.D. 602 Prescott, E.C., see Hodrick, R. 9, 1 2, 34, 428, 93 1 , 932 Prescott, E.C., see Kyd1and, F.E , 9, 42, 1 5 8, 428, 547, 549, 929, 953, 956, 957, 962, 980, 9 8 1 , 1 058, 1 059, 1 1 40, 1 1 4 1 , 1 145,

1319

Rabin, M . , see Bowman, D .

Rabinowitz, P. , see Davis, P.J. Radner, R.

A.

Prati,

Prescott, E.C.

Quadrini, Quadrini,

1 068, 1 1 26

Poterba, J.M.

1 1 67, 1 1 95, 1 400, 1405, 1 4 1 5, 1 449, 1485, 1 486, 1488, 1 673, 1 708 Prescott, E.C., see Lucas Jr, R.E. 547, 554 Prescott, E.C., see Mehra, R. 547, 96 1 , 1234, 1 236, 1 249, 1 25 1 , 1 264, 1 268, 1 270, 1 272, 1 289, 1 3 1 2 Prescott, E.C., see Parente, S.L. 672, 674, 708 Prescott, E.C., see Stokey, N.L. 95 1 , 998, 999 Prescott, E. S . 380 Press, W.H. 329-334, 343, 348, 356, 365 Preston, I., see Banks, J. 759, 783, 790, 791 Preston, I., see Blundell, R . 572, 764, 797 Priouret, P. , see Benveniste, A. 476, 5 3 1 Pritchett, L. 2 37 Pritchett, L., see Easterly, W 277, 278, 28 1 , 675 Przeworski, A. 1 466 Psacharopou1os, G. 685 Puterman, M.L. 336, 338, 339

1313 333

952

1 465 2 8 1 , 852, 1 1 57, 1 1 59 Ramey, G., see den Haan, WJ. 994, 1 1 66, 1 1 94, 1 203, 1 204, 1206, 1 207 Ramey, G., see Evans, G.W 455, 46 1 , 462 Ramey, VA . 67, 876, 885, 897, 902, 905-907, 909, 9 1 1 , 9 1 4, 1 084, 1 089 Ramey, VA., see Bresnahan, T.F. 9 1 1 , 9 1 2 Ramey, VA . , see Chah, E.Y. 775 Ramey, VA., see Ramey, G. 2 8 1 Ramos, J. 1 543 Ramsey, F. 643, 649 Ramsey, F.P. 1 673 Rankin, N. 1 025 Rankin, N., see Dixon, H . 537 Rapping, L., see Lucas Jr, R.E. 6 1 5, 6 1 6 Radner, R., see Benhabib, J .

Ramey, G.

I-23

Author Index

Rasche, R.H., see Hoffman, D.L. 5 1 , 4 1 2 Ratti, R.A. 1 497 Ravikumar, B., see Chatterj ee, S . 1 1 26 Ravikumar, B . , see Glomm, G. 7 1 2, 1472 Rawls, J. 1 662 Ray, D., see Esteban, J.-M. 264 Rayack, W 579 Razin, A. 1 7 1 5 Razin, A., see Frenkel, J.A. 1 630 Razin, A., see Helpman, E . 203, 1 5 80 Razin, A . , see Mendoza, E . 1439 Razin, A., see Milesi-Ferretti, G.-M. 1 5 97 Rebelo, S.T. 245, 260, 2 6 1 , 709, 952, 1 546, 1 568, 1 578-1 5 8 1 , 1 606 Rebelo, S.T., see Burnside, C . 399, 930, 980, 982-985, 994, 1 078, 1 1 42 Rebelo, S.T., see Correia, I. 974 Rebelo, S.T., see Easterly, W 703 Rebelo, S.T., see Gomes, J. 994, 1 1 59 Rebelo, S .T., see King, R.G. 9, 54, 369, 39 1 , 429, 435, 545, 549, 649, 672, 7 1 1-7 1 3, 929, 932, 945, 954, 995, 1 062, 1 1 40 Rebelo, S.T., see Stokey, N.L. 578, 583, 672, 709, 7 l l , 7 1 4, 954 Redish, A. 1 54, 1 5 5 , 166 Redish, A., see Betts, C.M. 2 1 7 Redmond, J. 1 6 1 Reichenstein, W 1 0 1 Reichlin, L . , see Evans, G . W. 1 1 25 Reichlin, L., see Lippi, M. 2 1 7 Reid, B.G., see Boothe, P. M . 1 658 Reinhart, C.M. 1 545, 1 546, 1 55 1 , 1 553, 1 5 6 1 , 1 572, 1 573 Reinhart, C.M., see Calvo, G.A. 1 538, 1 539, 1 552, 1 588, 1 600 Reinhart, C.M., see Kaminsky, G.L. 1 553, 1 590 Reinhart, C.M., see Ostry, J. 1 568 Renelt, D., see Levine, R. 269, 277-282, 390, 423, 67 1 , 694 Reserve Bank of New Zealand 1 500 Resnick, L.B., see Levine, J. 1 332 Restoy, F. 12 72 Revelli, R., see Contini, B. 1 1 77, 1 1 78, 1 1 80, 1 200, 1 222 Revenga, A., see Blanchard, O.J. 1 2 1 4 Rey, P., see Aghion, P. 1 1 57 Ricardo, D. 1 642 Rich, G. 1 5 1 4 Richard, S.F., see Hansen, L.P. 556 Richards, S., see Meltzer, A.H. 1 466

Rietz, T. 1 252, 1 272, 1 296 Riley, J. 1 4 6 1 , 1 465 Rios-Rull, J. 943 Rios-Rull, J.- V, see Castaneda, A. 380 Rios-Rull, J.-V 380 Rios-Rull, V , see Krusell, P. 1445, 1 473 Ritter, J.R. 1 32 1 Ritter, J.R., see Ibbotson, R. 1 3 2 1 Rivers, D . 840 Rivlin, T.J. 343 Rob, R., see Jovanovic, B. 702 Rob, R., see Kandori, M. 475 Robb, R., see Heckman, J.J. 752 Robbins, H. 476, 478 Roberds, W , see Hansen, L.P. 573, 574 Roberts, H . V 1 307 Roberts, J., see Milgrom, P. 475 Roberts, J.M. 1 0 1 3 , 1 033, 1 040, 1 1 1 6, l l 1 8, 1 505 Roberts, J.O., see Lebow, D.E. 2 1 5 Roberts, K. 1466 Robertson, J.C., see Pagan, A.R. 69, 1 08 Robinson, D. 2 1 7 Robinson, J. 1 054, 1 1 20 Robinson, S., see Meltzer, A.H. 204, 2 1 6, 2 1 7, 222 Rockafellar, R.T. 325 Rockoff: H . 1 55, 1 57 Rockoff, H . , see Bordo, M.D. 1 60 Rodriguez, C.A. 1 562, 1 563, 1 5 65 , 1 568 Rodriguez-Clare, A., see Klenow, P.J. 663, 673, 679, 680, 683-686, 694, 702, 705, 707 Rodrik, D., see Alesina, A. 278, 692, 1466, 1 469 Rogers, C. 1 449, 1 450 Rogers, D., see Fullerton, D. 576, 588, 6 1 6 Rogerson, R. 55 1 , 602, 976--978, 1 145 Rogerson, R., see Benhabib, J. 402, 550, 1 145 Rogerson, R., see Bertola, G. 1222 Rogerson, R., see Cho, J.O. 976 Rogerson, R., see Cole, H.L. 1 1 63, 1 1 94, 1 2 0 1 - 1 203, 1 207 Rogerson, R., see Greenwood, J. 550, 995 Rogerson, R., see Hopenhayn, H. 672, 708, 994 Rogerson, R., see Parente, S.L. 702 Rogoff, K. 96 1 , 1 4 1 5 - 1 4 1 8, 1420, 1422, 1425, 1429, 1 432, 1 434, 1 43 8 Rogoff, K . , see Bulow, J . 1448, 1 449 Rogoff, K., see Canzoneri, M.B. 1 507, 1 508

I-24

Author Index

Rogoff, K., see Obstfeld, M.

407, 1 507, 1 590,

1 630

Rojas-Suarez, L. 1 575 Roland, G., see Persson, T. 1460 Roldos, J. 1 578 Roll, R. 1 328 Romer, CD. 6, 69, 92, 1 37, 1 83, 1 87, 204, 205, 1 6 1 8

Romer, D.

237, 643, 649, 65 1 , 66 1 , 930, 1 0 1 3 ,

1 034, 1 1 40, 1 1 5 7, 1 1 63 , 1 635, 1 6 6 1

Romer, D., see Ball, L.

1 023, 1 037, 1 04 1 ,

1 1 27

Romer, D., see Frankel, J.A. 280, 2 8 1 Romer, D., see Mankiw, N . G . 244-246, 252255, 269-27 1 , 277-279, 289, 653, 655, 660, 673, 679-683, 685, 686, 1 63 8

Romer, D.H., see Romer, C.D. 69, 92, 1 3 7 Romer, P.M. 2 3 8 , 245, 260, 26 1 , 264, 265, 27 1 , 278, 280, 398, 424, 425, 64 1 , 65 1 , 665, 672, 705-707, 7 1 5-7 1 7, 7 1 9, 1 63 8

Romer, P. M . , see Evans, G . W

425, 426, 506,

521

277-279, 1 404,

1 423, 1 425, 1 460, 1 466, 1 47 1

Roubini, N., see Grilli, V 95 Roubini, N., see Kim, S. 95 Rouwenhorst, K.G. 1 296 Royer, D., see Balasko, Y 506 Rubinstein, A. 1 1 88 Rubinstein, A., see B inmore, K.G. 1 1 88 Rubinstein, M. 5 54-556 Rubinstein, M., see Jackwcrth, J.C 1 3 1 0 Rudd, J.B., see Blinder, A.S. 1 0 1 8, 1 1 1 8 Rudebusch, G.D. 69, 1 04, 1 96, 1 493 Rudebusch, G.D., see Diebold, F.X. 6 Rudebusch, G.D., see Oliner, S . D. 1 37, 820, 1 3 74, 1 376

Rudebusch, R.G. 1 1 Rudin, J. I 040 Ruhm, C. l l 52 Runkle, D., see Glosten, L. 1280 Runkle, D., see Keane, M.P. 608, 609, 786, 790

Rose, A., see Akerlot; G.A. 1 200 Rose, A.K., see Eichengreen, B. 1 590 Rose, A.K., see Frankel, J.A. 1 590 Rosen, A., see Meehl, P. 1 3 1 9 Rosen, S . 584, 5 8 5 , 976 Rosensweig, J.A. 1 659 Rosenthal, H., see A1esina, A. 1 425, 1426 Roseveare, D. 1 626 Ross, L. 1 3 1 9 Ross, S . , see Brown, S. 1 242 Ross, S.A. 1 3 3 1 Rossana, R.J. 879, 8 8 1 , 886, 907 Rossana, R.J., see Maccini, L.J. 8 8 1 , 893, 894, 903, 907

Rossi, P.E., see Jones, L.E.

380, 672, 7 1 1--7 1 3 ,

1 675, 1 7 1 1

Rotemberg, J.J.

Roubini, N. 1 439, 1 465 Roubini, N., see Alesina, A.

67, 68, 395, 397, 406, 407,

423, 429, 434, 838, 9 1 0, 974, 996, 1 020, 1 033, 1 034, 1 036, 1 040, 1 04 1 , 1 043, 1 044, 1 055, 1 056, 1058, 1 062, 1 063, 1 067-1069, 1 074, 1 08 1 , 1 082, 1 088--1 090, 1 092, 1 093, 1 1 06, 1 1 07, 1 1 1 4, 1 1 1 6, 1 1 1 8, 1 1 23- 1 1 25, 1 1 29, 1 1 43, 1 1 44, 1 365, 1464, 1 492, 1 494, 1 497

Rotemberg, J.J., see Mankiw, N.G. 785 Rotemberg, J.J., see Pindyck, R. 1 072 Rotemberg, J.J., see Potcrba, J.M. 1 59 Rothschild, M. 823 Rotwein, E. I 0 I 1

Runkle, D.E. 789, 790, 1 655 Rtmkle, D.E., see Geweke, J.F. 89 Runkle, D.E., see Mankiw, N.G. 1 3 5 Russek, F. S., see Barth, J.R. 1 657 Rust, J. 3 1 4, 3 1 7, 336 Rust, J., see Amman, H.M. 535 Rustiehini, A., see Benhabib, J. 400, 847, 1 449, 1 467, 1472

Rustichini, A., see Boldrin, M. Ryder, H. 587 Ryder Jr, H.E. 1284

400, 1 465

Sabelhaus, J., see Gokhale, J. 750 Sachs, J. 1 590, 1 59 1 Sachs, J., see Bruno, M . 1 090 Sachs, J., see Roubini, N. 1439, 1 465 Sachs, J.D. 252, 703 Sack, B., see Ga1eotti, M. 909 Sadka, E., see Razin, A. 1 7 1 5 Sahay, R. 1 535 Sahay, R., see Fischer, S . 1 538, 1 547, 1 5 6 1 Saint Marc, M. 222, 223 Saint-Paul, G. 1 1 62, 1 472 Saint-Paul, G., see Blanchard, O.J. 1 2 1 4 Sakellaris, P. , see Barnett, S . 83 1 Sala-i-Martin, X. 269, 277, 279--282, 659, 694

Author Index Sala-i-Martin, X ., see Barro, R.J. 237, 245, 246, 252, 269, 27 1 , 272, 278, 284, 643, 65 1 , 657, 659, 6 7 1 , 675, 1 63 7 Salge, M . 499 Salmon, C.K., see Haldane, A.G. 1485, 1 497 Salmon, M . 525 Salmon, P., see Kirman, A.P 536, 539-541 Saloncr, G., see Rotemberg, .T.J. 9 1 0, 1 058, 1 093 Salter, W. E.G. 848 Sampson, L., see Fauvel, Y. 1 573 Samuelson, PA. 46, 643, 6 6 1 , 1 3 1 1 , 1 634 Samwick, A. 609 Samwick, A.A., see Carroll, C.D. 567 Sandmo, A., see Atkinson, A.B. 1 7 1 8 Sandroni, A . 1 293 Sanguinetti, P. 1 540 Sanguinetti, P , see Heymann, D. 506 Sanguinetti, P., see Jones, M. 1 540 Santaella, J. 1 543 Santos, M . , see Caballe, J. 578 Santos, M.S. 321-323, 326, 327, 335, 353, 354, 382, 590, 1 266 Santos, M . S . , see Bona, J.L. 3 1 3 Santos, M.S., see Ladron de Guevara, A. 3 1 7 Santos, M.S., see Peralta-Alva, A . 374 Sargent, T. 1 62, 1 98, 929 Sargent, T. , see Ljungqvist, L . 1 2 1 4 Sargent, T., see Lucas Jr, R.E. 582 Sargent, T., see Marimon, R. 455, 523 Sargent, T.J. 73, 1 2 1 , 1 35 , 4 1 7, 4 1 8, 453, 455, 457, 458, 464, 465, 489, 504, 523, 524, 529-5 3 1 , 763, 888, 1 023, 1 024, 1 145, 1 506, 1 507, 1 5 1 9, 1 542, 1 543, 1 630, 1 63 1 Sargent, T.J., see Anderson, E.W 368, 369 Sargent, T.J., see Cho, I.-K. 455, 465, 524, 525 Sargent, T.J., see Evans, G.W. 530 Sargent, T.J., see Hansen, L.P 558, 573, 574, 882, 9 1 5, 1 294, 1 295 Sargent, TJ., see Marcet, A. 454, 464, 465, 468, 473--476, 480, 494, 499, 525, 528, 529, 532, 1 675, 1 705, 1 707 Sattinger, M . 577, 578 Sannders, A. 1 8 1 Sauvy, A . 222 Savage, L.J. 1 3 08, 1 324 Savage, L.J., see Friedman, M . 1 325 Savastano, M.A. 1 589 Savastano, M.A., see Masson, PR. 1 554, 1588

I-25 Savin, N., see Bray, M. 454, 465, 466, 473, 475, 527 Savin, N., see Ingram, B. 984 Savin, N.E., see McManus, D.A. 908 Savouri, S., see Jackman, R. 1 2 2 1 Sayers, R . S . ! 56 Sbordone, A. 983 Sbordone, A., see Cochrane, J. 1 1 20 Sbordone, A.M. 1 078, 1 099, 1 1 08, 1 1 1 8, 1 128 Scammell, W.M. 1 56 Scarpetta, S. 1 2 1 4 Schaling, E. 1 43 7 Schaling, E., see Eijffinger, S. 1 432, 1 438 Schaller, H., see Moore, B.J. 455 Scharfstein, D., see Chevalier, J.A. 1 1 22, 1 1 23 Scharfstein, D., see Hoshi, T. 1 344 Scheinkman, J., see Ekeland, I. 1 689 Scheinkman, J., see Heckman, J.J. 579 Scheinkman, J.A. 566 Scheinkman, J.A., see Benveniste, L.M. 3 2 1 Schiantarelli, F., see Ga1eotti, M . 909, I 086, 1 1 24 Schmidt, P, see Kwiatkowski, D. 2 1 2 Schmidt-Hebbel, K., see Easterly, W. 1 53 8 Schmitt-Grohe, S. 406, 407, 4 1 6, 4 1 8, 429, 43 1 , 435 Schmitt-Grohe, S., see Bcnhabib, J. 4 1 9, 42 1 , 423 Schmitz Jr, J.A. 672, 695-697, 699 Schnadt, N., see Capie, F. 1 54 Scholes, M., see Black, F. 1 3 1 0, 1 3 3 1 Scholz, J.K., see Gale, W.G. 1 646 Schiinhofer, M. 5 1 5 Schopenback, P., see Erlich, D. 1 3 1 4 Schotter, A. 1 4 1 5 Schuh, S. 877, 8 8 1 , 9 1 2 Schuh, S . , see Davi s, S .J . 1 1 5 1 , 1 1 52, 1 1 60, 1 1 6 1 , 1 1 78, 1 1 94, 1 1 99 Schuh, S., see Fuhrer, J.C. 905, 908 Schuh, S., see Hmnphreys, B.R. 909 Schultz, T.W. 653 Schmnaker, L.L. 344, 345 Schwartz, A., see Thaler, R.H. 1 3 1 3 Schwartz, A.J. 1 56, 1 6 1 , 1 73 , 1 80, 204, ! ) 1 ) Schwartz, A.J., see Bordo, M.D. 1 59, 1 65 , 1 84 , 1 94, 203, 204, 208, 2 1 7, 1 404, 1 5 90 Schwmiz, A.J., see Darby, M.R. 1 66 Schwartz, A.J., see Friedman, M. 6 1 , 1 37, 1 34. 1 62, 1 72, 1 76, 1 79, 1 80, 1 85, 1 89, 222

I-26 Schwert, G.W 1 236, 1 280 Schwert, G.W, see French, K. 1 280 Seater, J.J. 1 62 1 , 1 654, 1 656, 1 657 Sedlacek, G., see Heckman, J.J. 578, 579 Sedlacek, G.J., see Hotz, VJ. 792, 803 Segal, l.B. 1 1 57 Senhadji, A.S., see Diebold, F.X. 1 1 Sentana, E., see King, M . 1 333 Seppala, J., see Marcet, A. 1 675, 1 705, 1 707 Seslnick, D. 746, 75 1 Shafir, E. 1 3 1 6, 1 324, 1 329 Shafir, E., see Tversky, A. 1 3 24 Shapiro, C. 1 1 57 Shapiro, C., see Farrell, J. 1 1 2 1 Shapiro, M . 938, 980 Shapiro, M., see Barsky, R. 558, 564, 565 Shapiro, M.D. 1 38, 8 1 8, 1 069, 1 075, 1 65 5 Shapiro, M.D., see Dominguez, K. 1 82 Shapiro, M.D., see Mankiw, N.G. 1 35 Shapiro, M.D., see Ramey, VA. 67, 1 089 Sharma, S., see Masson, P.R . 1 554, 1588 Sharpe, S. 1 344 Shaw, E.S., see Gurley, J.G. 1 507 Shaw, K. 584 Shay, R.P., see Juster, F.T. 777 Shea, J. 402, 608, 790, 983, 1 1 1 7 Sheffrin, S.M., see Driskill, R.A. 1 042 Shefrin, H. 1 3 1 3 , 1 3 1 7, 1 32 1 , 1 330 Shell, K. 389, 3 9 1 , 5 1 6 Shell, K., see Balasko, Y. 427 Shell, K., see Barnett, W 540 Shell, K., see Cass, D. 389, 5 1 6, 662 Shepard, A., see Borenstein, S. 1 124 Sherali, D.H., see Bazaraa, M.S. 3 3 1 Sheshinski, E . 1 03 1 , 1 0 37 Shetty, C.M., see Bazaraa, M.S. 3 3 1 Shiller, R.J. 1 73, 1 234, 1 235, 1 238, 1 249, 1 290, 1 3 1 6, 1 3 1 7, 1 3 1 9, 1 320, 1 323, 1 3 24, 1 327, 1 33 0- 1 332 Shiller, R.J., see Campbell, J. Y. 1235, 1 265, 1 280, 1 320 Shiller, R.J., see Case, K.E. 1 323 Shiller, R.J., see Grossman, S.J 1 242, 1 246, 1 268, 1 29 1 Shin, M . C . , see Puterman, M . L . 3 3 9 Shin, Y. , see Im, K. 283 Shin, Y. , see Kwiatkowski, D. 2 1 2 Shleifer, A . 1 3 1 7 , 1 324 Shleifcr, A., see Barberis, N. 1 294, 1 322 Shleifer, A., see Bernheim, B.D. 1 646 Sh\eifer, A., see DeLong, .J.B. 1 290, 1 324

Author index Shlcifer, A., see L a Porta, R. 1 240 Sh\eifer, A., see Lakonishok, J. 1 323 Sh\eifer, A., see L ee, C. 1 324 Shleifer, A., see Murphy, K.M. 262, 278, 1 082 Shoemaker, C.A., see Johnson, S.A. 345, 3 8 1 Shor, N.Z. 33 1 Shoven, J.B. 705, 708 Shoven, J.B., see Ballard, C. 1 639 Sibert, A., see Rogoff, K. 1 4 1 6, 1 4 1 7, 1 420, 1 425 Sichel, D., see Oliner, S.D. 820 Siegel, J.J. 1 3 1 2, 1 3 1 3 Silberman, J. 1 3 1 6 Simkins, S . 93 1 Simmons, B. 1 63 Simon, H.A., see Holt, C.C. 882, 885, 888, 909, 9 1 0, 9 1 2 Simons, H.C. 852, 1 485 Simonsen, M.H., see Dornbusch, R. 1 543, 1 565 Sims, C.A. 34, 44, 69, 83, 93, 95, 99, I 05, 1 2 1 , 1 28, 1 29, 1 3 1 , 1 32, 1 34, 1 44, 397, 4 1 8, 539, 673, 694, 1 509, 1 5 1 8, 1 520, 1 63 1 Sims, C.A., see Hayashi, F. 788 Sims, C.A., see Leeper, E.M. 69, 74, 83, 93, 1 0 1 , 1 28, 1 32, 1 34, 1 036, 1 089, 1 369 Sinai, A., see Eckstein, 0. 1 344 Singer, B. 292 Singer, B., see Heckman, J.J. 1 1 66 Singleton, K. 1 270 Singleton, K.J., see Dunn, K.B. 800, 1 284 Singleton, K.J., see Hansen, L.P. 547, 555, 556, 768, 769, 784, 882, 1 234, 1 246, 1 250, 1 26 1 Siow, A., see Altonj i, J.G. 789 Skinner, B.F. 1 328 Skinner, J. S. 7 7 1 , 772 Skinner, J.S., see Hubbard, R.G. 567, 569, 572, 573, 593, 7 7 1 , 776, 794, 797, 1 660 Slade, M.E. 1 0 1 5 Slemrod, J., see Shapiro, M.D. 1 655 Slovic, P. , see Fischhoff, B. 1 3 1 9 Small, D.H., see Hess, G.D. 1 485, 1 509 Small, D.H., see Orphanides, A. 1 485 Smetters, K. A . 1 647 Smith, A.A., see Krusell, P. 380, 547, 566, 567, 994 Smith Jr, A.A., see Krusell, P. 1 293 Smith, C.W, see Nance, D.R. 1 3 1 8 Smith, E.L. 1 3 1 2

Author Index Smith, G.W., see Devereux, M. 952 Smith, G.W., see Gregory, A.W. 376, 377 Smith, R., see Alogoskoufis, G.S. 1 66, 2 1 4 Smith, R.P., see Lee, K . 284 Smithson, C.W., see Nance, D.R. 1 3 1 8 Snower, D., see Blanchard, O.J. 1 2 14 Soares, J., see Cooley, T.F. 1 463 Soderlind, P., see Hassler, J. 9, 1 238 Sodersh·om, T., see Ljung, L. 476 Soerensen, J.P 528 Solnick, A., see Judd, K.L. 340 Solon, G. 579, l 058, 1 1 02, 1 1 06 Solon, G., see Barsky, R. 43 Solow, R.M. 237, 244, 246, 257, 643, 656, 664, 68 1 , 929, 930, 942, 950-952, 1 1 40, 1 207, 1 63 8 Solow, R.M., see Blanchard, O.J. 1 2 1 4 Solow, R.M., see Blinder, A.S. 1 660 Solow, R.M., see Hahn, F. 661 Solow, R.M., see Samuelson, P.A. 46 Sommariva, A. 222 Sonnenschein, H., see Hildenbrand, W. 535, 537 Sorger, G., see Hommes, C.H. 529, 532 Souleles, N., see Jappelli, T. 790 Spear, S.E. 465 Spear, S.E., see Marimon, R. 455, 5 3 1 Spiegel, M.M., see Benhabib, J . 283 Spilerman, S . , see Singer, B. 292 Spulber, D., see Caplin, A.S. 80 1 , 1 03 1 , 1 03 2 Spynnewin, F. 803 Srba, F., see Davidson, J. 750 Srinivasan, T.N. 705 Stacchetti, E., see Jones, L.E. 720 Stafford, F., see Holbrook, R. 569 Stafford, F. , see Ryder, H. 587 Staiger, D. 49, 50 Staiger, R. 1 4 1 5 Staiger, R. W., see Bagwell, K . 1 1 25 Stambaugh, R.F., see French, K. 1 280 Stambaugh, R.F., see Kandel, S. 1 235, 1 252, 1 253, 1 265, 1 270, 1 272 Stark, T., see Croushorc, D. 1 485 Starr, R.M., see Chah, E.Y 775 Stmiz, R., see Nelson, C.R. 1 264 Stahnan, M., see Shefrin, H. 1 3 1 3, 1 3 1 7 , 1 33 0 Stedinger, J.R., see Johnson, S . A . 345, 3 8 1 Stein, J.C . , see Kashyap, A.K. 1 3 7 , 8 8 1 , 9 1 2, 1 344, 1 3 74, 1 376 Stengel, R.F. 904

1-27 Stephen, P, see Ryder, H. 587 Sterling, A., see Modigliani, F. 1 656, 1 657 Stigler, G. 1 0 1 8 Stigler, G.J. 1 1 73 Stigler, S.M. 275 Stiglitz, J., see Dixit, A. 1 1 1 5 , 1 1 2 1 , 1 1 26 Stiglitz, J., see Greenwald, B. 857, 1 1 22, 1 37 7 Stiglitz, J., see Jaffee, D.M. 1 376 Stiglitz, J.E. 1 675, 1 696, 1 7 1 8 Stiglitz, J.E., see Atkinson, A.B. 1 673, 1 676, 1 680, 1 682, 1 7 1 8 Stiglitz, J.E., see Shapiro, C . 1 1 5 7 Stock, J.H. 9, 1 1 , 39, 43, 45, 5 0-54, 821 , 878, 9 1 9, 934, 938, 939, 1 0 1 1 , 1 02 1 , 1404, 1 674 Stock, J.H., see Feldstein, M. 44, 1485, 1497, 1 498 Stock, J.H., see King, R.G. 54, 94 1 Stock, J.H., see Staiger, D. 49, 50 Stockman, A. 1 57 8 Stockman, A . C . 549 Stockman, A.C., see Baxter, M. 203, 938, 1 404 Stockman, A.C., see Darby, M.R. 1 66 Stockman, A.C., see Gavin, W. 1 485 Stockman, A.C., see Ohanian, L.E. 1 036 Stocks, Bonds, Bills and Inflation 1 639 Stockton, D.J., see Lebow, D.E. 2 1 5, 1 0 16 Stoer, J. 334 Stoker, T., see Blundell, R. 770, 788 Stokey, N., see Alvarez, F. 996 Stokey, N . , see Lucas Jr, R.E. 559, 5 6 1 Stokey, N . , see Milgrom, P 1 322 Stokey, N.L. 27 1 , 299, 3 14, 3 1 8-32 1 , 346, 578, 5 83 , 672, 705, 709, 7 1 1 , 7 1 4, 95 1 , 954, 998, 999, 1 674 Stokey, N.L., see Lucas, R.E. 380, 1 446, 1 449 Stokey, N.L., see Lucas Jr, R.E. 1 5 8 , 1 673, 1 675, 1 699, 1 723, 1 728 Stone, C.J., see Breiman, L . 289 Strang, G. 82 Strongin, S. 83-!lS, 87, 1 1 4 Strotz, R.H. 1 653 Strotz, R. H. , see Eisner, R. 1 3 1 0 Stroud, A.H. 334 Stuart, A. 1 485 Stulz, R.M. 1 3 1 7 Sturzeneggcr, F., see Dombu�ch, R . l 543 Sturzenegger, F., see Guo, J.-T. 427 Sturzenegger, F., see Mondino, G. 1 540

Author index

I-28 Suarez, J. 1 378 Subrahmanyam, A., see Daniel, K. 1 322 Sugden, R., see Loomes, G. 1 3 1 3 Suits, D., see Kallick, M . 1 32 5 Summers, L . H . 96 1 Summers, L.H., see Abel, A.B. 1 266, 1 65 1 Summers, L.H., see Alesina, A. 1432 Summers, L.H., see Bernheim, B.D. 1 646 Summers, L.H., see Blanchard, O.J. 4 1 6, 1 63 5 Summers, L.H., see Carroll, C.D. 759, 793, 1 65 5 Summers, L.l-1., see Clark, K . B . 602, 1 1 73 Summers, L.H., see Cutler, D.M. 1 290, 1 3 20, 1321 Summers, L.H., see DeLong, J.B. 279, 695, 1 042, 1 290, 1 324 Summers, L.H., see Easterly, W. 277, 278, 2 8 1 , 675 Summers, L.H., see Kotlikoff, L.J. 780, 1 646 Summers, L.H., see Mankiw, N.G. 785 Summers, L.H., see Poterba, J.M. 1 235, 1 320, 1 648 Srunmers, R. 238, 30 1 , 640, 673-675, 677, 680, 6 8 1 , 689, 720 Sun, T. 1 270 Sundaram, R. K., see Dutta, P. K. 3 80 Sundaresan, S .M . 1 284 Sunder, S . , see Marimon, R. 455, 472, 5 3 1 Surekha, K . 908 Sussman, 0., see Suarez, J. 1 378 Svensson, J. 1 466, 1 47 1 , 1 472 Svensson, L.E.O. 1 56, 1 97, 4 1 7, 1 033, 1 034, 1 273, 1 4 1 1 , 1432, 1 434, 1 489, 1 493, 1 494, 1 498, 1 504 Svensson, L.E.O., see Englund, P. 9 Svensson, L.E.O., see Kotlikoff, L. 1 448, 1 449, 1 465 Svensson, L.E.O., see Leiderman, L. 1432, 1 43 8, 1495 Svensson, L.E.O., see Persson, M. 1447, 1 449 Svensson, L.E.O., see Persson, T. 1 449, 1450, 1 454, 1 456, 1465 Swagel, P. , see Alesina, A. 277-279, 1 460, 1 466, 1 47 1 Swan, T.W. 244, 246, 247, 643 Sweeney, J., see Kneese, A. 656 Swoboda, A., see Genberg, H. 1 65 Symansky, S.A., see Bryant, R.C. 1 49 1 , 1 497, 1516 Szafarz, A., see Adam, M. 500

Szafarz, A , see Broze, L.

487, 488

Tabcllini, G. 1 4 1 4, 1 4 1 5, 1450, 1456, 1 464, 1 465 Tabellini, G., see Alesina, A. 1 446, 1 449, 1 450, 1 454, 1465, 1 5 1 8, 1 522 Tabellini, G., see Cukierman, A. 1 456, 1 465 Tabcllini, G., see Daveri, F. 1 220 Tabellini, G., see Edwards, S. 1 5 3 8 Tabellini, G., see Grilli, V 1 404, 1 432, 1 438, 1 439, 1 465 Tabellini, G., see Ozier, S . 1 457, 1 465 Tabellini, G., see Persson, T. 278, 692, 1 400, 1 403, 1 4 1 3 , 1 4 1 5- 1 4 1 8, 1 420, 1 42 1 , 1 425, 1 433, 1 435, 1 43 7 - 1 440, 1442, 1 445, 1448, 1 449, 1459, 1460, 1466, 1469, 1 470, 1 490 Taber, C., see Heckman, J.J. 576, 578, 582, 584, 586, 587, 590, 592, 593 Taguas, D., see Blanchard, O.J. 1 2 1 4 Tallarini Jr, T.D., see Hansen, L.P. 558, 1 294, 1 295 Tallman, E.W., see Rosensweig, J.A. 1 659 Talvi, E. 1 543, 1 57 1 , 1 604 Tan, K.S. 334 Tanner, S., see Banks, J. 758, 792 Tanzi, V 1 74 1 Tarshis, L . 939, 1 059 Tauchen, G. 367 Taylor, A., see Obstfeld, M. 1 64, 1 65 Taylor, C. 1 330 Taylor, J.B. 46, 1 82, 3 1 4, 397, 408, 4 1 7, 422, 454, 474, 487, 489, 495, 545, 1 0 1 1 , 1 0 1 3, 1 0 1 5, 1 0 1 7, 1 025, 1 027-103 1 , 1 037-1 039, 1 042, 1 043, 1 1 1 3, 1 3 64, 141 1 , 1 485, 1 487, 1 488, 1 490, 1 497, 1 505, 1 507, 1 5 1 2, 1 5 1 3 , 1 5 1 6, 1 5 1 8, 1 542, 1 582 Taylor, J.B., see Phelps, E . 1025, 1 02 6 Taylor, L.D., see Houthakkcr, H . S . 803 Taylor, S.E. 1 330 Tejada-Guibert, J.A., see Johnson, S.A. 345, 381 Teles, P. , see Correia, I . 1 537, 1 675, 1 720, 1 733 Tc lme r, C.!., see Backus, D.K. 1 3 1 6 Temin, P. 1 62, 179, 1 80, 1 83, 1 84 Temp le, J. 276 Terlizzese, D., see Guiso, L. 772 Tema, P., see Bellratti, A. 524, 525 Terrones, M. 1 425 Teruyama, H., see Fukuda, S.-i. 875 Tesar, L., see Mendoza, E. 1439

Author

I-29

Index

see Stockman, A.C. 549 see Fillion, J.F. 1 498 Teukolsk:y, S.A., see Press, W.H. 329-334, 343 ,

Tesar, L.,

Tetlow, R.,

Thaler, R.,

Thaler, R.H.,

see

Benartzi, S.

see

De Bondt, W.F.

1 290, 1 3 1 2, 1 307, 1 320,

see R.H., see

Shefrin, H.

Siegel, J.J.

Theunissen, A.J.,

see

1 083, 1 1 22

Brayton, F.

1 043, 1 344, 1 485

103 1

Tsiddon, D.

see Lach, S. 1 0 1 9 see Chow, C.-S. 326, 334 Y., see Shiller, R.J. 1 3 1 6

Tsutsui,

see

Thomas, J.K . ,

see

1 508

Whittaker, J.

Bernard, V.L.

1321

161

Thomas, T.J.

see Taylor, S.E. 1 330 see Carlson, J.B. 1 04

Thompson, S . C. , Thomson, J.B., Thornton, H. Thurow, L.

1485 759

Tieslau, M. A. ,

see

Tillmann, G .

474

Hoftinan, D. L .

Timberlake, R.H. Timmermann, A.G.

412

1 69, 1 74 454, 455, 500, 530

817 1 266, 1 650

Tinbcrgen, J.

see Fudenberg, D. 1 1 5 5 Tirole, J . , see Holmstrom, B. 1 376 Titman, S., see Jegadeesh, N. 1321 Tiro1e, J.,

7 7 3 , 8 1 7, 8 1 8, 1 643

see Brainard, WC. 8 1 7 see Eichengreen, B . 1 68 Todd, P., see Heckman, J.J. 578, 582 Todd, R., see Christiano, L.J. 1 365 Toharia, D., see Blanchard, O.J. 1214 Tobin, J.,

Tobin, J.,

1 74, 1 77, 1 87, 1 90 Goff, B.L. 1 59 Tommasi, M. 1 540 Tonunasi, M., see .Iones, M. 1 540 Tomrnasi, M., see Mondino, G. 1 540 Topel, R. 578 Topel, R., see .luhn, C. 6 1 9 Topel, R., see Murphy, K . 5 8 1 Tornell, A. 1466, 1 472, 1 590 Torncll, A., see Lane, P. 1 472 1 5 90, 1 5 9 1 Tornell, A. , see Sachs, J. Townsend, R.M. 453, 46 1 , 474, 529, 795, 796, 1 350, 1 37 6 Toma, M .

see

156

Tullio, G .

994

Thomas, J.

Toma, M. ,

Felli, E .

Tsitsiklis, J.N.,

1317 1 3 12

1238, 1 632

The Economist

Tobin, .1.

334

Tsiddon, D.,

1 323

Tirole, J.

A.

159

1 57, 1 65 Trostel, P.A. 1 652 Tryon, R.,

Thaler, R.H., Thaler,

see Papageorgiou,

see

Tria, G . ,

1313 Thaler, R.H.,

380, 575,

Triffin, R.

1313, 1317

Thaler, R.H.

Phelan, C .

338

Traub, J.F. Trchan, B.

see Froot, K. 1 3 1 6 see Lee, C . 1 324

see

796 Traub, J.F.,

348, 356, 365 Thaler, R.,

Townsend, R.M.,

see Sommariva, A. 222 Tullock, G., see Grier, K.B. 253 Tuncer, B . , see Krueger, A.O. 699

Tullio, G . ,

474 1 308, 1 3 1 5, 1 3 1 9, 1 324, 1 330 Tversk:y, A., see Kahneman, D. 1 308, 1 309, 131 1 Tversk:y, A., see Quattrone, G.A. 1 329 Tversky, A., see Shafir, E . 1 3 1 6, 1 324, 1 329 Tversky, A., see Thaler, R.H. 1313 Tybout, J., see Corbo, V 1 543 Tylor, E.B. 1331 Turnovsky, S.

Tversk:y, A.

Uhlig,

H.

Uhlig, H . , Uhlig, H.,

70

see Lettau, see Taylor,

524, 1 297 314

681

United Nations

see

M. J.B.

564 1 539, 1 578, 1 589 Uribe, M., see Benhabib, J. 4 1 9, 42 1 , 423 Uribe, M., see Mendoza, E. 1 5 7 1 , 1 579 Uribe, M., see Schmitt-Grohe, S . 4 1 6, 4 1 8 , 43 1 US Bureau of the Census 585 Uzawa, H. 578, 65 1 , 7 1 0 Uppal, R.,

Dumas, B.

Uribe, M.

R., see Dornbusch, R. 1 590 V., see Clu·istiano, L.J. 504 Van Huyck, J.B., see Grossman, I-I.J. 1 5 8, 1 4 1 5 ,

Valdes,

Valdivia,

1 449

see Beaudry, P 1 264 see Lettau, M . 470, 472

van Wincoop, E., Van Zandt, T., Vasicek, 0.

see

1 270

Guidotti, P.E. 1 675, 1 720 1 535, 1 53 8, 1 542, 1 543, 1 546, 1 550, 1 554, 1 5 8 8 158 Vegh, C . A . , see Bordo, M.D.

Vegh, C . ,

Vegh, C.A.

Author Index

1-30

see Calvo, GA 1 428, 1 535, 1 538, 1 539, 1 546, 1 554, 1 557, 1 563, 1 564, 1 568, 1 5 7 1 , 1 572, 1 5 82, 1 587-1589, 1 597, 1 605 Vegh, C.A., see De Gregorio, J. 1 546, 1 5 5 1 , 1 573, 1 575, 1 577 Vegh, C.A., see Edwards, S . 1 578-1580 Vegh, C.A., see Fischer, S . 1 538, 1 547, 1 5 6 1 Vegh, C.A., see Guidotti, P.E . 1 537, 1 5 88, 1 603 Vegh, CA, see Hoffinaister, A. 1 56 1 , 1 589 Vegh, C.A., see Lahiri, A. 1 597 Vegh, C.A., see Rebelo, S .T. 1 546, 1 568, 1 5 78, 1 5 79, 1 5 8 1 , 1 606 Vegh, C.A., see Reinhart, C.M. 1 545, 1 546, 1 55 1 , 1 553, 1 56 1 , 1 5 72, 1 573 1 53 5 Vegh, C.A., see Sahay, R. Vela, A . , see Santaella, J. 1 543 Velasco, A. 4 1 6, 1 446, 1 449, 1450, 1459, 1 465, 1 540 Velasco, A., see Sachs, J. ! 590, 1 5 9 1 Velasco, A., see Tommasi, M . 1 540 Velasco, A., see Tornell, A. 1 466, 1 472, 1 590 Venable, R., see Levy, D. 1 0 1 4, 1 0 1 5, 1 0 1 9 Venegas-Martinez, F. 1571 Ventnra, G., see Huggett, M . 380 Veracierto, M. 994 Verdier, T., see Saint-Paul, G. 1 472 Vetterling, W.T., see Press, W.H. 329-334, 343, 348, 356, 365 Viana, L. 1 543 Vickers, J. 1 4 1 4, 1 4 1 5 Vigo, J., see Santos, M.S. 3 2 1 , 322, 326, 327, 335 Vinals, J., see Goodha1i, C. EA 1 438, 1 495 1 294, 1 322 Vishny, R.W., see Barberis, N. Vishny, R.W., see La Porta, R. 1 240 1 323 Vishny, R.W., see Lakonishok, J. Vishny, R.W., see Murphy, K.M. 262, 278, 1 082 Vishny, R.W., see Shleifer, A. 1 324 Visscher, M., see Prescott, E.C. 700 Vives, X. 474, 532 Vives, X., see Jun, B. 474 Volcker, P.A. 1 630 von Furstenberg, G.M. 1333 von Hagen, J. 1 439, 1460, 1 465 von Hagen, J., see Eichengreen, B. 1 465 von Hagen, J., see Fratianni, M. 1431 von Hagen, J . , see Hallerberg, M. 1 460, 1 465 von Weizsiicker, C. 64 1 , 650, 657 Vredin, A.E., see Bergstrom, V 538 Vegh, CA,

Vuong, Q.H.,

see

Wachtel, P.

1 65 8

Rivers, D.

840

see Evans, M. 1 82 1 33 3 Wachter, S.M., see Goetzmann, WN. Wadhwani, S . , see King, M. 1 33 3 Wagner, R.E., see Buchanan, J.M. 1631 Waldmann, R.J., see DeLong, J.B. 1 290, 1 324 Walk, H . , see Ljung, L. 476 Walker, M., see Moreno, D. 481 Wallace, N., see Sargent, T.J. 4 1 7, 4 1 8 , 489, Wachtel, P.,

1 024, 1 506, 1 507, 1 5 1 9, 1 630 1 43 1 Waller, C., see Fratianni, M. 1 43 1 Wallis, K., see Kreps, D.M. 540 Walsh, C.E. 1433, 1 434, 1 437, 1 438, 1490 Walsh, C.E., see Trehan, B. 159 143 1 Walsh, C.E., see Waller, C . Wang, F.A. 1 322 Wang, J. 1 237, 1 293 Wang, L. -T., see Dezhbakhsh, H . 1 039 Wang, T., see Dumas, B. 564 Warner, A.M., see Sachs, J.D. 252, 703 Wamer, E.J. 1019 Wascher, W. , see Lebow, D.E. 1016 Watson, J., see den Haan, W.J. 994, 1 1 66, 1 1 94, 1 203, 1 204, 1 206, 1 207 Watson, J., see Ramey, G . 852, 1 1 57, 1 1 59 Watson, M . W 6, 50, 547, 93 1 144 Watson, M.W, see Bernankc, B.S. 1 266 Watson, M.W, see Blanchard, OJ. Watson, M.W., see Canjels, E. 55 Watson, M . W., see King, R.G. 46, 54, 939, 941 Watson, M.W., see Staiger, D. 49, 5 0 Watson, M . W , see Stock, J.H. 9, 43, 45, 50--52, 82 1 , 878, 9 1 9, 934, 938, 939, 1 0 1 1 , 1 0 2 1 , 1 404, 1 674 Webb, S., see Goodman, A 797 Webber, A., see Capie, F. 222 Weber, G. 774 Weber, G., see Alessie, R. 774, 775 Weber, G., see Attanasio, O.P. 6 1 1-6 1 3 , 756, 769, 7 8 1 , 783, 784, 787, 790, 7 9 1 , 793, 794, 1 264, 1 65 5 Weber, G . , see Blnndcll, R . 7 8 1 Weber, G . , see Brugiavini, A. 775 Weber, G., see Meghir, C. 61 1 , 6 1 3, 775, 804 Weber, M. l33l Weder, M . 403, 437 Wehrs, W , see Carlson, J.A. 904 Waller, C .

Author Index Weibull, J., see Lindbeck, A. 1465 Wei!, D.N., see Mankiw, N.G. 1 73 , 2 1 6, 244246, 252-255, 269-2 7 1 , 277-279, 289, 653, 655, 660, 673, 679-683, 685, 686, 1 63 8 Wei!, P. 547, 1 235, 1 250, 1 253, 1 256, 1 647 Wei!, P., see Blanchard, O.J. 1 650 Wei!, P., see Restoy, F. 1 272 Weingast, B., see North, D. 1 449 Weinstein, M.M. 1 82 Weisbrod, S.R., see Rojas-Suarez, L. 1 57 5 Weiss, A . , see Greenwald, B. 1 1 22 Weiss, L., see Scheinkman, J.A. 566 Weiss, Y. 583 Weiss, Y. , see Blinder, A. 587 Weiss, Y., see Lillard, L. 569, 572 Weiss, Y., see Sheshinski, E. 1 03 1 , 1 03 7 Weitzman, M . L . 1 689 Welch, F. 579 Welch, I., see Bikhchandani, S . 1 332 Wen, I.E , see Devereux, M. 1 466, 1 47 1 Wen, L. 427, 43 1 Wenzelburgcr, J., see Biihm, V 475 Werner, A., see Dornbusch, R. 1 543, 1 563, 1 568 West, K.D. 87 I , 876, 880, 882, 885, 887, 888, 894, 896, 897, 900, 902, 905-908, 913, 9 1 9, 1 028, 1 04 1 , 1 320, 1 497 Whalley, J. 705 Whalley, J., see Ballard, C . 1 639 Whalley, J., see Shoven, .l.B. 705, 708 Whalley, J., see Srinivasan, TN. 705 Wheatley, S. 1 242, 1 2 6 1 Wheelock, D.C. 1 77, 1 79 Wheelock, D.C., see Calomiris, C.W 1 87, 191 Whinston, M.D., see Segal, LB. 1 1 57 White, E., see Bordo, M.D. 1 59 White, E.N. 1 80 White, H. 524 White, H., see Chen, X. 476, 532 White, H., see Kuan, C.-M. 476 Whited, T. 1 344 Whited, T., see Hubbard, R.G. 1 344 Whiteman, C. 487 Whitt, W 326 Whittaker, .1. 1 508 Wickens, M.R., see Robinson, D. 2 1 7 Wicker, E . 1 62, 1 76, 1 77, 1 79-1 8 1 , 1 543 Wickscll, K. 203, 1485, 1 63 1 Wieland, V , see Orphanides, A. 1 485 Wigmore, B.A. 1 63 , 1 83

I-3 1 Wilcox, D. 1 242 Wilcox, D., see Kusko, A.L. 1 3 27 Wilcox, D.W 1 65 5 Wilcox, D.W, see Carroll, C.D. 769, 785 Wilcox, D. W , see Cecchetti, S.G. 876 Wilcox, D. W , see Kashyap, A.K. 1 3 7, 877, 886, 903, 906, 9 1 2 Wilcox, D. W , see Orphanides, A . 1 98, 1 485 Wilcox, D.W, see West, K.D. 908 Wildasin, D., see Boadway, R. 1 463 Wilkinson, M . 8 8 1 Williams, J.C., see Brayton, F. 1 043, 1 344, 1 485 Williams, J.C., see Gilchrist, S. 847 Williams, J.C., see Wright, B.D. 347, 348 Williamson, J. 1 597 Williamson, O.E. 852 Williamson, S. 1 3 7 6 Willis, R . , see Heckman, J.J. 602, 623 Wilson, B., see Saunders, A. 1 8 1 Wilson, C.A. 408 Wilson, R. 554, 796 Winter, S.G., see Phelps, E.S. 1 1 2 1 Woglom, G. 1 1 2 7 Wohar, M.E., see Fishe, R.P.H. 1 73 Wojnilower, A. 1 344 Wolf, H., see Dornbusch, R. 1 543 Wolf, H., see Ghosh, A.R. 202, 207, 208 Wolff, E . 664 Wolfowitz, J., see Kiefer, J. 476 Wolinsky, A. 1 1 88 Wolinsky, A., see Binmore, K .G . 1 1 8 8 Wolinsky, A., see Rubinstein, A. 1 1 88 Wolman, A.L., see Dotsey, M. 974, 1 032, 1 043 Wolman, A.L., see King, R.G. 1 036, 1 04 1 , 1 043, 1 3 64, 1 367 Wolters, J., see Tullio, G. 1 5 6 Wong, K . -E 1 08 Wood, G.E., see Capie, F. 1 63 , 1 43 8 Wood, G . E . , see Mills, T.C. 204 Woodford, M. 389, 395, 406, 407, 409, 4 1 8, 421-423 , 439, 454, 473-476, 48 1 , 483, 507, 5 1 6, 5 1 8, 52 1 , 662, 1 036, 1 1 57, 1 507, 1 509, 1 5 1 8- 1 520, 1 537, 1 630, 1 675, 1 676, 1 720, 1 73 1 Woodford, M . , see Bernanke, B.S. 1 3 6 1 , 1 3 63 Woodford, M., see Boldrin, M. 506 Woodford, M., see Farmer, R.E. 395, 396 Woodford, M . , see Guesnerie, R. 439, 454, 460, 465, 474, 475, 506, 5 1 1 , 5 1 6, 526

l-32

Author Index

Woodford, M., see Kehoe, T.J. 380 Woodford, M., see Lucas Jr, R.E. 1 023 Woodford, M., see Rotemberg, J.J. 67, 68, 395, 406, 407, 429, 434, 974, 996, 1 020, 1 04 1 , 1 043, 1 044, 1 05 5 , 1 056, 1 062, 1 063, 1 067-1069, 1 074, 1 08 1 , 1 082, 1 088-1 090, 1 092, 1 093, 1 1 06, 1 1 07, 1 1 1 8, 1 1 23-1 1 25, 1 1 29, 1 1 43 , 1 1 44, 1 365, 1 492, 1 494, 1 497 Woodford, M . , see Santos, M.S. 1 266 Woodward, P.A., see Baker, J.B. 1 1 25 Wooldridge, J., see Bollerslev, T. 1 280 Wozniakowski, H. , see Traub, J.F. 338 Wright, B.D. 347, 348 Wright, M.H., see Gill, P.E. 329 Wright, R. 1 1 58 Wright, R., see Benhabib, J. 402, 550, 1 1 45 Wright, R., see Boldrin, M. 399 Wright, R., see Burdett, K. 1 1 96 Wright, R., see Greenwood, J. 550, 995 Wright, R., see Hansen, G.D. 976 Wright, R., see Kiyotaki, N. 524 Wright, R., see Parente, S.L. 702 Wright, R., see Rogerson, R. 978 Wurzel, E., see Roseveare, D. 1 626 Wynne, M. 974 Wynne, M.A., see Huffman, G.W 437 Wyplosz, C., see Eichengreen, B . 1 68, 1 590 Xie, D. Xie, D., Xie, D., Xu, Y

425

see Benhabib, J. see Rebelo, S.T.

425 952

344

Yashiv, E. 1 200 Yellen, J.L., see Akerlof, G.A. 397, 1 034, 1 035, 1 039, 1 1 57, 1 200 Yeo, S., see Davidson, J. 750 Yi, K.-M., see Kocherlakota, N . R. 2 7 1 Yin, G . G . , see Kushner, H . .T. 476 Yong, W, see Bertocchi, G. 474 Yorukoglu, M., see Cooley, T.F. 847

Yorukoglu, M., see Greenwood, J. 576 Yotsuzuka, T. 1 649 Young, A. 664, 672, 673, 687, 7 1 6 Young, J., see Wachtel, P. 1 658 Yu, B., see Hashimoto, M. 1 1 52 Yun, T. 1026, 1 036

Zarazaga, C.E. 1 540 Zarazaga, C.E., see Kyd1and, F.E. 1 557, 1 56 1 Zamowitz, V 9, 40 Zcckhauser, R., see Degeorge, F. 1 32 1 Zeckhauser, R.J., see Abel, A.B. 1 266, 1 65 1 Zeira, J., see Galor, 0. 262, 263 Zejan, M., see Blomstrom, M. 277, 279, 280 Zeldes, S.P. 566, 607-609, 7 7 1 , 789, 790, 802, 1 344, 1 655 Zeldes, S.P., see Barsky, R.B. 1 653 Zeldes, S.P. , see Hubbard, R.G. 567, 569, 572, 573, 593, 77 1 , 776, 794, 797 Ze1des, S.P., see Mankiw, N.G. 790, 1 290 Ze1des, S.P., see Miron, J.A. 876, 907 Zeldes, S.P., see O 'Connell, S.A. 1 65 0 Zellner, A. 3 4 Zenner, M. 497 Zha, T., see Cushman, D.O. 95, 96 Zha, T., see Leeper, E.M. 69, 74, 83, 93, 1 0 1 , 1 28, 1 32, 1 34, 1 089, 1 369 Zha, T. , see Sims, C.A. 69, 83, 93, 99, 1 28, 1 29, 1 3 1 , 1 32, 134, 1 44 Zhang, L . , see Lockwood, B. 1 4 1 1 , 1 4 1 5 Zhou, Z., see Grossman, S.J. 1 237, 1 293 Zhu, X. 1 708 Zilcha, I., see Becker, R. 369 Zilibotti, F., see Gali, J. 405, 426 Zilibotti, F., see Marimon, R. 1 2 1 4 Zin, S.E., see Epstein, L.G. 556, 558, 564, 744, 769, 1 250, 1256 Zingales, L., see Kaplan, S.N. 856, 1 3 44

SUBJECT INDEX

accelerator 884, 890, 896, 909 accelerator model 8 1 6, 8 1 7 accelerator motive 8 67 , 902 activist vs. non-activist policies 1485 actual law of motion (ALM) 466, 472, 490,

asset-price chmmel 1 3 78 asset prices, variable 1 356 asset pricing models with feedback 500 asset pricing with risk neutrality 498 associated differential equation 5 1 9 asymmetric fixed costs 825 asymmetry in adjustment of employment

511 adaptive expectations 453, 465 adaptive learning 464, 472, 493, 5 1 0 stability under 47 1 adaptively rational expectations equilibrium

1 1 58 asymptotic stability 479, 639 autarky 853 automatic stabilizers 1 660 average cohort techniques 787

532 adjustment costs 800, I 072 employment 1075 hours 1 075 in investment 1 296 non-convex 82 1 , 839 production 867, 892, 893, 900 hazard 835, 836, 840 speed of 881 , 889, 908 age distribution 753, 848 aggregate convexity 843 aggregate demand 1 6 1 7 , 1 628, 1 630 aggregate human capital 583, 590-593 aggregate productivity 1 1 95 aggregate productivity shock 1 204 heterogeneous 1 2 1 4 aggregate shocks 578, 582, 865 aggregation 548-594, 604, 605, 61 4, 6 1 5 , 745,

backlog costs 884 backstop technology 656 balance-of-payments (BOP) crises

balanced-budget rule 1 63 1 balanced growth path 50, 392, 393, 424, 425,

427

band-pass filter, see B P filter bank lending channel 1 376 Barro, R. 1 640, 1 642-1 646 Bayesian learning 474 Bayesim1 updating 461 , 465 Belgium 1 6 1 9 Bellman's Principle o f Optimality 998 bequest motive 745, 780, 1 624, 1 646,

1 647

78 1 , 804, 836, 849, 9 1 0

strategic 1 646 best practice 848 {3-convergence 659 Beveridge curve 1 1 94, 1 1 96, 1 22 1 , 1222 bilateral bargaining problem 1 1 57 black market premium 67 1 , 688, 689, 691-694,

across commodities 782 AK model 672, 673, 709-7 1 5 , 720, 733 allocation rules 1 688, 1 723 alternative dating 499 amplification 841 , 1 145, 1 1 5 8, 1 1 59, 1 1 6 1 anchoring 1 3 14-1 3 1 7, 1 3 22 animal spirits 395, 5 1 7, 5 2 1 , 941 anomalies 1 307, 1 308, 1 3 1 6, 1 3 1 7, 1 3 2 1 , 1 3 22,

703

1 333, 1 334 approximation error 326-345, 3 5 1-382 arbitrage 1 246 ARMA models 489, 496, 501 Arrow-Debrcu equilib1ium 795

1 5 34, 1 535,

1 55 3

l-33

Blanchard-Kahn technique 505 Bolivia 1 63 1 boom-recession cycle 1 550, 1 552, 1 58 1 bootstrap methodology 79 BOP clises, see balance-of-payments crises borrowers' net worth 1 345

I-34

Subject Index

566, 575, 593, 595, 597, 598, 772, 775, 1 293 see also capital market imperfections;

borrowing constraint

credit market imperfections; liquidity constraints

1 39-142 842, 843 bounded rationality 454, 464 BP (band-pass) filter 1 2, 933, 934 Bretton Woods 1 52, 1 53, 1 63-1 68, 1 88, 1 90, 1 92, 1 99, 202-204, 206-209, 2 1 1 , 2 1 3, 2 1 5 , 2 1 8-220 Brownian motion 825, 845 regulated 845 bubble-free solution 1 524 bubble solutions 1 522 bubbles 499 explosive 499 budget deficit 1 6 1 9 budget surplus 1619 buffer-stock saving 77 1 , 1 653, 1 654 building permits 45 Boschen-Mills index

bottlenecks

Bums-Mitchell business cycle measurement

932

imperfections

business cycles

1 659 see also

865, 927-1002, 1 620, 1 62 1 ,

cycles; fluctuations in aggregate

934, 938, 939, 956 67 in RBC model 968 measuring 932 persistence of 939 table of summary statistics 956, 957 U S facts 934 USA 935 -938, 956

facts about

general equilibrium models

497 462 545, 550, 567, 601 , 6 14, 6 1 6

Cagan model of infia!ton calculation equilibrium calibration

45

capacity utilization modeling of rate of

4 1 , 427, 43 1 , 930

980

98 1

984 1 61 7 , 1 687 broad measure 70 I desired 8 1 6, 842 frictionless 832, 838 htunan 673, 678, 679, 68 1 --687, 701 , 7 1 0, 7 1 3 , 7 1 4, 7 1 6--7 1 8, 720, 732, 734 steady-state rate of

capital

1 6 6 1 , 1 708 1 693 capital utilization 848 CARA utility 794 capital taxation

optimality of zero

activity

Canada

see also human capital 700, 701 physical 678-683, 701 , 7 1 0, 7 1 3 , 7 1 4, 721 , 732 specific 1 1 54 stock of 1 629, 1 630, 1 632, 1 633, 1 636- 1 638, 1 648, 1 652, 1 656 target 820 uruneasurcd 70 1, 702 vintage 702 capital accumulation 942, 1 203 general equilibrium nature of 946 optimal 946 perpetual inventory method 944 capital budgeting 1 623 capital controls 1588 capital imbalances, establislnnents' 83 7 capital intensities 641 , 644, 679, 680, 682, 685, 686 capital investment decision 1 349 capital/labor substitution 856 capital market imperfections 1 648, 1 649 see also borrowing constraint; credit market organizational

397, 1 722 1 720, 1721 "catching up with the Jonescs" 1 284 certainty equivalence 762 Charnley result 1 698 characteristics model 578, 579, 582, 602 characterization of equilibria 487, 489 Cholesky factor 80 classification 262, 289, 303 classifier systems 465, 523 closed economy 1 7 1 4 closed-forn1 solution 769 club-convergence 660 cash-in-advance constraint cash--credit model

Cobb-Douglas production function in RBC model

944, 950 456

"cobweb" model

1 249 781 cohort effects 576, 577, 590-592, 6 1 7, 753, 754 cointegration 50, 750, 820, 838, 877-8 8 1 , 885-887, 903, 1 266 collateral 857 coefficient of relative risk aversion cohort data

Subject index commitment 574, 575, 1 488, 1 523 technology 1 688, 1 723 vs. flexibility 1 489 commodity space 1 686 comparative advantage 547, 548, 577-579,

584, 587 comparative dynamics measured by impulse response 967, 968, 970 competitive equilibrium 844, 845, 1 677, 1 688,

1 722 competitive trajectory 650 complementarity 1 1 6 1 complements 599, 601 , 6 1 1 -6 1 3, 855 complete markets 553, 558, 563, 595, 602,

786, 1 688 computation o f (approximate) solutions 525 computational general equilibrium (CGE) 705,

708 computational intelligence 465 computational tool 455 conditionally linear dynamics 475, 481 conditioning 556, 594, 597-599, 60 1 , 605, 6 1 2,

613 consistent expectations equilibria 529 constant returns to scale 639, 83 1 , 1 687 in RBC model production function 995 consumer expectations 45 consumer theory 603 consumer's budget constraint 1 264, 1 7 12,

1 728 40, 545, 546, 548-558, 560-564, 566, 567, 572-576, 5 87, 590, 594-603, 605-61 4, 6 1 6, 62 1 , 1 276 behavior in US business cycles 938 empirical 1 344 estimates 605-6 1 4 'excess' sensitivity 524 growth 1 233, 1 242, 1 276 inequality in 797 permanent-income hypothesis 943 private 1 687 procyclical 433 -435 smoothing 805 in RB C model 967 time-averaged data 1 242 consumption-based asset pricing 1249 consumption expenditure 745 Consumption Expenditure Survey (CEX) 750 consumption per capita 643 consumption taxes 1 692 contract multiplier 1 028 consumption

1-35 contractual problems 849 control rights 852 control variables 688, 689 convergence 240, 245-276, 284-288, 290, 295,

296, 659 global 486 local 5 1 9 probability o f 480 speed of 5 3 1 , 659 convergence analysis 454, 477-479 convertibility 1 53, 1 60 convertibility rules 209, 2 1 3 convex adjustment costs 8 1 8, 823 coordination failures 461 coordination o f beliefs 3 9 1 corner solutions 804 cost of capital 8 17, 1 3 44 cost shifters 906, 9 1 2 cost shock 867, 884, 899, 907, 908, 9 1 2 Costa Rican tariff reform 707 costly state verification 1 349 creative dcstmction 848, 1 2 10, 1 2 1 3 credibility 1 536, 1 603 credit chains 1 378 credit constraints 856 credit market 847 imperfections 1 343 see also borrowing constraint; capital market imperfections segmentation 1 575, 1 577 cross-country regression 276, 28 1 cross-section least-squares regression 269 cross-sectional density 840 of establishments' capital imbalances 837 cross-sectional growth regression 252, 269-

273, 275, 276, 284-289, 67 1 , 675, 694 literature 688 crossover 522 crowding out 1 632, 1 633, 1 636, 1638, 1 648,

1 652, 1 654 currency crises 15 34 current account deficit 1 598 Current Population Survey 796 curse of dimensionality 843, 847 customer markets 1 1 20 cycles 460, 507, 509, 526, 865 deadweight loss

1 63 1 , 1 632, 1 639, 1 640,

1 662 debt contract 1350 debt-deflation 1 372

Subject Index

I-36 debt neutrality 1644 debt-income ratio 1 630 debt-output ratio 1 6 1 9 decentralized economy 547, 575, 576, 602 decision rule 888-890 deficits 1 6 1 7 nominal 1621 real 1 62 1 demand shocks 865, 884, 889-892, 895, 898,

105 5 demographic transition 658 demographic variables 793 demographics 547, 55 1-6 1 5, 744 and retirement behavior 758 depreciation 642, 1 633 detrending and business cycle measurement

932 difference models of habit 1284 difference-stationary models 764 difference-stationary process 2 1 1 , 2 1 5, 1497 differential equation 472 diminishing returns 639 separately to capital and augmented labor

653 dirty floating 1 587 discount factor 548, 555-557, 5 6 1 , 567, 588,

595, 60� 607, 609, 6 1 0, 6 1 6 disinflation, output costs o f 1 542 disj unction effect 1 324 disparity in GDP 675 disparity in incomes 674 distribution dynamics 263, 290-295, 299 distribution of country incomes 674 distribution of relative GDP 674 dividend growth 1 233, 1 242, 1 276 dollarization 1 589 domestic debt 1 595, 1601 domestic policy regime 1 53 , 202 Dornbusch-type model 502 DSGE, see dynamic stochastic general equilibrium models durability 798, 1 242 durable goods 549, 746, 799, 1 550, 1 552, 1 573,

1 575 dynamic economic models 3 1 2, 3 1 3 Dynamic New Keynesian (DNK) framework

1 346 dynamic programming 834 dynamic stochastic general equilibrium (DSGE) models 930, I J 39, 1 145, 1 150, 1 1 57,

1 1 66

models with job search

1 1 58

546, 567-573, 577-588, 592, 593, 598, 605, 6 1 5, 623 see also wages structural equation 5 82 variance 569-572, 578, 586 econometric approaches 237 economic growth 1 6 1 7, 1 64 1 , 1 6 5 1 economic relationship 852 education 577, 578, 580, 584, 602, 607, 609, 6 1 3, 6 1 5, 622, 623, 653 eductive approaches 462, 464 effective labor 650 efficiency of terminations 1 1 52 efficiency units 566, 658 see also labor in efficiency units efficiency wages 577, 578, 1098, 1 1 57, 1 1 59, 1 160 efficient equilibrium 854 efficient markets 1 307, 1 308, 1 3 1 6, 1 3 1 9-1 322, 1 333 elastic labor supply 1 145 elasticity 545, 546, 550-552, 563, 579, 580, 592-594, 596-601 , 605, 607, 6 1 0, 6 1 4-61 7, 620 of capital supply 1 7 1 4 long run 838 of demand, varying 1 1 19 of intertemporal substihltion 552, 557, 5 6 1 , 564, 597, 600, 601 , 614, 6 1 5 , 769, 79 1 , 1 148, 1250 of investment 857 of labor supply schedule 1 147 of substitution 645 election 522 embodied technology 1 207 embodiment-effect 664 employment 39 employment contract 1 1 53 employment fluctuations 1 1 73, 1 1 94 employment protection 12 15, 1 2 1 7 employment relationship 1 1 57 endogenous fluctuations 506, 5 3 1 endogenous growth models 238, 241 , 243, 245, 257, 259, 26 1 , 264, 265, 269, 27 1 , 297, 506, 65 1 , 653, 1 7 1 1 entry 1 067 variable 1 125 entry and exit 5 5 1 , 602, 615, 6 1 6, 824, 844 envelope theorem in RBC model 998 earnings

Subject Index "episodic" approach 1 560 E-SSE 520 Epstein-Zin-Weil model 1 259 equipment 840 equity premium puzzle 1 234, 1 245, 1 249,

1 250 error correction model 750 E-stability 463, 466, 468, 471--473, 488, 490,

491 , 504, 5 1 1 iterative 463 strong 473, 483, 491 , 5 1 2 weak 473, 483, 5 1 2 Euler equation 3 1 4, 345-347, 349-352, 354,

355, 364, 368, 3 7 1 , 373, 374, 3 8 1 , 382, 555-558, 566, 567, 575, 597, 598, 606, 607, 609, 6 1 1 , 621 , 650, 765, 767, 794, 805 undistortcd 1 7 1 3 Euler equations 745, 79 1 excess bond returns 1 276, 1 277, 1 280 excess sensitivity 772, 784, 785, 790 excess smoothness puzzle 747 excess stock returns 1 249, 1 276, 1 277 excess volatility 1 3 1 9, 1 320 excessive destruction 856 exchange rate 527, 5 3 1 , 1 658 anchor 1 588 and markups 1 122 arrangements 1 67, 203 exchange-rate-based stabilization 1 535, 1 543, 1553, 1 559 empirical regularities 1 546 existence of competitive equilibrium in RBC model 1 002 exit, delayed 850 see also entry and exit exogenous growth models 261 exogenous technological progress 650 expectation functions 453, 461 , 464 expectational stability, see E-stability expectations, average 528 expectations hypothesis of term structure

1281 experience 582, 584, 590, 602 experimental evidence 530 exports 41 extensive margins 843 external effects 390, 399--40 1 , 403 -405,

424--427, 43 1 , 433--435, 437 external finance premiwn 1 345 external habit models 1 284 externalities in RBC model 1 002

I-37 factor-saving bias 641 factors of production 909 Family Expenditure Survey (FES) 746, 750 family income 564, 569, 589 Federal Reserve 1 53 , 1 68, 1 69, 1 72-1 82,

1 84-202, 2 1 9 feedback derivative 1 5 1 0 proportional 1 5 1 0 feedback rule 68, 7 1 feedforward networks 524 financial accelerator 1 345 financial development 67 1 , 688, 692 financial markets, role in economic growth

1 376 firing fiscal fiscal fiscal fiscal

cost 1 1 86, 1 2 1 4, 1 222 authorities 1 524 deficits 1 53 8, 1 594, 1604 increasing returns 416 policy 672, 692, 694, 7 1 2, 7 1 5, 1 5 80,

1 6 1 7, 1 624 countercyclical 1 6 1 7, 1 660 fiscal theory of price-level determination

1 520,

1 524 fixed costs 390, 426, 435, 828, 848, 9 1 1 flow-fixed costs 83 1 fixed effect 787 flexible accelerator 8 1 6, 865, 893, 903 flexible cyclical elasticity 842 flexible neoclassical model 8 1 7 floating exchange rate 1 582 fluctuations in aggregate activity 547, 549, 552,

556, 569, 1053 see also business cycles induced by markup variation 1 055, 1 104 France 45 free entry condition 844, 845 frictionless neoclassical model 8 1 7 Friedman rule 1 720 Frisch demands 595-597, 603 Frisch labor supply 1 146 full-order equilibrium 530 functional forms 550, 583, 584, 588, 598, 601 ,

607, 6 1 1 , 623 fundamental solution 498 fundamental transformation gain sequence 469, 475 decreasing 469 fixed 469 small 470

852

I-38

Subject Index

general equilibrium 543-625, 888 generational accounting 1 624 genetic algorithms 465, 5 2 1 , 525 Germany 45, 1 6 3 1 global culture 1 332, 1 333 GLS 788 gold standard 1 53-1 90, 1 99-220 Golden Rule 1 650 Gorman-Lancaster technology 800 government budget constraint 1 687, 1 7 1 9 consumption 67 1 , 691 , 694, 1 687, 1 736 rate to GDP 688, 689 debt 1 6 1 7, 1 687 production 672, 695, 701 production of investment 699 purchases 41 purchases and markups 1 1 20 share 692 in GDP 67 1 , 689 in investment 695, 696 in manufacturing output 696 in output 693 gradual adjustments 823 gradualism 849 Granger causality 34 Great Depression 1 53, 1 63, 1 75, 1 78, 1 80-1 84,

1 9� 200, 2 1 3, 1 343 Great Inflation of the 1 970s 1 53 great ratios of macroeconomics 939, 940 gross domestic product (GOP) per capita 674 per worker 67 1 gross substitutes 1 7 3 1 growth cycles 9 growth accounting 678, 687, 688 growth miracles in East Asia 709 growth-rate targets 1 5 24 maximum growth rate 677, 726, 728, 732 habit formation 798, 802, 1 237, 1 284 habits 564, 802 Harrod- Domar models 640 hazard rate constant 839 effective 836 increasing 840 hedging demand 1 275 Hcrfindahl index 824 heterogeneity 546, 547, 552, 553

in firms 1 366 in learning 527 in values of job matches 1 1 52 of preferences 545, 558, 563 unobserved 779, 83 1 heterogeneous agents 843, 1 237, 1 290 heterogeneous consumers 1686 Hicks composite commodity 766 Hicksian demand decomposition in RBC model

971 hiring rate I 1 6 1 histogram 840 historical counterfactual simulations 1 523 history-dependent aggregate elasticity 84 I Hodrick-Prescott filter, see HP filter hold-up problems 852 home production 402, 4 1 7, 43 1 , 702 home sector 435 homotheticity 1 725, 1 728, 1 733 Hotelling's rule 657 HP (Hodrick-Prescott) filter 1 2, 932, 933 human capital 527, 546, 547, 576, 577,

583-592, 594, 639, 653, 1 638, 1 7 1 2 405, 436, 1 374 hump-shaped profiles 7 55 hyperinflation (seignorage) 509, 520, 53 1 , 1 63 1 hysteresis and threshold effects 455, 530 hump-shaped impulse responses

i.i.d. model 1 739 identification problem 75-78 global identification 76, 77 local identification 76 unde1identification 76, 77 idiosyncratic risk 795, 1290 idiosyncratic shocks 840 in productivity I 1 83 imbalances 826 imperfect competition 665 implementability constraint 1 677, 1 689, 1 7 1 9,

1 729 implicit collusion 1 123 imports 4 1 impulse 1 140 impulse response measure of comparative dynamics 967 to productivity in RBC model 967 impulse response functions 74, 8 1 , 85, 86, 90,

98, 1 00, 1 02, 1 07, 1 1 0, 1 12, 1 33, 1 40, 397, 4 1 1 , 430, 43 1 ' 880, 894

I-39

Subject Index inaction range Inada conditions

832 645

instrumental variables (IV) regression insurance

income distribution, cross-country income elasticity income inequality income processes income tax

67 1

1681 797 569, 574, 6 1 0

672

1 652 853, 854, 856 incomplete markets 566-576, 1 742 indeterminacy 491 , 494, 506, 1 1 6 1 , 1 506, 1 69 1 nominal 4 1 8, 1 506, 1 524 of price level 2 1 5 , 2 1 6, 4 1 5, 417, 4 1 9, 423 real 4 1 3 , 4 1 5, 4 1 6, 4 1 8, 4 1 9, 423 indicator, cyclical 1 062

income uncertainty

incomplete contracts

indivisible labor model, role in RBC model

977 industry equilibrium inequality

888, 889

745, 795

647 42, 1 534, 1 536, 1 630 and business cycles 939 and markups 1 1 28 inertia 1 562 level 1 98 persistence 1 66, 2 1 1 , 2 1 3-2 1 5 rate 1 738 autocorrelation 1 738, 1 739 variability 207 inflation correction 1621 inflation forecast targeting 1 504 inflation-indexed bonds 1 27 1 inflation-indexed consol 1 269 inflation targeting 1 499, 1 505 vs. price-level targeting 1 497 inflation tax 1 538, 1 720 inflationary expectations 1281 information externality 849 information pooling 849 information set 455 informational problems 849 -85 1 , 858 infrequent actions 825 instability 4 8 1 , 5 1 9 o f interest rate pegging 5 1 4 of REE 507 institutional factors 852 instmment feasibility 1 507 instrument instability 1517 instrument variable 1 492, 1 524 instnm1ental variables (IV) estin1ator 787 infinite-horizon consumption program

inflation

1 261

745, 795

1 297 43, 1 620, 1 62 1 , 1 629, 1 630, 1 634, 1 635, 1 637, 1 639, 1 648, 1 652, 1 653, 1 657-1659 nominal 1 524 interest rate instrument 1 5 14 interest rate policy 1 596 interest rate smoothing 1 509 intermediate-goods result 1 684, 1 720, 1733 intermediate-goods taxation 1 676 intermediate input use 1 0 8 1 internal habit models 1 284 international capital flows 1 636-1638 International Financial Statistics (IFS) 1 238 international reserves 1 594 intertemporal allocation 761 intertemporal budget 555, 561, 647, 661 intertemporal budget constraint 1 259, 1 268 intertemporal CAPM 1 275 intertemporal channel 1 142 integrated world capital market

interest rate

intertemporal elasticity of labor supply

1 149

of substitution in leisme

1 147

intertcmporal marginal rate of substitution

1 245 77 5 745 intcrtemporal substitution 1 055, 1 1 50 "intervention" policy 1 5 87 intradistribution dynamics 274, 292 intratemporal first-order conditions 775 inventories, target 894 inventolics of finished goods 887 inventory fluctuations 1084 procyclical 872-882, 898, 900, 909 inventory investment 865 inventory --sales ratio 871 inventory-sales relationship 867 investment 40, 641 collapse 851 competitive equilibrium 844 delays 1 365 distortions 672, 695-698 empirical 1 344 expected 839 frictionless 832 lumpy 822, 823 share in output 693, 699 spike 823, 824, 857 intcrtemporal non-scparabilities

intertemporal optimization

Subject Index

I-40

labor contract 1 1 54 labor force 1 1 74 labor force status 602, 603, 607, 6 1 1 , 6 1 4,

investment (cant 'd) tax incentives 843 US manufacturing 840 investment episode 823 investment-output ratio 7 1 4 irrational expectations 1 237, 1 293

623 labor hoarding 1 076, 1 078, 1097 labor in efficiency units 650 see also efficiency units

irregular models 490, 493, 505 irreversibility constraint 832 irreversible investment 822, 828, 832 iso-elastic utility function ltaly 1 6 1 9 Ito's lemma 825 Japan 45 Jensen's inequality

606, 607, 6 1 0

restrictions 672, 695 labor power 1220 labor productivity 42

1 247

job-finding rate, cyclical behavior of job loss 1 1 5 1

I I 62

job search 1 143, 1 1 50, 1 1 58, 1 1 62 job-specific capital 1 1 52 job to job flows l 1 98, 1 200 job-worker separations 1 1 84 jobs creation 846, 1 1 50, 1 1 58, 1 1 6 1 , 1 1 73, 1 1 76,

1 1 78, 1 1 85, 1201, 1 2 1 9 cost 1 1 87, 1 193, 1 2 1 5, 1 222 creation and destruction, international comparison 1 1 78 destruction 846, I 1 50, 1 1 58, 1 1 60, 1 166,

1 1 73, 1 1 76, 1 1 78, 1 1 85, 1 1 97, 1 20 1 , 1219 rate 1 1 5 1 , 1 152 flow 1 1 97 international comparison 1 1 80 reallocation 1 222 termination 1 1 52 cost 1 1 93 joint production 853 j oint surplus 1 1 57 j ust-in-time 871 Kaldor facts about economic growth 94 1 Keynes, J.M. 1 660 Keynesian analysis 1 628 Keynesian consumption function 761 Krcps-Portcus axiomatization Krugman model 1 592 Kuhn-Tucker multiplier 774 labor 1 687 bargaining strength labor-augmentation

12 1 9 65 1

labor income 1 237, 1 275, 1290 labor market 855 policy 1 2 1 4

744

labor regulations 852 labor share I 059

546-553, 562, 577, 585, 587, 592, 594, 596, 598, 599, 601 , 602, 605, 606, 608, 6 1 0-621 , 623, 744, 777, 792, 1 1 50, 1 296 elasticity 975, 1 3 7 1 i n RBC model 975 empirical 1 148 endogenous in RBC model 945 extensive margin 976 female 6 1 1 fixed costs of working 976 indivisible labor model 976 male 6 1 1 substitution effect 975 unobserved effort of 930 labor tax rate, autocorrelation 1739 lack of credibility 1 569, 1 5 72, 1 58 1 Latin America 1 543 laws of large numbers 837 leading example 488, 493 learning 453, 488 by doing 664 in games 475 in misspecified models 528 least squares learning 465, 467, 526 social 849 stability tmder 496 statistical 493 leaming dynamics, persistent 455 learning equilibria 5 1 5 learning rules 439, 454 econometric 472 finite-memory 474 fixed-gain 5 ! 1 statistical 465 leaming sunspot solutions 494 leaming transition 5 3 1 labor supply

1-41

Subject Index Legendre--Clebsch condition 904 levels accounting 678-687 leverage 1 280 life cycle 583, 586-588, 593, 595, 601 , 603,

604, 609, 6 1 5, 620, 62 1 , 744, 749, 752, 754, 760, 792, 793 life cycle-permanent income model 760 life expectancy 691-693 lifetime budget constraint 647 see also intertemporal budget likelihood function 840 linear allocation rules 554, 563, 564 linear commodity taxes 1 677 linear filter 1 1 linear model 467, 487 , 842 with two forward leads 5 0 1 linear-quadratic model 457, 865, 876, 882, 903, 904 liquidity 1255, 1 59 1 liquidity constraints 745, 772, 773, 789, 1 654 see also borrowing constraint liquidity variables 8 1 7 log-linearization 788 long-term bonds 1 255, 1 280 low-equilibrium trap 646 Lucas aggregate supply model 457 Lucas critique 1 49 1 Lucas program 67 lumpy project 823 Lyapunov theorems 479 M2

44

Ml velocity 50 machinery, price of 696 macroeconomics 63 9 magical thinking 1 328, 1 329 maintenance 823 maintenance investment 83 9 major and infrequent adjustments 823 managed float 1 52, 1 53, 1 67, 202, 204, 207 manufacturers 870 marginal cost schedule 1 054 declining 1 066 marginal production costs 867, 890, 892, 896,

899, 902, 905, 907 marginal profitability of capital 830 marginal rate of substitution 549, 5 5 1 , 554- -557,

559, 560, 598, 622, 765 heterogeneity 620-623 marginal utility 767 market capitalization 1239

market clearing 1 02 1 -1 024-, 1 026, 1 035 expected 1 02 1 , 1 024-1 027 market imperfection 390, 405, 424, 426, 433 market structure 546, 553, 558, 575, 598 market tightness 1 1 85 market work 550, 594, 60 1 Markov chain 1 708, 1 736 Markov process 1 264 markup 399, 400, 406, 407, 426, 429, 43 1 ,

1 053 average 1 068 countercyclical 406, 1 1 1 3 for France ! 068 cyclical 1 092 desired 1 056 measurement 1 05 8 models o f variation 1 055, 1 1 1 2 procyclical 1 1 1 3, I l 2 8 variable 406, 407 variation in desired 1 129 Marshallian demands 597 martingale 767 martingale difference sequence 487 match capital 1 1 52 matching function 1 1 83 matching model 1 1 63 Maximum Ptinciple 650 measure of financial development 691 measurement error 5 1 8, 546, 5 6 1 , 572-574,

609, 6 1 6, 1 242 "mechanical" approach 1560 mechanism design 1 1 54 Medicare 1 622, 1 626 men 550, 552, 607, 6 1 5 , 620 mental compartments 1 3 1 7 menu costs 397 microeconomic data 543-625, 745 microeconomic Jumpiness 824 microfoundations 761 military purchases 1 088 Mincer model 568, 569, 5 8 1 , 582, 584, 592 minimal state variable solutions, see MSV solutions mismatch 1 2 2 1 mismeasurement o f average inflation 1 254 Modigliani-Miller theorem 1 343 monetary accommodation 1 539 monetary base 44, 1 507, 1 524 monetary economies 1 720 monetary model with mixed datings 500

1-42

Subject Index

692, 695, 7 1 5, 1 01 2, 1 0241 037, 1 2 8 1 , 1 630, 1 660, 1 720 optimal, cyclical properties of 1 736 monetary policy rule 1 3 64 monetary policy shocks 65-1 45 effect 69 on exchange rates 94-96 on US domestic aggregates 91-94 on volatility 1 23-1 27 identific ation schemes 68 -70, 1 369 Bernanke--Mihov critique 1 1 5--123 Bernanke-Mihov test 1 J 9-1 21 empirical results 1 2 1 - 1 23 Coleman, Gilles and Labadie 1 14, 1 1 5 narrative approach 1 36-14 1 see also Romer and Romer shock pitfalls 1 34-1 36 plausibility I 00-1 04 assessment strategies 1 1 4- 1 23 problems 1 43-145 interpretations 71-73 non-recursive approaches 1 27-134 output effects 1 1 29 recursiveness assumption 78- 1 27 see also recursiveness assumption responses to 1 368 monetary regimes 1 53, ! 68, 1 78, 202, 204, 2 1 1, 2 1 6, 220 money 44, 1 0 1 1 - 1 0 1 3 , 1 020- 1 029, 1 03 1- 1 033, 1 035, 1 036, 1 040, 1 04 1 money anchor 1 588 money-based stabilization 1 535, J 543, 1 554, 1 558, 1 582 money demand 50, 598, 1 603, 1 736 conswnption elasticity of 1 725 interest elasticity of 1 736 money growth rate 1 738 money-in-the-utility-function model 1 720, 1 728 money supply 1 536 money velocity 1 588 see also M 1 velocity monopolies 695 monopolistic competition I 033-1 036, I 041 , 1042 monotonicity 830 monetary policy

Morgan Stanley Capital International (MSCI)

1 23 8 M S V (minimal state variable) solutions

493, 502 and learning

503

488,

locally (in)determinate 490 non-MSV solutions 493 multiple competitive equilibria 1 679 multiple equilibria 1 539, 1 603 multiple REE, see under REE multiple solutions 487, 1 506, 1 524 multiple steady states 460 multiple strongly E-stable solutions 50 I multiplicity of steady states 658, 662 multivatiate models 502 with time t dating 505 mutation 522 Muth model 465, 484, 525 myopia 1 653, 1 654 Nash bargain, generalized 1 1 89 National Account 75 1 , 752 national accounting identities 1 628 National Bureau of Economic Research (NBER)

6, 8 national income 1 6 1 7 national saving 1 628, 1 629, 1 637, 1 639, 1 64 1 ,

1 652, 1 659-1662 natural expeiiments 822 natural rate 1 17 6 natural resources 639 negative income tax expetiments 1 1 48 neoclassical exogenous growth model 243, 26 1 ,

673 245, 246, 252, 259, 269, 272, 276, 639, 695, 697, 70 1 , 1 140 basis for RBC model 942 neoclassical theory of investment 8 1 7 net convergence effect 692, 693 net present value rule 835 net worth and the demand for capital 1 352 neural networks 465, 524 neurons 524 neoclassical growth model

noise case of small 5 1 3 inttinsic 507 noise traders 1290 noisy k -cycle 5 1 3 noisy steady states 483, 509 nominal anchor 207, 2 ! 1 , 2 1 5, 2 1 6, 1 535,

1 542, 1 557 nominal income targeting 1 505 non-durables 746 non-nested models g40 non-random atttition 787 non-Ricardian policy 4 1 8

Subject Index

I-43 418

non-Ricardian regime

473 1 3 1 9-1 3 22 overtaking 650 overvaluation 1 563 overparametrization

non-separability o f consumption and leisure

759 non-state-contingent nominal claims

1 722

oveneaction

Non-Accelerating Inflation Rate of Unemploy-

46 468 828, 839

ment (NAIRU)

275, 283-287, 295, 781 .559-564, 796 partial adj ustment model 821 , 838 participation 574, 601 , 1 2 1 8

nonlinear models

panel data

nonlinearity

Pareto weights

532 320, 324, 326, 328, 348,

nonparametric techniques numerical algorithms

path dependence of adaptive learning dynamics

358, 378 3 1 8, 326, 352, 805

numerical solutions

455 peacetime

848 685, 7 1 8, 7 1 9, 1 1 74

1 699

obsolescence

Penn World Table

OECD

pent-up demand

OECD adult equivalence scale

757

1 089 639

oil prices, effects of one-sector model

one-step-ahead forward-looking reduced form

506 1714

open market operations opem1ess

perceived law of motion (PLM) perceptron

524

703

1486, 1 523 8 5 1 , 858 opportunity costs 854 optimal control 1490 optimal debt policy 1 639, 1 659, 1 660, 1 662 optimal fiscal policy 1 686 optimal investment path 834 optimal national saving 1 6 1 7 optimal tax theory 1 692 optimal trajectory 650 optimal wedges 1 692 optimum quantity of money rule 1 537 option to wait 832, 834 operationality opportunism

ordinary differential equation (ODE)

468, 478 785 out-of-sample forecasting 840 out-of-steady-state behavior 649 output 1 687 output levels 206 output variability 208, 2 1 1 overconfidence 1 3 1 9- 1 323, 1 325, 1 326, 1 328 overhead labor I 065 ovcridcntif'ying restrictions 7 68 overlapping contracts models 495, 1 582 overlapping generations model 390, 395, 397, 398, 427, 458, 546, 549, 576-594, 660, 1 634, 1 635, 1 645-1647 approximation

orthogonality conditions

83 1 650 846

perfect competition perfect insulation

1 722

466, 472, 490,

511

perfect foresight

open economy

674, 680 841

perfect-insurance hypothesis periodic or chaotic dynamics

796 646

see also cycles pe1manent-income hypothesis

749, 1 64 1 ,

1 662 permanent shocks

2 1 6-2 1 9

680 870-882, 8 9 1 , 893, 900, 902, 904, 1 142, 1 1 62, 1 1 66, 1 739 of business cycles, see persistence under

perpetual inventory method persistence

business cycles

527 1 537 peso problem 1 252 pessimism 1 295 Phillips curve 46, 1 056, 1 363, 1 542 planner's problem in RBC model 997, 1 002 policy 455 affecting labor markets 672 distorting investment 695 impeding efficient production 672 policy accommodation 1 538 policy ftmction 320-3 8 1 political rights 67 1 , 689 political stability 67 1 , 688, 692 Ponzi scheme 1 650 population aging 1625, 1 640 population growth 941 endogenous 639 power utility 1 249 of fluctuations

of inflation

1-44

precautionary saving 744, 770, 1 253, 1288, 1 653 preference parameters 550, 555, 556, 558, 567, 601 , 605 preferences 546-550, 552, 553, 556-558, 564, 565, 567, 572, 582, 593, 601 , 604, 605, 607, 608, 6 10, 614, 6 1 6, 6 1 7, 623 additive 594 conditional 778 functional forms 550 Gorman polar 766, 783 heterogeneity 545, 552, 558-565, 567, 593, 594, 609, 621 , 623 homogeneity 553-556, 577 of representative agent in RBC model 942 quadratic 762, 770 present-value model of stock plices 1 264 log-linear approximation 1 265 present-value neutrality 573 price elasticity 1 6 8 1 price functions 1 723 plice puzzle 97-100 plice rules 1 688 price-cost margin I 053 see also markup price-dividend ratio 1 265, 1 266, 1 276 prices 42 of machinery 696 of raw materials I 082 pricing, equilibrium 555, 602, 845 primal approach 1 676 primary budget 1 6 1 9 plincipal-agent problems 1 345 principles of optimal taxation 1 676 private and public saving 1 629 private information 574-576, 849 production costs, non-convex 897, 9 1 1 production economy 1 686 production efficiency 1 684, 1 735 production function 548-550, 578, 579, 5 8 1 , 583-586, 588, 590, 5 9 1 , 594 non-Cobb--Douglas 1 064 production possibilities surface 40 I production smoothing 876, 877, 884, 895, 1 085 production to order 887 production to stock 887 productivity 552, 553, 566, 583, 602, 1 057 cyclical 93 8, I 094 deterministic growth of 943 general 1 1 92, 1 1 93

Subject Index growth of 942 shocks 930, 943, 965, 972 amplification of 963 modeled as first-order autoregressive process 963 persistence of (serial correlation) 952, 963 RBC model's response to 964 remeasurement of 982 slowdown 664 profit function 830 profits 1 057 cyclical 1 1 00 projection facility (PF) 480 propagation of business cycles 865 propensity to consume 762 property rights 852, 856 proportional costs 825 proportional taxes 1 687 prospect theo1y 1 308- 1 3 1 3 protection o f specific investments 1 1 54 "provinces" effect 1 540 proxies for capital utilization 1 080 prudence 7 7 1 PSID 783 public consumption 1 5 8 1 public debt 1 60 I , 1 603 public finance 1 676 public saving 1 629, 1 64 1 putty-clay models 847, 848 q-theory 8 1 7 see also Tobin's q average q 8 1 7, 8 1 8 "flexible q " 8 1 8 marginal q 8 1 8 fragility of 828 quadratic adjustment cost model 823, 838 Quandt Likelihood Ratio (QLR) 34 quantitative performance 1 578, 1 5 8 1 quantitative theory 671-673, 695-7 1 9 see also dynamic stochastic general equilibrium models quasi-magical thinking 1 329, 1330 Ramsey allocation problem 649, 1 679, 1 69 1 , 1 692, 1 7 1 3 , 1 7 1 9, 1 723, 1 729 Ramsey equilibrium 1 678, 1 688, 1 723, 1 729, 1 732 Ramsey growth model 1 65 1 , 1 652 Ramsey prices 1 679

Subject Index random walk 767, 1 3 1 6, 1 3 1 9, 1 702, 1 706, 1 738, 1 742 geometric 825 range of inaction 826 rate of arrival of shocks 1 193 rate of discount 1 1 93 rate of return 566, 577, 582, 595, 606, 6 1 0 ratio models o f habit 1 284 rational bubbles 499, 1 266 rational expectations 453 transition to 454 rational learning 461 rationalizability 464 rationing 857 RBC models, see real business cycle Reagan, R. 1 641 real balance model 489, 496 real business cycle (RBC) 394, 402, 4 1 3, 427, 428, 437, 442, 505, 843, 928, 1 296 amplification of productivity shocks in 958, 967 as basic neoclassical model 942 baseline model 1 1 43, 1 709, 1 736 failures 1 144 calibration 953-955, 959 competitive equilibrium 999 concave planning problem 1 002 contingent rules 1 000 ctiticisms 96 1 depreciation rate of capital 944 discount factor 942 modified 945 endowments in 943 extensions 994 firm's problem 1 00 1 government spending and taxes i n 974 high risk aversion model 1 709 high-substitution version calibration 985, 987 decision rules for 985 ingredients of 984 probability of technical regress 989, 990 role of capacity utilization in 985 role of indivisible labor in 985 sensitivity to measurement of output 992 sensitivity to parameters 990, 99 I simulation of 986 household's problem 1 000 importance of consumption smoothing in 967

I-45 Inada conditions on production function 996 interest rate effects 973 internal propagation in 967 labor demand for 956 supply of 956 Lagrangian for 946 lifetime utility 996 market clearing 1 00 1 production function in 943 RBC model as basic neoclassical model 942 simulations of 957 solution certainty equivalence 952 dynamic programming 95 1 linear approximations 949 loglinear approximations 952 rational expectations 95 1 steady state of 947 transformation to eliminate growth 944 transitional dynamics of 948 transversality condition for 946 wage effect in 973 wealth effects in 971 with nominal rigidities 974 real exchange rate 1 547 real interest rate 1 220, 1 233, 1 276, 1 286 measurement of 939 real marginal cost 1 053 real shocks 1 1 74 real wage 1 296 reallocation of workcrs 1 1 60, 1 1 83, 1 1 99 recession now versus recession later 1 535, 1 55 7 recursive algorithm 468, 475, 479, 486 recursive least squares 467 recursive least squares learning 494 recursive utility 557 recursiveness assumption 68, 73, 78- 1 27 benchmark identification schemes 83 -85 FF policy shock 87, 88 influence of federal funds futures data 1 04--1 08 NBR policy shock 88 NBR/TR policy shock 89 problems 97 results 85 robustness 96, 97 sample period sensitivity l OS 1 14

I-46

Subject Index

recursiveness assumption (cont'd) relation with VARs 78-83 REE (rational expectations equilibria) 452 cycles 458 multiple 454, 467 reduced order limited information 529 unique 484 reflecting barriers 828 regime switching 426 regression tree 289 regular models 490 regulation barrier 832 relative price of investment to consumption

risk premium 1 246, 1 247, 1 250 risk price 1 236, 1 280 risk-sharing in indivisible labor version of RBC model 977 riskfree rate puzzle 1 235, 1252 robustness approach 1 49 1 , 1 523 Romer and Romer shock 1 37-142 rule-like behavior 1 487, 1 522 rule-of-thumb decision procedure 524 rules 1 52-1 54, 1 56, 1 58, 1 60, 1 66, 1 68, 1 84,

200, 208, 2 1 9, 220 rules vs. discretion 1 485 Rybczinski theorem 404

696-698, 700, 701 reluctance to invest 82S, 832 renegotiation 1 1 53, 1 1 55 renewable/nonrenewable resources 655, 656 rental prices 588, 590, 592 of capital I 000 reorganization 1 1 60, 1 1 6 1 representative agent 556, 557, 560, 5 6 1 , 563,

587, 601 , 838, 1 249, 1 259, 1 268 in RBC model altered preferences in indivisivle labor

977 altruistic links 943 preferences of 942 representative household 643 representativeness heuristic 1 3 1 9, 1 3 22, 1 327 reproduction 522 research and development (R&D ) 664, 672,

692, 695, 708, 709, 7 1 5-7 1 9

residence-based taxation 1 7 1 5 restricted perceptions equilibrium 529 restr-ictions in job separation 1 222 restrictions on government policy 1 707 retailers 869 retirements 83 9 returns to seale 63 9 decreasing 656 increasing 652, 653, 664, 828, 830, I 066 social 460, 509, 5 2 1 Ricardian equivalence 4 1 8, 1 6 1 7, 1 640-1 659,

1661 Ricardian regime 4 1 8 Ricardo, D . 1 640 risk 546, 547, 552, 554--5 58, 563-567, 569,

572, 575, 593, 606 risk adj ustment 555, 557, 558 risk aversion 547, 552, 556--558, 564--5 66, 606,

771

(S, s) model

80 1 , 802, 83 1 , 9 1 0, 9 1 I sacrifice ratio 1 54 1 saddle point 405, 649 saddle point stability 490 Sargent and Wallace model 489 saving 64 1 private 1 628, 1 629, 1 632--1634, 1 637, 1 64 1 , 1 648 'saving for a rainy day' equation 764 scale effects 672, 7 1 5, 7 1 6, 7 1 8, 7 1 9 school attainment 691 school enrollment 68 1 , 684 post-secondary 683 primary 683 secondary 68 1 -683 schooling 576-578, 58 1-592 sclerosis 856 scrapping 844, 847, 855, 856 endogenous 844 search and matching approach 1 173, 1 1 83 search efficiency 1 1 62 search equilibrium 1 1 86 search externalities 506 seasonal adj ustment 1 242 seasonal variations in work volwne 1 1 49 second-best solutions 849 secondary job loss 1 163 sector-specific external effects 402 sectoral shifts hypothesis 1 22 1 securities market 1 722 seignorage model 460, 47 1 , 509, 525, 530,

1 74 1 selection criterion 468 selection device 454 self-fulfilling fluctuations 506 separability 556, 602, 603, 607, 608, 6 1 2, 6 1 3 ,

6 1 7, 1 725, 1 728, 1 733

Subject Index tests 6 1 1 separation rate 1 1 5 1 Sharpe ratio 1 249 shock absorber 1 699, 1 7 1 0, 1 739 shock propagation 1 203 shocks and accommodation 1 539 shopping-time model 1 720, 1 732 shopping-time monetary economy 1732 short-tenn bonds 1280 short-tenn maturity debt 1 603 a-convergence 659 Sims-Zha model 1 28-134 empirical results 1 3 1 - 1 34 skill-biased technology shock 1 2 1 5 , 1 2 1 6, 1218 skills 546, 547, 569, 576--579, 5 8 1 , 582, 584, 586-588, 590-594, 623 slow adaption 480 slow speed of adjustment 877, 894 small durables 798 small open economy 1 7 1 5 small sample 820 small versus large finns 1 373 smooth pasting conditions 827 Social Security 1 6 1 9, 1 622, 1 624, 1 626, 1 635 Solow residual 930, 1 140, 1 14 1 as productivity measure 962 in growth accounting 962 mismeasuremcnt 962 solvency conditions 575 specificity 85 1 , 852, 856 spectral analysis 1 1 SSE, see stationary sunspot equilibria stability conditions 454 stabilization 1 534, 1 562 stabilization goals 1 53 stabilization time profiles 1 547 stable equilibrium point 48 1 stable roots 393 staggered contracts model 1 0 1 2, 1 0 1 3 , 1 024, 1 027, 1 030, 1 032, 1 039 staggered price and wage setting 1 0 1 2, 1 0 1 3 , 1 027, 1 030, 1 03 1 , 1 033, 1 035-1037, 1 040 staggered price setting 397, 422, 423, 1 129, 1 363 staggered-prices formulation 1 582 standardized employment deficit 1 62 1 state-contingent claims 55 5, 602 state-contingent returns on debt 1 687, I 699 state-dependent pricing 1 03 1 , 1 032 state dynamics 477

l-47 state prices 1 294 stationary distribution of RBC model 999 stationary sunspot equilibria (SSE) 408, 5 1 7 E-SSE 5 1 7 near deterministic solutions 520 steady states 468, 507, 525, 549-5 5 1 , 576, 592, 598, 639 of RBC model 944 sterilization I 595 sticky price models 503, 1 1 1 3 stochastic approximation 468, 475, 476 stochastic discount factor 1234, 1 245 log-normal 1 246 stochastic growth model 546-577, 592 stochastic simulations 1 5 1 6, I 523 stock market 1 3 1 0, 1 3 1 2, 1 3 1 3 , 1 3 1 5, 1 3 16, 1 320-1 328, 1 33 1 , 1 333 stock market volatility puzzle 1 235, 1 236, 1 268, 1 276, 1 280 stock prices 43 stock return 1 233, 1 240 stockout costs 884, 885 Stolper-Samuelson theorem 404 Stone price index 783 storage technologies 5 74, 575 strategic complementarity 1 129 strategic delays 858 strong rationality 464 structural model 462 structural shifts 530 structures 840 subgame perfection 1 679 subjective discow1t factor 548, 552, 56 1 , 593 , 595, 609, 6 1 6 subsistence wage 657 substitutes 577, 590, 591, 6 1 3, 6 1 6 sunk costs 858 sunspot equilibria 454, 5 1 5 sunspot paths 662 sunspot solutions 495 see also learning sunspot solutions sunspots 489, 5 1 5 supply o f capital 846 supply price of labor 1 1 92, 1 1 93 supply shocks 1 129 supply-side responses 1 577 surplus 853 surplus consumption ratio 1 286 survivorship bias 1 242 sustainability 1597

I-48 T-mapping 467, 47 1 , 5 1 2 Tanzi effect 1 74 1 target points 826 target variables 1492, 1 523 tariff 672, 695, 703-707 taste shift 778 tax see also labor tax rate; capital taxation distortionary 1 65 1 , 1 652, 1 654 on capital income 1 686 on employment 1 220 on international trade 703 policy 672, 708 rate 1 441 on private assets 1 709 reforms 822 smoothing 1 655, 1 659, 1 662, 1 705 intertemporal 1 6 1 7 source-based 1 7 1 5 system 1 679 Taylor expansion 1 265 Taylor rule 1 364 technological change 1 708 technological embodiment 848 technological progress 64 1 , 1207, 1 2 1 3 disembodied 1 207, 1 208 endogenous 639 Harrod-neutral, Hicks-neutral 944 labor-augmenting 944 purely labor-augmenting 650 technological regress, probability of in RBC models 930 technology adoption 672, 708 technology shocks 1 1 4 1 , 1 142, 1 736 temporariness hypothesis 1 5 69, 1 572 temporary shocks 2 1 6 temporary work 1 1 65 term premium 1 255 term stmcture of interest rates 1270 termination costs 708 thick-market externality 1 1 6 1 threshold externalities 527 thresholds 258-262, 276, 289 time-additive utility function 661 time aggregation 8 8 1 time-consistent behavior 1 488 time dependency 799 time-dependent pricing 1 03 1 , 1 032 time-inconsistent behavior 1 653 time preference 547, 588 time preference rate 1 25 3

Subject Index time series 264, 272, 287, 288 time series volatility 756 time to build 832, 850 time-varying aggregate elasticity 84 1 timing assumption 469 Tobin's q 8 1 7, 1 296 see also q-theory total factor productivity (TFP) 42, 673, 678, 687, 688, 702 trade deficit 1 630, 1 658, 1659 trade policy 672, 692, 694, 702 training 577, 582-584, 586-592, 653 transition rates 1 1 66 transversality conditions 392, 393, 400, 650 Treasury bills 1 233 trend-stationary models 764 trend-stationary process 1 0, 2 1 1 , ! 497 trigger points 830 tuition costs 583, 588, 590 twin deficits 1 63 0 two-stage least squares estimation 1 2 6 1 uncertainty 545-547, 556, 5 5 8 , 564, 566, 567, 569, 572, 574, 575, 593, 605, 606, 620, 621 , 623, 744, 1 627, 1 653 undcrinvestment 852, 854 underrcaction 1 3 1 9-1 322 unemployment 546, 569-5 7 1 , 578, 579, 1 143, 1 1 50, 1 158, 1 1 6 1 , 1 1 62, 1 173, 1 174, 1 1 94, 1214 experiences o f OECD countries 1 2 1 3 natural level 1 1 57 rise in 1 1 82 serial correlation 1 163 unemployment compensation 1 2 1 7 unemployment income 1214 unemployment inflow and outflow rates I I 8 1 unemployment rates 1 1 76 unemployment spell duration hazard 1 1 84 tmemployment-skill profile 1 2 1 6 unified budget 1 6 1 9 uniform commodity taxation 1 676, 1 726 union bargaining 1 098 uniqueness of equilibrium in RBC model 1 002 unit root 1 1 United Kingdom 45 tmivatiate models 488, 497 unstable equilibrium point 481 utility function 548-550, 556 -558, 560, 594, 596, 59� 599-601 , 606, 607, 6 1 0

1-49

Subject index momentary in RBC model 944 offsetting income and substitution effects 944 utility recursion 557 utilization of capital 1 079

vacancies 4 1 , 1 1 94 vacancy chain 1 200 vacancy duration hazard 1 1 84 value function 3 1 9-327, 329, 335, 336, 340, 345, 3 5 1 -355, 357-359, 365, 368, 378 value matching 827 variable costs 828 variety, taste for 705 vector autoregression (VAR) 73, 438 definition 73 vintage capital models 847, 848 volatility employment 1 1 57 invent01ies 869, 870 monetary aggregates 1 599 vote share 1 455

wage bargaining 1 130 wage contract 1 1 73, 1 1 86 wage inequality 1 1 82, 1 21 4, 1 2 1 8, 1 2 1 9

wages 42, 547, 550-553 , 556, 566-569, 572, 577-579, 5 8 1 , 587, 593, 595-60 1 , 603-607, 6 1 1 , 6 1 2, 6 1 6, 6 1 7, 6 1 9, 62 1 , 62 3, 1 1 8 l , 1 629, 1 637 see also earnings cyclical 939 equilibrium 556 fixed 1 1 57 marginal I 069 rigidity 1 055 war o f attrition 1 540 wars 1 6 1 9, 1 642, 1 656, 1 66 1 -1 663, 1 699 wealth distribution 556, 5 6 1 , 567, 572, 593 wealth-output ratios 1 240 wealth shock 1 372 welfare costs of macroeconomic fluctuations 1 297 welfare theorems, role in R BC analysis 1 001 wholesalers 869 within-period responses 599 women 550, 552, 607, 6 1 5, 620, 623 worker flows 1 1 80 into unemployment 1 1 64 worker turnover 1 1 76 works in progress inventories 887

yield spread

1 256, 1 280