Research in Finance, Volume 20 (Research in Finance) (Research in Finance)

CONTENTS LIST OF CONTRIBUTORS vii INTRODUCTION ix IMPACT OF DIFFERENTIAL AND DOUBLE TAXATION ON CORPORATE FINANCIAL...

Author: A.H. Chen

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CONTENTS LIST OF CONTRIBUTORS

vii

INTRODUCTION

ix

IMPACT OF DIFFERENTIAL AND DOUBLE TAXATION ON CORPORATE FINANCIAL POLICIES IN AN INFLATIONARY WORLD Andrew H. Chen and Edward J. Kane

1

PRICE CEILING REGULATION OF A TAX EVADING MONOPOLIST Partha Sengupta

19

DEPOSITOR PREFERENCE LEGISLATION AND FAILED BANKS’ RESOLUTION COSTS William P. Osterberg and James B. Thomson

33

SECONDARY MORTGAGE MARKETS, GSEs, AND THE CHANGING CYCLICALITY OF MORTGAGE FLOWS Joe Peek and James A. Wilcox

61

INCREASING MARKET DISCIPLINE ON BANKS: SUBORDINATED DEBT AND BANK LOAN SALES Andrew H. Chen, Kenneth J. Robinson and Thomas F. Siems

81

v

vi

USING ZERO-NON-ZERO PATTERNED VECTOR AUTOREGRESSIVE MODELLING TO TEST FOR CAUSALITY BETWEEN MONEY SUPPLY, GDP GROWTH, THE LONDON STOCK MARKET INDEX AND THE EURO EXCHANGE RATE Edward J. Y. Lin, J. H. W. Penm, R. D. Terrell and Soushan Wu

99

FRAGILE FIXED EXCHANGE RATES WITH BANKING SAFETY NET GUARANTEES Stephen A. Kane and Mark L. Muzere

119

LONG MEMORY IN CURRENCY FUTURES VOLATILITY Ching-Fan Chung, Mao-Wei Hung and Yu-Hong Liu

139

VALUATION OF PENSION BENEFIT GUARANTEES AND TERMINATION CONDITIONS Jin-Ping Lee, Shih-Cheng Lee and Min-Teh Yu

159

ANNOUNCEMENT EFFECTS OF SPECIALLY DESIGNATED DIVIDENDS Ken Hung, Chang-Wen Duan and Gladson I. Nwanna

181

THE OPTIMIZATION OF EFFICIENT PORTFOLIOS: THE CASE FOR AN R&D QUADRATIC TERM John B. Guerard, Jr. and Andrew Mark

213

LIST OF CONTRIBUTORS Andrew H. Chen

Edwin L. Cox School of Business Southern Methodist University Dallas, TX, USA

Ching-Fan Chung

Institute of Economics, Academia Sinica, Taiwan

Chang-Wen Duan

Department of Banking and Finance, Tamkang University, Taiwan

John B. Guerard, Jr.

University of Pennsylvania, Philadelphia and GlobeFlex Capital, L. P., San Diego, CA, USA

Ken Hung

Department of Finance, National Dong Hwa University, Taiwan

Mao-Wei Hung

College of Management, National Taiwan University, Taipei, Taiwan

Edward J. Kane

Carroll School of Management, Boston College, MA, USA

Stephen A. Kane

Frank Sawyer School of Management, Suffolk University, Boston, MA, USA

Jin-Ping Lee

Department of Finance, Feng Chia University, Taichung, Taiwan

Shih-Cheng Lee

Department of Finance, Yuan Ze University, Jung-Li, Taiwan

Edward J. Y. Lin

Institute of Business and Management, National Chiao-Tung University, Hsinchu, Taiwan

Yu-Hong Liu

College of Management, National Taiwan University, Taipei, Taiwan

Andrew Mark

GlobeFlex Capital, L. P., San Diego, CA, USA

Mark L. Muzere

Frank Sawyer School of Management, Suffolk University, Boston, MA, USA vii

viii

Gladson I. Nwanna

Department of Accounting and Finance, Morgan State University, Baltimore, MD, USA

William P. Osterberg

Department of Economics and Finance, University of Wyoming, WY, USA

Joe Peek

School of Management Finance, University of Kentucky, KY, USA

J. H. W. Penm

Faculty of Economics and Commerce, The Australian National University, Canberra, Australia

Kenneth J. Robinson

Federal Reserve Bank of Dallas, Dallas, TX, USA

Partha Sengupta

R. H. Smith School of Business, University of Maryland, College Park, MD, USA

Thomas F. Siems

Federal Reserve Bank of Dallas, Dallas, TX, USA

R. D. Terrell

National Graduate School of Management, The Australian National University, Canberra, Australia

James B. Thomson

Federal Reserve Bank of Cleveland, Cleveland, OH, USA

James A. Wilcox

University of California, Berkeley, CA, USA

Soushan Wu

College of Management, Chang Gung University, Tao-Yuan, Taiwan

Min-Teh Yu

Department of Finance, Providence University, Taichung, Taiwan

INTRODUCTION

Eleven papers in this volume present some current interesting and important research in finance. Based upon the CAPM, Chen and Kane show that double taxation and differential tax rates on personal and capital-gains income affect corporate stock values and financial policies in nonneutral ways. Sengupta shows tax evasion decisions of a monopolist in a price-ceiling regulatory environment. In their paper, Osterberg and Thomson empirically examine the impact of state-level depositor preference laws on resolution type and costs for all operating FDIC-BIF insured commercial banks that were closed or required FDIC financial assistance from January 1986 through December 1992. Peek and Wilcox show that during periods of international financial crises or of domestic economic stress, the government-sponsored enterprises (GSEs) are well suited to stabilize mortgage markets. In their paper, Chen, Robinson and Siems empirically show the association between banks’ subordinated debt and their loan sales activities and its implications in the transmission mechanism of monetary policy. Also in this volume, Lin et al., use the Granger causality test to examine the linkage between the euro exchange rate and the money supply and GDP in the euro community as well as its impact on the U.K. exchange rate and the London stock exchange market index. In their paper, Kane and Muzere extend the DiamondDybvig model of bank runs to an open market economy and show that adding the central banks and the IMF guarantees will reduce, but not eliminate, the banking as well as currency crises. The paper by Chung et al., empirically shows the presence of a long memory property in currency futures market and discusses its hedging implications. In their paper, Lee, Lee and Yu develop a valuation model for the pension benefit guarantees that incorporates the plan termination conditions as well as a stochastic interest rate. In a case study, Hung et al., empirically show that the specially designed dividends (SDD) have positive signals in the Taiwan Stock Exchange. Finally, in their paper, Guerard and Mark show that the use of an R&D quadratic term enhances the mean-variance efficient portfolios and stockholder returns. Andrew H. Chen Series Editor ix

IMPACT OF DIFFERENTIAL AND DOUBLE TAXATION ON CORPORATE FINANCIAL POLICIES IN AN INFLATIONARY WORLD Andrew H. Chen and Edward J. Kane ABSTRACT This paper uses the capital asset pricing model to show that, in realistic circumstances, double taxation and differential tax rates on personal and capital-gains income affect corporate stock values and ﬁnancial policies in non-neutral ways. This non-neutrality holds whenever inﬂation is uncertain and tax-avoidance activity is neither costless nor riskless. The model also allows us to explore how a series of frequently proposed changes in the interplay of corporate and personal taxes would affect corporate dividend payouts and debt usage. Our analysis clariﬁes that conscientious efforts to integrate corporate and personal tax rates must make supporting changes in the size and character of capital-gains tax preferences built into the tax code.

1. INTRODUCTION Differential tax rates generate incentives for corporate and personal taxpayers to rework ordinary income so that it accrues formally in a more lightly taxed form. For a risk-averse taxpayer, tax-avoidance activities have two separate costs: the Research in Finance Research in Finance, Volume 20, 1–17 Copyright © 2003 by Elsevier Ltd. All rights of reproduction in any form reserved ISSN: 0196-3821/doi:10.1016/S0196-3821(03)20001-0

1

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ANDREW H. CHEN AND EDWARD J. KANE

expense of translating income into a tax-preferred form and the riskiness of the tax reduction the taxpayer hopes to achieve. Kane (1975) interprets avoidance costs as implicit tax payments received by someone other than the tax authority. Differences in statutory tax rates and tax-avoidance opportunities also influence the distribution of after-tax real income. Tax-avoidance opportunities weaken the progressivity built in the statutory structure of tax rates economically and politically. Economically, large corporations and wealthy households can spread the fixed costs of expert tax preparation and audit defense over a larger tax base. Politically, these same parties may be better able than other taxpayers to coordinate their lobbying activities to preserve or generate loopholes they value. This paper uses the capital asset pricing model to analyze two issues raised by differential taxation. First, we show how, when the rate of inflation is uncertain, different tax rates on stockholders’ nominal flows of dividend and capital-gains income generate tax-avoidance activity that affects the equilibrium value of a firm’s outstanding shares. Equilibrium conditions for the optimal dividend and debt policies for a value-maximizing firm indicate that financial policies would be irrelevant only under the unrealistic condition that implicit taxes are zero: i.e. if tax avoidance is costless and riskless. Second, we use our model to analyze the effects of two perennial tax-reform proposals on dividend policy and debt structure: proposals aimed at integrating personal and corporate income tax rates and proposals to adjust the size or character of capital-gains tax preferences. The Jobs and Growth Tax Relief Reconciliation Act of 2003 (signed into law by the President on May 28th, 2003) lowers the top capital-gains tax rate from 20 to 15% and the top dividend tax rate from 38.6 to 15%. However, this equality of top statutory rates is misleading. The effective capital-gains tax rate is still lower than the dividend-tax rate, because capital gains enjoy two imbedded options: capitalgains taxes are not due unless and until a gain is realized and taxes on unrealized gains are forgiven at death.

2. CORPORATE FINANCIAL POLICY WITH UNCERTAIN INFLATION AND DIFFERENTIAL NOMINAL-INCOME TAXES ON CORPORATE INCOME, DIVIDENDS, AND CAPITAL GAINS 2.1. Institutional Background In the U.S., corporate income that is distributed to stockholders has traditionally been taxed more heavily than other forms of income. Dividend income experiences

Impact of Differential and Double Taxation on Corporate Financial Policies

3

successive and substantial bites from two separate taxes: the corporate income tax rate, tc , and the personal income tax rate, tp . Ignoring differences in marginal tax rates as well as deductions, exclusions, credits and other forms of tax relief, a representative dollar of dividend income corresponds to only (1 − t c )(1 − t p ) dollars of after-tax income to shareholders. If tc were 40% and tp were 30%, a dollar of dividend income would have an after-tax worth of only 42 cents to shareholders. On the other hand, stockholder returns from a corporation’s retained income are taxed preferentially. This occurs because – always assuming that retained income is invested efficiently – these returns are realized as stock-price appreciation. Under the U.S. tax code, the effective tax rate on capital gains, tg , is lower than tp both because the statutory rate tgs has been low (often 1/2t p ) and because the tax does not become due until the stock is sold. Hence, tg equals the appropriately discounted present value of the statutory rate. Ignoring the value of the timing option, if gains were typically realized after three years with t gs = 1/2t p and the appropriate discount rate were 10%, t g = (0.375)t p . Under previous assumptions about tc and tp , a representative dollar of retained income would be worth (0.60)(1 − (0.375)(0.3)) dollars or 53.25 cents to stockholders. Moreover, the higher the applicable personal tax rate, the greater is the differential benefit to stockholders from corporate income retentions.

2.2. Simplifying Assumptions To keep our model lean, we restrict ourselves to a single period and make eight other convenient assumptions: (1) Each security’s dividend yield is perfectly predictable at the beginning of the period. However, price appreciation or depreciation on each security is random. (2) Corporate and personal taxes are due at known tax rates at the end of the period when corporate cash flows and dividends occur. To treat taxes on accrued capital gains symmetrically, we focus on the present discounted value of the statutory gains rate. Our model ignores the uncertainty that realistically attaches to effective tax rates,1 but we introduce this uncertainty in interpreting our results. (3) The corporate tax rates, tc , is the same for all corporations and the marginal rates on dividends, t ip , and capital gains, t ig , are constant for the ith investor. (4) Taxes are levied on nominal (rather than real) incomes, and interest payments are tax-deductible both for persons and for corporations.

4

ANDREW H. CHEN AND EDWARD J. KANE

(5) In calculating real rates of return, the inflation rate, ␲, ˜ is treated as an additive rather than a multiplicative factor. This abstracts from a conventionally neglected second-order “inflation on current interest” term. (6) Risk-free borrowing and lending opportunities are available to persons at an exogenously determined rate, but corporate borrowing may or may not carry a default risk. (7) Persons and corporations have identical expectations. (8) Each firm’s plans for business investment are fixed and unaffected by dividend and financial-structure decisions.

2.3. Notation Wi ˜ 1i W W Zij Yi Rf ˜j R ˜ i∗ R j ␦j g˜ j t ig t ip ␲ ˜

= the amount of ith investor’s initial real wealth; = the ith investor’s end-of-period real wealth after taxes; = m i=1 W i , the aggregate initial real wealth of all investors taken together; = the amount of the ith investor’s holding of the jth risky asset, where i = 1, . . ., m and j = 1, . . ., n; = the amount of the ith investor’s lending (Yi > 0) or borrowing (Yi < 0) at the risk-free nominal rate of interest; = the risk-free nominal rate of interest; = the random total before-tax nominal rate of return on the jth risky asset ˜ j ) are ¯ j and variance Var(R (with homogenous expectations, the mean R the same for all investors); ˜ j to the ith investor; = the after-tax value of R = the dividend yield; = the rate of net capital gains or losses; = the ith investor’s average and marginal tax rate on capital gains;2 = the ith investor’s average and marginal tax rate on ordinary personal income; = the random rate of inflation (again, with homogenous expectations, all or some of the moments of this variable’s probability distribution [␲, ¯ Var(␲), ˜ ˜ j , ␲] and Cov(R ˜ are the same across investors). 2.4. Analysis of the Individual Investor’s Mean-Variance Opportunity Set

Rational investors should focus on real after-tax returns. However, because personal-income and capital-gains tax rates vary across the population, the gross nominal yield on any security ordinarily generates different after-tax nominal

Impact of Differential and Double Taxation on Corporate Financial Policies

5

yields for different investors. A security’s after-tax yield to any investor may be expressed as the sum of two components: (i) the after-tax yield that would apply if proceeds accrued entirely in the tax-preferred form of capital gains; and (ii) the additional tax that must be paid on the portion of the proceeds received as dividends: i ˜ i i ˜ i∗ R j = (1 − t g )Rj − (t p − t g )␦j .

(1)

Treating the inflation rate as an additive rather than a multiplicative factor, the ith investor’s real end-of-period wealth after taxes becomes: ˜ 1i = W

n

˜ i∗ Z ij (1 + R ˜ + Y i [1 + R f (1 − t ip ) − ␲]. ˜ j − ␲)

j=1

˜ i∗ R j

Substituting for from Eq. (1) and using the balance-sheet constraint that Y i = W i − j Z ij , this becomes: ˜ j (1 − t ig ) − R f (1 − t ip ) − (t ip − t ig )␦j ] + W i [1 + R f (1 − t ip ) − ␲]. ˜ 1i = Z ij [R ˜ W j

(2) Taking the expected value and variance of these expressions for each investor establishes the taxpayer’s mean-variance opportunities in real-wealth space: ˜ 1i ) = ¯ j (1 − t ig ) − R f (1 − t ip ) − (t ip − t ig )␦j ] E(W Z ij [R j

+ W i [1 + R f (1 − t ip ) − ␲]. ¯ ˜ 1i ) = (1 − t ig )2 ˜ j, R ˜ k ) + W 2i V(␲) V(W Z ij Z ik Cov(R ˜ j

(3)

k

− 2(1 − t ig )W i

˜ j , ␲). Z ij Cov(R ˜

(4)

j

For a mean-variance investor, the preference function is defined completely by ˜ 1i . Letting the balance-sheet restraint determine Yi , the first two moments in W first-order optimality conditions can be developed for each risky-asset holding, Zij , j = 1, . . ., n: ¯ j (1 − t ig ) − R f (1 − t ip ) − (t ip − t ig )␦j ] = (1 − t ig )2 Z ij Cov(R ˜ j, R ˜ k) ␪i [R k

˜ j , ␲). ˜ − (1 − t ig )W i Cov(R ˜ 1i )/∂E(W ˜ 1i )]. In Eq. (5), the “audacity index” ␪i = −(1/2)[∂V(W

(5)

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ANDREW H. CHEN AND EDWARD J. KANE

This parameter is the investor’s marginal rate of substitution between the mean and variance of end-of-period real wealth.3 The higher is ␪i , the less reluctant the investor is to accept additional risk in exchange for a promised increase in portfolio return. Simplifying the left-hand side of Eq. (5) and dividing both sides by (1 − t ig )2 , we obtain: ␪i ¯ j − Rf ] = ˜ j, R ˜ k ) − W i Cov(R ˜ j , ␲) [R Z ij Cov(R ˜ i 1 − tg 1 − t ig k

+

␪i (t ip − t ig ) 1 − t ig

(␦j − R f ).

(5a)

For a world with differential taxes and uncertain inflation, individual demand functions for a firm’s shares, derived from the first-order condition Eq. (5a), would be sensitive not only to covariances with returns on other assets, but also to the firm’s inflation risk and dividend policy.

2.5. Analysis of Market Equilibrium By summing this expression across the m investors and imposing market clearance, we obtain market-equilibrium relationships between risk and return for each risky asset j: m m ␪i Wi ¯ j − R f ] = W Cov(R ˜ j, R ˜ m) − ˜ j , ␲) [ R Cov(R ˜ 1 − t ig 1 − t ig i=1 i=1 t ip − t ig (␦j − R f ). ␪i (6) + 1 − t ig i

¯ j as a linear function of three weighted-average We may solve Eq. (6) explicitly for R trade-off parameters: ¯ j = R f + ␭1 Cov(R ˜ j, R ˜ m ) − ␭2 Cov(R ˜ j , ␲) R ˜ + ␭3 (␦j − R f ). The three ␭ parameters may be interpreted as follows: (i) ␭1 = W

␪i i 1−t ig

−1

(7)

Impact of Differential and Double Taxation on Corporate Financial Policies

7

is the market’s unweighted aggregate tax-adjusted “timidity” or reluctance to trade market-volatility risk for aggregate return; ␪i −1 Wi (ii) ␭2 = i i i i 1−t g

1−t g

is the market’s weighted-average “timidity” with respect to inflation risk; t ip −t ig ␪i −1 (iii) ␭3 = ␪ i i i i i 1−t g

1−t g

is a weighted-average yield-adjustment factor that prices the after-tax advantage (if ␦j < R f ) of being able to generate “tax losses” by means of leveraged investments in asset j. This factor imposes a penalty on securities whose dividend yields exceed the risk-free rate. In passing, we note three points: (i) Assets whose inflation risk is positive have less undiversifiable risk than their standard beta coefficient would suggest. Moreover, an asset’s undiversifiable risk is decreased by a ceteris paribus increase in its covariance with the inflation rate. (ii) In the absence of uncertain inflation, Eq. (7) reduces to Brennan’s (1970) result: ¯ j = R f + ␭1 Cov(R ˜ j, R ˜ M ) + ␭3 (␦j − R f ). R

(8)

(iii) As long as personal tax rates exceed capital-gains tax rates, a firm would ¯ j by setting its dividend at its corner minimize its required rate of return R value. Because of institutional constraints, this corner value may exceed zero. 2.5.1. Assuming Homogeneous Tax Rates Equations (6) and (7) simplify if all investors are subject to the same two tax rates, tp and tg : i ␪i ¯ ˜ j, R ˜ M ) − W Cov(R ˜ j , ␲) [Rj − R f ] = W Cov(R ˜ 1 − t ig 1 − t ig

  t ip − t ig i ␪i  (␦j − R f ). + (6a) 1 − t ig ˜ j , ␲) ˜ Cov(R ¯ j = R f + ␭ Cov(R ˜ j, R ˜ M) − R + (t p − t g )(␦j − R f ). 1 − tg

(7a)

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ANDREW H. CHEN AND EDWARD J. KANE

In (7a), ␭ = W(1 − t g )/ i ␪i may be interpreted as tax-adjusted aggregate level of “timidity” in the market.4 It is interesting to note that, in determining equilibrium expected rates of return, inflation risk receives a higher weight than volatility risk. In Eq. (7a), inflation risk is grossed-up for capital-gains taxes to avoid double-counting the indirect effects ˜ M along with its direct effects onR ˜ j . In this model, of inflation operating through R the capital-gains tax rate influences the market price of risk-bearing, the gross-up rate for inflation risk, and the coefficient attached to the difference between the dividend yield and the riskless rate. As a result, changes in tg should alter the relative prices of assets and therefore the pattern of resource allocation. 2.5.2. Market Price of Risk-Bearing With a Uniform Personal Tax Rate Because Eq. (7a) must price the market portfolio as well, we can solve explicitly ˜ M for R ˜ j , Eq. (7a) becomes for the market price of risk-bearing. Substituting R ¯ M = R f + ␭ ␴2M − ␴M␲ + (t p − t g )(␦M − R f ), R (7b) 1 − tg ˜ M , ␲). where ␴M␲ = Cov(R ˜ If the bracketed coefficient is not zero, we may solve Eq. (7b) for ␭, the market price of risk bearing: ␭=

¯ M − R f − (t p − t g )(␦M − R f ) R ␴2M − ␴M␲ /(1 − t g )

(9)

˜ M − R f )/␴2 , in the This expression differs from the market price of risk, ␭0 = (R M traditional capital asset pricing model (CAPM) or the Sharpe-Lintner-Mossin version by the negative final terms added to both the numerator and the denominator. Our model may clear up two problems encountered in trying to apply the CAPM empirically. First, empirical estimates of the market price for risk-bearing have evidenced nonstationarity. Changes in tax rates, inflation risk, and dividend usage could easily explain this. Second, the market risk premium has proved too high on average to respect CAPM restrictions on the regression intercepts. We note that the more weakly the market portfolio hedges against inflation risk and the more the average dividend rate exceeds the risk-free rate, the greater the divergence between ␭0 , the market price of risk in the traditional CAPM, and the corresponding ␭ of our differential-tax model. With t p > t g , for ␭ to be less than ␭0 on average, it is sufficient that on average (i) ␦M > R f , and (ii) ␴M␲ < 0.

Impact of Differential and Double Taxation on Corporate Financial Policies

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This explanation is very flexible, in that if either condition is violated, the other inequality need only be proportionately greater. Comparison with other models establishes testable implications by which to evaluate the importance of differential taxes statistically. The differential-tax model provides at least a potential explanation for observations that seem anomalous within the narrower frameworks either of the traditional CAPM or the standard model of the Fisher Effect. We invite others to test whether the variables featured in the differential-tax model can improve the outcome of time-series tests of these two theories.

3. DIFFERENTIAL TAXATION FROM THE CORPORATION’S POINT OF VIEW 3.1. Cash Flow Version of the Differential-Tax Model ˜ j to represent the total end-of-period return on asset j, where X ˜ j is the We use X ˜ sum of dividends, Dj , and random price appreciation, Gj . Introducing Vj to stand for the initial market value of asset j, the asset’s rate of total return becomes: ˜j ≡ R

˜j Dj + G − 1. Vj

(10)

Substituting Eq. (10) into Eq. (7a), we can solve explicitly for the equilibrium value of Vj : ˜ j , ␲) ˜ Cov(X 1 ˜ ˜ ˜ Vj = E(Xj ) − ␭ Cov(Xj , RM ) + ␭ 1 + R f (1 − t p + t g ) 1 − tg − (t p − t g )D j .

(11)

This formulation makes it clear that, with t p > t g , a value-maximizing firm would set dividends at zero, using its cash flow to repurchase its own shares to the extent ˜ j , ␲), that is feasible. It also shows that – since an asset’s inflation risk, Cov(X ˜ is grossed-up for the effect of capital-gains taxes – unit for unit, inflation risk plays ˜ j, R ˜ M ). a larger role in determining asset value than traditional market risk Cov(X Equation (11) states that the equilibrium value of firm j is simply the certaintyequivalent of the firm’s end-of-period cash flow, discounted at the tax-adjusted risk-free rate of interest. The certainty-equivalent is found by adjusting the firm’s expected cash flow at the end of the period for its market risk, inflation risk, and expected dividend.

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The corner solution for optimal dividend policy found here repudiates the Miller and Scholes (1982) proposition that dividend policy is irrelevant. Miller and Scholes assume costless opportunities for tax avoidance, which allows all investors to pay taxes at the low capital-gains tax rate. In their model, optimizing taxpayers effectively eliminate the statutory differential between tp and tg . Under this assumption, our Eq. (11) makes dividend policy irrelevant also.5 Models that assume costless and riskless opportunities for tax avoidance effectively negate the government’s ability to collect corporate taxes. Perfect tax avoidance could not exist in stationary political and economic equilibrium. Taxation is essentially a forcible taking by (and for) authorized government officials and tax revenue is the fuel on which the government runs. To preserve their jobs, power, and dignity, government officials must be expected to take legislative, administrative, and judicial action to keep the costs and risks of tax avoidance high enough to prevent tax loopholes from destroying their tax-collection capacity.

3.2. Explicitly Introducing Corporate Income Taxes into the Model ˜ ∗ stand for the jth corporation’s after-tax cash flow before dividends. Using We let X j Bj for the book value of outstanding debt and rj the coupon rate on this debt, we can write: ˜ j∗ = (X ˜ j − r j B j )(1 − t c ) + r j B j = X ˜ j (1 − t c ) + r j B j t c . X Employing this expression in the valuation Eq. (11), we obtain: ˜ j , ␲) ˜ Cov(X 1 − tc ˜ j, R ˜ M) + ␭ ˜ j ) − ␭ Cov(X Vj = E(X 1 + R f (1 − t p + t g ) 1 − tg (t p − t g )D j rj Bj tc . + − 1 − tc 1 − tc

(12)

(13)

3.2.1. What are the Critical Assumptions for Debt and Dividend Irrelevance and How Attractive are They? In the model summarized in Eq. (13), the value-maximizing firm should not only set dividends as low as possible, but to take advantage of the tax deductibility of bond interest should make maximum use of debt. Moreover, not only is ∂V j /∂B j positive, but the incremental tax saving achieved by issuing additional debt increases with the differential between tp and tg : ∂V j rj tc = > 0; ∂B j 1 + R f (1 − t p + t g )

Impact of Differential and Double Taxation on Corporate Financial Policies

∂ ∂t g ∂ ∂t p

∂V j ∂B j ∂V j ∂B j

11

< 0; > 0.

Finally, Eq. (13) indicates that increases in the tax rate on capital gains would raise the value of firms whose after-tax cash flow rises with the inflation rate while lowering the value of firms whose after-tax cash flow correlates negatively with the inflation rate. Drawing on Miller (1977), Fama (1977) develops a market-equilibrium model in which dividend and financial-structure decisions do not affect the value of the firm. Fama’s model sets t g = 0 and t c = t p . These assumptions turn Eq. (13) into: 1 − tp ˜ j ) − ␭[Cov(X ˜ j, R ˜ M ) − Cov(X ˜ j , ␲)] Vj = E(X ˜ 1 + R f (1 − t p ) tp + [r j B j − D j ] . (13 ) 1 − tp This formulation helps us to identify what assumptions must be added to our model to render dividend and financial-structure decisions irrelevant. Either firms and individuals must engage in sufficient tax avoidance to drive the effective tax rate on dividend income to zero or firms must be constrained by outside forces to keep total interest payments and total dividends equal. If tax-avoidance activities are costless at the margin, either condition may be reconciled with our model. Both approaches make use of the further condition that corporate and personal tax payments remain non-negative. Although neither alternative is easy to defend, the second alternative is less elegant. The condition that r j B j = D j makes sense only under the further restriction that D j = X j , which requires in turn that the firm’s cash flow be non-random. If a firm plans to distribute all of its income, r j B j = D j corresponds to the corner solution for its debt policy. Once a firm has issued enough bonds to shelter every dollar of earned income, it receives no benefit from issuing additional debt. Since zero and negative taxable incomes all map into a zero value for taxes due, B j > X j /r j represents an “overkill” situation. In effect, with X j = D j , the mechanics of tax avoidance would convert bonds and stock shares into financial joint products. In contrast, with costless tax avoidance, the ﬁrst alternative is relatively easy to justify. It requires only that firms and individuals be sufficiently relentless in their use of tax-avoiding leverage to drive their effective tax rates to zero. Since all individuals know the dividend that they will receive at the end of the period, they know precisely how much debt to issue to make their taxable incomes zero. Since

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each corporation’s cash flow is random, to be sure of avoiding all taxes, firms may set Bj at max (X j )/r j (which must in turn be assumed finite). However, complete tax avoidance would deprive the Treasury of revenue from capital income and make every asset-market participant an issuer of bonds. The Treasury would be led to reduce investor tax avoidance by taxing capital gains more aggressively and/or limiting the deductibility of interest payments. Similarly, debt markets would find it hard to stand still, too. To put the debt-market problem most dramatically, let us suppose that all firms as well as all households can issue riskless debt. To defend the exogenous value of Rf , an outside agency must buy debt from every market participant. In this model, no way exists for the riskless-asset market to clear endogenously. Endogenous clearance requires that personal income tax rates differ sufficiently (progressively with income in Fama and Miller) to allow riskless lending to offer some low-bracket investors higher incomes even after paying taxes on their interest receipts than they could earn if they insisted on leveraging their portfolios to avoid taxes all together. Since, in principle, discontinuities in tax brackets or in the distribution of wealth could prevent tc and tp from reaching equality at the margin, some degree of continuity must be assumed as well. Our analysis is designed to bring out the critical role that the assumed costlessness and risklessness of tax-avoidance activity plays in theorems that hold debt and dividend policies irrelevant. Completely contrary to this assumption, the theory and practice of tax law portray tax-avoidance activity as a difficult game played for uncertain benefits against an unpredictable opponent (the IRS) before unpredictable referees (the courts). Documentation requirements set by the IRS and fees set by tax-law practitioners make marginal tax-avoidance costs far from negligible. Under Section 385 of the Tax Code, the IRS can add to these costs by contesting the deductibility of interest payments claimed by highly levered corporations. Moreover, when the bondholders are themselves shareholders, the law places the burden on them to disprove the presumption that challenged “loans” are in fact disguised equity investments (Smith & Warner, 1979). Hence, for any particular firm, the applicable maximum use of debt is uncertain and presumptive tax-avoidance benefits should be discounted for risk. Models that posit costless and riskless opportunities for tax avoidance are not fundamentally different from models that assume no taxes at all. Sleight-of-hand tricks are performed to make the effects of taxes disappear: “Now you see them; now you don’t.” Basic price theory requires taxpayers to engage in tax avoidance only until the marginal costs of avoidance activities rise to the level of their risk-adjusted marginal benefits (Kane, 1975). In a world with differential taxation and uncertain inflation, when the marginal costs or risks of tax avoidance are nonzero, dividend and debt policies are far from irrelevant.

Impact of Differential and Double Taxation on Corporate Financial Policies

13

4. EFFECTS OF ALTERNATIVE TAX REFORMS 4.1. Dividend Tax Credit Providing stockholders with a tax credit against their personal income taxes for tax paid on dividends they receive would require us to reinterpret tp in Eq. (13) as the net extra personal-income tax on dividends, t p − t c . Substituting t p − t c , for tp everywhere it appears in Eq. (13) raises the algebraic values of the tax-adjusted discount rate and of the coefficient of dividends. Most importantly, the coefficient of Dj becomes: tc + tg + tp . 1 + R f (1 + t c + t g − t p ) For value-maximizing firms, t p = t c + t g becomes a switching point. If t p < t c + t g , asset values would be maximized by full payout of current earnings. On the other hand, if the inequality were reversed, zero payouts would remain optimal. In the real world where personal-income tax rates range up to 35% at the margin, a dividend tax credit would intensify clientele effects by making stocks with low (high) payouts relatively more attractive than before to investors in high (low) tax brackets. Tax-avoiding realignments of corporate dividend policies and investor stockholdings would make the decline in Treasury revenues much greater than prereform balance sheets might suggest. One would suppose that the larger the volume of stocks traded in the wake of tax change between high-bracket and low-bracket investors, the more the credit would hurt Treasury revenues. 4.2. Dividend Deductibility Making a firm’s dividend payouts tax-deductible would have much the same effect as allowing a dividend tax credit against personal-income taxes. With deductible dividends, the firm’s after-tax cash flow before dividends becomes: ˜ j − r j B j − D j )(1 − t c ) + r j B j + D j = X ˜ j (1 − t c ) + r j B j t c + D j t c . X ∗j = (X (12a) Hence, the value of the firm would be: ˜ j , ␲) ˜ ␭ Cov(X (1 − t c ) ˜ j ) − ␭ Cov(X ˜ j, R ˜ M) + Vj = E(X 1 + R f (1 − t p + t g ) 1 − tg (t c + t g − t p )D j rj Bj tc + . (13a) + 1 − tc 1 − tc

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ANDREW H. CHEN AND EDWARD J. KANE

Gathering the terms in Dj , we obtain its coefficient as: tc + tg − tp . 1 + R f (1 + t g − t p ) Although the denominator differs, the numerator is the same as in the tax-credit case. Hence, a value-maximizing firm’s payout policy shows the same switching point.

4.3. Imputing a Fraction of Undistributed Corporate Proﬁts to Stockholders’ Personal Incomes In our one-period model, when management employs undistributed profits efficiently, each dollar of undistributed profits raises a stock’s price by at least a dollar. For this reason, imputing a share of undistributed profits to the personal incomes of stockholders is much like imposing tp on a fraction of their current capital gains. We let ␤ represent the fraction of current appreciation in asset j’s price to be taxed as ordinary income with (1 − ␤) of the appreciation still taxed at the preferential capital-gains tax rate. Corresponding to Eq. (1), security j’s after-tax rate of return then becomes: ˜ i∗ R ˜ j [1 − ␤t p − (1 − ␤)t g ] j = (1 − t p )␦j + g ˜ j − (1 − ␤)(t p − t g )␦j . = [1 − t g − ␤(t p − t g )]R

(14)

¯ j becomes: Corresponding to Eqs (7), (7a) and (8), the mean equilibrium of R ˜ j , ␲) ˜ Cov(R ¯ ˜ ˜ Rj = R f + ␭ Cov(Rj , RM ) − 1 − t g − ␤(t p − t g ) + (1 − ␤)(t p − t g )(␦j − R f ).

(15)

Applying Eq. (15) to the market portfolio, we obtain the analogue to Eq. (7b): ␴M␲ ¯ M = R f + ␭ ␴2M − R + (1 − ␤)(t p − t g )(␦j − R f ). (16) 1 − t g − ␤(t p − t g ) Solving Eq. (16) for ␭ , the market price of risk-bearing yields: ␭ =

¯ M − R f − (1 − ␤)(t p − t g )(␦j − R f ) R ␴2M − ␴M␲ /(1 − t g − ␤(t p − t g ))

.

(17)

Impact of Differential and Double Taxation on Corporate Financial Policies

Finally, the equilibrium value of asset j becomes: 1 − tc ˜ j ) − ␭ Cov(X ˜ j, R ˜ M) Vj = E(X 1 + R f [1 − (1 − ␤)(t p − t g )] ˜ j , ␲) (1 − ␤)(t p − t g )D j ␭ Cov(X ˜ rj Bj tc + . + + 1 − t g − ␤(t p − t g ) 1 − t c 1 − tc

15

(18)

Differentiating Eqs (17) and (18) with respect to ␤ produces messy expressions that are difficult to evaluate. But for realistic values of the interest-rate and tax parameters, the sign of ∂␭ /∂␤ can be seen to vary with the sign and magnitude of ␴M␲ The more poorly the market portfolio hedges against inflation, the smaller algebraically would this partial slope be.

4.4. Complete Integration of the Corporate Income Tax In our model, complete corporate tax integration may be achieved straightforwardly by setting t c = 0. However, if the marginal costs of personal tax avoidance are nonzero, this approach would enhance corporations’ ability to convert individual taxpayers’ capital incomes into tax-favored capital gains. Governmental concern for the integrity of the personal income tax makes it likely that a reduction in capital-gains tax preferences would have to accompany such a reform. 4.4.1. With No Change in Capital-Gains Tax Preferences in Our Model Setting t c = 0 does not affect any asset’s rate of return or the market price of riskbearing. However, because tc enters the expression for the equilibrium value of individual assets, Eq. (13) becomes: Vj =

1 ˜ j, R ˜ M ) − ␭ Cov(X ˜ j , ␲) ˜ j ) − ␭ Cov(X ˜ E(X 1 + R f (1 − t p + t g ) − (t p − t g )D j . (13b)

In Eq. (13b), debt policy no longer affects the value of the firm, but an incentive to minimize dividends remains. Appreciation on corporate shares would loom as an easy and hard-to-regulate avenue for personal tax avoidance. 4.4.2. Simultaneously Raising ␤ to 100% By setting t c = 0 and ␤ = 100%, authorities could integrate the corporate tax and establish tax neutrality for capital incomes. In this case, Eqs (15),

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(16), (17), and (18) become ˜ j , ␲) ˜ Cov(R ˜ j, R ˜ M) − ¯ j = R f + ␭ Cov(R , R 1 − tg ˜ ˜ ¯ M = R f + ␭ Var(R ˜ M ) − Cov(RM , ␲) R , 1 − tp ¯ M − Rf R , ˜ M ) − Cov(R ˜ M , ␲)/(1 Var(R ˜ − tp) ˜ j , ␲) ˜ ␭ Cov(X 1 ˜ ˜ ˜ Vj = E(Xj ) − ␭ Cov(Xj , RM ) + . 1 + Rf 1 − tp ␭ =

(15a) (16a) (17a) (18a)

As Eq. (18a) should make clear, these tandem changes would make debt and dividend policies irrelevant once again.

5. POSSIBLE EXTENSIONS OF THE ANALYSIS The model presented here makes no provision for uncertainty in dividend yields or tax-avoidance benefits and it treats expectations as exogenous. Implications are only occasionally drawn for cases where expectations and marginal tax rates differ across investors. The model assumes that the burden of corporate profits taxes fall entirely on stockholders, who are afforded no opportunity to shift their tax burdens to the corporation’s customers or employees. Our analysis also ignores a number of asymmetries that complicate U.S. tax law. Among other things, the Internal Revenue Code limits: the exemption for dividends received; the maximum annual write-off of capital losses; and the use of loss carry-backs and carry-forwards. It also authorizes a myriad of tricky ways for tax-wise firms and investors to shelter personal and corporate income flows and makes some types of income tax-exempt. Although incorporating any of these features would change the details of our analysis, as long as the Internal Revenue Code taxes nominal income and implicitly taxes avoidance activity, after-tax implications of dividend and debt policy will vary with the level of inflation risk.

NOTES 1. To predict effective tax rates, one must forecast successfully not only the date on which each asset is to be liquidated, but also interim changes in tax statutes, regulations, and

Impact of Differential and Double Taxation on Corporate Financial Policies

17

judicial rulings. Recent years have seen substantial changes in capital-gains tax preferences: adjusting the minimum holding period for eligibility, raising and lowering the statutory rate, and introducing minimum-tax and maximum-tax complications. 2. Our formulation ignores the current limitation on the maximum amount of capital losses that may be deducted in any year. 3. The term “audacity” is due to Bierwag and Grove (1965), who further incorporate the risk inherent in an individual’s forming expectations. 4. If t p = t g , Eq. (7a) reduces to Eq. (38) in Chen and Kane (1977). 5. Based upon the results of their empirical study, Black and Scholes (1974) argue that a change in dividend policy would have no effect on the firm’s stock price. Graham (2003) reviews some relevant theoretical arguments and empirical evidence on how taxes affect corporate financial policies and firm value.

ACKNOWLEDGMENTS The authors wish to thank Jeffrey Fisher, John Glascock, George Kaufman, George Racette, and Gordon Roberts for valuable comments on an earlier draft of this paper.

REFERENCES Bierwag, G. O., & Grove, M. A. (1965). On capital asset prices: Comment. Journal of Finance, 20(March), 89–93. Black, F., & Scholes, M. (1974). The effects of dividend yield and dividend policy on common stock prices and returns. Journal of Financial Economics, 1(May), 1–22. Brennan, M. J. (1970). Taxes, market valuation and corporate financial policy. National Tax Journal, XXIII, 417–427. Chen, A. H., & Kane, E. J. (1977). Tax effects on risk-taking in an inflationary context, presented at the TIMS XXIII International Meeting (July). Fama, E. F. (1977). Taxes and optimal financing decisions by firms, mimeo, Graduate School of Business, University of Chicago. Graham, J. R. (2003). Taxes and corporate finance: A review. Review of Financial Studies (forthcoming). Kane, E. J. (1975). A cross-section study of tax avoidance by large commercial banks. In: D. Belsley, E. Kane, P. Samuelson & R. Solow (Eds), Inﬂation, Trade and Taxes (pp. 218–246). Columbus: Ohio State University Press. Miller, M. H. (1977). Debt and taxes. Journal of Finance, 32(May), 261–275. Miller, M. H., & Scholes, M. (1982). Dividends and taxes. Journal of Financial Economics, 6, 333–364. Smith, C. W., Jr., & Warner, J. B. (1979). On financial contracts and optimal capital structure: An analysis of bond convenants. Journal of Financial Economics, 7(June), 117–161.

PRICE CEILING REGULATION OF A TAX EVADING MONOPOLIST Partha Sengupta ABSTRACT This paper uses a simple analytic model to analyze the problem of tax evasion by a monopolist subject to price ceiling regulation. Prior research had explored tax evasion decisions of a monopolist in a non-regulatory environment. However, since monopolies often operate in a regulatory environment, it is important to examine how a regulated monopolist makes its tax reporting decisions. This paper shows that under certain conditions, an increase in the effective price ceiling increases tax evasion. The production decision of the monopolist however is unaffected by tax evasion parameters. A social planner, attempting to maximize social welfare, subject to a revenue constraint, can achieve optimality in a number of ways; with or without full compliance.

1. INTRODUCTION Since the seminal papers by Allingham and Sandmo (1972) and Srinivasan (1973), a large body of literature has modeled the determinants of individuals’ tax evasion decision.1 Recently some attention has been devoted to understanding the tax evasion decision of a monopolist. This line of research explores a monopolist’s tax evasion and production decisions under the assumption that its production costs are not observable by the tax collector and thus can be misreported. Kreutzer and Lee (1986) was the first paper to use this framework. They showed that a Research in Finance Research in Finance, Volume 20, 19–32 Copyright © 2003 by Elsevier Ltd. All rights of reproduction in any form reserved ISSN: 0196-3821/doi:10.1016/S0196-3821(03)20002-2

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risk neutral monopolist who faces no penalty from detection of their misreporting would produce more than the optimal level under no tax evasion suggesting that the profit tax is not neutral in terms of monopolist’s production decision. Subsequently, Wang and Conant (1988) showed that a risk averse monopolist facing a probability of detection and penalty for misreporting would set output levels independent of tax evasion, indicating that the profit tax is in fact neutral. Further research by Wang (1990), Yaniv (1996) and Lee (1998) explores the tax neutrality issue under the more general scenario where the probability of detection and penalty upon detection varies endogenously with the overstated amount. The results of these papers suggest that neutrality of the profit tax is dependent on the particular form of cost overstatement and the nature of endogeneity of the audit probability and penalty rates. This paper extends prior research by examining the tax evasion decision of a monopolist facing a price ceiling regulation. This issue is important for at least two reasons. First, monopolies often operate in a regulatory environment, so it is of interest to examine if the monopolist’s production and tax evasion decisions continue to be separate under this setting. Second, prior research on the effects of regulation on a monopolist generally identifies the government’s (or regulator’s) optimal policy in a setting where the regulatory instrument is the only one under their control.2 Once tax evasion is allowed for, the government’s choice becomes more complex as it has to decide between optimal production levels, tax compliance and revenue generation. Changes in regulatory parameters can affect tax revenues so there may be a need for coordinated analysis of the two functions of the government. Using a simple model of tax evasion by a monopolist subject to price ceiling regulation this paper shows that under certain conditions, an increase in the effective price ceiling increases tax evasion also. Tax evasion decisions however are found not to affect output decisions of the monopolist. So the optimal price ceiling is set at the same level as without tax evasion, i.e. at the point where price equals expected marginal cost. The government, attempting to maximize social welfare, subject to a revenue constraint, can choose its parameters in a number of ways. If it can adjust its policy parameters costlessly, optimality can be achieved with or without tax evasion. Thus, elimination of tax evasion is not necessarily the best policy of the government. Because optimality can be achieved in a number of ways, the optimal tax, audit, and penalty rates are not uniquely determined.

2. THE MONOPOLIST’S PROBLEM The model developed here extends the framework of Wang and Conant (1988) by introducing a binding price ceiling. The model involves a monopolist producing

Price Ceiling Regulation of a Tax Evading Monopolist

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a single output q at a cost c(q). Costs are assumed to be increasing in output so that c (q) > 0. The inverse demand for the firm’s product is given by p(q) with p (q) < 0. The monopolist is subject to a proportional profit tax at the rate of t. The government also regulates the activity of the monopolist by setting a price ceiling on the monopolist’s product, which takes the form p ≤ p, ¯ where p¯ is the ceiling price specified. It is assumed here that the government is fully informed about the demand for the monopolist’s product and the price that it charges. So it is not possible for the monopolist to misreport its revenues. The government however is incompletely informed about the monopolist’s cost of production.3 The government, if it wants, can perform an audit of the monopolist’s tax return, in which case it can learn the monopolist’s costs accurately. Auditing a tax return, however, involves some costs so that for budgetary reasons only a certain fraction of tax returns are audited each period, returns being chosen at random for audits. It is assumed that the way in which the government’s tax revenues are spent, have no impact on the monopolist’s decision making. The fact that there is asymmetry of information between the monopolist and the government and the fact that only a fraction of all tax returns are audited, provides the monopolist with an opportunity to misreport costs to evade taxes. If the monopolist over-reports its cost by a fraction ␮(␮ ≥ 0), total reported cost is c r (q) = (1 + ␮)c(q) Such over-reporting would reduce the tax burden of the monopolist by t␮c(q) in the event he is not audited. If he is audited, however, his true cost is correctly identified and he is forced to meet all his tax obligations and pay a fine of (␪ − 1) times the evaded tax (␪ > 1) as penalty for tax evasion. The government is assumed to announce the penalty rate ␪ before the monopolist makes the production decisions and is also assumed to commit to the announcement. The monopolist is aware of the fact that if he misreports costs he might be audited. Suppose that the monopolist perceives that he is likely to be audited with some probability ␣.4 He then makes his decisions so as to maximize his expected utility from net profits5 (after tax and penalty, if any) given by EU = ␣U(␲d ) + (1 − ␣)U(␲nd )

(1)

subject to the price ceiling constraint p ≤ p¯ where ␲nd = (1 − t)[R(q) − c(q)] + t␮c(q)

(2)

refers to the net profits of the monopolist in the event that he over-reports costs and is not detected, and, ␲d = (1 − t)[R(q) − c(q)] − (␪ − 1)t␮c(q)

(3)

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refers to the net profits of the monopolist in the event that he misreports costs and is detected, where R(q) ≡ p(q) · q is the revenue of the monopolist. Regarding the monopolist’s utility function, it is assumed that U (·) > 0. The monopolist is also assumed to be risk averse so that U (·) < 0. Regarding the penalty rate ␪ and the audit probability ␣ it is assumed that these are exogenous (from the monopolist’s point of view) and independent of the volume of taxes evaded. For simplicity, it is assumed that the monopolist cannot adjust the quality of the product. Problems relating to inefficiency arising from quality adjustments are thus ignored. The problem of the monopolist then is to choose q and ␮ so as to maximize his expected utility from profits given by Eq. (1) subject to the regulatory constraint p ≤ p¯ (with ␲nd and ␲d being given by Eqs (2) and (3) respectively). The Lagrangian for the problem is given by L = EU + ␭[p¯ − p]

(4)

where ␭ is the Lagrange multiplier. Assuming that the price ceiling is binding and confining attention to interior solutions only, the F.O.C.’s for a maximum are: ∂L = (1 − ␣)tc(q)U (␲nd ) − ␣(␪ − 1)tc(q)U (␲d ) = 0 ∂␮

(5)

∂L = ␣U (␲d )[(1 − t){R − c } − (␪ − 1)t␮c ] + (1 − ␣)U (␲nd ) ∂q × [(1 − t){R − c } + t␮c − ␭p = 0

(6)

And, ∂L = p¯ − p = 0 ∂␭

(7)

where R ≡ ∂R(q)/∂q represents the marginal revenue of the monopolist, p ≡ ∂p(q)/∂q refers to the slope of the monopolist’s demand curve, c ≡ ∂c(q)/∂q refers to the marginal cost of the monopolist and U (␲i ) ≡ ∂U(␲i )/∂␲i , i = d, nd; refers to the marginal utility of the monopolist in the two states of nature. The solution to Eqs (5)–(7) gives the optimal choice of the monopolist (␮, ˜ q˜ ). It is easy to show that a necessary condition for the monopolist to evade some taxes is that 1 > ␣␪. The net expected profits of the monopolist can be defined as E␲ ≡ ␣␲d + (1 − ␣)␲nd = (1 − t)[R(q) − c(q)] + t␮(1 − ␣␪)c(q)

(8)

From Eq. (8) it is clear that net expected profits are larger with tax evasion than without tax evasion (in which case the net gain is (1 − t){R(q) − c(q)}) so long

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as (1 − ␣␪) > 0. It is assumed here that the parameter values are such that this condition is satisfied. The determinant of the bordered Hessian for the second order condition is given by 2 ∂ L || = − (p )2 (9) ∂␮2 where, ∂2 L = ␣t 2 (␪ − 1){c(q)}2 U (␲d ) + (1 − ␣)t 2 {c(q)}2 U (␲nd ) < 0 ∂␮2

(10)

and U (␲i ) ≡ ∂U (␲i )/∂␲i < 0, i = d, nd. From Eqs (9) and (10) it is clear that || > 0 so long as the monopolist is risk averse. Thus, the second order conditions for a maximum are globally satisfied. Note that the second order conditions are satisfied irrespective of any assumptions on the marginal cost function. This is because under an effective ceiling constraint, output is determined solely by the demand function. Before proceeding to the comparative static results of the model, it is useful to state the following result. Proposition 1. Assuming that the price ceiling is binding, the monopolist’s optimal output occurs where R < c .6 The proposition implies that the monopolist’s optimum output under regulation is larger than that without regulation. This is the same result obtained for the no tax evasion case.

3. COMPARATIVE STATIC RESULTS The model reveals a number of interesting results. These are summarized in the form of the propositions given below. Propositions 2.1 and 2.2 refer to the effect of changes in the government policy parameters ␪, ␣, t, and p¯ on optimal output produced by the monopolist. Propositions 3.1, 3.2 and 3.3 refer to the effect of the same policies on the optimal proportion ␮ by which the monopolist overreports costs. The results are obtained simply from differentiating the first order conditions, so that the proofs are omitted. Proposition 2.1. When the price is binding the monopolist’s optimal output choice is unaffected by alterations in the profit tax rate, the penalty rate and the audit probability of the government.

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Proposition 2.2. An increase in the effective price ceiling leads to a fall in the monopolist’s optimal output. That is, ∂q/∂p¯ < 0. Propositions 2.1 and 2.2 are intuitively clear. With the price ceiling being effective, the firm’s output is obtained solely from the demand curve for the product. Moreover, since the monopolist’s price and output are both costlessly observed by the government, there is no room for misreporting these. Proposition 3.1. An increase in the penalty rate or the audit probability of the government leads to a reduction in the fraction by which costs are over-reported. That is ∂␮/∂␪ and ∂␮/∂␣ < 0. This is also an intuitively clear result. It says that stricter enforcement laws reduce tax evasion. This is the usual result in tax evasion literature. Proposition 3.2. A reduction in the price ceiling, other things remaining constant, leads to a reduction in the fraction by which costs are over-reported, if the Arrow-Pratt measure of absolute risk aversion of the monopolist is nonincreasing in income. In other words, ∂␮/∂p¯ > 0 if, R A (d) ≥ R A (nd), where R A (i) = −U (␲i )/U (␲i ), i = d, nd; is the Arrow-Pratt measure of absolute risk aversion. The result is not very difficult to explain. So long as the price ceiling is effective, an increase in the ceiling results in an increase in profits of the monopolist. This would induce him to greater risk taking, if his preferences exhibit decreasing absolute risk aversion. So he tends to mis-report costs by a higher fraction. Proposition 3.2 is very interesting. It indicates that a reduction in the price ceiling in this simple model is not only welfare improving in terms of increasing the output of the monopolist but it has also the added “advantage” of reducing tax evasion and hence increasing tax collections. This clearly points out a need for coordinating the activities of the regulatory authority and the tax authority. Propositions 2.1, 2.2, 3.1 and 3.2 show that changes in tax enforcement parameters ␣ and ␪ have no impact on the optimal output of the monopolist, this being determined solely by the ceiling constraint p. ¯ Alterations in the ceiling price however have impact on the amount of evasion since ␮ depends on p. ¯ This indicates that the one-sided separability between tax evasion and production decisions observed by Marrelli (1984), Wang and Conant (1988), Wang (1990) and Yaniv (1996) continues to exist with the introduction of a binding price ceiling regulation. Proposition 3.3. An increase in the proportional profit tax rate leads to a reduction in the fraction by which costs are over-reported if the Arrow-Pratt measure of absolute risk aversion of the monopolist is non-increasing in income. That is, ∂␮/∂t < 0 if, R A (d) ≥ R A (nd).

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This proposition can be explained in the same way as Proposition 3.2. An increase in the profit tax reduces the monopolist’s after-tax profits or net income. This leads him to reduce tax evasion (a reduction in ␮) if his preferences exhibit decreasing absolute risk aversion. This result is similar to those obtained by Yitzhaki (1974) for individual income taxes and Wang and Conant (1988) and Kreutzer and Lee (1986) for monopolist’s profit taxes. The result however goes against the common belief that increasing evasion is a direct consequence of increasing marginal tax rates.

4. THE GOVERNMENT’S OPTIMIZATION PROBLEM The last section set out the problem of a single monopolist and discussed the effects of changes in various government policy parameters on the monopolist’s output and tax evasion decisions. To consider optimal government policies, suppose the economy consists of N firms, firms being indexed by i (i = 1, 2, . . ., N). These may be various local monopolies of the same good or could be monopolies over distinct goods. It is assumed that the N markets are sufficiently separated from one another that the action of the ith firm has no impact on the profits of the jth firm. The government regulates the activities of these monopolies by imposing a price ceiling p¯ i on each of them and taxes them at the proportional rate t. Whereas the government has costless knowledge about the output of the monopolists, it does not have complete knowledge about the monopolists’ costs. It is aware that the cost of production of the ith firm takes the form ci (qi , ␥i ) where ␥i is a parameter that is unknown to the government (but known to the monopolist). The government however has some subjective prior probability distribution for this unknown parameter. It is assumed that fi (␥i ) represents the density function for this probability distribution. The function is assumed to be continuous in ␥i with f i (␥i ) > 0 over the interval [␥0i , ␥1i ]. The government makes its decisions on the basis of this distribution of ␥i . The government is also aware that firms can evade taxes due to the asymmetry of information and if it so desires, it can prevent this (at least partially) by auditing a fraction ␣ of all tax returns and collecting penalty at the rate of ␪ from any firm that is found to have evaded taxes. The objective of the government is to set the tax rates, the price ceilings, the audit rate and the penalty rate so as to maximize some measure of social welfare to be defined below. Note that whereas the tax rates, the price ceilings and the penalty rate can be imposed without incurring any administrative costs, auditing tax returns involve some cost which can be given by g(␣) with g (␣) > 0. (The audit costs should also depend on N, the total number of firms, but this is taken as constant in our model). The government has to raise at least T¯ dollars per period, in (expected) revenues, net of audit costs.7

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PARTHA SENGUPTA

Before formulating the government’s optimization problem, it is of interest to find out how changes in policy variables affect the expected revenue of the government. The gross expected revenue of the government can be given by ␥i Tg = t[R i (q i ) − {1 + ␮i (1 − ␣␪)}c i (q i , ␥i )] f i (␥i ) d␥i (11) 0 t=1 ␥i

The qi and ␮i ’s in Eq. (11) actually should be written as q˜ i and ␮ ˜ i – the optimal values for the ith monopolist, but the tilde’s are suppressed in (11) and subsequently, for notational convenience. For the same reason, in subsequent equations the limits of the sum and the limits of the integration of the parameter ␥ are omitted (but understood). A sufficient condition for Tg to be positive is that each monopolist “on average” reports nonnegative profits. Positive profits on average implies that [R i (q i ) − {1 + ␮i }c i (q i , ␥i )] f i (␥i ) d␥i ≥ 0, ∀i From Eq. (11) it is clear that this implies that T g > 0. Proposition 4.3. The effect of a change in the ceiling price on the expected revenue of the government is ambiguous even when the Arrow-Pratt measure of absolute risk aversion is non-increasing in income. Since an increase in the price ceiling leads to higher profits of the monopolist, it might seem that revenues of the government should be increasing. However a higher price ceiling induces higher mis-reporting and evasion so that the final outcome is not clear. The first step towards deriving optimal policies of the government is to derive some measures of social welfare that the government should be maximizing. The literature analyzing the issues of social optimum under regulatory policies usually uses the notion of consumer surplus to characterize social optimum. Such use is justified if it is assumed that all consumers are identical and have utility functions separable in the monopoly good and all other goods, and if the utility function is linear in all other commodities. Under these circumstances, consumer’s surplus can be directly identified with utility.8 Total surplus, which is the sum of consumer surplus and profits of the firm, is then taken as the measure of social welfare which the regulator maximizes. Basically the same measure of social welfare is used here. One difference is that with N firms, the aggregate consumer surplus (the sum of consumer surplus from each market) is used. Also with tax evasion the net profits of the firm depends on the exact state of nature. So aggregate expected profits (instead of actual profits) of the firms are considered.

Price Ceiling Regulation of a Tax Evading Monopolist

27

Lastly, the government is subject to a fixed revenue constraint which requires that its expected revenue, net of any audit costs be at least T¯ . The aggregate consumer surplus in this model is given by CS = p i (x i ) dx i f i (␥i ) d␥i − R i (q i )f i (␥i ) d␥i (12) x=0

The aggregate of the monopolists’ expected profits is given by E␲ = (1 − t)[R i (q i ) − c i (q i , ␥i )] f i (␥i ) d␥i + (1 − ␣␪) ×

t␮i c i (q i , ␥i )f i (␥i ) d␥

(13)

Social welfare can then be written as W = CS + E␲ = p i (x i ) dx i f i (␥i ) d␥i − c i (q i , ␥i )f i (␥i ) d␥i −

x=0

t[R i (q i ) − {1 + ␮i (1 − ␣␪)}c i (q i , ␥i )] f i (␥i ) d␥i

The expected revenue of the government, net of audit cost is given by Tn = t[R i (q i ) − {1 + ␮i (1 − ␣␪)}c i (q i , ␥i )] f i (␥i ) d␥i − g(␣)

(14)

(15)

The government’s problem then is to choose qi , t, ␣ and ␪ so as to maximize W subject to the constraint that T n ≥ T¯ . (To be very accurate, the ceiling prices p¯ i ’s should be taken as the choice variable of the government instead of the qi ’s However, in this model both p and q are costlessly observable so that any of the two can be considered.) The Lagrangian for the government’s optimization problem is M = (␾ − 1) t[R i (q i ) − {1 + ␮i (1 − ␣␪)}c i (q i , ␥i )] f i (␥i ) d␥i + −

x=0

p i (x i ) dx i f i (␥i ) d␥i

c i (q i , ␥i )f i (␥i ) d␥i − ␾[g(␣) + T ]

where ␾ is the Langrange multiplier.

(16)

28

PARTHA SENGUPTA

The F. O. C.’s for an interior solution are ∂M = (␾ − 1) [R i (q i ) − {1 + ␮i (1 − ␣␪)}c i (q i , ␥i )] f i (␥i ) d␥i ∂t ∂␮ − (␾ − 1)(1 − ␣␪) tc i (q i , ␥i ) i f i (␥i ) d␥i = 0 (17) ∂t ∂M = p i (q i )f i (␥i ) d␥i + (␾ − 1) [R i − {1 + ␮i (1 − ␣␪)}c i ] f i (␥i ) d␥i ∂q i ∂␮ − (␾ − 1)(1 − ␣␪) tc i (q i , ␥i ) t f i (␥i ) d␥i ∂q i − c i (q i , ␥i )f i (␥i ) dγi = 0 (18) ∂M = (␾ − 1)␪ t␮i c i (q i , ␥i )f i (␥i ) d␥i − (␾ − 1)(1 − ␣␪) ∂␣ ∂␮ × c i (q i , ␥i ) i f i (␥i ) d␥i − ␾g (␣) = 0 ∂␣ ∂M = (␾ − 1)␣ t␮i c i (q i , ␥i )f i (␥i ) d␥i − (␾ − 1)(1 − ␣␪) ∂␪ ∂␮ × tc i (q i , ␥i ) i f i (␥i ) d␥i = 0 ∂␪ ∂M = t[R i (q i ) − {1 + ␮i (1 − ␣␪)}c i (q i , ␥i )] f i (␥i ) d␥i ∂␾ − g(␣) − T¯ = 0

(19)

(20)

(21)

Tax evasion literature, however, usually assumes that there are some costs associated with eliminating tax evasion. Thus audits are assumed to involve resource costs. Also it is usually assumed that there are social and political costs to raising the penalty rate. So it is assumed here that the penalty rate cannot ¯ Under these circumstances it is clear that eliminating exceed some upper limit ␪. tax evasion may not be the optimal policy. Two interesting questions arise here. The first is what the optimal price ceiling should be in the presence of tax evasion and second, is if there is a trade-off between selecting the audit and the penalty rates. These questions are addressed below. Proposition 5.1. The optimal policy of the government is to set the price ceiling for the each monopolist where it equals the expected marginal cost if the preferences of the monopolists exhibit non-increasing absolute risk aversion.

Price Ceiling Regulation of a Tax Evading Monopolist

That is:

p¯ i =

c i (q i , ␥i )f i (␭i ) d␥i

29

if R iA (nd) ≤ R iA (nd)∀i.

Proof: If monopolists on average report positive profits, [{R i (q i ) − (1 + ␮i )c i (q i , ␥i )} + ␮i ␣␪c i (q i , ␥i )] f i (␥i ) d␥i > 0 Moreover, Proposition 3.3 implies that ∂␮ (1 − ␣␪) tc i (q i , ␥i ) i f i (␥i ) d␥i < 0, ∂t

if R iA (nd) ≤ R iA (d)∀i.

(22)

(23)

Comparing Eqs (17), (22) and (23) it is clear that Eq. (17) would be satisfied only if ␾ = 1 Setting ␾ = 1 in Eq. (18), the result follows. Thus, as in the case of costless audits, the price ceiling is set independent of the tax parameters at the point where price equals expected marginal cost. Proposition 5.2. The government has incentives to set the audit rate as low as possible. Proof: To answer the second question, suppose that the penalty rate is increased and the audit rate is decreased simultaneously to keep expected tax revenues of the government constant. If such a change leads to an unambiguous increase in welfare, then it should be clear that the government will always have the incentive to reduce the audit rate. Total differential of Eq. (15) holding T n , t and p¯ i (i.e. qi )as constant, yields ∂␮i t␣␮i c i (q i , ␥i ) − t(1 − ␣␪)c i (q i , ␥i ) f (␥ ) d␥i d␪ = ∂␪ i i ∂␮ − t␪␮i c i (q i , ␥i ) − t(1 − ␣␪)c i (q i , ␥i ) i f i (␥i ) d␥i d␣ − g (␣) d␣ ∂␣ (24) Total differential of Eq. (14) holding T n , t and p¯ i (i.e. qi ) as constant, yields ∂␮ dW = − t␣␮i c i (q i , ␥i ) − t(1 − ␣␪)c i (q i , ␥i ) i f i (␥i ) d␥i d␪ ∂␪ ∂␮ − t␪␮i c i (q i , ␥i ) − t(1 − ␣␪)c i (q i , ␥i ) i f i (␥i ) d␥i d␣ ∂␣ (25)

30

PARTHA SENGUPTA

Equations (23) and (24) can be combined to give dW = −g (␣) d␣

(26)

From Eq. (26) it is clear that welfare can be increased unilaterally by reducing the audit rate (and increasing the penalty rate), so long as audits are costly. It is important to note two points. First, the audit rate cannot be set equal to zero in this model as some audits are needed to enforce the tax. Second, the model does not necessarily imply that the government would always set the penalty rate ¯ In fact, from Eq. (20) it is clear that so long as ␾ = 1, ∂M/∂␪ is always at ␪ = ␪. zero. As seen already for the case where audits are costless, the government has a number of ways of raising its required revenues. So the constraint on the penalty rate may not necessarily be binding.

5. CONCLUSION This paper brought together the literature on tax evasion and regulation by exploring the decisions of a tax-evading monopolist subject to price ceiling regulation. A simple model was used to highlight a number of interesting issues. One interesting finding was that a reduction in the effective price ceiling led to a reduction in tax evasion. However, the analysis showed that optimal regulatory policies are not affected by tax evasion considerations since their optimal price ceiling policies do not change when tax evasion is allowed. Lastly, it was found that optimality in the model can be achieved with or without evasion (even when the government can reduce tax evasion costlessly). Many of the findings of this model depend crucially on the exact nature of regulatory policy considered and the nature of the asymmetry of information between the government and the monopolist. With price as the regulatory instrument, there was no scope of cheating on this instrument. The results are likely to be different in situations where the monopolist can also cheat on the regulatory instrument. Another point to note is that in practice there could also be asymmetry of information on the demand side. Thus the firm may well have more accurate information on the demand for its product as compared to the regulator. This also would affect the results of this paper.

NOTES 1. See Andreoni, Erard and Feinstein (1998) for a recent survey of this research. 2. See, for example, Caillaud, Guesnerie, Rey and Tirole (1988), Sappington and Stiglitz (1987) and Baron (1989) for surveys of research on the effects of regulation on monopolist’s decisions.

Price Ceiling Regulation of a Tax Evading Monopolist

31

3. The exact nature of information available to the government will be discussed in detail in the next section, when the government’s optimization problem is introduced. 4. The audit probability as perceived by the monopolist may equal the actual audit probability of the government. 5. The general tradition in the industrial organization literature is to assume that the firm is risk neutral. Risk neutrality in tax evasion models however leads to corner solutions so that following Wang and Conant (1988) it is assumed that the monopolist is risk averse. 6. The proof follows from Eqs (5) and (6). 7. The number of firms is considered to be sufficiently large that expected revenues reasonably approximate actual collections. 8. See Sheshinski (1976).

ACKNOWLEDGMENTS I am indebted to my dissertation committee, Helmuth Cremer (co-chair), Firouz Gahvari (co-chair), Catherine Eckel, Djavad Salehi-Isfahani, and Richard Steinberg for their guidance and suggestions. Remaining errors are my responsibility.

REFERENCES Allingham, M., & Sandmo, A. (1972). Income tax evasion: A theoretical analysis. Journal of Public Economics, 1, 323–338. Andreoni, J., Erard, B., & Feinstein, J. (1998). Tax compliance. Journal of Economic Literature, 36(June), 818–860. Baron, D. P. (1989). Design of regulatory mechanisms and institutions. In: R. Schmalensee & R. Willig (Eds), Handbook of Industrial Organization (Chap. 24, pp. 1347–1447). North Holland. Caillaud, B., Guesnerie, R., Rey, P., & Tirole, J. (1988). Government intervention in production and incentives theory: A review of recent contributions. Rand Journal of Economics, 19(Spring), 1–26. Kreutzer, D., & Lee, D. R. (1986). On taxation and understated monopoly profits. National Tax Journal, 39(June), 241–243. Lee, K. (1998). Tax evasion, monopoly, and nonneutral profit taxes. National Tax Journal, 51(June), 333–338. Marrelli, M. (1984). On indirect tax evasion. Journal of Public Economics, 25(November), 181–196. Sappington, D., & Stiglitz, J. (1987). Information and regulation. In: E. Bailey (Ed.), Public Regulation: New Perspectives on Institutions and Policies. Cambridge: MIT Press. Sheshinski, E. (1976). Price, quality and quantity regulation in monopoly situations. Economica, 43(May), 127–137. Srinivasan, T. (1973). Tax evasion: A model. Journal of Public Economics, 2, 339–346. Wang, L. (1990). Tax evasion and monopoly output decisions with endogeneous probability of detection. Public Finance Quarterly, 18, 480–487.

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Wang, L., & Conant, S. (1988). Corporate tax evasion and output decisions of the uncertain monopolist. National Tax Journal, 41(December), 579–581. Yaniv, G. (1996). Tax evasion and monopoly output decisions: Note. Public Finance Quarterly, 24(October), 501–505. Yitzhaki, S. (1974). A note on income tax evasion: A theoretical analysis. Journal of Public Economics, 3(May), 201–202.

DEPOSITOR PREFERENCE LEGISLATION AND FAILED BANKS’ RESOLUTION COSTS William P. Osterberg and James B. Thomson ABSTRACT The Omnibus Budget Reconciliation Act of 1993 included depositor preference legislation intended to reduce Federal Deposit Insurance Corporation (FDIC) resolution costs. However, depositor preference might induce an offsetting reaction by general creditors and may affect resolution type. We examine the empirical impact of state-level depositor preference laws on resolution type and costs with call-report data and FDIC data for all operating FDIC-BIF insured commercial banks that were closed or required FDIC ﬁnancial assistance from January 1986 through December 1992. Our major ﬁndings are that depositor preference has: (1) tended to increase resolution costs; and (2) induced the FDIC to choose assisted mergers over liquidations.

1. INTRODUCTION On August 10, 1993 Congress passed the Omnibus Budget Reconciliation Act of 1993. Contained in this legislation was a provision that revised the priority of claims on failed depository institutions by making other senior claimants junior to depositors. Congress apparently hoped to reduce the losses to the Federal Deposit Research in Finance Research in Finance, Volume 20, 33–59 Copyright © 2003 by Elsevier Ltd. All rights of reproduction in any form reserved ISSN: 0196-3821/doi:10.1016/S0196-3821(03)20003-4

33

34

WILLIAM P. OSTERBERG AND JAMES B. THOMSON

Insurance Corporation (FDIC) of resolving bank failures by changing the capital structure of banks to enhance the priority of depositors and the FDIC.1 An important element in any assessment of the impact of such depositor preference legislation involves the behavior of general creditors, the main category of claimants made junior to depositors. It is possible that these claimants might react so as to offset the intended cost savings. For example, general creditors such as sellers of federal funds might collateralize their claims by shifting to repurchase agreements in which government securities are collateral. Such collateralized claims would become senior to those of the depositors and thus the FDIC. Other responses by general creditors, such as shortening of maturities could also increase the FDIC’s costs. While there have been theoretical analyses of how depositor preference affects the values of various bank claimants, there has been little empirical analysis of whether the FDIC’s losses have been reduced, or whether responses to the legislation have offset its intended benefits.2 The biggest wave of bank failures had passed by the time of national depositor preference’s passage in 1993. However, some individual states already had depositor preference laws in effect, and in this paper, we examine the impact of such legislation on FDIC resolution costs from 1986 through 1992.3 The theoretical framework follows Hirschhorn and Zervos (1990) and Osterberg and Thomson (1994, 1999), where depositor preference legislation reduces the value of the FDIC claim unless general creditors undertake some offsetting action.4 The empirical analysis extends studies of closed-bank resolution costs by James (1991), Osterberg and Thomson (1995) (henceforth, OT), and Osterberg (1996). We improve on previous studies by controlling for the endogeneity of book measures of bank capital, correcting for sample selection bias introduced by regulatory closure rules, and taking account of depositor preference’s possible impact on the FDIC’s choice of resolution type.

2. LEGISLATIVE AND REGULATORY PROVISIONS Two complications arise for the interpretation of our results in terms of the likely impact of the 1993 Act. First, the various state level depositor preference statutes are applicable to state-chartered banks, which may differ from national banks along several dimensions.5 These state depositor preference laws also vary somewhat, such as in terms of the account size covered. However, there is no reason to assume that such differences were material to either the eventual cost or to the way in the FDIC resolved bank failures.6 Appendix A presents some details on the 1993 Act. Table 1 lists the state depositor preference laws for banks and thrifts.

Depositor Preference Legislation and Failed Banks’ Resolution Costs

35

Table 1. State Depositor Preference Legislation for Banks. State

Date Effective

Alaska Arizona California Colorado Connecticut Florida Georgiaa Hawaii Idahob Iowa Kansas Louisiana Maine Minnesota Missouri Montana Nebraska New Hampshire New Mexico North Dakota Oklahoma Oregon Rhode Island South Dakota Tennessee Utah Virginia West Virginia a Legislation

10/15/78 9/21/91 6/27/86 5/1/87 5/22/91 7/3/92 1974 6/24/87 1979 1/1/70 7/1/85 1/1/85 4/16/91 4/24/90 9/1/93 1927 1909 6/10/91 6/30/63 7/1/87 5/26/65 1/1/74 2/8/91 7/1/69 1969 1983 7/1/83 5/11/81

became effective on either January 1 or July 1.

b Passed by both houses on July 1, enactment date unclear. In other cases when only the year is indicated,

neither the month nor the day of enactment is available.

Second, the Federal Deposit Insurance Corporation Improvement Act (FDICIA) of 1991 reduced the FDIC’s flexibility as receiver in deciding whether or not to impose losses on uninsured claimants.7 During the 1986–1992 period analyzed in this paper, the FDIC appears to have had substantial latitude in interpreting the priority of claimants in the resolution of bank failure. For example, the status of foreign depositors under state depositor preference legislation was unclear.8 The sample period we study precedes the implementation of FDICIA (1991), which while not materially changing the resolution options available to the FDIC, did place limits on its ability to extend de facto guarantees to uninsured depositors

36

WILLIAM P. OSTERBERG AND JAMES B. THOMSON

and general creditors. Specifically, unless the FDIC seeks and secures a systemic risk exemption it cannot extend de facto guarantees to uninsured depositors or non-deposit creditors of the insolvent institution. As a result, depositor preference laws may no longer affect the FDIC’s choice of resolution type. One possibility is that this provision of FDICIA may induce general creditors to shorten maturities or to increase collateralization. On the other hand, if FDICIA’s prompt corrective action provisions result in the closure of capital deficient but book solvent banks, then depositor preference should have no impact on FDIC resolution costs. In general, without depositor preference, general or other senior liabilities have the same priority of payment as deposits. However, with or without depositor preference, secured creditors of the failed depository will have their claims satisfied first, up to the amount of the collateral. Thus, general or senior creditors could conceivably protect their claim from depositor preference by increasing collateral. With most bank closures, the FDIC charged with choosing among types of procedures to resolve the failure. The FDIC could resolve bank insolvency in one of three ways. First, they could choose to liquidate the institution, in what is commonly referred to as a payout. While there are several different ways to implement a payout the implications for the FDIC, uninsured depositors, and unsecured general creditors are the same for each; they receive no de facto guarantees of their claims and thus are fully exposed to loss. The second way in which the FDIC could resolve insolvency is through a purchase and assumption transaction (P&A). Prior to FDICIA, a P&A typically involved the transfer of all deposits and general creditor obligations to another bank, thereby providing de facto guarantees to senior creditors. The third method has the FDIC infusing capital into an open institution. The net effect of such open-bank assistance (OBA) is the extension of de facto deposit insurance coverage to depositors and general creditors.9 The impact of depositor preference legislation on costs and the choice of resolution type will depend on the reactions of the various claimants (particularly non-depositor general creditors). Although equity holders and subordinated debenture holders cannot collateralize their claim so as to improve priority, federal fund sellers can shift to repurchase agreements, which are collateralized by government securities. In addition, depositors can take out loans which can be used as offsets to the deposit, trade creditors can use related commodities as collateral, and foreign depositors can offer convert their deposits into collateralized forms (see Ely, 1993; Kaufman, 1997). Hirschhorn and Zervos (1990) find evidence that supports this conjecture, showing that following the passage of state depositor preference laws, general creditors of affected savings and loans increased collateralization and interest rates on uninsured certificates of deposits fell. Resolution cost could also be increased by non-depositors shortening the

Depositor Preference Legislation and Failed Banks’ Resolution Costs

37

maturity of loans (which could lead to earlier withdrawal of funds), cutting off credit in certain circumstances, increasing interest rates to compensate for the increased risk of loss to the general creditors, or using put options or acceleration clauses.

3. EMPIRICAL METHOD Our main focus is on the empirical impact of state-level depositor preference legislation on closed-bank resolution costs. A secondary focus is on the impact on the FDIC’s choice of resolution type. We estimate three equations in addition to the equation for resolution costs. The first controls for the endogeneity of book capital (net worth). The second allows us to adjust standard errors from the resolution cost and resolution type equations for sample selection bias induced by regulatory closure rules. The third allows us to control for the endogeneity of the FDIC’s choice of resolution type. This allows us to distinguish between the legislation’s direct impact on costs and its indirect impact operating through its influence on resolution type. Our four-equation model has the following form: Net Wortht = ␣11 +

k

␣1j X 1jt + e 1t

(1)

j=2

ˆ Wortht + Failuret = ␣21 + ␣22 Net

m

␣2l X 2lt + e 2t

(2)

l=3

ˆ Wortht + Resolution typet = ␣31 + ␣32 Net

p

␣3n X 3nt + e 3t

(3)

n=3

ˆ Wortht + ␣43 Resolution ˆ Resolution costt = ␣41 + ␣42 Net typet +

r

␣4q X 4qt + e qt

(4)

q=4

Equation (1) is based on Thomson (1992) and Maddala’s (1986) discussion of the importance of generating a prediction for net worth, a key determinant of bank closure. The predicted value from the estimation of Eq. (1) is included as a proxy for net worth on the right-hand side of the closure, resolution-type, and resolution-cost equations. We rely on previous studies (e.g. Barth, Bartholomew & Bradley, 1990)

38

WILLIAM P. OSTERBERG AND JAMES B. THOMSON

of the decision to close banks to specify the determinants of closure, in Eq. (2). Estimation of this equation generates a term included on the right-hand sides of Eqs (3) and (4) to correct each for selectivity bias in the analysis of closed banks. We will mainly focus on Eq. (3) for resolution type and Eq. (4) for resolution costs. We know of no previous empirical analysis of the FDIC’s choice of resolution type. However, Buser, Chen and Kane’s (1981) theoretical analysis views the FDIC as maximizing the value of a troubled institution’s charter in the handling of its resolution. In addition, Kane (1986) suggests a framework in which the FDIC jointly minimizes its fiduciary, political, and other costs associated with resolving the closed bank. Our choices of the determinants of bank failure resolution costs follows Bovenzi and Murton (1988), James (1991), and Osterberg and Thomson (OT, 1995) all of whom view resolution costs as determined by problem assets, risky assets, and core deposits.

3.1. Determinants of Resolution Type In Eq. (3) the dependent variable equals 0 when failure is resolved by liquidation, which provides no de facto deposit guarantees to uninsured depositors and general creditors and equals 1 otherwise (P&A).10 Ideally, we would specify this equation from a formal model of the FDIC’s choice of resolution type. However, if the FDIC chooses resolution type so as to maximize net recoveries from receivership, resolution type would be subject to many of the same influences as costs. Unfortunately, including the same variables on the right-hand sides of both Eqs (3) and (4) would hamper econometric identification. We deal with this potential problem by choosing the variables for Eq. (3) from a stepwise regression. Variables are defined in Table 2. Table 3 indicates the signs expected for the coefficient on the determinants of resolution type. The coefficient on the depositor preference dummy would be positive if depositor preference induces the FDIC to P&As over liquidations. For Hirschhorn and Zervos (1990) the explanation for this result would be that depositor preference clearly benefits the FDIC with P&As but not with liquidations. Silverberg (1986) argues that depositor preference laws render contingent liabilities worthless, making P&As less costly vis-`a-vis liquidations. The coefficient on Core Deposits is expected to be positive. Keeley (1990) claimed they control for the franchise (charter) value and are sources of unbooked gains while Buser, Chen and Kane (1981) argue that the FDIC will try to minimize its losses by closing banks in a manner that preserves the value of the charter. Thus higher levels of Core Deposits would be expected to be associated with the choice of P&A over liquidation since charter values are preserved by the former but not

Depositor Preference Legislation and Failed Banks’ Resolution Costs

39

Table 2. Variable Definitions. Variable

Definition

BHC Dummy

= 1 if bank is in a bank-holding company = 0 otherwise = 1 if bank’s home state has statewide branching = 0 otherwise Deposits received from brokers or dealers for the account of others, either directly or ultimately Domestic deposits under $10,000 = 1 if state bank in a depositor preference state = 0 otherwise Annualized non-interest expense/Total Assets Yearly total business failure liabilities by state (from Dun and Bradstreet) Federal funds purchased or securities sold under agreements to repurchase Federal funds sold or securities purchased under agreements to resale Core Deposits multiplied by Predicted Resolution Type from Eq. (3) Loans to insiders Purchased Funds/Total Assets Herfindahl index constructed using portfolio shares of major loan categories (see Thomson, 1992) Charge-offs minus recoveries (annualized) Annualized net income Book equity plus reserves: bank capital Net worth from previous call report = 1 if bank is in Boston, New York, or Philadelphia Federal Reserve districts = 0 otherwise

Branch Dummy Brokered Deposits Core Deposits Depositor Preference Dummy Efficiency Ratio Failed Business Liabilities Fed Funds Purchased Fed Funds Sold ICORE Inside Loans Liquid Liability Ratio Loan Herfindahl Index Net Charge-offs Net Income Net Worth Net Worth (t − 1) Northeast Dummy

Off-Balance Sheet Items Other Borrowed Money

Other Real Estate Owned Other Risky Assets Per Capita Income Predicted Net Worth Predicted Resolution Type Problem Loans Purchased Funds

Activities that generate revenues, expenses or risk but do not result in a booked asset or liability Miscellaneous borrowings, including: loans from Federal Reserve and Federal Home Loan Banks, repurchase agreements not included in Fed Funds Purchased, etc. Real estate assets acquired by the bank through forclosure Risky assets not in Other Real Estate Owned, Problem Loans, or Inside Loans Yearly state level per capita income Net Worth predicted from Eq. (1) Resolution Type predicted from Eq. (3) Loans 90 days past-due or non-accruing Foreign deposits + Fed Funds Purchased + Other Borrowed Money + Brokered Deposits

40

WILLIAM P. OSTERBERG AND JAMES B. THOMSON

Table 2. (Continued ) Variable

Definition

Resolution Type

= 1 for purchase and assumptions or open bank assistance = 0 for Payouts (i.e. Deposit Transfers, Liquidations) Correlation coefficient between the errors in the failure and resolution type equations Net Income/Total Assets Mills’ ratio from failure equation Natural logarithm of total assets = 1 if bank is in the Dallas Federal Reserve district = 0 otherwise Interest income earned on loans that is uncollected

Rho Return on Assets Selectivity Correction Size Southwest Dummy Uncollected Interest

by the latter. The coefficient on Problem Loans should be negative since higher values of which these might be associated with low franchise values and thus with liquidations.11 We also include Branch Dummy, which equals 1 if a bank’s home state has statewide branching (and equals 1 otherwise). The coefficient on this variable should be positive since intrastate branching could length the list of potential acquirers and thus improve the relative attractiveness of P&As. Since we would expect high levels of contingent liabilities to induce the FDIC to choose liquidations, the coefficient on Other Real Estate Owned should be negative. This also is expected for Predicted Net Worth, since closed banks with high capital ratios might have high levels of unbooked losses.12 A positive coefficient on Size would be consistent with the too-big-to-let fail doctrine, which suggests that all senior claimants are de-facto insured, and thus that larger banks are less likely to be liquidated (see Carnell, 1993; Todd & Thomson, 1991). We would expect negative coefficients on Northeast Dummy and Southwest Dummy if depressed regional Table 3. Estimated and Expected Signs on Independent Variables in Eq. (3). Variable Problem Loans (log) Southwest Dummy Depositor Preference Dummy Predicted Net Worth Branch Dummy Size Core Deposits Northeast Dummy Other Real Estate Owned

Expected Sign

Estimated Sign

Significant

− − + − + + + − −

− + + − − + + − −

Yes Yes Yes Yes Yes Yes Yes Yes Yes

Depositor Preference Legislation and Failed Banks’ Resolution Costs

41

economic conditions are associated with lower franchise values. However, at least in the case of the Southwest, the estimated coefficient might be influenced by the constraints faced by the FDIC in resolving large and complex failures.

3.2. Determinants of Resolution Cost Table 4 lists the signs expected for the coefficients on all of the variables appearing on the right-hand side of Eq. (4). This list of variables is based partly on previous analyses such as OT and Osterberg (1996).13 The variables can be seen as representing the sources of FDIC costs of resolving bank failures. In one category are losses reflecting the underlying insolvency of the bank and the realization of downside risk associated with a bank’s investment and financing decisions. On an economist’s extended balance sheet, these losses equal the negative market net worth of the firm (excluding the value of government guarantees). In a second category are losses related to forbearance, incurred after the depository is no longer economically viable but before it is closed.14 Third are the costs Table 4. Estimated and Expected Signs on Proxy Variables in Eq. (4). Variable

Proxy for

Predicted Net Worth Predicted Resolution Type Uncollected Interest Problem Loans Other Real Estate Owned Inside Loans Other Risky Assets Off Balance Sheet Items Core Deposits Size

Solvency Resolution type Unbooked losses Unbooked losses Unbooked losses Fraud Portfolio Risk General creditor claims Franchise or charter value Resolution/closure constraints Depositor preference status Lending opportunity set General creditor claims General creditor claims Market discipline Charter value given resolution type Correction for sample selection bias

Depositor Preference Dummy Fed Funds Sold Fed Funds Purchased Other Borrowed Money Brokered Deposits ICORE Selectivity Correction

Expected Sign

Estimated Sign

Significant

− − + + + + + − − +

− + + + + + + − − +

Yes No No Yes Yes Yes Yes Yes Yes Yes

−

+

Yes

+ − − − −

+ − − − −

Yes Yes No No No

N/A

+

No

42

WILLIAM P. OSTERBERG AND JAMES B. THOMSON

associated with receivership, including administrative and legal expenses.15 Since little case-specific data on receivership costs is available, let alone the marginal receivership cost for each closed institution, we include all three types of resolution costs in the dependent variable for Eq. (4). Net worth (book equity plus reserves) represents the cushion between the value of assets and the promised payments to debt holders, so Predicted Net Worth should be negatively related to costs. Unbooked losses should be positively related to resolution costs and are proxied here by two measures of losses on the asset portfolio, Other Real Estate Owned and Problem Loans (“past-due and non-accruing loans”). On the other hand, Core Deposits should be negatively related to costs, perhaps because they are sources of unbooked gains, such as the value of real options for profitable business opportunities. ICORE, the product of Predicted Resolution Type and Core Deposits, is intended to capture the fact that with P&As the franchise value (proxied by Core Deposits) is saved and thus costs should be lower. We also include Predicted Resolution Type. If it is true that the FDIC minimizes resolution cost by choosing resolution type, the coefficient on Predicted Resolution Type will equal zero. It is also true that if the claims of the proponents of depositor preference legislation are valid, the coefficient on the Depositor Preference Dummy will be negative. Bovenzi and Murton (1988) note that distressed banks have incentives to cover up the amount of problem assets in their portfolio, possibly by booking income on a non-performing loan to prevent it from being classified as past due or non-accruing. This motivates our inclusion of Uncollected Interest as a measure of unbooked losses not reported by the bank, which should be positively related to costs. Other Risky Assets are included as a proxy for portfolio risk and should be positively related to losses. Inside Loans are included as a proxy for fraud and should be positively related to costs. Fed Funds Sold is included based on previous work where it was found to increase resolution costs, possibly being an indicator of depressed regional economies with limited lending opportunities. Fed Funds Purchased, Off-Balance Sheet Items, and Other Borrowed Money are included as proxies for general creditor claims. Previous research found that Fed Funds Purchased and Off-Balance Sheet Items reduced costs, possibly due to market discipline whereby banks able to utilize these funding sources are seen as having lower unbooked losses.16 On the other hand, Fed Funds Purchased includes repurchase agreements, which are collateralized. If the proportion of repurchase agreements in the Fed Funds Purchased variable increases as a bank slides towards insolvency, then it is possible that higher levels of Fed Funds Purchased might be associated with higher costs. Other Borrowed Money and Brokered Deposits might also provide market discipline and thus lower costs. Previous work found such an impact for Brokered Deposits.

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OT found significant impacts of dummy variables for filer types and for size categories. A standard specification test supports replacing the size categories by Size, which would be positively related to costs if regulators adhered to the too-big-to-let-fail doctrine.17

3.3. Data and Procedures Our sample includes all operating FDIC-BIF insured commercial banks on December 31, 1992 and those FDIC-BIF insured commercial banks that were closed or required FDIC financial assistance to remain open from January 1, 1986 through December 31, 1992. Quarterly balance sheet and income data for these banks are from the Federal Financial Institution Examination Council’s Quarterly Reports of Condition and Income (call reports) from March 31, 1984 through December 31, 1992. Closure data, estimated resolution cost (to the FDIC) and resolution type are from FDIC (1993). We estimate Eq. (1) with least squares, both in levels and with all variables divided by total assets. The predicted values from the former estimation appear on the right-hand side of Eq. (4). Equations (2) and (3) include the predicted values from Eq. (1) when estimated in ratio form. Equations (2) and (3) are estimated as probits and Eq. (4) is estimated as weighted-least squares with all variables divided by the square root of total assets to take account of heteroscedasticity as suggested by Maddala (1986). The inclusion of the predicted value of net worth on the right-hand side of the other three equations and the inclusion of a predicted value of resolution type on the right-hand side of the resolution cost equation requires that the standard errors be adjusted, following Murphy and Topel (1985). The implementation of this procedure is discussed in Appendix B. All four equations are estimated using LIMDEP 6.0. The net worth equation is estimated for all observations for all banks while the failure equation includes one observation per bank. For failed banks, Eq. (2) uses the last “good” call report, one quarter before closure. For other banks, Eq. (2) uses the 1992: Q4 observation. This procedure is consistent with Thomson’s (1992) analysis of the joint determination of net-worth and closure and is suggested by other analyses of resolution costs. In addition, while the procedure appears to ignore information in the panel, we account for some of the time-series variation by including economic conditions variables. Equation (3) uses the last good observation on all failed banks and thus includes observations at different points in time. In this case, we included some regional dummies and other measures of economic conditions in the list of variables from which the stepwise procedure chose. Equation (4) also uses data from the last good call report and thus aligns

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WILLIAM P. OSTERBERG AND JAMES B. THOMSON

banks that failed at different points in time. Here again we include regional dummies and conditions variables.

4. RESULTS The results from estimating the net worth (Eq. (1)) and closure equations (Eq. (2)), presented in Tables 5 and 6, are consistent with those found in previous studies. The two-equation closure model of Thomson (1992) suggests that we include these equations and the adjusted R2 of 0.8989 for Eq. (1) is higher than for the net worth equation in Thomson. Moreover when we estimate Eq. (2) independently from Eq. (3), our closure equation has lower classification error than the 7.271% Table 5. OLS Estimation of Net Worth/Total Assets Equation.a Variable

Coefficient

Std. Error

t-Ratio

Probability

Constant Net Worth (t − 1) Net Charge-offs Loan Herfindahl Index Other Risky Assets Purchased Funds Return on Assets Off-Balance Sheet Items Failed Business Liabilities Core Deposits Problem Loans Other Real Estate Owned Per Capita Income

0.26596 8.8246 −0.76341 0.00003 0.0192 −0.3208 1.8497 0.0180 −0.0047 −0.3004 0.1349 −0.3510 0.00676

0.0223 0.0362 0.0515 0.00001 0.0096 0.0247 0.0563 0.0016 0.0009 0.0170 0.0615 0.0757 0.0006

11.947 243.587 −14.816 2.661 2.004 −12.981 32.869 11.084 −5.231 −17.755 2.195 −4.640 10.565

0.0000 0.0000 0.0000 0.0078 0.0451 0.0000 0.0000 0.0000 0.0000 0.0000 0.0282 0.0000 0.0000

Anova Source

Variation

Degrees of Freedom

Mean Square

Regression Residual

2478.675 278.835

12 12541

206.5562 2.2234

Total

1757.510

12553

0.2197

Notes: Estimation generates Predicted Net Worth to be used as a regressor in the closure Eq. (2) and the resolution type Eq. (3). Number of observations = 12554; Mean of dependent variable = 0.9635; R-squared = 0.8989; Adjusted R-squared = 0.8988; F[12, 12541] = 9290.161. a All of the right-hand side variables have been divided by total assets.

Depositor Preference Legislation and Failed Banks’ Resolution Costs

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Table 6. FIML-Probit Estimation of Closure Eq. (2).a Variable

Coefficient

Std. Error

t-Ratio

Probability

Constant Predicted Net Worth Uncollected Interest Purchased Funds Off-Balance Sheet Items Inside Loans Size Other Risky Assets Per Capita Income Failed Business Liabilities BHC Dummy Efficiency Ratio Core Deposits Rho

8.7640 −6.2562 1.0707 −0.18146 −0.29323 0.10611 −1.3255 −0.0899 −13.614 4.9775 −0.3016 0.0968 −4.9905 0.0213

0.5580 0.1528 0.0405 0.0356 0.3041 0.0121 2.6390 0.2061 1.0480 2.0290 0.0766 0.0139 0.2881 0.0889

15.705 −40.937 44.511 −5.092 −0.964 8.790 −0.502 −0.436 −12.990 2.453 −3.936 6.957 −17.323 −0.240

0.0000 0.0000 0.0000 0.0000 0.3350 0.0000 0.6155 0.6627 0.0000 0.0142 0.0000 0.0000 0.0000 0.8102

a These

results are used to adjust the estimated standard errors as in Table 7 for the resolution type Eq. (3).

reported by Thomson (see Tables B1 and B2). The improved performance of our model can be traced to two sources. First, the list of regressors here is somewhat different.18 Second, we estimate Eqs (2) and (3) as a bivariate probit (allowing for possible correlation between error terms) rather than estimating the closure equation with logit. Overall, the results in Tables 5 and 6 are consistent with those found in previous studies. Table 7 presents the estimated coefficients for the resolution type equation. Of the 9 estimated coefficients 7 have the expected sign and are significant. In the other two cases the coefficients are significant and of the “wrong” sign. The negative and significant coefficient on Problem Loans implies that the FDIC is more likely to liquidate a closed bank when the value of banking franchises is low. A similar interpretation applies to the negative and significant coefficient on Northeast Dummy. The negative and significant coefficients on Predicted Net Worth and Other Real Estate Owned are consistent with our expectation that the FDIC would choose liquidation when faced with large contingent liabilities. The positive and significant coefficient Core Deposits is consistent with our view that the FDIC would utilize P&As in attempt to lower costs by preserving franchise values. The positive and significant coefficient on Size is consistent with de facto insurance of all senior claimants (uninsured depositors and general creditors) under the too-big-to-let fail doctrine prior to FDICIA.

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WILLIAM P. OSTERBERG AND JAMES B. THOMSON

Table 7. FIML-Probit Estimation of Resolution Type Eq. (3).a Variable

Coefficient

Std. Error

t-Ratio

Probability

Constant Problem Loans (log) Southwest Dummy Depositor Preference Dummy Predicted Net Worthb Branch Dummy Size Core Deposits Northeast Dummy Other Real Estate Owned

8.7391 −53.737 0.51140 0.53849 −0.50081 −0.35542 0.18602 0.86907 −0.03819 −0.21659

3.8740 20.140 0.1074 0.1164 0.1940 0.1136 0.0413 0.3058 0.0196 0.0993

2.256 −2.668 4.760 4.626 −2.581 −3.129 4.506 2.842 −1.948 −2.181

0.0241 0.0076 0.0000 0.0000 0.0098 0.0018 0.0000 0.0045 0.0514 0.0292

a Selection b Net

criterion (closure) provided by estimation of Eq. (2) as reported in Table 6. Worth predicted from Eq. (1); results in Table 5.

The coefficient on the Southwest Dummy is positive and significant, contrary to our expectation of a negative sign. The interpretation of this result must take into account the prohibition of branching in Texas that led to the creation of large multi-bank holding companies. The collapse of the depository institutions sector in the Southwest included FDIC resolution of five of the eight largest Texas holding companies and the death-bed acquisition of two of the other three large Texas holding companies by out-of-state banking organizations. Finally, despite the economic problems in Southwest in the mid-1980s this region was expected to be a high growth region in terms of both population and income. Hence, the positive and significant sign on Southwest Dummy appears to be controlling for constraints faced by the FDIC in resolving the insolvency of large multi-bank holding companies and the value of Texas banking franchises to out-of-state holding companies. The sign of the coefficient on the Branch Dummy is also inconsistent with our expectation. Since the number of potential acquirers for a closed bank is higher in states without intrastate branching restrictions, we expected that the Branch Dummy would be positively related to the use of the P&As. As conjectured by analysts, we find that depositor preference induces the FDIC to choose P&As. There are three channels thorough which depositor preference could affect the FDIC’s choice of resolution type. First, general creditors in banks subject to depositor preference might successfully exit the bank or effectively collateralize their exposure before the bank is closed, thereby raising the cost of a liquidation vis-`a-vis purchase and assumption and open-bank assistance transactions. Hirschhorn and Zervos (1990) provide evidence of this type of response in their study of thrifts. Second, depositor preference might

Depositor Preference Legislation and Failed Banks’ Resolution Costs

47

render contingent liabilities worthless so that P&As become less costly vis-`a-vis liquidations (Silverberg, 1986). Finally, constraints faced by the FDIC may cause it to choose the resolution option that jointly minimizes its fiduciary, political, and other costs associated with resolving the closed bank. In a liquidation the FDIC would have to strictly observe depositor preference, whereas, in P&A and OBA it could choose to ignore it. Hence, depositor preference could increase the non-fiduciary costs to the FDIC associated with liquidations, increasing the relative attractiveness of alternative failed-bank resolution options. Table 4 presents a list of the hypothesized and estimated coefficient signs for Eq. (4). Fourteen of the 17 coefficients have the expected sign and 11 of the 17 are significantly different from zero. The estimated coefficients appear in Table 8.19 The coefficient on predicted book capital, Net Worth, is negative and significantly different from zero and from negative one, corroborating James (1991) and OT’s findings of significant unbooked losses on the balance sheets of failed banks. On the other hand, the coefficient on income earned but not Table 8. Weighted-Least Squares Estimation of Resolution Cost Eq. (4).a Variable

Coefficient

Std. Error

t-Ratio

Probability

Constant Predicted Net Worthb Predicted Resolution Type Uncollected Interest Problem Loans Other Real Estate Owned Inside Loans Other Risky Assets Off Balance Sheet Items Core Deposits Size Depositor Preference Dummy Fed Funds Sold Fed Funds Purchased Other Borrowed Money Brokered Deposits ICORE Selectivity Correction

−18520.0 −1.5649 848.73 4.0097 1.2300 1.0600 2.4934 0.3915 −0.0423 −0.2127 1810.7 3061.1 0.3197 −0.3268 −0.1764 −0.1078 −0.0238 1163.5

11570.0 0.2942 4207.0 2.500 0.1881 0.1784 0.7669 0.0664 0.0237 0.0396 1100.0 1798.0 0.0642 0.0803 0.1760 0.1002 0.0263 2359.0

−1.6010 −5.3190 0.2020 1.6040 6.5390 5.9410 3.2510 5.8950 −1.7830 −5.3700 1.6470 1.7030 4.9820 −4.0670 −1.0020 −1.0760 −0.9040 0.4930

0.1094 0.0000 0.8401 0.1087 0.0000 0.0000 0.0011 0.0000 0.0745 0.0000 0.0996 0.0887 0.0000 0.0000 0.3162 0.2821 0.3658 0.6219

Note: Number of Observations = 1240; Mean of dependent variable = $7.8566 million; R-squared = 0.3763; Adjusted R-squared = 0.3676; F[17, 1222] = 43.37303. N(0, 1) used for significance levels. a All variables divided by the square-root of total assets. Selection criterion (closure) provided by estimation of Eq. (2), results given in Appendix B, Table B2. b Predicted Net Worth from estimation of Eq. (1), results given in Table B1.

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WILLIAM P. OSTERBERG AND JAMES B. THOMSON

received (Uncollected Interest), although positive, is no longer significant at the 10% level.20 Problem Loans and Other Real Estate Owned control for unbooked losses and have the expected positive and significant impacts. As in OT loans to insiders and portfolio risk have significantly positive impacts on resolution costs. In addition, we confirm Osterberg’s (1996) finding of a positive impact of Fed Funds Sold, which might proxy for the quality of the loan portfolio. Off-Balance Sheet Items are still negatively related to resolution costs consistent with the market discipline hypothesis of Boot and Thakor (1991) and the hypothesis that banks use derivative contracts to hedge against on-balance sheet risks.21 The positive impact of Size is consistent with higher FDIC administrative and legal expenses for larger banks. Neither Predicted Resolution Type nor ICORE (Predicted Resolution Type times Core Deposits) has significant effects on resolution cost. The former is consistent with the FDIC choosing resolution type so as to minimize resolution cost. However, the latter is inconsistent with the loss of franchise under liquidation being a significant influence on costs. As in previous work, the coefficient on Fed Funds Purchased is negative and significant. This fails to provide confirmation of general creditors increasing collateralization. The negative coefficients on Fed Funds Purchased, Other Borrowed Money, and Off Balance Sheet Items might be explained by all three providing market discipline – that is, banks with higher levels of unbooked losses than have been captured with the other variables has less access to these funding channels. Finally, the positive coefficient on Depositor Preference Dummy in the resolution cost equation is inconsistent with the hypothesis that depositor preference laws lower the FDIC’s costs. However, the sources of the higher costs from depositor preference are unclear. The FDIC might be providing de facto guarantees of all senior creditors. Or, there might be offsetting responses by general creditors. Which of these explanations is correct has important implications for the efficacy of depositor preference under FDICIA. If higher resolution costs associated with depositor preference laws are driven by FDIC behavior then reforms in FDICIA (1991) could eliminate or reverse this effect. On the other hand, if general creditor behavior is driving the positive coefficient on Depositor Preference Dummy then depositor preference may increase FDIC closed-bank resolution costs. Our model specification and econometric corrections allowed us to investigate the robustness of previous empirical results to sample selection bias and the endogeneity of book measures of bank capital. However, while there are strong theoretical reasons for all of our econometric corrections, we find that neither our results here nor the results of previous studies are sensitive to these corrections. Table 6 shows that the coefficient on Rho, the correlation between the errors in the closure and resolution type equations, is not significant. The results of

Depositor Preference Legislation and Failed Banks’ Resolution Costs

49

the closure probit run separately from the type equation (Table B2) thus do not appear different from the results in Table 6. The coefficient on the selectivity correction term (Mills’ ratio) in the resolution cost equation in Table 4 also is not significant. This result is confirmed in Table B3, which differs from Table 4 by excluding ICORE from the resolution cost equation. However, by including Predicted Resolution Type in the cost equation we have controlled for any possible influence of depositor preference on cost through its effect on resolution type. This might explain why, contrary to Osterberg (1996), ICORE no longer influences costs.

5. CONCLUSIONS AND POLICY RECOMMENDATIONS We extend the depositor preference literature and the bank resolution cost literature by incorporating deposit preference into an econometric model of bank resolution costs. This model allows us to directly test the impact of state-level depositor preference on the FDIC’s choice of resolution type and closed bank resolution costs while controlling for any impact on type in our analysis of the impact on costs. Moreover, our framework allows us to test the sensitivity of previous findings to sample selection bias and Maddala’s (1986) concerns about the endogeniety of book measures of net worth used as proxies in this literature. Our examination of bank failures from 1986 through 1992 provides little support for claims that depositor preference will result in lower FDIC closed bank resolution costs. In fact, we find a marginally significant positive relationship between depositor preference and costs. Consistent with Silverberg’s (1986) analysis of depositor preference, we also find a positive relationship between the presence of depositor preference laws and the use of P&A and OBA transactions. These two results are consistent with Kane’s (1986) analysis of FDIC behavior, where the FDIC jointly minimizes its fiduciary, political, and other costs associated with resolving the closed bank. In other words, to the extent that depositor preference increases the non-fiduciary costs faced by the FDIC we would expect depositor preference to change the trade-off between fiduciary and non-fiduciary costs and lead to higher fiduciary resolution costs. Although we have analyzed the impact of state depositor preference legislation, we would expect the qualitative nature of our results to carry over to an analysis of the 1993 national depositor preference statute. First of all, as Marino and Bennett (1999) point out, the relatively heavy reliance of state banks on insured deposits biases our analysis away from finding a significant impact on costs. Second, variation among the state laws introduces into our regression noise not likely to be present in an analysis of the national law. Third, the systemic risk exemption

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WILLIAM P. OSTERBERG AND JAMES B. THOMSON

provision of FDICIA – which went into effect after our sample period and before national depositor preference – should increase the incentives of general creditors to improve the security of their claims in troubled depositories through greater collateralization and/or shortened maturity. The impact of general creditor behavior on FDIC resolution costs for large banks would be material as foreign deposits are considered general credits under existing interpretations of the national depositor preference law. Finally, since FDICIA explicitly precludes the FDIC from disregarding depositor preference in a closed bank resolution (it doesn’t allow the FDIC to protect uninsured depositors or unsecured creditors) it reduces the resolution forbearance incentives that bias the FDIC’s choice of resolution options away from liquidations. Therefore, under FDICIA depositor preference laws are less likely to have a significant impact on FDIC’s choice of resolution type. To the extent that FDICIA’s prompt corrective action provisions result in the closure of capital deficient but book solvent banks, then depositor preference should have no impact on FDIC resolution costs.

NOTES 1. Kaufman (1997) noted that the passage of national depositor preference legislation was surprising to many observers and resulted from an effort to find a source of revenue as an alternative to charging state banks for FDIC examinations. Most claims about the impact were voiced only after enactment. 2. See Thomson (1994) for an example of how FDIC losses may increase as a result of depositor preference laws. 3. At the time national depositor preference legislation was enacted, 29 states had similar laws covering state-chartered banks and 18 had depositor preference statutes covering statechartered thrift institutions. 4. Birchler (1997) provides a contract-theoretic explanation of the priority structure of bank deposits. 5. For example, during the sample period state-chartered banks typically enjoyed more liberal powers. 6. Osterberg (1996) examined a wide range of portfolio measures and found no significant differences among banks depending on whether they were subject to depositor preference. However that analysis was not restricted to banks that eventually failed. 7. See Carnell (1993) for a discussion of FDICIA. 8. Marino and Bennett (1999) provide a discussion of the importance of foreign deposits for assessing the impact of the 1993 Act. 9. The Competitive Equality Banking Act of 1987 gave the FDIC an intermediate option for handling a failed bank, the bridge bank. Under bridge bank authority (which was expanded by the Financial Institutions Reform, Recovery, and Enforcement Act of 1989) the FDIC can pass the assets and liabilities of the failing bank into a specially chartered National bank which the FDIC can operate for up to three years. The bridge bank option

Depositor Preference Legislation and Failed Banks’ Resolution Costs

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gives the FDIC more flexibility in resolving closed banks by extending the time it has to weigh its alternative resolution options. 10. Given the small number of open-bank assistance transactions, we group the OBA banks and the P&A banks into a single category. 11. The joint maximum likelihood estimation of Eqs (3) and (4) required the scaling of some of the regressors in Eq. (3), hence, we use the natural logarithm of problem loans in (3). 12. Thomson (1992) found that the probability that a bank is closed is inversely related to its capitalization. This effect should be taken account of with the selection rule. 13. Unlike the analysis in this paper, Osterberg (1996) included interactive terms intended to test whether the impact of general credit categories varied with depositor preference status. Such terms are omitted here because they were not jointly significant. 14. Kane (1986) argues that information, funding, administrative and legal, and political constraints cause bank regulators to adopt sub-optimal closure rules. Allen and Saunders (1993) model deposit insurance as a callable perpetual put option. The value of forbearance is the difference between the value of the call option under unconstrained regulatory closure rules and its value under constrained closure rules. 15. For example, expenses for the FDIC’s division of liquidation averaged 8.3% of collections in 1991 (see the FDIC’s 1991 Annual Report). Moreover, at the end of 1992, the FDIC’s estimated contingent liability for unresolved legal cases was $404 million. Costs of receivership also include losses that arise from the inefficient asset salvage operation of the receiver (see Kane, 1990). 16. See Avery and Berger (1991), Boot and Thakor (1991), and Koppenhaver and Stover (1991). 17. The significance of individual filer type dummies is eliminated when federal funds variables are included. 18. For example, Thomson (1992) used capital net of problem loans as the dependent variable whereas the resolution cost literature uses net worth as a regressor. The post-1992 literature on the determinants of resolution cost suggests further changes to the specification of Eqs (1) and (2). 19. Table B3 shows the results when ICORE (Core Deposits times Predicted Resolution Type) is excluded. The selectivity condition from estimating Eq. (2) alone was used to correct the standard errors in the resolution cost equation. Table B2 shows the results of estimating Eq. (2) separately from the resolution type Eq. (3). The selectivity correction generated by estimating Eq. (2) alone is not much different from that resulting from joint estimation with Eq. (3) since the correlation between the errors from Eqs (2) and (3) is not significant. 20. However, the coefficient on Uncollected Interest is positive and significant when Eq. (2) omits measures of fed funds sold, fed funds purchased and other borrowed money. 21. OT finds similar results when Off-Balance Sheet Items was split into off-balance sheet loan items and other off-balance sheet activities. 22. Foreign depositors are junior to uninsured domestic depositors and the FDIC under the new legislation since the “deposit” is defined as in the FDIC act where it refers to domestic deposits. See Kaufman (1997, footnote 2, p. 62). 23. See Federal Register (1993). 24. Given that the failure/closure and resolution type equations as an ordered probit, R is retrieved as the appropriate quadrant of the variance matrix from the two equations.

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WILLIAM P. OSTERBERG AND JAMES B. THOMSON

ACKNOWLEDGMENTS The work was completed while William P. Osterberg was an economist at the Federal Reserve Bank of Cleveland. The views stated herein are those of the authors and not those of the Federal Reserve Bank of Cleveland or of the Federal Reserve Board of Governors. The authors thank Jim Barth, Ben Craig, William Greene, Joe Haubrich, Chris James, Ed Kane, Stanley Longhofer, Randy Olsen, Walker Todd, Haluk Unal, and seminar participants at the Eastern Finance Association, Federal Reserve Bank of Chicago Bank Structure Conference and East Tennessee State University for helpful comments and suggestions. Sandy Sterk provided outstanding research assistance.

REFERENCES Allen, L., & Saunders, A. (1993). Forbearance and the valuation of deposit insurance as a callable perpetual put. Journal of Banking and Finance, 16(June), 629–643. Avery, R., & Berger, A. (1991). Loan commitments and bank risk exposure. Journal of Banking and Finance, 15(September), 173–192. Barth, J., Bartholomew, P., & Bradley, M. (1990). Determinants of thrift institution resolution costs. Journal of Finance, 45(July), 731–754. Birchler, U. (1997). Bankruptcy priority for bank deposits: A contract theoretic explanation. Discussion Paper No. 9709, Department of Economics, University of St. Gallen, Switzerland (May). Boot, A., & Thakor, A. (1991). Off-balance-sheet liabilities, deposit insurance, and capital requirements. Journal of Banking and Finance, 15(September), 825–846. Bovenzi, J., & Murton, A. (1988). Resolution costs of bank failures. FDIC Banking Review, 1(Fall), 1–11. Buser, S., Chen, A., & Kane, E. (1981). Federal deposit insurance, regulatory policy, and optimal bank capital. Journal of Finance, 36(September), 775–787. Carnell, R. (1993). A partial antidote to perverse incentives: The FDIC Improvement Act of 1991. Annual Review of Banking Law, 12, 317–321. Ely, B. (1993). Surprise Congress just enacted the core banking system. American Banker, 158(September 21), 24. Federal Deposit Insurance Corporation (1993). Failed bank cost analysis: 1986–1992. Washington, DC (FDIC). Federal Register (1993). Friday, August 13, 58(155), 43069–43070. Greene, W. (1993). Econometric analysis. New York: MacMillan. Hirschhorn, E., & Zervos, D. (1990). Policies to change the priority of claimants: The case of depositor preference laws. Journal of Financial Services Research, 4, 111–125. James, C. (1991). The losses realized in bank failures. Journal of Finance, 46(September), 1223–1242. Kane, E. (1986). Appearance and reality in deposit insurance reform. Journal of Banking and Finance, 10, 175–188. Kane, E. (1990). Principal-agent problems in S&L salvage. Journal of Finance, 45(July), 755–764.

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Kaufman, G. (1997). The new depositor preference Act: Time inconsistency in action. Managerial Finance, 23, 56–63. Keeley, M. (1990). Deposit insurance, risk, and market power in banking. American Economic Review, 80(December), 1183–1200. Koppenhaver, G., & Stover, R. (1991). Standby letters of credit and bank capital: Evidence of market discipline. Proceedings from a Conference on Bank Structure and Competition, Federal Reserve Bank of Chicago (May), pp. 373–394. Maddala, G. (1986). Econometric issues in the empirical analysis of thrift institutions’ insolvency and failure. Working Paper, University of Florida. Marino, J., & Bennett, R. (1999). The consequences of national depositor preference. FDIC Banking Review, 12(2), 19–38. Murphy, K., & Topel, R. (1985). Estimation and inference in two-step econometric models. Journal of Business and Economic Statistics, 3(4), 370–379. Osterberg, W. (1996). The impact of depositor preference laws. Federal Reserve Bank of Cleveland Economic Review (Quarter 3), 2–11. Osterberg, W., & Thomson, J. (1994). Depositor preference and the cost of capital for insured depository institutions. Federal Reserve Bank of Cleveland, Working Paper 9404 (April). Osterberg, W., & Thomson, J. (1995). Underlying determinants of closed-bank resolution costs. The Causes and Costs of Depository Institution Failures, 75–92. Kluwer. Osterberg, W., & Thomson, J. (1999). Depositor preference laws and the cost of debt capital. Federal Reserve Bank of Cleveland Economic Review (Quarter 3), 10–20. Silverberg, S. (1986). A case for depositor preference. Banking and Economic Review, Federal Deposit Insurance Corporation, pp. 7–9. Thomson, J. (1992). Modeling the bank regulator’s closure option: A two-step Logit regression approach. Journal of Financial Services Research, 6, 5–23. Thomson, J. (1994). The National Depositor Preference Law. Federal Reserve Bank of Cleveland Economic Commentary (February 15). Todd, W., & Thomson, J. (1991). An insider’s view of the political economy of the too big to let fail doctrine. Public Budgeting and Financial Management: An International Journal, 3, 547–617.

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APPENDIX A Omnibus Budget Reconciliation Act of 1993 Title III of the Omnibus Budget Reconciliation Act of 1993 instituted depositor preference for all insured depository institutions by amending Section 11(d)(11) of the Federal Deposit Insurance Corporation Act [12 U.S. C. 1821(d)(11)]. The amendment establishes the following priority of payment in the resolution of a failed depository institution: (1) (2) (3) (4) (5)

Administrative expenses of the receiver. Deposit liabilities.22 General or senior liabilities. Subordinated obligations. Shareholder claims.

On August 13, 1993 the FDIC issued an interim rule clarifying its interpretation of “administrative expenses of the receiver,” indicating that these include “post appointment obligations incurred by the receiver as part of the liquidation of an institution” and that “this priority also covers certain expenses incurred prior to the appointment of the receiver.”23 Thus the receiver (which for most banks and thrifts is the FDIC) may pay expenses it deems consistent with the orderly closure of the institution, even if those expenses were incurred prior to closure. These prereceivership expenses include the payment of the institution’s last payroll, guard services, data processing, utilities and lease payments. Excluded are items such as golden parachute claims, severance pay claims, and liabilities arising from the repudiation of contracts.

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APPENDIX B Table B1. OLS Estimation of Net-Worth Equation.a Variable

Coefficient

Std. Error

t-Ratio

Probability

Constant Net Worth (t − 1) Uncollected Interest Problem Loans Other Real Estate Owned Inside Loans Other Risky Assets Off-Balance Sheet Items Core Deposits Net Charge-offs Loan Herfindahl Index Purchased Funds Net Income Failed Business Liabilities Per Capita Income

−1949.5 0.89404 0.08942 −0.10858 0.28048 −0.06186 0.00928 0.00404 0.00639 0.04095 0.36495 0.00019 0.13298 −0.00006 90.4660

650.9 0.00327 0.04122 0.00354 0.00755 0.02824 0.00055 0.00001 0.00036 0.00887 0.69960 0.00031 0.00925 0.00002 35.62

−2.995 273.440 2.169 −30.679 37.135 −2.190 16.832 27.524 17.562 4.615 0.522 0.628 14.373 −3.115 2.540

0.0027 0.0000 0.0301 0.0000 0.0000 0.0285 0.0000 0.0000 0.0000 0.0000 0.6019 0.5297 0.0000 0.0018 0.0111

Anova Source

Variation

Degrees of Freedom

Mean Square

Regression Residual

0.6981E + 15 0.1139E + 13

14 12539

0.4987E + 14 0.9081E + 08

Total

0.6993E + 15

12553

0.5571E + 11

Note: Number of Observations = 12,554; Mean of Dependent Variable = $25.74261 million; R-squared = 0.9984; Adjusted R-squared = 0.9984; F[14, 12539] = 549153.3. a Estimation generates Predicted Net Worth used as a regressor in Eq. (4).

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Table B2. FIML-Probit Estimation of Closure Eq. (2).a Variable

Coefficient

Std. Error

t-Ratio

Probability

Constant Predicted Net Worth Uncollected Interest Purchased Funds Off-Balance Sheet Items Inside Loans Size Other Risky Assets Per Capita Income Failed Business Liabilities BHC Dummy Efficiency Ratio Core Deposits

9.1148 −6.2946 101.55 −1.8881 −0.25905 10.566 −2.5163 −0.0133 −13.393 3.9552 −0.29586 0.93649 −5.0985

0.6272 0.1973 5.964 0.4685 0.2271 1.889 3.018 0.2463 1.3280 2.083 0.0717 0.1339 0.3436

14.533 −31.898 17.026 −4.031 −1.141 5.593 −0.834 −0.054 −10.149 1.899 −4.124 6.997 −14.832

0.0000 0.0000 0.0000 0.0001 0.2540 0.0000 0.4044 0.9569 0.0000 0.0576 0.0000 0.0000 0.0000

Note: Used to adjust standard errors in Eq. (4) for selectivity. N(0, 1) used for significance levels. a All of the variables have been divided by total assets.

Frequencies of Actual and Predicted Outcomes Predicted Failure?

Total

No

Yes

Failed? No Yes

11251 199

63 1041

11314 1240

Total

11450

1104

12554

Table B3. Estimation of Resolution Cost Equation without ICORE.a Variable

Coefficient

Std. Error

t-Ratio

Probability

Constant Predicted Net Worthb Predicted Resolution Type Uncollected Interest Problem Loans Other Real Estate Owned

−14897.0 −1.458 67.653 3.9812 1.1814 0.9845

10850.0 0.2693 4119.0 2.500 0.1804 0.1577

−1.372 −5.413 0.016 1.592 6.551 6.242

0.1699 0.0000 0.9869 0.1113 0.0000 0.0000

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Table B3. (Continued ) Variable

Coefficient

Std. Error

t-Ratio

Probability

Inside Loans Other Risky Assets Off Balance Sheet Items Core Deposits Size Depositor Preference Dummy Fed Funds Sold Fed Funds Purchased Other Borrowed Money Brokered Deposits Selectivity Correction

2.5614 0.3737 −0.0410 −0.2070 1495.6 2983.5 0.30626 −0.3120 −0.1900 −0.0892 983.64

0.7635 0.0625 0.0237 0.0391 1043.0 1796.0 0.0624 0.7868 0.1754 0.0981 2352.0

3.355 5.889 −1.732 −5.292 1.434 1.661 4.905 −3.965 −1.083 −0.909 0.418

0.0008 0.0000 0.0834 0.0000 0.1517 0.0968 0.0000 0.0001 0.2787 0.3632 0.6757

Note: Number of Observations = 1240; Mean of dependent variable = $7.786 million; R-squared = 0.3759; Adjusted R-squared = 0.3677; F[16, 1223] = 46.041; N(0, 1) used for significance levels. a All variables are divided by the square-root of total assets. b Predicted Net Worth from Table B1 estimation.

APPENDIX C Adjustment of Standard Errors for Inclusion of Predicted Values as Regressors We follow Murphy and Topel (1985) in deriving the correct standard errors when one or more variables on the right-hand side of the failure/closure, resolution type, or resolution cost equation has been generated by a prior estimation. In the case of the failure/closure equation, and the resolution type equation, which are estimated by probit (maximum likelihood [MLE]), the right-hand side includes the predicted value of net worth/total assets, which was generated by ordinary least squares (OLS). In the case of resolution cost, the right-hand side includes the predicted level of net worth, estimated by OLS, and the predicted resolution type, predicted by probit (MLE). Murphy and Topel present the correct adjustment when the first stage estimation is maximum likelihood and the second MLE or when both are MLE. Here we detail the derivation for the slightly different case when the first stage is OLS and the second MLE. The OLS estimation yields: √

n(␪ˆ 1 − ␪∗1 ) =

1 X X1 n 1

−1

1 X U1, n 1

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where X, U, and ␪ denote the right-hand side variables, estimated residuals, and parameters, respectively. The MLE estimation yields: 1 ∂ 2 (y 2 , ␪∗1 , ␪∗2 ) 1 1 ∂2 2 (␪∗1 + ␭(␪ˆ 1 − ␪∗1 )) √ ˆ −√ = d␭ n(␪1 − ␪∗1 ) ∂␪2 n ∂␪2 ∂␪1 n 0 1 1 ∂2 2 (␪∗ + ␭(␪ˆ 2 − ␪∗2 )) √ ˆ + d␭ n(␪2 − ␪∗2 ), n ∂␪2 ∂␪2 0 where 2 denotes the log-likelihood for the second equation, ␪2 denotes the parameters in the second equation (including those associated with the predicted values from prior equations). Substitution yields: n √ 1 ∂ (y 2 , ␪∗1 , ␪∗2 ) −1 ∗ ∼ ˆ n(␪2 − ␪2 ) = −R 2 √ ∂␪2 n + R −1 2 R3

i=1

1 X X1 n 1

−1

1 √ X 1 U 1 , n

where R2 is Fisher’s information matrix which can be written as −E[∂2 2 /∂␪2 ∂␪2 ] and will be easily retrieved from the estimation of the second equation.24 R3 must be derived and is equal to −E{∂ 2 /∂␪2 ∂␪1 }. Then we need the form of the variance-covariance matrix where     ∂ 2 1 ∂ 2 2 n ∂ 2 E U X1 − E 1 n ∂␪∂␪ ∂␪2 1 . √  i=1 ∂␪2  ∼ = N(0, ) and =    ∂ 1 2 n n E X1 U1 ␴ (X1 X1 ) i=1 X1 U1 ∂␪1 n Then, for the estimated parameters for the second equation (␪ˆ 2 ) we have √ n(␪ˆ 2 − ␪∗2 ) ≈ N(0, ) where −1 2 −1 −1 −1 −1 = R −1 2 + R 2 [R 3 ␴ (X 1 X 1 ) nR 3 + Q 2 Q 0 R 3 + R 3 Q 0 Q 2 ]R 2

where R2 and R3 are defined as above, Q2 is the lower-left hand quadrant of , and ˆ 0 = 1/n(X X 1 )−1 , which is easily retrievable from the results of the first-stage Q 1 OLS estimation. For the standard error adjustment for both the failure and resolution type equations, the log-likelihood is based on the bivariate probit as discussed by

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Greene (1993). As mentioned in the text, since neither the failure dummy nor the resolution type dummy appears in the other’s equation, while the failure equation supplies the selection rule for the resolution type equation, the two are better thought of as an ordered probit. However, although there is no simultaneity the presence of selectivity implies that ␳ = 0.

SECONDARY MORTGAGE MARKETS, GSEs, AND THE CHANGING CYCLICALITY OF MORTGAGE FLOWS Joe Peek and James A. Wilcox ABSTRACT In recessions, depository institutions accounted for most declines in mortgage ﬂows. Recently, they partially offset their withdrawals from primary markets with accumulations of mortgage-backed securities. Increases in direct ﬂows into agency and private pools also countered the declining ﬂows elsewhere. As the less-procyclical secondary mortgage markets grew and matured, they increasingly stabilized mortgage ﬂows. During periods of international ﬁnancial crises or of domestic economic stress, GSEs may have been particularly effective in stabilizing mortgage markets and moderating business cycles.

1. INTRODUCTION Congress chartered the Federal Home Loan Mortgage Corporation (Freddie Mac) and the Federal National Mortgage Association (Fannie Mae) as housing-related, government-sponsored enterprises (GSEs). The missions of Fannie Mae and Freddie Mac are to: (1) promote the flow of capital to residential mortgage markets; and (2) stabilize residential mortgage markets by facilitating “a continuous supply of mortgage credit for U.S. homebuyers in all economic environments” (Federal Home Loan Mortgage Corporation, 2000). Research in Finance Research in Finance, Volume 20, 61–80 Copyright © 2003 by Elsevier Ltd. All rights of reproduction in any form reserved ISSN: 0196-3821/doi:10.1016/S0196-3821(03)20004-6

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Numerous studies have concluded that Freddie Mac and Fannie Mae raised homeownership rates by promoting the flow of capital to (residential) mortgage markets. By providing guarantees of the timely payment of principal and interest on mortgages, Freddie Mac and Fannie Mae have contributed mightily to the development of secondary markets in mortgages (McCarthy & Peach, 2002). Secondary mortgage markets, in turn, have increased the efficiency and liquidity of primary mortgage markets and the integration of U.S. mortgage markets into world capital markets (Devaney & Pickerill, 1990; Federal Reserve Bank of Minneapolis, 2001; Goebel & Ma, 1993; Rudolph & Griffith, 1997). Apart from the reductions in mortgage interest rates generally that may be attributed to the maturation of secondary markets, interest rates on conforming mortgages averaged a bit more than 25 basis points lower than those on jumbo mortgages before the 1990s, and a bit less than 25 basis points lower since the middle of the 1990s (Congressional Budget Office, 2001; Hendershott & Shilling, 1989). The total lowering of mortgage interest rates attributable to GSEs benefited homeowners substantially. By increasing the aggregate, longer-term supply of mortgage credit, and thereby lowering mortgage interest rates and raising homeownership rates, GSEs can be said to have achieved the first part of their missions. Less attention has been devoted to the second aspect of the GSEs’ public missions. The volumes of assets and trading associated with secondary mortgage markets and the GSEs, anecdotal evidence, and introspection support the hypothesis that large, active secondary mortgage markets have altered the procyclicality of residential mortgage flows and construction.1 Nonetheless, in spite of the widely held view that the mortgage markets now operate fundamentally differently, little systematic evidence exists that secondary mortgage markets have altered mortgage flows during recessions.2 In contrast to the studies about GSEs that predominantly focus on the average effects of GSEs on mortgage rates, here we focus on fluctuations in mortgage flows at depository institutions and at other private sector suppliers of funds, as well as at GSEs. In particular, we quantify how much these total mortgage flows changed during national economic recessions. We calculate how much the flows of mortgage funds that were provided by depository institutions, pensions, insurance companies, and other suppliers of mortgage funds changed during recessions. We calculate how much GSEs intermediated mortgage flows during recessions, how their intermediation compared with others’, and how it shifted through time. Of special interest to us was how much, or even whether, GSEs offset others’ declines in mortgage intermediation and thereby stabilized the aggregate supply of mortgage credit during recessions. By stabilizing mortgage flows, Freddie and Fannie could dampen fluctuations in real activity, both in the housing sector and in the macroeconomy.3 For that

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reason, which stands quite apart from their continuing value to the longer-term operation and development of secondary mortgage markets, the housing GSEs may contribute to the broader aims of public policy. How can GSEs stabilize mortgage flows? First, they may directly increase mortgage flows during recessions by purchasing whole mortgages and mortgagebacked securities to at least partially offset the procyclicality of supplies by others. GSEs may be more willing or able to act countercyclically than the private sector because they have “deeper pockets.” Second, GSEs may reduce the procyclicality of other mortgage suppliers indirectly. One way to do that is to make mortgages more attractive to less-procyclical investors. The expansion of secondary markets, the increase in their liquidity, and the implicit government guarantee of GSEs’ obligations are likely to have attracted more funds both from foreign investors, whose home business cycles are imperfectly correlated with those of the United States, as well as from sectors, such as insurance and pension funds, whose shares of whole mortgages held had been in longer-term decline. Large, active secondary mortgage markets may alter financial and real magnitudes in housing markets during recessions for several reasons. The first revolves around differences between the average riskiness of home mortgages and of business loans in bank (and thrift) portfolios. Bank portfolios consist of investments, mortgages, and other, primarily business, loans. Home mortgages tend to have lower expected default rates and risk premiums than the average bank loan. During recessions, the default rates and associated risk premiums in their interest rates for business loans tend to increase relative to those for home mortgages. Since depository institutions’ costs for their own liabilities reflect their entire portfolios, the risk-based spread between the secondary market yield on mortgages and depository institutions’ liabilities’ costs may shrink during recessions, thereby reducing the quantity of mortgages demanded by depository institutions. Secondary mortgage markets can cushion declines in mortgage flows during recessions, then, by absorbing the mortgages that depository institutions are willing to originate but not hold. Typically, recessions are preceded by tighter monetary policy in the form of significantly higher short-term interest rates. Secondary mortgage markets may reduce the declines in mortgage flows attributable to higher interest rates, and therefore reduce the extent to which total home mortgage flows decline during recessions. When tighter monetary policy reduces the supply of their less expensive, “core” deposits, depository institutions’ funding costs rise relative to secondary mortgage market yields. By absorbing more mortgages, secondary mortgage markets can cushion housing markets when depository institutions accumulate mortgages on their balance sheets more slowly.

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Recessions can also result from disruptions to financial markets. Disruptions stem from various sources. Contributing to the severity of the 1990–1991 recession, for example, was the “bank capital crunch,” during which loan losses reduced banks’ capital enough to reduce their supplies of credit, including mortgage credit. Banks can ease capital constraints by securitizing or selling mortgages that they have on their balance sheets. Given the structure of the Basle capital regulations, secondary mortgage markets likely cushion mortgage flows against bank capital shocks by enabling banks to convert whole mortgages into secondary mortgage market securities that have a lower capital requirement, thus “stretching” bank capital. Thus, when housing-related GSEs increase their supplies of mortgage activities in response to financial disruptions, they serve as shock absorbers that lessen the fall-off in the supplies of home mortgages. GSEs may act either as conduits to ultimate holders of home mortgages or as the ultimate holders themselves. An increase in GSEs’ holdings of home mortgages further mitigates the decline in depository institutions’ supplies of mortgage credit. In that way, secondary markets for guaranteed mortgages play the role that some envisioned for Fannie Mae and Freddie Mac after the mortgage credit crunch associated with disintermediation from depository institutions in the 1960s. In this paper, we provide evidence that, as secondary mortgage markets grew, the procyclicality of primary mortgage markets diminished. The next section provides background on the growth of the secondary mortgage market and of two mortgage-related GSEs. The third section focuses on the (pro-) cyclicality of mortgage flows and calculates how much GSEs have reduced their cyclicality. The final section summarizes our findings and suggests fruitful directions for further research on the effects of secondary mortgage markets on the financial and real sides of housing markets.

2. DIRECT AND INDIRECT HOLDINGS OF MORTGAGES BY THE PRIVATE SECTOR AND GSES Two basic activities of Fannie Mae and Freddie Mac increase the supply of mortgage funds: (1) providing credit guarantees; and (2) investing in mortgages or mortgage-backed securities (MBS). The term “retained portfolio” generally refers to the sum of the whole mortgages plus the MBS that Fannie Mae and Freddie Mac each hold. After purchasing mortgages, Fannie Mae and Freddie Mac can either: (1) securitize the mortgages upon which they have placed their credit guarantee by issuing guaranteed MBS and then sell these securities to investors; or (2) retain these mortgages for their own portfolio.4 Fannie Mae and Freddie Mac fund their holdings of mortgages and of MBS by issuing non-mortgage-backed securities.

The Changing Cyclicality of Mortgage Flows

65

When they retain mortgages or issue guaranteed MBS, Freddie and Fannie assume the credit risk associated with the mortgages. Unlike providing credit guarantees, the retained portfolio imposes interest rate and prepayment risks on Fannie Mae and Freddie Mac. Fannie Mae and Freddie Mac mitigate these risks with derivative financial instruments. The revenues to Fannie Mae and Freddie Mac differ across the basic two activities: Fannie Mae and Freddie Mac receive a guarantee fee for the mortgages that they securitize, while they earn the differential of the yields on their retained portfolio above those of their own liabilities. The market for MBS developed slowly, beginning in the early 1960s with the issuance of securities backed by pools of Farmers’ Home Administration (FmHA) mortgages. The outstanding stock or volume of these pools did not reach $1 billion until late 1968. Growth of mortgage pools accelerated in the 1970s after the Government National Mortgage Association (Ginnie Mae) and Freddie Mac began pooling mortgages in the early 1970s. Growth accelerated again in the early 1980s after Fannie Mae and the private sector began to pool mortgages. The outstanding volumes of both GSE pools and private mortgage pools again grew rapidly in the early 1990s, a time when the total volume of mortgages outstanding grew slowly. The absence of the typical decline in total mortgages during the 1990–1991 recession coupled with the large increase in the size of secondary markets suggests that secondary markets somewhat reduced the effects of recessions on mortgage flows. Figure 1 plots quarterly data for MORTBAL, which is the outstanding total of residential mortgage balances, as a percentage of (nominal) potential GDP for 1968Q1–2001Q3.5 MORTBAL is clearly procyclical, declining during the 1970, 1974–75, and the two 1980s recessions. However, during the 1990 recession and the ensuing slow recovery, the total dollar stock of mortgages outstanding grew at about the same rate as GDP, rather than following its typical procyclicality. Idiosyncrasies of the 1990–91 recession, such as the favored treatment of mortgages and agency securities by the 1988 Basle Accord, may explain the missing procyclicality of MORTBAL. Alternatively, MORTBAL may have become less procyclical as a result of the maturation of secondary markets for mortgages. Figure 2 plots holdings of whole mortgages by Fannie Mae (DFANNIE) and Freddie Mac (DFREDDIE), as a percentage of potential GDP. Fannie Mae acquired whole mortgages rapidly during the 1970s. Since then, DFANNIE has been nearly trendless. DFANNIE fluctuates considerably over shorter spans. Relative to potential GDP, Fannie Mae’s holdings of whole mortgages peaked near each of the recessions since the early 1970s. Freddie Mac’s holdings of whole mortgages relative to potential GDP, DFREDDIE, were smaller and fluctuated less than those of Fannie Mae. DFREDDIE, too, peaked in the mid-1970s, in the mid-1980s, and in the early 1990s. In contrast to DFANNIE, DFREDDIE did

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Fig. 1 Note: End-of-quarter total residential mortgage balances outstanding, not seasonally adjusted, 1968Q1–2001Q3, as a percentage of potential GDP. Data sources: Board of Governors of the Federal Reserve System, Federal Reserve Bank of St. Louis FRED database, and www.freelunch.com.

not rise as much during the two recessions at the beginning of the 1980s. Note that Fig. 2 plots data only for holdings of whole mortgages, and therefore ignores the growing holdings by Fannie Mae and Freddie Mac of MBS and the growing volume of guaranteed MBS held outside the GSEs. Figure 3 plots total residential mortgage intermediation by Fannie Mae (TFANNIE) and Freddie Mac (TFREDDIE), calculated for each GSE as its holdings of whole mortgages plus its guaranteed MBS outstanding. Figure 3 also plots the intermediation by private mortgage conduits (TPRIVATE), calculated as the sum of private (i.e. not guaranteed by a GSE) MBS. Data for each series in Fig. 3 are expressed as a percentage of potential GDP for 1968Q1–2001Q3. TFANNIE and TFREDDIE grew quite slowly until the early 1980s. Both then accelerated. Thereafter, TFANNIE maintains its rapid growth rate. While TFREDDIE grew more rapidly than TFANNIE through the mid-1980s, it grew more slowly for the ensuing decade. Clearly, GSEs accounted for the overwhelming share of growth in total intermediation until the early 1990s. But, once secondary markets became well established, non-GSE issuance of MBS grew rapidly, too: TPRIVATE grew

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67

Fig. 2 Note: End-of-quarter residential mortgage balances outstanding, not seasonally adjusted, 1968Q1–2001Q3, as a percentage of potential GDP. DFANNIE consists of residential mortgages directly held in portfolio by FNMA. DFREDDIE includes residential mortgages directly held in portfolio by FHLMC. Data sources: Board of Governors of the Federal Reserve System, Federal Reserve Bank of St. Louis FRED database, and www.freelunch.com.

relatively slowly through the 1980s, but then accelerated in the 1990s to growth rates similar to those of TFANNIE and TFREDDIE. Figure 4 plots total mortgages outstanding and total intermediation by GSEs, each relative to potential GDP. FANFRED is the sum of total residential mortgage intermediation activities by Fannie Mae and Freddie Mac, calculated as the sum of TFANNIE and TFREDDIE from Fig. 3. MORTBAL is the total residential mortgage balances outstanding series from Fig. 1. DIFF, calculated as the difference between MORTBAL and FANFRED, measures the volume of mortgages that do not pass through Fannie Mae or Freddie Mac. After having been approximately trendless until the early 1980s, MORTBAL rises by about 20 percentage points, or about 70%, through the end of the period. From 1968 through 2001, DIFF was approximately trendless. By contrast, FANFRED rose from near zero to about 20% since the late 1960s. Thus, the major, longer-term increase in homeownership, as measured by mortgages relative to

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Fig. 3 Note: End-of-quarter residential mortgage balances outstanding, not seasonally adjusted, 1968Q1–2001Q3, as a percentage of potential GDP. TFANNIE includes residential mortgages directly held in portfolio by FNMA plus outstanding principal balances of residential-mortgage-backed securities insured or guaranteed by FNMA. TFREDDIE includes residential mortgages directly held in portfolio by FHLMC plus outstanding principal balances of residential-mortgage-backed securities insured or guaranteed by FHLMC. TPRIVATE consists of outstanding principal balances of residential-mortgagebacked securities issued by private mortgage conduits. Data sources: Board of Governors of the Federal Reserve System, Federal Reserve Bank of St. Louis FRED database, and www.freelunch.com.

potential GDP, coincided not with an increase in DIFF, but rather with a strikingly similar increase in the extent to which GSEs participated in mortgage markets. Such evidence supports the notion that the housing GSEs have succeeded in the first part of their missions. The second part of their missions is to stabilize mortgage finance. Figure 4 shows that, until about the mid-1980s, fluctuations in MORTBAL coincide impressively with fluctuations in DIFF, the mortgages not held or securitized by the GSEs. And, the fluctuations in both series were visibly procyclical.

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Fig. 4 Note: End-of-quarter residential mortgage balances outstanding, not seasonally adjusted, 1968Q1–2001Q3, as a percentage of potential GDP. MORTBAL is from Fig. 1. FANFRED is the sum of TFANNIE and TFREDDIE from Fig. 3. DIFF is the difference between MORTBAL and FANFRED.

Although the procyclicality of DIFF appears unabated, MORTBAL seems much less procyclical after the mid-1980s for two reasons. First, the upward trend in FANFRED offset the contributions of DIFF to the procyclicality of MORTBAL. And, second, FANFRED itself seems to have been somewhat countercyclical: its growth was somewhat faster during the macroeconomically weaker periods of the early 1990s and early 2000s and somewhat slower during the macroeconomically stronger periods of the late 1980s and mid-1990s.

3. THE DECLINING PROCYCLICALITY OF MORTGAGE FLOWS Figure 4 illustrated that total residential mortgages outstanding were clearly procyclical prior to the 1990s, but much less clearly so after 1990. An important issue is to what extent the two housing GSEs offset the reductions in supplies

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Table 1. Changes in Total Residential Mortgage Balances and Changes in Intermediation by GSEs Near Recessions. RECESSION PERIODS COMPARISON PERIODS TOTAL GSE TOTAL-GSE RATIOS (%) GSE/TOTAL (TOTAL-GSE)/TOTAL GSE/(TOTAL-GSE)

1973:4– 1975:1 1972:4– 1974:4

1980:1– 1980:3 1978:4– 1980:2

1981:3– 1982:4 1980:4– 1982:3

1990:3– 1991:1 1989:4– 1991:1

2001:1– 2001:4 2000:2– 2000:4

Average over five most recent recessions

-1.82 0.44 -2.26

0.05 0.22 -0.17

-2.65 0.67 -3.32

-0.16 1.52 -1.68

1.11 0.68 0.42

-0.69 0.71 -1.40

-24 124 -19

440 -340 -129

-25 125 -20

-950 1050 -90

61 38 162

-103 203 -51

Note: First differences of not-seasonally adjusted outstanding balances as a percentage of potential GDP. Recession periods span the quarters that contain the peak and trough months designated by the National Bureau of Economic Research (NBER). Comparison periods span the quarter with the (local) maximum (seasonally adjusted) flows of total home mortgages outstanding to the quarter with the (local) minimum flow of total home mortgages outstanding. GSE is the sum of balances of residential mortgages that FNMA or FHLMC directly held in their own portfolios plus outstanding principal balances of residential mortgage-backed securities insured or guaranteed by FNMA or FHLMC. Data sources: Board of Governors of the Federal Reserve System, Federal Reserve Bank of St. Louis FRED database, and www.freelunch.com.

of mortgage credit by others during recessions. To the extent that Fannie Mae and Freddie Mac operated countercyclically, they stabilized mortgage flows and likely the macroeconomy as well. Table 1 shows the changes in total residential mortgage balances and the changes in (total) intermediation by Fannie Mae and Freddie Mac for the five most recent recessions. These are the five recessions that have occurred since Fannie Mae and Freddie Mac became substantial participants in secondary mortgage markets. Table 1 also shows the difference between those two series and the averages across the five recessions for each series in Table 1. Recession periods in Table 1 span the quarters that contain the peak and trough months designated by the National Bureau of Economic Research (NBER). The comparison period associated with each recession was based on seasonally adjusted, quarterly data for total flows of home mortgages. These data came from the Flow of Funds accounts of the Board of Governors of the Federal Reserve System. Data for mortgage flows were expressed as a percentage of potential GDP. Tables 1–5 focus on mortgage flows during recessions. That is, they focus on cyclical rather than trend-like developments. In Table 1, each comparison period spans the period from the calendar quarter that contains the (local) maximum flow

RECESSION PERIODS COMPARISON PERIODS ALL HOLDERS D-DEP D-NDEPFIN D-INS D-PENS D-NFCORP D-HH D-GOVT D-GSE D-POOL D-ABS

1953:2– 1954:2 1953:1– 1954:1

1957:3– 1958:2 1955:1– 1958:1

1960:2– 1961:1 1959:2– 1961:1

Credit Crunch 1965:3– 1967:2

1969:4– 1970:4 1968:4– 1970:2

1973:4– 1975:1 1972:4– 1974:4

1980:1– 1980:3 1978:3– 1980:2

1981:3– 1982:4 1980:3– 1982:3

1990:3– 1991:1 1989:3– 1991:1

2001:1– 2001:4 2000:2– 2000:4

-0.33 -0.12 0.02 0.03 0.00 0.00 -0.06 -0.21

-1.54 -1.28 -0.09 -0.35 0.01 0.00 0.04 0.01 0.11

-0.61 -0.83 -0.04 0.01 0.02 -0.00 0.54 -0.18 -0.14

-1.38 -1.22 0.00 -0.20 -0.03 0.00 0.06 0.06 -0.08 0.03

-0.85 -0.93 0.08 0.02 0.01 0.01 -0.35 -0.06 0.32 0.04

-1.51 -1.74 -0.28 0.10 0.02 -0.04 -0.17 0.29 0.31 0.01

-3.14 -2.83 -0.27 0.08 0.03 0.25 -0.16 0.13 -0.26 -0.09

-2.44 -2.56 -0.03 -0.02 0.02 -0.24 -0.14 -0.24 0.16 0.61

-2.10 -1.28 -0.68 -0.06 -0.07 -0.19 -0.09 0.13 0.06 -0.29 0.20

-0.81 -2.12 -0.04 0.01 0.00 0.00 0.00 0.01 -0.03 1.19 0.18

Average over five most recent recessions -2.00 -2.11 -0.26 0.02 0.00 -0.04 -0.11 0.06 0.05 0.29 0.19

The Changing Cyclicality of Mortgage Flows

Table 2. Changes in Flows of Home Mortgages Near Recessions: Direct Holdings, by Holder.

Note: First differences of seasonally adjusted net flows of direct holdings of home mortgages by holder, all expressed as a percentage of potential GDP. Recession periods are the same as in Fig. 1. Comparison periods span the first quarter of the two adjacent quarters that contain the (local) maximum flows of total home mortgages outstanding to the quarter with the (local) minimum flow of home mortgages outstanding. The amounts in the table are the differences between: (1) the average of the flows of the maximum-flow quarter and the higher of the two adjacent quarters; and (2) the average of the flows during the minimum-flow quarter and the quarter that preceded the minimum-flow quarter. The 1966 credit crunch period was not a recession. Prefix D- indicates direct holdings. Mnemonics for holders are described in the text. Data sources: Board of Governors of the Federal Reserve System, Federal Reserve Bank of St. Louis FRED database, and www.freelunch.com.

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Table 3. Changes in Flows of Home Mortgages Near Recessions: Direct-plus-Indirect Holdings, by Holder. RECESSION PERIODS COMPARISON PERIODS

1957:3– 1958:2 1955:1– 1958:1

1960:2– 1961:1 1959:2– 1961:1

Credit Crunch 1965:3– 1967:2

1969:4– 1970:4 1968:4– 1970:2

1973:4– 1975:1 1972:4– 1974:4

1980:1– 1980:3 1978:3– 1980:2

1981:3– 1982:4 1980:3– 1982:3

1990:3– 1991:1 1989:3– 1991:1

2001:1– 2001:4 2000:2– 2000:4

-0.33 1.33 0.02 0.03 0.01 0.00 -1.07 -0.13

-1.54 -0.23 -0.09 -0.35 0.04 -0.10 -0.41 -0.07

-0.61 -0.50 -0.04 0.06 -0.01 -0.21 -0.54 0.00

0.11

-0.14

-1.38 -0.86 0.00 -0.11 -0.07 -0.14 -0.04 0.08 -0.01 -0.07 0.03

-0.85 -0.75 0.08 0.03 -0.04 -0.11 0.45 -0.50 -0.00 0.32 0.04

-1.51 -2.11 -0.28 0.10 0.02 -0.01 1.20 -0.12 -0.10 0.32 0.01

-3.14 -2.77 -0.00 -0.13 0.27 0.31 -0.37 -0.62 -0.05 -0.20 -0.09

-2.44 -2.48 0.33 0.03 0.13 -0.33 -0.08 0.04 -0.08 0.17 0.61

-2.10 -0.39 -0.10 0.05 -0.09 -0.27 -1.29 -0.19 -0.20 -0.12 -0.29 0.30

-0.81 -1.42 0.98 -0.01 0.14 -0.21 -1.46 -0.05 0.39 1.12 1.19 0.11

Average over five most recent recessions -2.00 -1.83 0.19 0.01 0.09 -0.10 -0.40 -0.19 0.01 0.26 0.29 0.21

Note: First differences of seasonally adjusted net flows calculated as the sum of (1) flows of direct holdings of home mortgages and (2) holdings of home mortgage-backed securities, by holder, all expressed as a percentage of potential GDP. Recession periods are the same as in Fig. 1. Comparison periods span the first quarter of the two adjacent quarters that contain the (local) maximum flows of total home mortgages outstanding to the quarter with the (local) minimum flow of home mortgages outstanding. The amounts in the table are the differences between: (1) the average of the flows of the maximum-flow quarter and the higher of the two adjacent quarters; and (2) the average of the flows during the minimum-flow quarter and the quarter that preceded the minimum-flow quarter. The 1966 credit crunch period was not a recession. Mnemonics for holders are described in the text. Data sources: Board of Governors of the Federal Reserve System, Federal Reserve Bank of St. Louis FRED database, and www.freelunch.com.

JOE PEEK AND JAMES A. WILCOX

ALL HOLDERS DEP NDEPFIN INS PENS NFCORP HH GOVT FOREIGN GSE POOL ABS

1953:2– 1954:2 1953:1– 1954:1

RECESSION PERIODS COMPARISON PERIODS D-DEP D-NDEPFIN D-INS D-PENS D-NFCORP D-HH D-GOVT D-GSE D-POOL D-ABS

1953:2– 1954:2 1953:1– 1954:1 36 -6 -9 0 0 18 64

1957:3– 1958:2 1955:1– 1958:1 83 6 23 -1 0 -3 -1 -7

1960:2– 1961:1 1959:2– 1961:1 136 7 -2 -3 0 -89 30 23

Credit Crunch 1965:3– 1967:2 88 0 14 2 0 -4 -4 6 -2

1969:4– 1970:4 1968:4– 1970:2

1973:4– 1975:1 1972:4– 1974:4

109 -9 -2 -1 -1 41 7 -38 -5

115 19 -7 -1 3 11 -19 -21 -1

1980:1– 1980:3 1978:3– 1980:2 90 9 -3 -1 -8 5 -4 8 3

1981:3– 1982:4 1980:3– 1982:3 105 1 1 -1 10 6 10 -7 -25

1990:3– 1991:1 1989:3– 1991:1 61 32 3 3 9 4 -6 -3 14 -10

2001:1– 2001:4 2000:2– 2000:4 262 5 -1 0 0 0 -1 4 -147 -22

Average over five most recent recessions 127 13 -1 0 3 5 -4 -4 -31 -16

The Changing Cyclicality of Mortgage Flows

Table 4. Contributions to Changes in Mortgage Flows Near Recessions: Direct Holdings, by Holder.

Note: First differences of seasonally adjusted net flows of direct holdings of home mortgages by holder, all expressed as a percentage of the first difference of total flows of home mortgages. Recession periods are the same as in Fig. 1. Comparison periods span the first quarter of the two adjacent quarters that contain the (local) maximum flows of total home mortgages outstanding to the quarter with the (local) minimum flow of home mortgages outstanding. The amounts in the table are the differences between: (1) the average of the flows of the maximum-flow quarter and the higher of the two adjacent quarters; and (2) the average of the flows during the minimum-flow quarter and the quarter that preceded the minimum-flow quarter. The 1966 credit crunch period was not a recession. Prefix D- indicates direct holdings. Mnemonics for holders are described in the text. Data sources: Board of Governors of the Federal Reserve System, Federal Reserve Bank of St. Louis FRED database, and www.freelunch.com.

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Table 5. Contributions to Changes in Mortgage Flows Near Recessions: Direct-plus-Indirect Holdings, by Holder. RECESSION PERIODS COMPARISON PERIODS

-403 -6 -9 -3 0 324 39

1957:3– 1958:2 1955:1– 1958:1

1960:2– 1961:1 1959:2– 1961:1

15 6 23 -3 6 27 5

82 7 -10 2 34 89 0

-7

23

Credit Crunch 1965:3– 1967:2 62 0 8 5 10 3 -6 1 5 -2

1969:4– 1970:4 1968:4– 1970:2 88 -9 -4 5 13 -53 59 0 -38 -5

1973:4– 1975:1 1972:4– 1974:4 140 19 -7 -1 1 -79 8 7 -21 -1

1980:1– 1980:3 1978:3– 1980:2 88 0 4 -9 -10 12 20 2 6 3

1981:3– 1982:4 1980:3– 1982:3 102 -14 -1 -5 14 3 -2 3 -7 -25

1990:3– 1991:1 1989:3– 1991:1 19 5 -2 4 13 61 9 10 6 14 -14

2001:1– 2001:4 2000:2– 2000:4

Average over five most recent recessions

175 -121 1 -17 26 180 6 -48 -138 -147 -14

105 -22 -1 -6 9 35 8 -5 -31 -31 -14

Note: First differences of seasonally adjusted net flows calculated as the sum of (1) flows of direct holdings of home mortgages and (2) holdings of home mortgage-backed securities, by holder, all expressed as a percentage of the first difference of total flows of home mortgages. Recession periods are the same as in Fig. 1. Comparison periods span the first quarter of the two adjacent quarters that contain the (local) maximum flows of total home mortgages outstanding to the quarter with the (local) minimum flow of home mortgages outstanding. The amounts in the table are the differences between: (1) the average of the flows of the maximum-flow quarter and the higher of the two adjacent quarters; and (2) the average of the flows during the minimum-flow quarter and the quarter that preceded the minimum-flow quarter. The 1966 credit crunch period was not a recession. Mnemonics for holders are described in the text. Data sources: Board of Governors of the Federal Reserve System, Federal Reserve Bank of St. Louis FRED database, and www.freelunch.com.

JOE PEEK AND JAMES A. WILCOX

DEP NDEPFIN INS PENS NFCORP HH GOVT FOREIGN GSE POOL ABS

1953:2– 1954:2 1953:1– 1954:1

The Changing Cyclicality of Mortgage Flows

75

of total home mortgages that occurred just prior to the national economic peak quarter to the calendar quarter with the ensuing (local) minimum flow of total home mortgages. Measured this way, the comparison period spans the period of peak to trough in the flow of total home mortgages. Table 1 shows that the trough in mortgage flows occurred in either the quarter of the trough in the national economy or the quarter immediately prior for each of the five recessions, except for the 2001 recession. We expected most financial and economic stocks and flows to decline (relative to potential, rather than actual, GDP) during recession or comparison periods. We also expected that the longer or more severe the recession, the larger the decline during that recession or its comparison period. Those patterns show up in Table 1. Table 1 shows that total residential mortgage balances fell during the longer and more severe recessions of 1973–1975 and 1981–1982. During the 1990–1991 recession, which was less severe, total balances declined by a smaller amount. During the 1980 recession, which was very brief and anomalous for having been much influenced by government-induced credit controls, total mortgage balances actually rose by a small amount. By contrast, during the most recent recession, which began in 2001, total residential mortgage balances actually rose considerably, increasing by over one full percentage point of potential GDP during the middle of 2000. Here we use the standard that cyclicality is measured by changes in financial quantities relative to potential rather than to actual GDP. On average over these five recessions, total residential mortgage balances fell by 0.69% of potential GDP. By that measure, total balances were procyclical. The procyclicality of total balances has waned, however, through time. During the 1990–1991 recession, total balances fell by only 0.16%. And, during the most recent recession, total balances actually rose by 1.11%, which is about as countercyclical as the average decline for the first four recessions in Table 1 of 1.14% was procyclical. Thus, total balances, and thus presumably mortgages and real activity in housing markets, have become much less procyclical over the postwar period. Table 1 next shows that total intermediation by Fannie Mae and Freddie Mac during recessions has typically been countercyclical. It also shows that GSE intermediation has been increasingly countercyclical. The two rows under the row labeled TOTAL show the changes in the components of TOTAL. The row labeled GSE contains data for the changes in total intermediation by Fannie Mae and Freddie Mac. These data are based on the data used for FANFRED in Fig. 4. Having increased during (the comparison period associated with) each recession, intermediation by Fannie Mae and Freddie Mac combined was countercyclical. On average, the combined total intermediation rose by 0.71% of potential GDP. During the two most recent recessions, it rose by an average of 1.1 percentage points, which is more than twice as much as it rose on average (0.44 percentage

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points) during the three prior recessions. By contrast, the non-GSE portion of mortgage intermediation, calculated as TOTAL-GSE, fell in each but the most recent recession. These declines mean that, taken together, the behavior of the other participants in the mortgage market was procyclical. Nonetheless, non-GSE intermediation has also become notably less procyclical recently. Whether that decline in procyclicality is connected to increasingly countercyclical total intermediation by GSEs is a question worthy of further investigation. The bottom panel in Table 1 shows the changes in the components of total balances relative to changes in total balances. Thus, the sums of the data in the first two rows of the bottom panel equal 100%. The data in the rightmost column in both the top and bottom panels show that, on average over these five recessions, total intermediation by Fannie Mae and Freddie Mac rose by half as much as non-GSE holdings declined. In that sense, Table 1 indicates that the countercyclicality of Fannie Mae and Freddie Mac offsets half of the procyclicality of others. To further investigate the cyclicality of GSEs and others, we used the Federal Reserve’s Flow of Funds accounts (FOF) to obtain data for the flows of home mortgages that are disaggregated by sector of holder. The FOF data show the major holders of home mortgages by sector, but do not similarly show holdings of MBS by sector. To approximate holdings of MBS by sector, we used FOF data for holdings of agency securities. These data overstate holdings of MBS by sector and overstate the direct obligations of Fannie Mae and Freddie Mac. The sum of MBS issued by agencies plus the bonds, notes, and short-term debt issued by Fannie Mae and Freddie Mac accounts for nearly all of the total stock of agency securities. On the other hand, the data for agency securities exclude the large and growing stock of MBS that has been issued by the private sector. We used data for direct holdings (of whole mortgages) and direct-plus-indirect holdings (i.e. holdings of whole mortgages plus MBS) in Tables 2 and 3. In addition to the recessions analyzed in Table 1, Table 2 includes data for the other postwar recessions and data for the 1966 credit crunch, which is the only non-recession period when the flow of total home mortgages (relative to potential GDP) declined for at least four consecutive quarters. (Hereafter, we include the 1966 credit crunch in the set of postwar recessions). Because quarterly flows of mortgages are so volatile, for Tables 2–5 we calculated changes in the two-quarter averages of flows by first-differencing the seasonally adjusted, net flows (relative to potential GDP) of direct holdings of home mortgages by each holder. The comparison periods span the quarters with the peak and trough flows for total home mortgages (relative to potential GDP). We calculated the first-differences reported in Table 2 by subtracting the average value for the minimum flow quarter and the quarter preceding the minimum flow quarter from the average value for the maximum flow quarter and the higher of the two adjacent quarters. The two

The Changing Cyclicality of Mortgage Flows

77

exceptions are that a single quarter is used for the minimum flow quarter for both the 1980 recession, because it was immediately followed by the next recession comparison period, and the 2001 recession, because the total home loans series rose strongly after 2000Q4. Table 2 shows changes in the flows of holdings of whole home mortgages for each recession, for the 1966 credit crunch, and on average over the most recent five recessions. Table 2 shows changes in total flows (ALL HOLDERS) and changes in the flows for each of ten sectors. The sectors are depository institutions (D-DEP), which includes the commercial banking sector, savings and loans, and credit unions; non-deposit financial institutions (D-NDEPFIN), which includes finance companies, mortgage companies, REITs, money market mutual funds, mutual funds, and brokers and dealers; insurance companies (D-INS), which includes life insurance companies and other insurance companies; pensions (D-PENS), which includes private pension funds and state and local government retirement funds; non-financial corporate business (D-NFCORP); households (D-HH); government (D-GOVT), which includes the federal, state, and local governments; government-sponsored enterprises (D-GSE); federally related mortgage pools (D-POOL); and private issuers of asset-backed securities (D-ABS). Table 2 shows that the flow of home mortgages to all holders declined during each recession. Over the most recent five recessions, the decline averaged 2% of potential GDP. Depository institutions reduced the rate at which they acquired whole mortgages in each episode. In fact, over the most recent five recessions, the average decline for depository institutions was larger than that for all holders. In contrast, on average over the five most recent recessions, countercyclicality was most prominent among issuers of MBS: federally related mortgage pools and private sector issuers of MBS. Although the other Federal Reserve data used for Figs 1–4 and for Table 1 allowed it, FOF accounts data did not allow us to separate data for Fannie Mae and Freddie Mac from the reported aggregate data for all GSEs. Table 3 shows data for changes in flows of direct-plus-indirect holdings of home mortgages. Indirect holdings consisted of MBS. This table, as well as Table 5 below, includes the foreign sector (FOREIGN), which had no whole mortgages reported in the FOF accounts and thus was omitted from Table 2. The data for the ALL HOLDERS row is from Table 2. As with direct holdings, direct-plus-indirect holdings by depository institutions accounted for most of the declines. Thus, in Table 2 and Table 3, depository institutions were generally the most procyclical holders of mortgages. Households were typically procyclical, too, as were the government and non-financial corporate sectors. The most countercyclical sectors were the federally related mortgage pools, GSEs, and private issuers of MBS. In Table 3, GSEs contributed more to countercyclicality than in Table 2 because of the rapid growth of their holdings of MBS.

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Table 4 re-expresses the changes in flows in Table 2 relative, not to potential GDP, but rather to the changes in flows of total home mortgages. That is, for Table 4, the numerators in Table 2 were divided by the changes in flows to all holders. Since this denominator was negative for each recession, positive entries in Table 4 show the shares of the declines in the total flows by sector. A negative entry indicates the percentage of the change in the total flows that was offset by a sector. In five of the ten recessions, depository institutions accounted for more than 100% of the decline in the flow of total home mortgages. In the most recent recession, they accounted for more than twice the actual decline in the flow of total home mortgages. The contrast with the actions of federally related mortgage pools is particularly striking. During the most recent recession, the increase in the flow of home mortgages to federally related mortgage pools rose significantly. In fact, the increase in the pools’ rate of acquisition of home mortgages was far greater than the net decline in the flow of total home mortgages. Table 5 re-expresses the flows of the sum of direct-plus-indirect holdings of home mortgages relative, not to potential GDP, but rather to the changes in flows of total home mortgages. Even with this broader measure, depository institutions remain very procyclical, on average accounting for 105% of the declines in total mortgage flows over the five most recent recessions. By this broader measure, households are significantly procyclical, on average accounting for about one-third of the declines over the five most recent recessions. Although they had no consistent pattern before that, the large negative entry for non-depository financial institutions for the most recent recession shows that they partially offset the procyclicality of depositories. By the broader measure of mortgage flows in Table 5 that included their holdings of MBS, GSEs were more countercyclical than suggested by Table 4.

4. SUMMARY, IMPLICATIONS, AND FUTURE DIRECTIONS The housing-related GSEs have contributed to the growth and maturation of secondary mortgage markets. In doing so, they have contributed to higher, long-term homeownership rates by lowering mortgage interest rates. Here, we have focused on the cyclical, rather than the longer-term, effects of secondary mortgage markets and GSEs. Not surprisingly, total residential mortgage flows declined relative to potential GDP during post-WW II recessions. Declines of direct flows into depository institutions typically accounted for most of the declines of total flows. Especially during more recent recessions, depository institutions tended to partially offset their withdrawals from primary mortgage markets by relatively increasing their accumulations of MBS. At the same time,

The Changing Cyclicality of Mortgage Flows

79

increases in direct flows of mortgages into federally related and private sector pools also countered the declining flows of mortgages into depository institutions. GSEs also speed up their accumulations of MBS for their own portfolios during the 2001 recession. As less-procyclical secondary mortgage markets grew and matured, aggregate primary mortgage flows became less procyclical. In that sense, secondary mortgage markets stabilized mortgage flows. The values that world capital markets place on the association of GSEs with the U.S. government seem to fluctuate with conditions here and abroad. During periods of international financial crises or of domestic economic stress, those values seem to rise appreciably. Thus, in such periods, GSEs may be particularly well suited to facilitating mortgage flows. So long as there are such crises and stresses, GSEs may be particularly effective in stabilizing mortgage markets and moderating business cycles. Further analysis of the declining countercyclicality of mortgage markets awaits. Two issues present themselves immediately. One is how much secondary mortgage markets have altered the responses of real activity in the housing sector and in the macroeconomy to various shocks. A second is the extent to which the apparently declining procyclicality of non-GSE intermediation is connected to the increasingly countercyclical total intermediation by GSEs. In contrast to our analysis here, those analyses may benefit from more statistical and econometric approaches.

NOTES 1. Some studies have noted the roles that Fannie Mae and Freddie Mac played during recent financial disruptions, such as the Russian bond market and Long Term Capital Management crises of the late 1990s. 2. Studies based on data for the 1970s found some evidence that GSEs stabilized mortgage flows (Jaffee & Rosen, 1978, 1979). 3. By “stabilize,” we mean “reduce recession-related fluctuations of.” 4. Equivalently, they can issue and exchange MBS for whole mortgages with the mortgage originator. 5. Unless otherwise noted, all data in the figures and tables are quarterly. The data for residential mortgage debt outstanding are associated with Table 1.54 in the Federal Reserve Bulletin and were provided by the Board of Governors of the Federal Reserve System.

REFERENCES Congressional Budget Office (2001). Federal subsidies and the housing GSEs. Devaney, M., & Pickerill, K. (1990). The integration of mortgage and capital markets. Appraisal Journal, 58, 109–113.

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Federal Home Loan Mortgage Corporation (2000). Again and again Freddie Mac delivers. Annual Report. Federal Reserve Bank of Minneapolis (2001). Mortgage rates, homeownership rates, and governmentsponsored enterprises. Annual Report. Goebel, P. R., & Ma, C. K. (1993). The integration of mortgage markets and capital markets. Journal of the American Real Estate and Urban Economics Association, 21, 511–538. Hendershott, P. H., & Shilling, J. D. (1989). The impact of the agencies on conventional fixed-rate mortgage yields. Journal of Real Estate Finance and Economics, 2, 101–115. Jaffee, D. J., & Rosen, K. T. (1978). Estimates of the effectiveness of stabilization policies for the mortgage and housing markets. Journal of Finance, 33, 933–946. Jaffee, D. J., & Rosen, K. T. (1979). Mortgage credit availability and residential construction activity. Brookings Papers on Economic Activity, 333–386. McCarthy, J., & Peach, R. W. (2002). Monetary policy transmission to residential investment. Economic Policy Review, 139–161. Rudolph, P. M., & Griffith, J. (1997). Integration of the mortgage market into the national capital markets: 1963–1993. Journal of Housing Economics, 6, 164–183.

INCREASING MARKET DISCIPLINE ON BANKS: SUBORDINATED DEBT AND BANK LOAN SALES Andrew H. Chen, Kenneth J. Robinson and Thomas F. Siems ABSTRACT While subordinated debt can be used to increase market discipline on banks by playing a corporate governance role in the presence of a federal safety net that encourages risk taking, it also has implications for banks’ loan sales. Using two measures of banks’ loan sales activity, we ﬁnd greater proportions of subordinated debt increase the likelihood that banks engage in loan sales activity, and are associated with greater proportions of loan sales. Our results have implications about banks’ lending efﬁciency as well as their transparency and disclosure policies that could play a role in the transmission mechanism of monetary policy.

1. INTRODUCTION As the banking system becomes larger and more complex, regulatory oversight can provide only a partial substitute for the corporate governance services provided by shareholders and creditors. As a result, an increasing number of both academic and regulatory economists have advocated the use of subordinated debt as a way

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to increase market discipline on banks. The Federal Reserve recently completed a study on the feasibility of using subordinated debt as an instrument to augment market discipline (Federal Reserve System, 1999). And the Gramm-Leach-Bliley Act of 1999 mandates that the top 100 banks have at least one issue of subordinated debt outstanding.1 While subordinated debt can play a role in corporate governance by offsetting some of the moral hazard incentives present with the existence of a federal safety net, such debt also has important implications for banks’ loan sales. Using a dynamic inventory control model, Chen and Mazumdar (1999) show that banks that issue more subordinated debt will engage in greater loan sales. This result, which flows from a liquidity-based rationale for banks’ loan sales, follows from the proposition that banks with more subordinated debt will suffer greater underinvestment losses as defined in Myers (1977), and is consistent with James’ (1988) collateralization hypothesis. Greenbaum and Thakor (1987) argue that the existence of a federal safety net has a dampening influence on loan sales. This result follows from the incentives for banks to prefer the deposit funding mode over securitization due to the subsidies from the safety net. To the extent that subordinated debt increases market discipline and reduces regulatory subsidies, greater subordinated debt issues should be associated with greater loan sales. An alternative view regarding the relationship between loan sales and subordinated debt can be found in Pennacchi (1988) and Pavel and Phillis (1987). These authors develop a regulatory tax argument in which greater regulatory oversight imposes implicit taxes on banks that increase their cost of capital. Banks have an incentive to avoid such taxes through loan sales. If subordinated debt increases market discipline and this serves to reduce the regulatory costs banks face, then we would expect a negative relationship between subordinated debt and loan sales. Off-balance sheet activities have grown in importance for banks (Berger & Udell, 1993; Boyd & Gertler, 1994). One of the more prominent of these activities is loan sales. For example, banks’ sales of mortgage loans stood at roughly $10 billion in 1990, and by 2000 sales of these loans reached almost $60 billion. Haubrich and Thompson (1996) also report strong growth in sales of what are mostly assumed to be business loans between 1984 and 1990. Because of a well-developed market for bank loans, banks no longer exclusively use their deposits to fund their lending activity. Instead, banks can engage in both loan sales and purchases, plus other nontraditional activities, to manage their liquidity. There are a number of both direct and indirect ways that banks can engage in loans sales, including securitization (both with and without recourse), loan syndications, and loan participations. Loan sales also offer banks the opportunity to decompose the traditional lending process into more elemental

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activities such as originating, servicing, funding and guaranteeing (Greenbaum & Thakor, 1987). Corresponding to the growth in the loan sales market, a number of researchers have investigated the motives for banks to engage in loan sales. Our focus in this paper is on the models developed by Chen and Mazumdar (1999), Greenbaum and Thakor (1987), Pavel and Phillis (1987) and Pennacchi (1988). If banks with greater proportions of subordinated debt in their portfolios have greater underinvestment losses and reduced regulatory subsidies, then the higher a bank’s subordinated debt to asset ratio the greater should be its loan sales. On the other hand, if regulatory taxes are decreased by issuing subordinated debt, then banks with higher proportions of subordinated debt should record lower proportions of loan sales. After accounting for some other factors that might also influence loan sales activity at banks, we investigate the role of subordinated debt. We estimate two sets of regressions that coincide with two series available on bank loan sales. While these two series differ in some important ways, they offer a test of the robustness of our results. From 1983 through 1993, banks reported sales of what were mostly business loans. Beginning in 1989, banks began to report the volume of mortgage loans sold. Using annual data for both series, we first estimate probit models of the likelihood that banks will engage in loan sales. Then, using the available data on loan sales volume, we supplement this information with Tobit regressions of the determinants of the amount of loan sales in banks’ portfolios.2 We estimate our models over different time periods and bank asset sizes. Our results point to the importance of underinvestment losses and regulatory subsidies in banks’ C&I loan sales activity. We find evidence that subordinated debt increases the likelihood of banks engaging in C&I loan sales. In our Tobit results, the importance of subordinated debt in explaining the volume of C&I loan sales by banks is evidenced by the finding that greater proportions of subordinated debt are associated with greater proportions of loan sales. Our results using sales of mortgage loans indicate mostly statistically insignificant relationships between subordinated debt and loan sales. This could reflect that sales of mortgage loans are more affected by institutional arrangements in the mortgage market, including the existence of Government Sponsored Enterprises, than by liquidity or regulatorybased factors. However, when we restrict our estimation period to one of rapid growth in mortgage sales, we find support for the importance of underinvestment losses and regulatory subsidies. We also find support for some other hypotheses regarding banks’ motivations to engage in loan sales that have been identified in the literature. Our results suggest that banks’ efforts to manage their liquidity through loan sales, spurred in part by subordinated debt, could have important implications

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for monetary policy. Higher portfolio proportions of subordinated debt lead to increases in liquidity-management efforts by banks. Such efforts give rise to greater lending efficiency. Moreover, greater amounts of subordinated debt create incentives for improved transparency and disclosure by banks. Given recent findings on the importance of a credit channel for monetary policy, a more efficient and transparent banking system could play a role in the transmission mechanism of monetary policy. We proceed as follows. Section 2 offers a review of the literature on bank loan sales. In Section 3, we describe the data we use and present the empirical models employed in the estimations. Section 4 presents our empirical results, which are followed by some conclusions and policy implications in Section 5.

2. RELATED LITERATURE 2.1. Overview A number of both theoretical and empirical explanations have been offered to account for loan sales (and purchases) by banks. Berger and Udell (1993) provide a comprehensive overview of theories of asset securitizations, several of which are related to loan sales. Gorton and Haubrich (1990) offer some background on the loan sales market in particular. Regulation plays a role in several of these explanations. Benveniste and Berger (1987) argue that a flat-rate deposit insurance system prompts banks to increase the insurance subsidy by increasing leverage through loan sales. Pennacchi (1988) and Pavel and Phillis (1987) consider a regulatory tax hypothesis in which reserve requirements and capital requirements increase banks’ cost of capital. Banks have an incentive to avoid such regulatory taxes through loan sales. Greenbaum and Thakor (1987) show that with asymmetric information about borrowers’ payoff distributions, banks have an incentive to sell off their best quality loans. In the presence of regulatory subsidies flowing from deposit insurance and other features of the federal safety net, however, banks will increase their reliance on deposits for funding. A corollary of their result is that reductions in the federal safety net subsidy may spur greater loan sales by banks. Gorton and Pennacchi (1995) develop a model of loan sales that assumes banks provide unique (and unobservable) credit services. If a loan is not fully (implicitly) guaranteed by the bank, then it will not undertake the full amount of evaluation and monitoring. Because the buying bank recognizes this moral hazard problem, it pays less for such loans.

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Pennacchi (1988), Carlstrom and Samolyk (1995), and Demsetz (1994, 1999) consider the comparative advantage hypothesis in which those banks that engage in loan sales have a comparative advantage in originating loans, but a disadvantage in funding loans. This advantage could reflect such factors as an information advantage about profitable lending opportunities in a particular locale. Pavel and Phillis (1987), Berger and Udell (1993), and Demsetz (1994, 1999) find support for this hypothesis. Pavel and Phillis (1987) and Demsetz (1999) also find support for the diversification hypothesis, which argues that banks that lack the ability to diversify internally use loan sales (and purchases) to enhance portfolio diversification. Mester (1992) hypothesizes that economies of scale and scope may lead banks to engage in loan sales. These scale and scope economies would be expected to grow and develop over time as bank managerial expertise improves. As a result, bank loan sales should also grow over time. James (1988) argues that loan sales are similar to collateralized debt. As such, loan sales (and standby letters of credit) can help banks avoid the underinvestment problem that arises when a firm issues risky debt. Myers (1977) shows that firms with risky debt outstanding will pass up valuable investment opportunities that could make positive net contributions to the market value of the firm. Because these positive net present value projects would effectively transfer wealth from shareholders to debtholders, they are not undertaken. According to James, loans sales, like collateralized debt, can reduce the underinvestment problem by permitting banks to sell claims to a portion of the payoffs of new loans that would otherwise accrue to existing depositors. Chen and Mazumdar (1999) develop an inventory-control model that highlights the dynamic nature of financial intermediation and the joint roles of loan originations, sales and purchases in overall bank liquidity management. Their model provides a consistent explanation for the empirical findings of Haubrich and Thompson (1996) regarding bank loan sales and purchases. Moreover, in Chen and Mazumdar’s dynamic liquidity model, underinvestment losses will increase the tendency of banks to sell loans, similar to James’ (1988) argument. Banks with greater proportions of subordinated debt have greater underinvestment losses since they would be more inclined to reject profitable investment projects. A testable hypothesis from Chen and Mazumdar (1999) and Greenbaum and Thakor (1987) is that the higher a bank’s uninsured subordinate debt to total asset ratio, the greater should be its loan sales (and the lower its loan purchases). However, because greater regulatory taxes motivate banks to sell more loans, more subordinated debt may, by reducing these taxes, decrease loan sales, as discussed in Pavel and Phillis (1987) and Pennacchi (1988).

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2.2. Recapitulation of Empirical Hypotheses From previous research in the motivations behind bank loan sales, we identify several empirical hypotheses. First, and foremost in our approach are the underinvestment hypothesis and the regulatory subsidy hypothesis, which conclude that banks with greater portfolio proportions of subordinated debt will engage in greater loan sales activities. We also focus on the regulatory tax hypothesis that suggests a negative relationship between subordinated debt and loan sales.3 Greenbaum and Thakor (1987) also show that under the regulatory subsidy hypothesis, banks with lower capital ratios or with greater losses on loans would likely face stricter regulatory supervision in order to offset any regulatory subsidies. As such, those banks with weaker capital ratios or greater loan losses would face greater incentives to sell off loans. These variables could also reflect aspects of the comparative advantage hypothesis where loan sales might reflect a funding disadvantage. The scale hypothesis of Mester (1992) suggests an important role for increases in bank size in expanding loan sales. The diversiﬁcation hypothesis in Demsetz (1994, 1999) and Pavel and Phillis (1987) suggests that a greater portfolio concentration of loans might motivate greater loan sales. A higher proportion of fee income might motivate fewer loan sales, also reflecting the diversiﬁcation hypothesis. Our focus in this paper is on the relationship between banks’ subordinated debt and their loan sales. Including other control variables in our empirical model consistent with these other hypotheses, though, also allows us to isolate the influence of subordinated debt, and at the same time offers some evidence on the importance of these other hypotheses in influencing loan sales. It should also be pointed out that despite Congressional and regulatory focus on the feasibility of mandatory subordinated debt issuance, the amount of subordinated debt in banks’ portfolios is strictly a choice variable over the time period of our investigation. A number of factors can influence a bank’s decision to issue subordinated debt. Banks could be voluntarily altering their capital structure to minimize their cost of capital and to maximize any regulatory subsidies flowing from the safety net. For some banks (and bank holding companies), exposure to institutional investors, and to financial markets in general, can create a favorable impression of the issuer by signaling self-induced market discipline in an attempt to lower regulatory costs. A recent study found that the issuance costs of subordinated debt are quite low compared to equity issuance, at least for large banking organizations (Board of Governors of the Federal Reserve System and United States Department of the Treasury, 2000, p. 18). However, greater amounts of subordinated debt increase banks’ financial risks. As a result, despite the voluntary nature of subordinated

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debt issues, banks with more subordinated debt in their portfolios are more likely to engage in loan sales in an attempt to manage their financial and liquidity risks.

3. DATA AND EMPIRICAL MODEL We test the relationship between subordinated debt and loan sales using data from banks’ Report of Condition, or call reports. Our data are collected at the organization level to take account of any intracompany transactions. Two series on banks’ loan sales are available. From 1983 through 1993, bank call reports contain data on all loans originated by the reporting bank that it has sold or transferred to others during the calendar quarter, regardless of when the loan was originated. This series excludes one-to-four family residential real estate loans and loans to individuals for household, family, and other personal expenditures. As such, Demsetz (1999) points out that these loans are primarily business or C&I loans. This series has been used by several researchers, including Demsetz (1994, 1999) and Haubrich and Thompson (1996). We call this particular series C&ISALES, and it is expressed as a percent of average assets.4 Bank call reports also contain a series on loan sales beginning in 1989. This series includes the principal balance outstanding for first lien one-to-four family residential loans that have been transferred with recourse. These include residential mortgage loans transferred to both Fannie Mae and Freddie Mac, and to private mortgage pools. We refer to this series as MORTSALES and it is expressed as a percent of assets. However, there are some important qualitative differences between C&ISALES and MORTSALES, especially with regard to risk, information asymmetry, and maturity. Moreover, the existence of Fannie Mae and Freddie Mac and their willingness to purchase conforming loans could have a significant impact on the motives behind sales of mortgage loans vs. C&I loans. Sales of mortgages are almost always undertaken for securitization purposes, while few C&I loans are securitized. Therefore, while we offer results for both C&ISALES and MORTSALES, these two series that are available are not considered close substitutes, but each may offer some insights into the motivations behind banks’ loan sales activities. Data are also available from the call reports on the amount of banks’ subordinated notes and debentures outstanding, which we refer to as SUBDEBT, and express as a percent of assets. While the potential exists for subordinated debt to effect loan sales, it is possible that subordinated debt’s role in enhancing market discipline can be muted. There are some data from supervisory reports that bank-issued subordinated debt is often held by the parent holding company and is

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not publicly traded. However, there is no public data source available that identifies who owns bank-issued subordinated debt (Federal Reserve System, 1999, p. 30). For analyzing C&ISALES we construct a panel of organizations using annual data from 1983 through 1993 consisting of 4,667 banking organizations. For MORTSALES, we construct a panel of 4,278 banking organizations over the period from 1989 through 2000. All of our data are structure adjusted to account for mergers and acquisitions. Mergers and acquisitions were identified and pro-forma banking organizations were created. We provide two empirical specifications for each of our loan series. The first is a probit model that estimates the likelihood of a bank engaging in loan sales. Then, we estimate a Tobit regression to exploit the available data on the actual volume of loan sales activities from the call reports. A Tobit regression is necessary because a large number of banks do not report any loan sales activity. We expect a positive sign on SUBDEBT in both models if the underinvestment and regulatory subsidy hypotheses hold, and a negative sign on SUBDEBT under the regulatory tax hypothesis. We also include a number of other variables in our models to account for previous researchers’ hypotheses into the motivations behind loan sales by banks. We include EQUITY, defined as equity capital as a percent of assets, and CHARGE, defined at net chargeoffs, expressed as a percent of average assets, to account for Greenbaum and Thakor’s (1987) regulatory subsidy argument and the comparative advantage hypothesis described in Demsetz (1999) and others. A negative sign on EQUITY and a positive sign on CHARGE would be consistent with greater regulatory scrutiny of banks’ loan portfolios, and the funding constraints faced by banks under the comparative advantage hypothesis. SIZE, defined as the log of total assets, is hypothesized to possess a positive sign to account for Mester’s (1992) scale hypothesis that economies of scale may lead to increased loan sales. Also, Pennacchi (1988) argues that larger banks may have stronger lending opportunities and potentially higher funding costs, inducing them to engage in more loan sales.5 NONINT, or non-interest income expressed as a percent of average assets, is intended to account for the current proportion of fee income in banks’ portfolios. The higher this proportion, the lower might be a banks’ propensity to engage in loan sales from the diversiﬁcation hypothesis. LOANASS, the loan to asset ratio, is included to reflect overall origination activity. A positive sign on this variable would be consistent with the diversiﬁcation hypothesis. HC and MBHC, dummy variables that equal one if a banking organization is part of a holding company, or multibank holding company, respectively, and zero otherwise, are included to account for the possibility that holding company affiliation might affect both the probability of engaging in loan sales and the amount of such activity.

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Table 1. Summary Measures for Banking Organizations, 2000 (% of Assets Except Where Noted). Variable

All Observations Mean

MORTSALES C&ISALES (1993) EQUITY CHARGE SIZE ($ billion) NONINT LOANASS SUBDEBT

0.129 2.243*** 10.590*** 0.077*** 1.3*** 0.252*** 59.880*** 0.033***

Standard Deviation 4.523 9.308 4.143 0.230 17.4 1.236 13.933 0.257

Assets ≥$500 Million Mean 0.936 3.838*** 8.840*** 0.093*** 11.0*** 0.363*** 64.480*** 0.226***

Standard Deviation 13.612 11.042 2.281 0.250 51.8 0.483 12.560 0.634

Note: MORTSALES is the principal outstanding balance as of the report date for residential mortgage loans that have been pooled and transferred with recourse to FNMA and FHLMC and to private mortgage pools, expressed as a percent of assets; C&ISALES are the total amount of all loans originated by the reporting bank that the bank has sold or transferred to others during the calendar year ending with the report date, regardless of when the loan was originated; excludes 1 to 4 family residential real estate loans and loans to individuals for household, family, and other personal expenditures, and expressed as a percent of average assets; EQUITY is equity capital, expressed as a percent of assets; CHARGE is net chargeoffs, expressed as a percent of average assets; SIZE is the log of total assets; HC is a dummy variable that equals 1 if a banking organization is part of a holding company, zero otherwise; MBHC is a dummy variable that equals 1 if a banking organization is part of a multibank holding company, zero otherwise; NONINT is non-interest income, expressed as a percent of average assets; LOANASS is total loans expressed as a percent of assets; SUBDEBT is the amount outstanding of subordinated notes and debentures, expressed as a percent of assets. All data are from the Report of Condition. Data are collected at the organization level and are structured adjusted for mergers and acquisitions. All data are from year-end 2000, except for C&ISALES, which are for year-end 1993 (the last available). For purposes of size classification, ASSETS are expressed in 1993 dollars when considering CI&SALES, and in 2000 dollars for all other variables. ∗∗∗ Significance at the one-percent level; significance levels are for t-tests of the hypothesis that mean values are greater than zero.

Demsetz (1999) finds that banks that are part of multibank holding companies are more likely to engage in both loan sales and loan purchases. Table 1 provides some summary statistics for the organizations in our sample. We provide mean values along with standard deviations for our variables based on year-end 2000 data, with the exception of C&ISALES, whose values are for year-end 1993, the latest data available. Statistics are provided for both all of the organizations in our sample and for those with assets greater than $500 million, since we also estimate our empirical models using this group of larger-sized banks to judge the robustness of our results.

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4. RESULTS 4.1. Entire Sample We first estimate both the probit and Tobit regressions with C&ISALES and MORTSALES as dependent variables using all the banks in our sample. These results are found in Table 2. From the probit models, organizations with lower capital ratios are more likely to engage in both C&ISALES and MORTSALES as hypothesized under the regulatory subsidy hypothesis. The sign on CHARGE is positive and significant for C&ISALES which supports the regulatory subsidy hypothesis but is negative and significant for MORTSALES, which is inconsistent with the regulatory subsidy arguments for engaging in loan sales. SIZE is positive for both measures of loan sales, but is significant only for MORTSALES as expected under the scale hypothesis. Organizations that are part of holding company structures are more likely to engage in C&ISALES, but those that are part of a multibank holding company face a reduced likelihood of engaging in MORTSALES. NONINT is positive and significant in both probit models, which is inconsistent with the diversiﬁcation hypothesis. However, LOANASS is positive and significant for both measures of sales, as anticipated under the diversiﬁcation hypothesis. Turning to our variable of interest, SUBDEBT is positive and significant when using C&ISALES as the dependent variable in the probit models, and is positive but insignificant when using MORTSALES. Those organizations with higher ratios of subordinated debt to assets are more likely to engage in C&I loan sales, consistent with the underinvestment hypothesis and the regulatory subsidy hypothesis. The Tobit results in Table 2 are mostly consistent with the estimates obtained from the probit models of our two measures of loan sales activity. The exceptions are SIZE, which is now negative and significant in the Tobit model using C&ILOANS, and MBHC which is now insignificant. When considering MORTSALES, HC and LOANASS possess different signs in the Tobit model, and NONINT is not significant in the Tobit model. SUBDEBT contains a positive and significant sign in the Tobit model using C&ILOANS, again consistent with the underinvestment/regulatory subsidy hypotheses. However, SUBDEBT is not significant in the Tobit model when MORTSALES is the dependent variable. Our two loan sales measures are the only series available. Their report dates differ and, as we pointed out above, these two sales variables have some important qualitative differences between them. These factors could lie behind the different signs in the regressions for some of our explanatory variables.

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Table 2. Regression Results for Models of Bank Loan Sales. Variables

C&ISALES: 1983–1993 All Banks

Constant EQUITY CHARGE SIZE HC MBHC NONINT LOANASS SUBDEBT Log likelihood Obs. with dep. = 1 Obs. with dep. = 0 Left censored obs. Uncensored obs.

MORTSALES: 1989–2000

Banks ≥$500 million

All Banks

Banks ≥$500 million

Probit

Tobit

Probit

Tobit

Probit

Tobit

Probit

−0.8971*** (0.0681) −0.0351*** (0.0019) 0.0511*** (0.0143) 0.0085 (0.0056) 0.5532*** (0.0126) 1.0495*** (0.0296) 0.1475*** (0.0221) 0.0179*** (0.0004) 0.0818*** (0.0264)

0.1195*** (0.0377) −0.1007*** (0.0015) 0.2647*** (0.0066) −0.0780*** (0.0030) 0.9142*** (0.0039) 0.0249 (0.0603) 0.7617*** (0.0199) 0.0622*** (0.0004) 3.7175*** (0.0199)

−2.6748*** (0.4219) −0.0496*** (0.0124) 0.0620 (0.1121) 0.1572*** (0.0278) 0.6213*** (0.1025) 1.0756*** (0.0797) 0.0743 (0.1131) 0.0188*** (0.0023) −0.0997 (0.0554)

29.2253*** (8.6340) 0.2522 (0.2182) 0.8179 (2.2443) 1.3929** (0.5486) 1.5699 (3.3486) 2.0300 (2.1686) 3.9730** (1.8073) 0.0921** (0.0408) 8.1487*** (0.6718)

−8.5257*** (0.1942) −0.0225*** (0.0074) −0.2762*** (0.0989) 0.4733*** (0.0115) 0.1907*** (0.0586) −0.1462*** (0.0429) 0.0353** (0.0160) 0.0133*** (0.0013) 0.0612 (0.0442)

−0.7555*** (0.0109) 0.0064*** (0.0003) −0.0120*** (0.0034) 0.0722*** (0.0011) −0.0368*** (0.0017) −0.1779*** (0.0181) 0.0005 (0.0073) −0.0005*** (0.0001) −0.0130 (0.0285)

−10.1772*** (0.4489) −0.0189 (0.0152) −0.5100*** (0.1856) 0.5622*** (0.0238) 0.4161** (0.1757) −0.1521** (0.0601) −0.0201 (0.0780) 0.0142*** (0.0023) 0.0525 (0.0529)

−30122.26

−148420.8

−917.53

−12858.36

−3304.02

−39610.08

−1304.45

29088

418

1140

732

22249

2879

50172

3290

Tobit 13.0558*** (0.8303) 0.0636*** (0.0105) −0.6852*** (0.1069) −0.8060*** (0.0629) −0.4610** (0.2193) 0.3664** (0.1583) 0.1650 (0.0970) −0.0293*** (0.0017) −1.3216*** (0.1097) −5393.52

22249

2879

50172

3290

29088

418

1140

732

Note: MORTSALES is the principal outstanding balance as of the report date for residential mortgage loans that have been pooled and transferred with recourse to FNMA and FHLMC and to private mortgage pools, expressed as a percent of assets; C&ISALES are the total amount of all loans originated by the reporting bank that the bank has sold or transferred to others during the calendar year ending with the report date, regardless of when the loan was originated; excludes 1–4 family residential real estate loans and loans to individuals for household, family, and other personal expenditures, expressed as a percent of average assets; EQUITY is equity capital, expressed as a percent of assets; CHARGE is net chargeoffs, expressed as a percent of average assets; SIZE is the log of total assets; HC is a dummy variable that equals 1 if a banking organization is part of a holding company, zero otherwise; MBHC is a dummy variable that equals 1 if a banking organization is part of a multibank holding company, zero otherwise; NONINT is non-interest income, expressed as a percent of average assets; LOANASS is total loans expressed as a percent of assets; SUBDEBT is the amount outstanding of subordinated notes and debentures, expressed as a percent of assets. All data are quarterly from the Report of Condition. Data are collected at the organization level and are structure adjusted for mergers and acquisitions. Standard errors are in parentheses. ∗∗ Significance at the 5% level; Assets variables used to classify bank size are expressed in 1993 dollars for the models using C&ISALES and in 2000 dollars in models using MORTSALES. ∗∗∗ Significance at the 1% level.

4.2. Large Organizations Because larger organizations are more likely to issue subordinated debt, we also estimate our empirical models using only those organizations with assets of $500 million and above. When estimating models using C&ISALES, asset values used

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to classify banks are expressed in 1993 dollars coinciding with the last year this loan sales variable was available. In models using MORTSALES, asset values are expressed in 2000 dollars. From Table 2, when considering C&ISALES, results from the probit model indicate that CHARGE is now insignificant when compared to the probit model using all banks, while SIZE is now positive and significant and NONINT is insignificant. More importantly, SUBDEBT is negative but is not statistically significant. When using MORTSALES, the probit results for larger organizations indicate that EQUITY and NONINT are no longer statistically significant as they were when using all banks, and SUBDEBT is positive but not statistically significant. Turning to the Tobit models for larger organizations, with C&ISALES, EQUITY, CHARGE, and HC are now statistically insignificant compared to the Tobit model that uses all banks, and SIZE possesses a positive sign. SUBDEBT, though, remains positive and significant. Considering MORTSALES, the Tobit model for large banks indicates that SIZE and MBHC, change signs when compared to the Tobit model for all banks. Moreover, SUBDEBT is now negative and statistically significant, providing some support for the regulatory tax hypothesis.

4.3. Loan Sales Post-1996 The MORTSALES measure of loan sales began to increase dramatically in the late 1990s. At the end of 1996, MORTSALES totaled approximately $8 billion, as compared to about $6.5 billion at the end of 1989. By 2000, MORTSALES climbed to almost $60 billion. To judge the robustness of our results, we estimated both our probit and Tobit regressions beginning in 1997. These results are found in Table 3. Focusing on the SUBDEBT variable, in both the probit and Tobit models using all banks, this variable is positive and significant, providing support for the underinvestment hypothesis and the regulatory subsidy hypothesis. When considering large banks, SUBDEBT in the probit model is positive but not statistically significant, while SUBDEBT is positive and significant in the Tobit regression, again supporting the underinvestment/regulatory subsidy hypotheses.

4.4. The Role of Subordinated Debt: A Summary Because our main focus is on the influence of subordinated debt on loan sales, Table 4 summarizes our findings on the relationships between loan sales and subordinated debt from both the probit and Tobit approaches. We find strong

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Table 3. Regression Results for Models of Bank Loan Sales. Variables

MORTSALES: 1997–2000 Banks ≥$500 million

All Banks

Constant EQUITY CHARGE SIZE HC MBHC NONINT LOANASS SUBDEBT Log likelihood Obs. with dep. = 1 Obs. with dep. = 0 Left censored obs. Uncensored obs.

Probit

Tobit

Probit

Tobit

−7.7756*** (0.2987) −0.0184 (0.0101) −0.3221** (0.1592) 0.4321*** (0.0173) 0.2133*** (0.0789) −0.1923*** (0.0632) 0.0305** (0.0146) 0.0099*** (0.0020) 0.1421** (0.0614)

−0.4493*** (0.0648) −0.0010 (0.0011) 0.0577 (0.0424) 0.0549*** (0.0055) −0.0337*** (0.0046) −0.1553*** (0.0503) 0.0143 (0.0105) −0.0013*** (0.0002) 0.1919** (0.0880)

−9.8225*** (0.8682) 0.0109 (0.0260) −0.7885** (0.3729) 0.5205*** (0.0417) 0.2119 (0.3045) −0.1704 (0.0940) 0.0541 (0.1263) 0.0169*** (0.0038) 0.0983 (0.0812)

21.1021*** (1.2884) −0.6290*** (0.0411) 5.7429*** (0.5356) −0.4861*** (0.0687) −0.9466** (0.4515) 3.1489*** (0.2995) −0.5310*** (0.1722) −0.1704*** (0.0049) 6.5479*** (0.2632)

−1635.11

−13834.51

−587.93

−2350.03

542

314

16562

1371 16562

1371

542

314

Note: MORTSALES is the principal outstanding balance as of the report date for residential mortgage loans that have been pooled and transferred with recourse to FNMA and FHLMC and to private mortgage pools, expressed as a percent of assets; EQUITY is equity capital, expressed as a percent of assets; CHARGE is net chargeoffs, expressed as a percent of average assets; SIZE is the log of total assets; HC is a dummy variable that equals 1 if a banking organization is part of a holding company, zero otherwise; MBHC is a dummy variable that equals 1 if a banking organization is part of a multibank holding company, zero otherwise; NONINT is non-interest income, expressed as a percent of average assets; LOANASS is total loans expressed as a percent of assets; SUBDEBT is the amount outstanding of subordinated notes and debentures, expressed as a percent of assets. All data are annual from the Report of Condition. Data are collected at the organization level and are structure adjusted for mergers and acquisitions. Standard errors are in parentheses. ∗∗ Significance at the 5% level; Assets variables used to classify bank size are expressed in 2000 dollars in models using MORTSALES. ∗∗∗ Significance at the 1% level.

support for the underinvestment and regulatory subsidy hypotheses especially for the CI&SALES measure. Results from the probit and Tobit models using all banks provide a positive and significant sign on SUBDEBT. When considering large organizations, the probit model produces a statistically insignificant sign on SUBDEBT, but the Tobit model shows a positive and significant sign for SUBDEBT. Our results are mixed when considering MORTSALES. The only statistically significant effect when considering the entire time period is found in the Tobit model for large banks, where SUBDEBT possesses a negative and significant sign,

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Table 4. Summary Results for the Influence of Subordinated Debt on Loan Sales. Loan Sales Measure

Sign on SUBDEBT Assets ≥$500 Million

Organization Size All C&ISALES

Probit Model: Tobit Model:

+ +

Probit Model: Tobit Model:

0 +

MORTSALES

Probit Model: Tobit Model:

0 0

Probit Model: Tobit Model:

0 −

MORTSALES97

Probit Model: Tobit Model:

+ +

Probit Model: Tobit Model:

0 +

Note: MORTSALES is the principal outstanding balance as of the report date for residential mortgage loans that have been pooled and transferred with recourse to FNMA and FHLMC and to private mortgage pools, expressed as a percent of assets; C&ISALES is the total amount of all loans originated by the reporting bank that the bank has sold or transferred to others during the calendar year ending with the report date, regardless of when the loan was originated; excludes 1–4 family residential real estate loans and loans to individuals for household, family, and other personal expenditures, expressed as a percent of average assets. MORTSALES97 is the MORTSALES variable collected from 1997 to 2000. SUBDEBT is the amount outstanding of subordinated notes and debentures, expressed as a percent of assets. Assets variables used to classify bank size are expressed in 1993 dollars for the models using C&ISALES and in 2000 dollars in models using MORTSALES. All data are annual from the Report of Condition. Data are collected at the organization level and are structure adjusted for mergers and acquisitions. + = positive and significant; − = negative and significant; 0 = statistically insignificant.

providing support for the regulatory tax hypothesis. However, when we consider the time period of rapid growth in MORTSALES (identified as MORTSALES97), our results indicate positive and significant signs on SUBDEBT, with the exception of the probit model for large banks.

5. CONCLUSIONS AND POLICY IMPLICATIONS The motives for banks to engage in loan sales have been investigated both theoretically and empirically by a number of researchers. In this paper, we consider the results of a dynamic inventory control model that provides a liquidity-based rationale for loan sales, purchases, and originations. In this model, bank loan sales are motivated by underinvestment losses resulting from issues of subordinated debt. Banks optimally increase loan sales (and reduce purchases) in an attempt to offset these losses. We also consider how reductions in the federal safety

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net subsidy that might be associated with subordinated debt can increase loan sales. Alternatively, if subordinated debt increases market discipline and lowers regulatory taxes, then reductions in these taxes motivate fewer loan sales. Using annual data, we construct panels of banking organizations. For two measures of loan sales, we are able to investigate the underinvestment hypothesis and the regulatory subsidy hypothesis, as well the regulatory tax hypothesis regarding the relationship between subordinated debt and loan sales. We also can account for other factors that might influence banks’ loan sales. We find some support for the scale hypothesis and the importance of the diversiﬁcation hypothesis as factors behind loan sales. After controlling for variables hypothesized to be important determinants of loan sales, when considering all organizations, our probit results indicate that the presence of subordinated debt increases the likelihood that a bank will engage in C&I loan sales. Further, results from Tobit regressions reveal that the portfolio proportions of C&I loan sales are positively related to the portfolio proportions of subordinated debt, with this relationship also holding for large organizations. These results provide support for the underinvestment hypothesis and the regulatory subsidy hypothesis. Our results are mixed when considering sales of mortgage loans. Using the entire time period of availability for this measure produces mostly insignificant results for the influence of SUBDEBT on loan sales. Restricting the estimation period to coincide with rapid growth in loan sales, however, provides further support for the underinvestment/regulatory subsidy hypotheses. Our results show the possible effects on banks’ portfolio management of increasing the reliance on issues of subordinated debt to enhance market discipline. Greater portfolio proportions of subordinated debt appear to motivate banks to engage in greater loan sales. This portfolio restructuring is likely related to underinvestment losses that are associated with firms’ issues of collateralized debt, and reductions in the federal safety net possibly associated with subordinated debt issues that lead banks to rely less on deposits as funding sources. A number of macroeconomic models stress the importance of a credit channel for monetary policy and how financial factors may amplify and propagate business cycles.6 Banks’ ongoing efforts to manage their liquidity can be expected to increase lending efficiency. Moreover, greater amounts of subordinated debt create incentives for improved transparency and disclosure by banks. Purchasers of subordinated debt need a clear picture of banks’ risk profiles in order to price risk appropriately. If this information is not forthcoming, investors will require higher yields (Board of Governors of the Federal Reserve System and United States Department of the Treasury, 2000). A more efficient, transparent banking system, then, could have important implications for monetary policy given recent findings on the importance of a credit channel for monetary policy.

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NOTES 1. See Bliss (2001) for an overview of issues related to market discipline and subordinated debt. 2. A Tobit or censored regression model is appropriate in that most banks do not report any loan sales activity. 3. It is important to point out that changes in regulatory subsidies or taxes could have varying effects on different banks. For example, Chen et al. (1999) find that the wealth effects and the impact on risk from passage of FDICIA in 1991 varied by banks’ capital ratios and size. 4. C&ISALES is expressed as a flow variable in the call reports necessitating the use of average assets in the denominator. For ease of exposition, even though our data are collected at the organizational level, we use the term bank throughout the analysis rather than banking organization. 5. Demsetz (1999) points out, though, that smaller banks might face limited diversification opportunities making them more likely to participate in both loan sales and purchases. Smaller banks could also face binding legal lending limits, making them more likely to engage in loan sales. 6. See Bernanke and Blinder (1988), Bernanke and Gertler (1995) and Kashyp and Stein (2000). However, Ramey (1993) and Oliner and Rudebusch (1995) do not find evidence consistent with the credit view.

ACKNOWLEDGMENTS The views expressed are the authors and do not necessarily represent those of the Federal Reserve System or the Federal Reserve Bank of Dallas.

REFERENCES Benveniste, L., & Berger, A. N. (1987). Securitization with recourse. Journal of Banking and Finance, 11, 403–424. Berger, A. N., & Udell, G. F. (1993). Securitization, risk, and the liquidity problem in banking. In: M. Klausner & L. White (Eds), Structural Change in Banking. Homewood, IL: Irwin. Bernanke, B. S., & Blinder, A. S. (1988). Credit, money, and aggregate demand. American Economic Review, 78(May), 435–439. Bernanke, B. S., & Gertler, M. (1995). Inside the black box: The credit channel of monetary policy transmission. Journal of Economic Perspectives, 9(Fall), 27–48. Bliss, R. R. (2001). Market discipline and subordinated debt: Review of some salient issues. Federal Reserve Bank of Chicago Economic Perspectives, 25, 24–45. Board of Governors of the Federal Reserve System and United States Department of the Treasury (2000). The feasibility and desirability of mandatory subordinated debt, Report by the Board of Governors of the Federal Reserve System and the Secretary of the U.S. Department of the Treasury, submitted to the Congress pursuant to section 108 of the Gramm-Leach-Bliley Act of 1999 (December).

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Boyd, J. H., & Gertler, M. (1994). Are banks dead, or are the reports greatly exaggerated? Federal Reserve Bank of Minneapolis Quarterly Review, 18, 2–22. Carlstrom, C. T., & Samolyk, K. A. (1995). Loan sales as a response to market-based capital constraints. Journal of Banking and Finance, 19, 627–646. Chen, A. H., Cornett, M. M., Mazumdar, S. C., & Tehranian, H. (1999). An empirical analysis of the effects of the FDICIA of 1991 on commercial banks. Research in Finance, 17, 41–64. Chen, A. H., & Mazumdar, S. C. (1999). Loan sales and bank liquidity management. International Journal of Theoretical and Applied Finance, 2, 113–129. Demsetz, R. (1994). Evidence on the relationship between regional economic conditions and loan sales activity. Federal Reserve Bank of Chicago, Proceedings of the 30th Annual Conference on Bank Structure and Competition, 370–380. Demsetz, R. (1999). Bank loan sales: A new look at the motivations for secondary market activity. Federal Reserve Bank of New York Staff Reports, No. 69 (March). Federal Reserve System (1999). Using subordinated debt as an instrument of market discipline. Study Group on Subordinated Notes and Debentures, Staff Study 172 (December). Greenbaum, S. I., & Thakor, A. V. (1987). Bank funding modes: Securitization vs. deposits. Journal of Banking and Finance, 11, 379–401. Gorton, G. B., & Haubrich, J. G. (1990). The loan sales market. In: G. Kaufman (Ed.), Research in Financial Services: Private and Public Policy (Vol. 2, pp. 85–135). Greenwich, CT: JAI Press. Gorton, G. B., & Pennacchi, G. G. (1995). Banks and loan sales: Marketing nonmarketable assets. Journal of Monetary Economics, 35, 389–411. Haubrich, J. G., & Thompson, J. B. (1996). Loan sales, implicit contracts, and bank structure. Review of Quantitative Finance and Accounting, 7, 137–162. James, C. (1988). The use of loan sales and standby letters of credit by commercial banks. Journal of Monetary Economics, 22, 395–442. Kashyp, A. K., & Stein, J. C. (2000). What do a million observations on banks say about the transmission of monetary policy? American Economic Review, 90(June), 407–428. Mester, L. M. (1992). Traditional and non-traditional banking: An information-theoretic approach. Journal of Banking and Finance, 16, 545–566. Myers, S. C. (1977). Determinants of corporate borrowing. Journal of Financial Economics, 5, 145– 175. Oliner, S. D., & Rudebusch, G. D. (1995). Is there a bank lending channel for monetary policy? Federal Reserve Bank of San Francisco Economic Review, 2, 3–20. Pavel, C., & Phillis, D. (1987). Why commercial banks sell loans: An empirical analysis. Federal Reserve Bank of Chicago Economic Perspectives, 14, 3–14. Pennacchi, G. C. (1988). Loan sales and the cost of bank capital. Journal of Finance, 43, 375–396. Ramey, V. (1993). How important is the credit channel in transmission of monetary policy? CarnegieRochester Conference Series on Public Policy (December), 1–46.

USING ZERO-NON-ZERO PATTERNED VECTOR AUTOREGRESSIVE MODELLING TO TEST FOR CAUSALITY BETWEEN MONEY SUPPLY, GDP GROWTH, THE LONDON STOCK MARKET INDEX AND THE EURO EXCHANGE RATE Edward J. Y. Lin, J. H. W. Penm, R. D. Terrell and Soushan Wu ABSTRACT In this paper the techniques of zero-non-zero (ZNZ) patterned vector autoregressive modelling are utilized to examine two issues associated with the European single currency – the euro. First, “Granger causality” is employed to examine the causal linkages between the euro exchange rate, the euro area money supply and the gross domestic product (GDP) growth in the euro area. Second, we examine the hypothesis that the euro has become a major inﬂuence on international stock markets by testing for the causal relationships between movements in the euro exchange rate, the U.K. pound exchange rate and the London stock market index.

Research in Finance Research in Finance, Volume 20, 99–117 © 2003 Published by Elsevier Ltd. ISSN: 0196-3821/doi:10.1016/S0196-3821(03)20006-X

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1. INTRODUCTION With the introduction on 1 January 1999 of the single European currency, the euro has become the official currency in the eleven participating countries of the European Union (EU). The increasing popularity of the euro as a pegging currency reflects the internationalisation of the euro. Also the euro has been used as the largest weighting element in a basket of currencies for foreign exchange (forex) arrangements adopted by several Central European countries. In this paper the zero-non-zero (ZNZ) patterned vector autoregressive (VAR) modelling, using the pre-windowed case, is utilised first to investigate Granger causal relations between the joint money supply in the euro area – which comprises all countries of the EU using the euro – and the euro exchange rate relative to the U.S. dollar. Second, the causality test between this euro exchange rate and the joint GDP growth in the euro area is also undertaken. Third, the hypothesis that the euro exchange rate is a major influence on international stock markets is then tested. This is done by examining the cause and effect relationship between the London stock market and two related forex markets using the ZNZ patterned VAR modelling. The body of this paper is organised as follows. Section 2 reviews background information on the money supply and GDP in the euro area and the euro’s potential influence on stock markets. In Section 3 we discuss the procedures for selecting the optimal ZNZ patterned VAR model by using the pre-windowed case.1 Section 4 first assesses the causal relationships between the movements in the euro exchange rate and the money supply, second the euro movements and the growth in GDP; and third the impact of the euro on the London stock market. A summary is provided in Section 5.

2. MONEY SUPPLY AND GDP GROWTH IN THE EURO AREA AND THE EURO’S IMPACT ON THE LONDON STOCK MARKET 2.1. Introduction of the Euro The introduction of the euro has been a significant recent event in global financial markets. The euro is intended to create broader, deeper and more liquid financial markets in Europe, and thus its main purpose is to improve the price stability, productivity and economic activity in the European economy. Rather than experiencing constant fluctuations in the member exchange rates, there is intended to be a more consistent and predictable environment for international trade. Another reason why the European Central Bank introduced the euro is based on its belief that the new currency will foster low inflation.2

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The euro has already established itself as a credible and important currency in the world. To date the euro/US dollar trading has been very active in the world’s forex markets through a wide range of instruments, offering significant hedging possibilities. Over the period January 1999 to December 2002 the relative weakness of the euro has been a significant feature in international forex markets. During this period the value of the euro relative to the U.S. dollar and the U.K. pound, in general, fell. The euro’s weakness throughout this period confounds earlier general expectations that it would trend upwards relative to the U.S. dollar and the U.K. pound (see ECB, 2001).

2.2. European Money Supply and GDP Growth Money supply in the euro area is measured by the standard stock of money (M3). It consists of short-term deposits, shorter deposits of up to two years, and marketable instruments. In a large number of months over the period 1999–2002 the monthly measures of M3 growth rate have been higher than the reference value of 4.5% set by the Governing Council of the European Central Bank. That is, the growth rate of M3 has exceeded the 4.5% benchmark for nearly the entire period.3 In a floating exchange rate system, currencies fluctuate according to supply and demand. One tool that has been used to manage the exchange rate is through the money supply. However such action can only be successful in the short-term. Governments are not able to control the exchange rate over a long period without regard to economic fundamentals. The most widely held view is that, ceteris paribus, an expansion in money supply leads to a decrease in domestic interest rates. This leads to a depreciation in the domestic currency. In the overshooting hypothesis, the immediate depreciation of the spot exchange rate will temporarily exceed, or overshoot, that of the long-term equilibrium exchange rate. Conversely, a tightening of monetary policy will lead to an appreciation of the domestic currency. Lewis (1993) utilises VAR modelling to investigate the impact of U.S. monetary shocks on the U.S. dollar exchange rate. The findings indicate that a loosening of monetary policy is associated with a depreciation of the currency. Eichenbaum and Evans (1995) investigate the effects of money shocks on the U.S. dollar exchange rate. Their results show that monetary policy is important in explaining exchange rate movements, but does not explain the majority of these movements. Cushman and Zha (1997) examine the effects of monetary shocks on the Canadian dollar exchange rate movements. They conclude that a contraction in U.S. monetary supply leads to an appreciation of the U.S. dollar against the Canadian dollar. The three above-mentioned studies do not give any evidence of support for the

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overshooting hypothesis. However the findings of Bonser-Neal et al. (1998) support the overshooting hypothesis. They use event study methodology to investigate the impact of monetary shocks on exchange rates. Their findings suggest that the immediate response of the exchange rate to U.S. monetary policy is statistically and economically significant in most cases, and the overshooting hypothesis is acceptable in seven of the eight cases they examine (Bonser-Neal et al., 1998). GDP is the annual aggregate money value of all final goods and services produced by an economy. Economic growth occurs when the total output of goods and services increases. GDP growth – changes in GDP – is commonly viewed as one of the most important measures of overall economic activity. A successful euro would lower transaction costs, increase price transparency, and then attract and encourage international investment. This environment would sustain low interest rates, then lead to a stable and attractive euro, and then increase GDP. In contrast, the international trade of the euro area would be disturbed if the euro currency were to rapidly move up and down in value against other currencies. Such an unstable euro would cause price instability and productivity deterioration in the euro area, and thus provide little contribution to economic growth, with a deteriorating GDP. Beenstock (1995) develops an econometric model of the oil importing developing countries. The model investigates the relationship between GDP, the exchange rate and capital flows. Kim (1998) tests the effects of the Australian GDP announcements on the value of the Australian dollar. His results indicate a causal relationship between GDP growth and the Australian dollar’s exchange rate. Crompton (2000) uses the rate of growth in GDP to forecast future trends in Japanese steel consumption. His findings show that a low GDP growth causes a reduction Japanese steel consumption. There is already literature examining the causal relationships between the euro exchange rate and economic activity indicators in the euro area (see BIS, 2000). However an investigation of the direct causal relationships between the euro exchange rate and economic indicators such as money supply and GDP growth, using the patterned VAR modelling, has so far not been attempted. Thus, the first major area of interest in this paper is to investigate whether there exist causal linkages between the euro exchange rate, the money supply and GDP growth. 2.3. Forex and Stock Markets This section examines the linkage between the forex and stock markets. It seeks to explain how the euro could impact on world stock markets, and uses the London stock market to examine the euro’s influence. First, previous evidence has shown that exchange rate changes have a significant impact on stock prices, implying the former contain relevant information about

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stock prices. For instance, Froot et al. (2001) demonstrate that flows of capital influence exchange rate movements and such flows are related to equity returns. Therefore we propose an underlying hypothesis that a causal relationship exists among the euro exchange rate relative to the U.K. pound, the U.S. dollar relative to sterling and the London stock market. Second, as described in Section 2.1, during the test period 1 January 1999 to 31 December 2002 the weakness of the euro has been a significant feature in international forex markets. The Annual Report of BIS in (2000) observed: “The Eurosystem had indicated that it would not react automatically to deviations of money growth from the reference value.” During the test period interest rates on the marginal lending facilities are maintained by the ECB at about 3.5% (see ECB, 2002), while the interest rate in the U.S. is for much of the period above 6%, thereby creating a flow of capital from the euro area to other markets, such as London and U.S. markets. During this period the average lending rate in London is above 5.5% (see BOE, 2003). Third, London is an important banking and financial centre and generally allows free entry and exit of international funds. The London stock market is the second largest in the world after New York. International investors are willing to place their money in London stocks while assessing other investment opportunities. Hence it is hypothesised that the decline in the euro had implications for London’s stock market in the test period. Therefore the second major area of interest is to test this hypothesis by examining the causal relationship between the London stock market and forex markets. Further, the common approach used to study these two areas of interest includes the use of empirical data to identify the mechanisms associated with market movements. Model building is an essential task and new techniques for vector time series modelling are used in interpreting and explaining the behaviour and impacts of the euro exchange rate. In contrast to conventional techniques this paper explicitly explores the situation of the presence of subset structures and zero coefficients (or entries) in ZNZ patterned VAR modelling to detect Granger causality. We refer to a VAR model, with allowance for possible zero entries in all coefficient matrices as a ZNZ patterned VAR, while commonly employed full-order VARs assume nonzero entries in all their coefficient matrices.

3. VAR MODELLING 3.1. ZNZ Patterned VAR Modelling The use of VAR models for investigating the causal relationship, or simply the causality, which exists among economic and financial variables has become

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more prevalent in the finance literature. Granger (1969) introduces a definition of causality which is based entirely on the predictability of the objective variables, such that they make no explicit use of economic and financial laws to provide a priori restrictions on the structure. Granger then proposes to fit a VAR for empirical model building to detect Granger causality and Granger non-causality. Sims (1972, 1977) suggests that we should treat all variables as jointly dependent, and then fit a VAR to avoid imposing on the model spurious or false restrictions for causality testing. Both Granger and Sims ignore important constraints on the coefficient matrices, because they wish to avoid possible misspecification. After this, Hsiao (1982) suggests a step-wise procedure based on Granger’s definition of causality together with Akaike’s FPE criterion and classical large-sample hypothesis tests to identify univariate equations in a multivariate framework. Geweke (1982) recommends a means of measuring two-way linear causality and instantaneous causality in VAR modelling. Subsequently Whitelaw (1994) investigates a VAR for assessing the time series properties of the expected value and the volatility of stock market returns. Thorbecke (1997) uses impulse-response functions from a VAR to analyse the relationship between monetary policy and stock returns. Bhattacharya et al. (2000) utilise a sequential hypothesis testing procedure using standard likelihood ratio tests to analyse the causal direction of volatility transmission between two different classes of shares in the framework of a VAR. Although full-order VAR models assume all non-zero entries in all their coefficient matrices, the number of entries to be estimated in these potentially over-parameterised models grows with the square of the number of variables, the degrees of freedom will thus be heavily reduced. Therefore, overcoming the problem of over-parameterisation needs to be carefully considered when assessing the value of the proposed VAR modelling system. Avoiding over-parameterisation has the benefits of improved efficiency with a reduced computational burden and greater numerical reliability. To overcome over-parameterisation Penm et al. (1984a, 1999) propose algorithms in conjunction with model selection criteria to investigate the ZNZ patterned VAR models. The selected optimal ZNZ patterned VAR model is then used as a basis for detecting Granger causality, Granger non-causality and instantaneous causality. It is appropriate to note that recent cointegration work suggests that, if cointegrating relations exist between the variables, then the use of the vector error-correction model (VECM), which is equivalent to the VAR model with unit roots, may be more effective for testing Granger causality. Interested readers are referred to Penm et al. (1997) for details.

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3.2. Estimation for ZNZ Patterned VAR Modelling In VAR modelling, let z(t) = {z 1 (t), z 2 (2), . . . , z m (t)} be a zero mean, wide-sense stationary time series of dimension m. We consider the VAR(p) model of the form p

B k z(t − k) = ␧(t)

(1)

k=0

where B 0 = I, Bk , k = 1, . . ., p, are the mxm parameter matrices and ␧(t) is an mx1 stationary vector process with E{␧(t)} = 0, and thus E{␧(t)␧ (t − k)} = G E{␧(t)␧ (t

− k)} = G

as k = 0 as k > 0

(2)

Time-series model designers often use the assumption that if a coefficient matrix in the model is non-zero, then all the lower-order ones will be non-zero too. For example, in a bivariate VAR model when p = 5, then the coefficients, B1 , B2 , up to and including B5 are assumed non-zero. That is they neglect all possible models with zero coefficient elements. However there are 220 = 65,536 possible models in this example. More important, if the underlying true VAR process has a ZNZ patterned structure, the sub-optimal model design (for instance, a full-order structure) can produce misleading inferences and inferior projections. Of course it is hard to find the optimal model without an effective approach. As mentioned in Section 3.1, Penm et al. (1984a, 1999) develop a tree-pruning algorithm to select the optimal AR model. For short data records, Kay and Marple (1981) show that the AR model design using the pre-windowed case produces more statistical accuracy in the parameter estimation. Thus, in this paper the pre-windowed approach to estimate a ZNZ patterned VAR is proposed to utilise the tree-pruning algorithm in conjunction with model selection criteria for the selection of the optimal VAR. Two model selection criteria are employed to select the optimal ZNZ patterned VAR. They are 2 ˆ AIC = log|Gp | + I, N log N ˆ SC = log|Gp | + I, N where N is the sample size, and I is the number of functionally independent parameters estimated. The procedures to select the optimal ZNZ patterned VAR with the smallest value of each selection criterion are summarised in the following steps.

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3.2.1. Step 1: To Assign a Maximum Lag P Clearly we must choose a maximum lag P, so we are confident that the order of the true model is less than this maximum lag. One suggestion is to use the classical sequential way as proposed in Penm et al. (1984a, 1999) to determine P. This means choosing Q P and using each criterion to select the best full-order model among all full-order models with p = 0, 1, . . ., Q. The order of this best full-order model is assigned as the value of P for each criterion.

3.2.1.1. Fitting of the full-order VAR models. To fit a full order VAR(p) model of (1) for a given set of observations {z(t), t = 1, . . ., N}, the estimated G using the pre-windowed approach method is as follows: N

ˆ = 1 G ␧ˆ t ␧ˆ t N

(3)

t=1

where ␧ˆ t denotes the estimate of ␧(t). Since the sample lag covariance matrices are N−k

Rk =

1 z(t + k)z (t), N t=1

we can re-write (3) as: p p p N 1 ˆ = ˆ k z(t − k) z(t) − ˆ k z(t − k) = R 0 + ˆ k R −k , z(t) − G B B B N t=1 k=1 k=1 k=1 (4) where z(t) = 0 as t ≤ 0. Also, the associated linear regression model can be expressed as                 z (N − 1) · · · z (N − p) ␧N z                .. .. .. ..    −A  ...     1 . . . .               (1)   ..  +  ␧   =  z (p) z (p + 1) · · · z Y  p+1  .                .. .. .    −A  ..     .. p   . . 0   .             z (1) 0 0 0 ␧1       Xp

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The usual least squares estimate of ␤ = −A 1 . . . − A p in the model Y = X p ␤ + ␩ is then: ␤ˆ = (X p X p )−1 X p Y. Hence we have U p = X p X p . Analogously, to fit a VAR (p − 1) model, we have U p−1 = X p−1 X p−1 , which indicates   .. U p =  Up−1 . . ... · Since Up is a block symmetric matrix, we can conduct the inverse of Up by applying the block Choleski decomposition method, which provides an iterative improvement on reducing numerical error generation and propagation. Thus, we can have     .. .. .. U p = L p D p L p  Lp−1 .  Dp−1 .  Lp−1 . , (5) ... · ... · ... · and U p−1 = L p−1 D p−1 L p−1 ,

(6)

where Lp is a lower block triangular matrix, and Dp is a block diagonal matrix with diagonal block entries di , i = 1, . . ., p. More importantly, in the course of computing both Lp and Dp for the VAR(p) model, Li and Di , i = 1, . . ., p will be obtained by using Eqs (5) and (6). Since Li and Di are required to conduct matrix inversions for all the lower order VAR models, therefore a considerable amount of computational cost can be avoided. 3.2.2. Step 2: To Select the Optimal Subset VAR for Each Criterion The subset VAR models include the VAR models with intermediate lags constrained to zero matrices. The subset VAR with the deleted lags i1 , i2 , . . ., is has the representation p

B k (I s )z(t − k) = ␧(t),

(7)

k=0

where Is represent an integer set with elements i1 , i2 , . . ., is , and B k (I s ) = 0, as k ∈ Is .

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We then use a leaps and bounds algorithm proposed in Penm et al. (1984a, 1999) to search for the “best” VAR model of size k, where k is the number of lags with non-zero coefficient matrices, k = 1, 2, . . ., p. 3.2.2.1. Fitting of the subset VAR model. In fitting the subset VAR model of Eq. (7), the coefficient elements can be estimated by the following relationship: p (I s )U p (I s ) = −p (I s ) where p (I s ) and p (I s ) are formed by placing zero block matrices 0m in the (i 1 . . . i s )th column of blocks of p and p . Up (Is ) is formed by placing Im in the {(i 1 , i 1 ) . . . (i s , i s )}th diagonal block of Up and zero block matrices everywhere else in the (i 1 . . . i s )th row of blocks and also in the (i 1 . . . i s )th column of blocks of Up . Thus the estimate of the G p (I s ) for the VAR(p) model is ˆ p (I s ) = R 0 + G

p

ˆ k (I s )R −k B

k=1

3.2.3. Step 3: To Select the Optimal ZNZ Patterned VAR for Each Criterion 3.2.3.1. Fitting of the ZNZ patterned VAR models. In fitting of VAR models of Eq. (1) with zero-non-zero patterned coefficient matrices, the coefficient estimates obey the following relationship: Z p (C r )␣(C r ) = ␥(C r ),

(8a)

where Z p = {I m ⊗ U p }, ␣ = vec{p }, ␥ = vec{p }. Cr is an integer set which contains c1 , c2 , . . ., cr , and the (c1 , c2 , . . ., cr ,)th entries of ␣ are constrained to zero. Then ␣(Cr ) and ␥(Cr ) are formed by placing 0 in the (c1 , c2 , . . ., cr ,)th row entries of ␣ and ␥, and Zp (Cr ) is formed by placing 1 in the {(c1 , c1 ), (c2 , c2 ), . . ., (cr , cr )} diagonal entries of Zp and 0 everywhere else in the (c1 , c1 , . . ., cr ) rows and columns of Zp . From Eq. (3) we have the estimate of G as ˆ = R0 + G

p k=1

ˆ k (I s )R −k + B

p j=1

ˆ j (I s ) + Rj B

p p

ˆ k (I s )R j−k B ˆ j (I s ). B

(8b)

j=1 k=1

Thus, similar to the above two steps, only the coefficient elements of Up required ˆ by using Eqs (8a) and (8b). ˆ k and G to compute B We note that consideration of the contemporaneous correlation in ␧(t) cannot be ignored. A ZNZ patterned VAR model can be viewed as a system of “seemingly unrelated regressions” as originally proposed by Zellner (1962). As the regressors

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in each equation of the VAR model are no longer necessarily the same, the GLS ˆ is positive estimator is more efficient than the estimator using Eq. (8a). Since G ˆ −1 = K ˆ such that G ˆK ˆ . As definite, there exists an mxm non-singular matrix K, −1 ˆ , and then follow described in Penm et al. (1984a, 1999), we premultiply z(t) by K the proposed pre-windowed method for fitting of VAR models, and so obtain the GLS coefficient estimates of the ZNZ patterned VAR model.

4. CAUSALITY ANALYSIS OF THE M3, GDP GROWTH AND THE EURO, AND THE EURO’S IMPACT ON THE LONDON STOCK MARKET 4.1. Data First, to investigate the causal relationships between movements in the euro exchange rate and the money supply, monthly average data on the euro exchange rate relative to the U.S. dollar (Ee ) and seasonally adjusted M3 are collected from DataStream™ over the period September 1997 to December 2002.4 To examine stationarity for each series Microfit 4.0 is used to carry out the augmented DickeyFuller (ADF) unit root test. The results indicate that both log Ee and log M3 are non-stationary. Second, to test the causal relationships between movements in the euro exchange rate relative to the U.S. dollar and growth in GDP, quarterly average data on the euro exchange rate (Eq ) and seasonally adjusted GDP are collected from DataStream™ over the period the first quarter of 1991 to the first quarter of 2003. The first difference of log GDP is used to measure growth in GDP. To examine stationarity of log Eq and log GDP, the augmented ADF test also indicates that detrending using a first-order polynomial is required before fitting the VAR models. Third, to examine the euro’s impact on the London stock market, all data are sampled weekly between 1 January 1999 and 31 December 2002 from DataStream™ . Weekly indices are chosen in preference to daily indices to avoid the problem of non-synchronous trading when daily indices are in use, or to avoid the influence on daily indices of thinly traded stocks. The Financial Times-Stock Exchange (FTSE) 100 Index is used as a proxy for the London stock market. It is the main stock market indicator in London, which is updated throughout the trading day in real time. This index comprises 100 constituent stocks which are the largest in the UK. Within this context, the following three variables are studied contemporaneously in a stochastic vector system using the ZNZ patterned vector AR modelling proposed above:

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(i) euro to U.K. pound – exchange rate (ER) (ii) London’s FTSE – stock price index (FTSE) (iii) UK pound to U.S. dollar – exchange rate (UX). The variables are log transformed such that z 1 (t) = log (ER), z 2 (t) = log (FTSE) and z 3 (t) = log (UX). Forsythe’s (1957) method is initially used for generating orthogonal polynomials to assess the data for suitable detrending to produce stationarity. The results show that a first-order polynomial detrending is required before fitting the VAR models. Thus all three variables are mean-corrected and detrended to achieve stationarity.

4.2. The Causal Relationship Between the Movements of the Euro Exchange Rate, the Money Supply and the Growth in GDP In detecting the causal relationships between the movements of the euro exchange rate and the money supply, the identification algorithms for ZNZ patterned VAR modelling as proposed in Section 3.2 are utilised to select the optimal VAR models for both mean-corrected and detrended log (M3) and log (Ee ) at T = 60, 61, 62, 63 and 64. The five cases correspond to August, September, October, November and December 2002 respectively. To demonstrate the usefulness of the proposed algorithms in a small sample environment, a maximum order of 12 is selected to cope with this small sample environment. Each of two order selection criteria – Akaike and Schwarz – is used to determine the best specification. The ability of these order selection criteria to determine the true specification of a ZNZ patterned VAR has been examined using a simulation approach suggested by Penm et al. (1984b, 1999). The simulation results suggest that SC is superior in order-identification to the alternative in ZNZ patterned VAR modelling for causality studies. Therefore only the specification determined by SC is applied and used as the benchmark model for analysing causal relations. The proposed algorithms are used to obtain the optimal ZNZ patterned VAR models at T = 60, T = 61, up to T = 64 using SC. The resulting estimates at each T show the same causal structure. The optimal models selected are estimated using the GLS techniques and are shown in Table 1. These models are then used as the benchmark models for analysing the causal relationships. To check the adequacy of the fit of these models, the strategy suggested in Tiao and Tsay (1989)5 is used, with the proposed algorithm applied to test the residual vector series, using the SC criterion. The results in Table 1 support these residual vector series being white noise processes.

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Table 1. The VARsa,b Selected by SC for Detecting the Causal Relationships Between Ee and M3. Sample Size (T )

60

Non-zero Lag Coefficient Structure for z(t) = {log E e log M3} −0.985(0.058) 0.178(0.096) lag 1 0 −0.988(0.036)

61

lag 1

62

lag 1

63

lag 1

64

lag 1

−0.968(0.057) 0.285(0.156) 0 −0.938(0.035) −0.953(0.056) 0.322(0.171) 0 −0.935(0.033) −0.950(0.052) 0.380(0.198) 0 −0.933(0.032) −0.945(0.048) 0.452(0.232) 0 −0.928(0.030)

Pattern of Granger Causalityc

log Ee

log M3

log Ee

log M3

log Ee

log M3

log Ee

log M3

log Ee

log M3

a Using

the GLS estimation procedure. errors in parentheses. c In the pattern x → y: x Granger causes y. b Standard

The patterned VAR selected by SC at all times shows Granger causality from M3 to Ee , Granger non-causality from Ee to M3, and no instantaneous causality (see Penm & Terrell, 1984a) between M3 and Ee . This outcome confirms that M3 is an independent source of financial and economic disturbance and influences movements of the euro exchange rate during the test period. A change in M3 causes changes in the value of the euro. These results are consistent with both theory and prior evidence. In testing the causal relationships between the movements of the euro exchange rate and the euro area GDP growth, the identification algorithms for ZNZ patterned VAR modelling are also utilised to select the optimal VAR models for both mean-corrected and detrended log (GDP) and log (Eq ). Following the proposed algorithms, the optimal ZNZ patterned VAR model is chosen by using SC. The optimal model selected is estimated using the GLS techniques and is shown in Table 2. The strategy suggested in Tiao and Tsay (1989) is applied to test the residual vector series, using the SC criterion. The results support the residual vector being a white noise process. The patterned VAR selected shows Granger causality from Eq to GDP growth, instantaneous causality between GDP growth and Eq , but Granger non-causality from GDP growth to Eq . These findings indicate that Eq affects GDP growth during

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Table 2. The Optimal ZNZ Patterned VAR Selected by SC.a,b z(t) = { log GDP log Eq } Maximum order assigned for search Order of the optimal VAR selected Coefficient estimator Type of coefficient matrices selected

12 1 LS ˆ B1 0 −0.193(0.090) 0 −0.829(0.082)

0.244 LS estimate of residual variance-covariance −0.621 −4 matrix (×10 ) Causal pattern detected in the three variable system selected by SCc GDP growth

GLS ˆ B1 0 −0.149(0.082) 0 −0.849(0.085) −0.621 15.493

Eq

a SC

is also applied to the residual vector. The results support the hypothesis that the residual vector is a white noise process. b The values in parentheses are standard errors of the non-zero coefficient estimates. c x → y denotes that x Granger causes y; x – y denotes that instantaneous causality exists between x and y.

the test period. A change in Eq causes changes in the euro area GDP growth. These results are consistent with both theory and prior evidence.

4.3. Detecting Granger Causality in the London Stock Market In this section, causality between the euro and the London stock market is examined. The identification approach of ZNZ patterned VAR modelling as proposed in Section 3.2 is utilised to conduct the selection of the optimal ZNZ patterned model. Since there is a huge number of candidate ZNZ patterned models, the search algorithm proposed in Penm et al. (1984a, 1999) is carried out. This search algorithm employs a block Choleski decomposition in conjunction with model selection criteria to identify the optimal patterned VAR without evaluating all possible candidate models. The optimal model is then used as a basis for detecting causal relations among the variables. To assess the euro’s impact on the London stock market, a maximum order of 36 is assigned to the vector system described in Section 4.1, and the search algorithm is undertaken to obtain the optimal ZNZ patterned VAR model, using SC. The optimal model selected is estimated using the GLS techniques and is shown in Table 3. The algorithm suggested in Tiao and Tsay (1989) is also applied to test

Maximum order assigned for search Order of the optimal VAR selected Coefficient estimator Type of coefficient matrices selected

36 1



LS ˆ1 B

GLS ˆ1 B

  −0.940(0.023) 0 0 −0.941(0.023) 0 0  0.060(0.027) −0.941(0.021)   0.063(0.025) −0.945(0.020)  0 0 −0.253(0.086) 0 −0.862(0.035) −0.061(0.023) 0 −0.815(0.039) 

1.265  −0.367 1.046

 −0.367 1.046 1.247 −1.295 −1.295 8.235

LS estimate of residual variance-covariance matrix (×10−4 ) Causal pattern detected in the three variable system selected by SCc

Using Zero-Non-Zero Patterned Vector Autoregressive Modelling

Table 3. The Optimal ZNZ Patterned VAR Selected by SC.a,b z(t) = { log ER log FTSE log UX}

a SC

is also applied to the residual vector. The results support the hypothesis that the residual vector is a white noise process. values in parentheses are standard errors of the non-zero coefficient estimates. c x → y denotes that x Granger causes y; x – y denotes that instantaneous causality exists between x and y. b The

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the residual vector series, using SC. The results support the residual vector being a white noise process. The detected causal pattern is also presented in Table 3. The estimated residual variance-covariance matrix produces some telling results. The non-diagonal Vˆ shown in Table 3 indicates the existence of instantaneous causality in the system. This outcome could result from the effect of time aggregation on instantaneous causality in weekly data. Hence, the causality within the system is complete and current shocks to any one of the variables will be processed through the system. The determined specification also indicates some interesting results. The lagged level of FTSE does not enter the UX equation, indicating that variations in the London stock market index provide little leading information about the movements of the U.K. pound relative to the U.S. dollar. The lagged level of the sterling exchange rate relative to the U.S. dollar does not enter the FTSE equation, indicating that variations in the sterling exchange rate provide little leading information for the movements of the FTSE index. Since instantaneous causality does exist between the London stock market index and the sterling exchange rate, a well-established efficient market exists between the London stock market and the U.S. dollar market. The flows of international funds enjoy free entry and exit between the U.S. and London markets. Further, the lagged level of the ER does enter both the FTSE and the UX equations, indicating that variations in the euro to sterling exchange rates provide leading information for the London stock market and relevant forex markets. This gives evidence that the emerging currency – the euro – provides significant impacts on the economic activities of the neighbouring countries of the euro area.

5. SUMMARY This paper examines two issues in the context of ZNZ patterned VAR modelling. The first issue concerns the causal relationships between movements of the euro exchange rate and economic activity indicators, such as money supply and growth in GDP, while the second examines the relationship between the London stock market and forex markets. First, the results show that money supply shocks contribute to movements of the euro exchange rate, but no causal relationship is detected from the euro to money supply. These findings are consistent with the standard theory which proposes that an expansion/contraction in monetary policy is associated with a decrease/increase in domestic interest rates for a given expected inflation rate, thus leading to a depreciation/appreciation of the domestic currency. The results also show that

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exchange rate shocks affect movements of the euro area GDP growth. This supports the theory that a successful euro leads to strong economic growth. Second, the findings indicate that movements in the euro are related to movements in the London market. Both a current shock and a lagged shock to the euro’s forex market impacts on the movements of both local London stock market and forex markets. However only a current shock, not a lagged shock, to either the local London stock market or forex markets yield a response from other components of the system. These findings confirm that the London stock market is responsive to external shocks. Third, the outcome suggests there might be a need to form a currency union in Asia in order to achieve such aims as diminishing forex risks, improving economic growth, and increasing employment opportunities. A single Asian currency would expand economic activities, and then accelerate the process of further financial integration in Asia. Since financial integration increases competition and allocation efficiency in the financial sector, it thereby will increase the amount of market-induced capital flows into the region. Recent studies have shown that the action of globalising stock markets significantly increases stock prices without a concurrent increase in stock return volatility (Kim & Singal, 2000). To successfully compete for capital in a global economic environment, capital markets should become more open and transparent, rather than have controls imposed on capital flows. A single currency in the Asian region would improve cost-competitiveness, and could contribute to stock market integration in the region. The cost of capital would be lowered by reducing uncertainty about exchange rates, and by reducing the cost of obtaining funds. Hence investment opportunities, employment growth, and potential prosperity should speed up in this region (Moshirian, 2001).

NOTES 1. For the estimation of model coefficients, the pre-windowed case utilises all available observations, and assumes that the unavailable observations prior to the sample period have zero values (see Penm et al., 1995). 2. Several EU countries have chosen not to participate in the new currency, namely Great Britain (U.K.), Sweden and Denmark. 3. The Governing Council adopts a price stability-oriented monetary policy strategy for the Eurosystem. That is, the rate of monetary expansion is set to achieve the objective of price stability. 4. The euro was at a tentative stage prior to 1 January 1999. The currency was then an artificial construct comprising a basket – the European currency unit – used by the member states of the EU as their internal accounting unit for the currency area called the European Monetary System (EMS). Thus, the data pre-1999 are indicative figures.

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5. Tiao and Tsay (1989) propose an algorithm using the crit(m, j) criterion to select the vector autoregressive moving average process with zero entries. After the final model is selected, their algorithm is then applied to the residual series to test whether this series is a vector white noise process.

REFERENCES Bank for International Settlements (2000). 70th Annual Report, March. Bank of England: Monetary & Financial Statistics (2003). January. Beenstock, M. (1995). An econometric model of the oil importing developing countries. Economic Modelling, 12, 3–14. Bhattacharya, U., Daouk, H., Jorgenson, B., & Kehr, C. (2000). When an event is not an event: The curious case of an emerging market. Journal of Financial Economics, 55, 69–101. Bonser-Neal, C., Roley, V. V., & Sellon, G. H. (1998). Monetary policy actions, intervention, and exchange rates: A re-examination of the empirical relationships using Federal funds rate target data. Journal of Business, 71(2), 147–177. Crompton, P. (2000). Future trends in Japanese steel consumption. Resources Policy, 26(2), 103–114. Cushman, D. O., & Zha, T. (1997). Identifying monetary policy in a small open economy under flexible exchange rates. Journal of Monetary Economics, 39, 433–448. Eichenbaum, M., & Evans, C. L. (1995). Some empirical evidence on the effects of shocks to monetary policy on exchange rates. Quarterly Journal of Economics, 110, 975–1009. European Central Bank (2001). Monthly Bulletin, February. European Central Bank (2002). Monthly Bulletin, December. Forsythe, G. E. (1957). Generation and use of orthogonal polynomials for fitting data with a digital computer. SIAM Journal on Applied Mathematics, 5, 74–88. Froot, K. A., O’Connell, P., & Seasholes, M. (2001). The portfolio flows of international investors. Journal of Financial Economics, 59, 151–193. Geweke, J. (1982). Measurement of linear dependence and feedback between multiple time series. Journal of the American Statistical Association, 77, 304–313. Granger, C. W. J. (1969). Investigating causal relations by econometric models and cross-spectral methods. Econometrica, 37, 424–438. Hsiao, C. (1982). Autoregressive modelling and causal ordering of economic variables. Journal of Economics Dynamics and Control, 4, 243–259. Kay, S. M., & Marple, S. L. (1981). Spectrum analysis – a modern perspective. Proceedings of the IEEE (November), 1380–1419. Kim, E., & Singal, V. (2000). The fear of globalizing capital markets. Emerging Markets Review, 1(3), 11, 183–198. Kim, S. J. (1998). Do Australian and the U.S. macroeconomic news announcements affect the USD/AUD exchange rate? Some evidence from E-GARCH estimations. Journal of Multinational Financial Management, 8(2–3), 233–248. Lewis, K. K. (1993). Are foreign exchange intervention and monetary policy related and does it really matter? No. 4377, NBER Working Paper. Moshirian, F. (2001). Financial systems in the new millennium. Journal of Multinational Financial Management, 11, 315–320. Penm, J. H. W., Penm, J. H. C., & Terrell, R. D. (1995). On the sequential fitting of subset autoregressions using the prewindowed case. IEEE Trans. on Signal Processing, ASSP-43, 322–326.

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Penm, J. H., Penm, J. H. W., & Terrell, R. D. (1997). The selection of zero-non-zero patterned cointegrating vectors in error-correcting modelling. Econometric Reviews, 16, 281–304. Penm, J. H. W., Penm, J. H. C., & Terrell, R. D. (1999). Economic forecasting – Subset time series models with zero coefﬁcients. ISBN 0–7315–3312–7. Penm, J. H. W., & Terrell, R. D. (1984a). Multivariate subset autoregressive modelling with zero constraints for detecting causality. Journal of Econometrics, 3, 311–330. Sims, C. A. (1972). Money, income and causality. American Economic Review, 62, 540–552. Sims, C. A. (1977). Comment. Journal of the American Statistical Association, 72, 23–24. Thorbecke, W. (1997). On stock market returns and monetary policy. Journal of Finance, 52, 635–654. Tiao, G. C., & Tsay, R. S. (1989). Model specification in multivariate time-series. Journal of Royal Statistical Society B, 51, 157–213. Whitelaw, R. F. (1994). Time variations and co-variations in the expectation and volatility of stock market returns. Journal of Finance, 49, 515–541. Zellner, A. (1962). An efficient method of estimating seemingly unrelated regressions and tests for aggregation bias. Journal of the American Statistical Association, 57, 348–368.

FRAGILE FIXED EXCHANGE RATES WITH BANKING SAFETY NET GUARANTEES Stephen A. Kane and Mark L. Muzere ABSTRACT Our paper presents an extension of the Diamond-Dybvig (1983) model of bank runs to an open market economy. We examine domestic banks that are subject to potential runs by domestic depositors who worry that they will not be able to be repaid in full, because the domestic banks may not be able to reﬁnance in the international ﬁnancial markets. A loss in conﬁdence in the banking system might precipitate a bank run. A bank run might be costly to safety net guarantors, for example, the central bank. Further, a bank run might lead to a breaking of the ﬁxed exchange rate. Our model shows that adding central bank and International Monetary Fund guarantees, increasing long term debt as well as more equity ﬁnancing reduces ﬁnancial fragility, but consistent with economic intuition, these policy levers cannot eliminate the possibility of a bank run or a banking crisis leading to a currency crisis.

1. INTRODUCTION We model a country’s policy of an exchange rate peg together with government safety net guarantees to the domestic banks. We show that adding central bank and International Monetary Fund (IMF) guarantees, long term debt as well as Research in Finance Research in Finance, Volume 20, 119–138 Copyright © 2003 by Elsevier Ltd. All rights of reproduction in any form reserved ISSN: 0196-3821/doi:10.1016/S0196-3821(03)20007-1

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equity financing reduces financial fragility. Due to a large amount of uncertainty in developing economies, foreign creditors often prefer short term debt contracts. This is because foreign creditors make less of a commitment and may not roll over their loans to mitigate losses if investments turn sour. Borrowers may be willing to accept short term debt contracts because they may reduce uncertainty premiums associated with long term debt and equity financing. Unfortunately, a developing country makes a long term commitment to these investments. Policy makers cannot reduce uncertainty premiums much without facilitating corporate governance reforms.1 We link a banking crisis with a currency crisis. Domestic investors who fear a loss of purchasing power or weak government guarantees to domestic banks might withdraw their funds from the domestic banks and deposit the funds into foreign currency denominated accounts at the local branches of foreign banks. With a fixed exchange rate, a run by depositors on the domestic banks may be equivalent to a run on the domestic currency. Since a central bank has limited foreign currency reserves, it may be difficult to remove the possibility of a banking crisis leading to a collapse of the fixed exchange rate. Central bank financial support may have the beneficial effect of increasing confidence in the domestic banking system by reducing the incentive for depositors to withdraw their funds. Our model may be applied to the Asian crisis. We build and extend the intuition of Obstfeld and Rogoff (1995), Rogoff (1999) and Kane (2000). Our modeling also employs insights from Goldfajn and Valdes (1997) and Chang and Valesco (2000a) by linking a banking crisis with a currency crisis in an open market economy. Similar to Chang and Valesco (2000b) and Chui, Gai and Haldane (2002), our model is an adaptation of the Diamond and Dybvig (1983) model. Chang and Valesco (2000b) acknowledge that the introduction of a “sun spot” probability is a controversial issue. Because the “sun spot” probability is not based on economic variables, we choose to preserve the multiple equilibriums in the original Diamond and Dybvig model – even though a single equilibrium facilitates comparative static analysis. We advance on the existing models by including a role for foreign creditors both in forecasting and in provoking a financial crisis. We discuss the need for corporate governance reforms that will facilitate more long term debt and equity financing. Our modeling demonstrates that more long term debt and equity financing will reduce but not eliminate financial fragility. Related work also includes Krugman (1998) and Corsetti, Pesenti and Roubini (1998), who attribute the Asian crisis to structural and policy distortions in East Asian economies, Radelet and Sachs (1998) and Krugman (1999), who attribute the Asian crisis to shifts in market expectations and confidence. We have organized the paper as follows. Section 2 describes the basic model. Section 3 describes a banking crisis, and extends the basic model to include

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long term debt and equity financing of domestic projects. Section 4 describes a currency crisis. Section 5 describes an application of our model to the 1997–1998 Asian financial crisis. Section 6 concludes the paper.

2. THE ECONOMY We extend the Diamond-Dybvig (1983) model of bank runs to an open market economy. There are two assets, a risky productive process located in a developing country and a risk free asset that facilitates lending and borrowing in the international financial markets. We assume that capital flows freely in the international financial markets. Assumption 1 below formalizes the cost of premature liquidation of the productive process, because the productive process needs time to generate cash flows. The cost of premature liquidation of the productive process makes a bank’s loans less liquid. Assumption 1. For each unit of investors’ wealth invested in the productive process, the premature liquidation value is substantially less than one. The domestic banking system consists of banks and a central bank. The domestic banks offer identical deposit returns, so we may assume that there is only one domestic bank that intermediates the productive process. Output from the productive process is tradable in the international goods market. Since the underlying foreign asset is financial in nature, we assume that transportation costs are negligible. We let e denote the domestic currency price of one unit of foreign currency, for example, the United States dollar. We let the price of the domestic good be p units of the domestic currency and the price of the foreign good be p∗ units of the foreign currency. There is one consumption good which may be imported. To introduce currency or exchange rate risk into the model, we assume that the price of the consumption good is expressed in units of the foreign currency. For simplicity, we normalize the price of the foreign good to 1, p ∗ = 1. We assume a continuum of domestic investors, who are uniformly distributed. Each investor has an increasing, concave and twice continuously differentiable expected utility function. The utility function satisfies the Inada conditions. That is, the utility function, which we denote by u(c), satisfies u (0) = +∞ as c → 0+ and E[u (c)] = 0 as c → + ∞. For ease of modeling, we assume that the domestic bank is mutually owned by the domestic investors. The domestic bank offers depositors demand deposit contracts that satisfy the sequential service constraint.2 The domestic bank

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performs maturity transformation, using short term deposits to finance long term projects. The domestic bank also performs currency transformation, that is, it borrows in foreign currency and lends in domestic currency. By accepting these credit terms, the domestic bank adds more exchange rate risk to its portfolio. Assumption 2 below ensures that investors do not undermine a bank in its role of providing liquidity (Jacklin, 1987). Assumption 2. There are no side trades in demand deposit contracts. Foreign investors, for instance, Japanese and Western commercial banks, lend their funds to domestic banks and to domestic firms through their subsidiaries in that country. We assume that foreign creditors are risk neutral. We model time as discrete, using dates 0, 1, and 2. We conceive the first period to be the time period between date 0 and date 1, and the second period to be the time period between date 1 and date 2. At date 0, all domestic investors are homogeneous. At date 1, investors privately decide whether or not to discontinue their investment. Early consumers consume at date 1 while late consumers consume at date 2 after the productive process has reached full fruition. We assume that the fraction of early consumer is ␪, where ␪ ␧ (0, 1). The number ␪ is publicly known at time 0. Based on ␪, each domestic investor has an independent and identically distributed chance of being an early consumer. Domestic investors are endowed with the amount of domestic currency w in the aggregate. We make further simplifying assumptions. Each unit of foreign currency invested in the risk free asset yields a constant gross return of r∗ at the end of each period. Returns on each unit of domestic currency invested in the productive process are given by rm = v at t = 1 rm = x at t = 2

if liquidated if not liquidated at t = 1

where v is a constant liquidation value and x is a random variable whose distribution is publicly known. For simplicity, we assume that x has the following Bernoulli distribution: x = vL with probability q, and x = vH with probability 1 − q, where r ∗ v < vL < 1 < vH and q ␧ (0, 1). The condition r ∗ v < vL is imposed to ensure that it is cheaper to borrow from the international financial markets than to liquidate the productive process. The expected value of the random variable x satisfies qvL + (1 − q)vH > er ∗2 or else the risk free asset will dominate the productive process. Returns on each unit of domestic currency deposited in the domestic bank are given by rb = r1

at t = 1

if a depositor chooses to cash out then

rb

at t = 2

otherwise

= r2

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where r1 is a fixed return and r2 is a random variable corresponding to a fractional share of assets remaining in the domestic bank, assuming no bank run occurs. This is a promise the domestic bank makes, but in the case that the bank is illiquid or insolvent the bank may not be able to honor the promise. We introduce the equilibrium concept for the implicit game played by agents in our economy. We use the equilibrium concept in Schmeidler (1973), which is also used in Chang and Valesco (2000a), because there is a continuum of domestic investors. We obtain an equilibrium when, given the decision of the other agents, no agent may improve the agent’s expected utility by making a different decision. A bank run is an event when depositors rush to a bank to withdraw their deposits due to the chance that the bank will be illiquid or will fail. A bank run is an equilibrium, since the sequential service constraint induces a negative externality when everyone runs at the same time, because late depositors will receive nothing. We model the reaction function (decision) of the central bank. The central bank could provide liquidity to the domestic banking system by printing additional currency, but the foreign creditors would induce a run on the domestic currency by converting their domestic currency holdings into their own currencies. The central bank could support the currency peg through intervention in the financial markets, but this would not be sustainable due to the country’s limited foreign currency reserves. We assume that the central bank provides financial support to the domestic banking system by using its foreign currency reserves and financial support (credit line) from the International Monetary Fund (IMF). Based on information available at date 0, bank managers believe that the probabilities of a devaluation of the domestic currency or the event of a bank run at date 1 are negligible. If the central bank bails out the foreign creditors, then domestic banks have an incentive not to fully hedge the foreign exchange risk. Information asymmetry between foreign creditors and domestic investors leads to the usual moral hazard problems. To mitigate the moral hazard problems, foreign creditors demand collateral. Often this collateral will be backed by government guarantees that are not ironclad. Governments have failed to live up to their obligations from time to time. For instance, governments can default, use sovereign immunity, or change laws to their benefit. Even so, it is increasingly difficult for governments to use the above mechanisms because they want to be part of the international community and may properly fear that they might be excluded from treaties and other agreements if they do not play fairly. Nevertheless, the lack of ironclad government guarantees and the domestic investors’ aggregate wealth will constrain foreign currency borrowing.3 The collateral in Assumption 3 below seems to be enforceable because of the threat to deny borrowers access to international financial markets.

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Assumption 3. The domestic bank is subject to an exogenous foreign currency borrowing limit given by e(b 02 + b 12 ) ≤ mw, where b01 is the amount of date 0 short term foreign currency borrowing, b02 is the amount of date 0 long term foreign currency borrowing, b12 is the amount of date 1 short term foreign currency borrowing that includes all the rolled over funds b01 , w is the domestic investors’ aggregate wealth, which acts as collateral, and m ≤ 1 is a fraction of aggregate domestic wealth. In this section we only consider short term borrowing, so we set long term borrowing to zero, b 02 = 0. Short term lending enables foreign creditors make less of a commitment. Foreign creditors will reduce their funding to mitigate losses when investments turn sour. Borrowers are willing to accept short term debt contracts because they reduce uncertainty premiums associated with long term debt and equity financing. The domestic bank borrows foreign currency at date 1 to finance the demand for liquidity and to service its foreign debt that has become due.

2.1. Social Welfare Optimization We analyze a fixed exchange rate regime, which could collapse due to various factors. However, based on information available at date 0, participants view this probability as negligible. Social welfare is optimized by solving the following problem. Problem 1. Aggregate society chooses date 0 foreign currency borrowing b01 , date 1 foreign currency borrowing b12 and per capita consumption c1 to maximize expected utility ␪u(c 1 ) + (1 + ␳)−1 (1 − ␪)[qu(c 2 (␪, e, vL )) + (1 − q)u(c 2 (␪, e, vH ))]

(1)

subject to ␪c 1 + r ∗ b 01 ≤ b 12

(2)

eb 12 ≤ mw

(3)

(1 − ␪)c 2 (␪, e, x) = (w + eb 01 )x/e − r ∗ b 12

(4)

b 12 , c 1 ≥ 0.

(5)

The utility function (1) reflects the currency peg. Constraint (2) says that the domestic bank will use foreign currency borrowing to finance the aggregate consumption of early consumers and rolled over short term debt. This is because premature liquidation of the productive process is prohibitively costly relative to

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debt. There are insufficient resources for the bank to borrow locally, so the bank borrows from abroad. Constraint (3) is an exogenous limit imposed on foreign currency borrowing. The domestic investors’ aggregate wealth is collateral. Constraint (4) is the resource constraint, which says that late consumers consume all proceeds from their investment. It is also assumed that foreign creditors will roll over their short term loans at date 1. Constraint (5) describes non-negative conditions. Lemma 1. The social optimum is given by date 0 foreign currency borrowing r ∗ b 01 = (mw)/e − ␪c 1 , date 1 foreign currency borrowing b 12 = (mw)/e and per capita consumption c1 , where c1 is a solution to the equation (1 + ␳)u (c 1 ) = qu (c 2 (␪, e, vL ))vL + (1 − q)u (c 2 (␪, e, vH ))vH .

(6)

We derive Lemma 1 by interchanging the partial derivative operators with respect to the three choice variables (b01 , b12 , c1 ) with the expectation operator and solving the first order conditions. Lemma 1 tells us that the bank borrows the maximum amount of foreign currency funds, borrowing just enough at date 1 to finance the early consumers’ aggregate consumption. The domestic bank may achieve the social optimum by offering domestic investors demand deposit contracts. Domestic investors deposit their entire endowment in the domestic bank. The domestic bank then invests the funds on behalf of the domestic depositors. The domestic bank solves the following problem. Problem 2. Writing a = w + eb 01 , the domestic bank chooses date 0 foreign currency borrowing b01 , date 1 foreign currency borrowing b12 and deposit return r1 to maximize expected utility ␪u(ar 1 /e − r ∗ b 01 ) + (1 + ␳)−1 (1 − ␪)[qu(ar 2 (␪, e, vL )/e) +(1 − q)u(ar 2 (␪, e, vH )/e)]

(7)

subject to ␪r 1 + r ∗ b 01 ≤ b 12

(8)

eb 12 ≤ mw

(9) ∗

u(ar 1 /e − r b 01 ) ≤ (1 + ␳)

−1

[qu(ar 2 (␪, e, vL )/e)

+ (1 − q)u(ar 2 (␪, e, vH )/e)] ∗

(1 − ␪)ar 2 (␪, e, x) = ax − e(r b 12 ).

(10) (11)

In the expected utility (7), domestic currency returns are converted into foreign curiency which are then exchanged for units of the consumption good. Constraint

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(8) says that the domestic bank undertakes enough short term borrowing at date 1 to finance early consumers’ returns and rolled over short term debt obligation. Constraint (9) is the foreign currency borrowing constraint described in Assumption 3. Constraint (10) is the incentive compatibility condition, which implies that late consumers are better off delaying their consumption until date 2. Constraint (11) is a restatement of the resource constraint. Foreign investors care about returns from their investments. They do not hedge their investment risk because they are assumed to be risk neutral. In the absence of a bank run, the domestic bank can achieve the social optimum in the following manner. Lemma 2. At date 0, the domestic bank borrows the amount of foreign currency b01 , where r ∗ b 01 = (mw)/e − ␪r 1 . At date 1, the domestic bank borrows the amount of foreign currency b 12 = (mw)/e, and chooses deposit return r1 , which is determined from the equation c 1 = (w + eb 01 )r 1 /e − r ∗ b 01 where the per capita consumption c1 is a solution to Eq. (7) in Lemma 1. Solving Problem 2 is similar to solving Problem 1 because the first-order conditions have the same form, but with some different variables.

3. BANKING CRISIS A combination of cut back of foreign credit and depositors running on the domestic banks might induce the domestic banks to liquidate some of their assets in order to satisfy demand deposit requests. This may precipitate a financial crisis. Sophisticated depositors may realize that acknowledged non-performing loans augmented with unacknowledged bad loans (for instance, loans used to finance recently constructed real estate that is less than fully utilized, but has not yet been recognized as a problem) would strain the domestic banking system and place pressure on the government safety net guarantees.4 Sophisticated depositors fear that in a banking crisis the government may not make the safety net guarantees. Further, sophisticated depositors may seek to protect the purchasing power of their domestic currency denominated investments should the domestic currency be devalued. Consequently, sophisticated depositors may engage in a run by removing their bank deposits from domestic banks and moving their funds to local branches of foreign banks (Kane, 2000). The depositors place their funds in foreign currency denominated accounts.5 There are feedback effects between the actions of domestic investors and the actions of foreign creditors. If foreign creditors refuse to roll over their short term loans, or if they refuse to provide new loans, domestic investors may respond by

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withdrawing their bank deposits and placing them in subsidiaries of foreign banks. The advent of a run on domestic banks or foreign creditors reducing their lending may create a liquidity crisis for the domestic banks, which may have to sell their assets to meet the demand for liquidity. We determine a critical fraction of domestic investors that the domestic banking system can support without defaulting on foreign currency loans. That is, the domestic bank pays off the foreign currency loans and distributes the remaining proceeds to late consumers. This critical fraction influences the central bank’s behavior. For example, when the fraction of domestic depositors withdrawing their funds early reaches the critical fraction the central bank might decide to stop supporting the currency peg.

3.1. Central Bank Intervention We treat the central bank as a lender of last resort, which is buttressed by the International Monetary Fund. We assume that there are no political constraints and no conditions imposed by the IMF. The IMF financial support comes in the form of a credit line that augments the central bank’s foreign currency reserves.6 We let = r ∗ 2 b 02 + r ∗ b 12 denote the amount of foreign currency from the central bank that will be used to support the domestic banks.7 Here, the maximum amount of financial support from the central bank is sufficient to fully bail out all the foreign creditors. If depositors run on the domestic banks, we assume that foreign creditors are accorded seniority. Thus, with this amount of guarantee, it is optimal for the domestic banks to not hedge foreign currency risk and international interest rate risk. We analyze the scenario where foreign creditors do not roll over their loans, and do not provide new funds to domestic investors. This scenario might be caused by depositors moving large amounts of their bank deposits to local subsidiaries of foreign banks. The domestic investors want to protect the purchasing power of their domestic currency denominated investments. We introduce additional uncertainty by letting f 1 ≥ ␪ denote the fraction of domestic depositors who withdraw their bank deposits at date 1. We shall examine situations where some sophisticated domestic depositors choose to move their deposits from the domestic bank to subsidiaries of foreign banks. For example, these domestic investors may seek to protect the purchasing power of their domestic currency denominated investments. The sophisticated domestic investors may also fear weak government guarantees. Thus, the fraction of domestic depositors who withdraw their funds early is greater than or equal to the fraction of early consumers. Since bank deposit withdrawals are uncertain, we model the fraction f1 as stochastic.

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The domestic bank finances the demand for liquidity by liquidating its assets. Thus, the resource constraint takes on the form (1 − f 1 )(w + eb 01 )r 2 ( f 1 , , e, x) = (w + eb 01 )x − ((w + eb 01 )f 1 r 1 − e( − r ∗ b 01 ))x/v − er ∗ . By setting date 2 returns to zero, r 2 ( f 1 , , e, x) = 0, we obtain f 1∗ ( , e, x) = v/r 1 + e (x − r ∗ v)/((w + eb 01 )r 1 x) − er ∗ b 01 /((w + eb 01 )r 1 ). (12) Thus, we rewrite the resource constraint in the form (1 − f 1 )r 2 ( f 1 , , e, x) = ( f 1∗ − f 1 )r 1 x/v. Since we are concerned with the effect of the central bank financial support to the domestic banking system, we may assume that changes to f 1∗ are caused by changes to only . Notice that the deposit return r1 has been determined in Lemma 2. So r1 is constant with respect to f1 . Thus, taking partial derivatives with respect to f 1∗ , we get [(1 − f 1 )∂r 2 /∂f 1 − (r 2 − r 1 )]∂f 1 /∂f 1∗ = r 1 .

(13)

Since date 2 returns decrease as f1 increases, because there are fewer funds to invest in the productive process, the partial derivative ∂r2 /∂f1 is negative. In the absence of bank run, date 2 returns are generally greater than the deposit return r1 . Thus, the partial derivative ∂f1 /∂f 1∗ is negative. This implies that the incentive to withdraw bank deposits early drops when investors think that the chance of getting their funds during a run on the bank is high. This is consistent with economic intuition about the effect of financial support in building confidence among investors. Define the critical fraction f m ( , e) = maximum f 1∗ ( , e, x) where x ␧{vL , vH }. We notice that f m (0, e) < f m ( , e), which implies that a credit line from the central bank augmented with IMF financial support reduces financial fragility. Further, if the fraction of domestic investors who withdraw their bank deposits early satisfied f 1 > f m ( , e), the domestic bank would be illiquid. This would imply that the fraction (1 − f m ( , e)/f 1 ) of the domestic investors would not get anything during a run on the bank. Thus, it would be optimal for late consumers to run on the domestic bank. Lemma 3. Let f1 denote a fraction of domestic investors who withdraw their bank deposits at date 1. Then we have two pure strategy equilibrium outcomes

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f 1 = ␪ and f 1 = 1. There is also a mixed strategy equilibrium outcome f 1 = h ∗ ␧ (␪, fm ), but we do not see any policy implications for this equilibrium. We give a formal proof in the Appendix. The central bank will bail out the foreign creditors to honor its guarantees. For definiteness with intermediate values of f1 , ␪ < f 1 < f m ( , e), we suppose that the central bank will try to quell the run. It will drop the exchange rate peg if it has insufficient resources to quell the bank run.8

3.2. Long Term Debt We extend our model to include long term foreign debt b02 , that is, date 0 to date 2 foreign currency borrowing. If date 1 withdrawals of bank deposits satisfy (w + e(b 01 + b 02 ))f 1 r 1 > e(b 12 + ), the resource constraint takes on the form (1 − f 1 )(w + e(b 01 + b 02 ))r 2 ( f 1 , , e, x) = (w + e(b 01 + b 02 ))x − ((w + e(b 01 + b 02 ))f 1 r 1 − e(b 12 + ))x/v − er ∗ (b 12 + + r ∗ b 02 ). By setting date 2 returns to zero, r 2 ( f 1 , , e, x) = 0, we obtain f 2∗ ( , e, x) = v/r 1 + e[(b 12 + )(x − r ∗ v)]/((w + e(b 01 + b 02 ))r 1 x) − er ∗2 b 02 v/((w + e(b 01 + b 02 ))r 1 x).

(14)

Define the critical fraction h m ( , e) = maximum f 2∗ ( , e, x) where x ␧{vL , vH }. From Eqs (12) and (14) we get f 1∗ ( , e, x) < f 2∗ ( , e, x) for every x. Thus, we get f m ( , e) < h m ( , e). In particular, f m (0, e) < h m (0, e). Echoing the results of Diamond and Dybvig (1983), long term debt in the capital structure of the country’s banks leads to less financial fragility compared to short term debt. This result is especially relevant if there is little central bank financial support to the banking system. Furthermore, the actions of foreign creditors are less destabilizing if the capital structure of the country’s banks contains long term debt.

3.3. Equity We extend our model to include foreign equity financing of domestic projects. For simplicity, there is one domestic firm that controls a productive process. Domestic investors and foreign minority equity investors share ownership rights to the domestic firm. Domestic investors may use foreign currency borrowing to

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finance their equity position in the productive process. As in the basic model, the domestic investors have mutual ownership of the domestic bank that intermediates the investment on their behalf. We model a secondary market for the firm’s equity. This market facilitates portfolio rebalancing at date 1 by the investors. Unfortunately, this secondary market may not be a source of new funds for the firm during a financial crisis. Due to corporate governance difficulties, the firm may be closely held and may have opaque accounting. This may discourage potential minority investors who may not be able to properly assess the firm’s prospects and who may have adverse selection concerns. At date 1, we suppose that equity trades at a substantial discount and this makes issuing additional equity unattractive to the firm. We also suppose that if foreign equity investors liquidate their positions, then they do so on net to domestic investors. When meeting withdrawal demands of depositors, the bank may suffer from a liquidity crisis at date 1. The bank may be unable to liquidate enough of its equity position at a reasonable price by selling some of its equity to foreign investors. Consequently, the bank may prefer to exercise its majority control of the firm to force asset liquidations to the determinant of foreign minority shareholders and society. Equity and long term debt may differ in their ownership, price and payout, but both are similar from a liquidity perspective since they are committed to the productive process from date 0 until date 2. We assume that the amount of capital invested in the productive process is fixed, so foreign minority equity will displace domestic borrowing and thus will lower leverage.9 Let y be the amount of date 0 foreign minority equity invested in the project, which is a choice variable of foreign investors and is thus exogenous to the choice problem of the domestic investors. The utility maximization problem of the domestic investors and the domestic bank’s problem are similar to those considered in the basic model. If date 1 withdrawals of bank deposits satisfy (w + e(b 01 + b 02 − y))f 1 r 1 > e(b 12 + ), then the resource constraint is of the form (1 − f 1 )(w + e(b 01 + b 02 − y))r 2 ( f 1 , , e, x, y) = (w + e(b 01 + b 02 − y))x − ((w + e(b 01 + b 02 − y))f 1 r 1 − e(b 12 + ))x/v −er ∗ (b 12 + + r ∗ (b 02 − y)). By setting date 2 returns to zero, r 2 ( f 1 , , e, x, y) = 0, we obtain f 3∗ ( , e, x, y) = v/r 1 + e[(b 12 + )(x − r ∗ v)]/((w + e(b 01 + b 02 − y))r 1 x) − r ∗2 (b 02 − y)/((w + e(b 01 + b 02 − y))r 1 x).

(15)

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Fig. 1 Effect of Foreign Equity on Per Capita Consumption of Early Consumers. Note: The parameters are ␪ = 0.20, q = 0.25, vL = 0.25, vH = 1.75, r ∗ = 1.12, m = 0.25, e = 1.025 and ␳ = 0.03. Figure 1 plots the per capita consumption of early consumers vs. foreign equity. Foreign equity enhances per capita consumption of early consumers. Similarly, since foreign equity displaces foreign borrowing, this plot demonstrates that increasing foreign borrowing will decrease per capita consumption of early consumers.

From Eqs (14) and (15) we see that increasing equity financing reduces financial fragility. If foreign equity in the productive process were zero, that is, y = 0, we would have the relation f 3∗ ( , e, x, 0) = f 2∗ ( , e, x). We provide a simulation of date 1 per capita consumption vs. leverage in Figs 1 and 2. The simulation shows that leverage may improve per capita consumption until an optimal level. Beyond the optimal level, per capita consumption falls as leverage increases. We argue that many domestic firms in developing countries are beyond the optimal level of debt. Equity financing is unduly costly due to a lack of protection of minority shareholders. This leads to a high ownership concentration among managers and majority shareholders (Coffee, 1999). Concentrated ownership raises the cost of equity financing since investors do

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Fig. 2 Effect of the Fraction of Early Consumers on Per Capita Consumption. Note: The parameters are q = 0.25, vL = 0.25, vH = 1.75, r ∗ = 1.12, m = 0.25, e = 1.025, y = 0.35 and ␳ = 0.03. Figure 2 plots per capita consumption of early consumers vs. the fraction of early consumers. The bank borrows the largest amount of foreign currency to finance domestic investment and consumption of early consumers. If too many depositors are early consumers, then this lowers their per capita consumption, due to liquidity constraints and the depletion of economic resources that deprives society of some investment returns at time 2.

not fully benefit from diversification.10 Consistent with the intuition of Rogoff (1999), our simulation shows that increased equity financing of domestic firms will mitigate some financial fragility.

4. CURRENCY CRISIS We link a banking crisis with a currency crisis by introducing a fixed exchange rate policy coupled with government safety net guarantees for the domestic banking system and firms. An important implication of Lemma 3 is the following: when a bank run occurs, the central bank may not have the resources to defend the fixed exchange rate.

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Kaminsky and Reinhart (1999) consider 26 banking crises and 76 currency crises, and document the following stylized facts.11 First, banking crises are highly correlated with currency crises. More than 25% of banking crises occur within one year of currency crises and 33% of banking crises occur within three years of currency crises. Second, capital inflows increase before a crisis and fall sharply during the crisis. The ratio of domestic credit to nominal GDP increases steadily and markedly as a crisis approaches. Third, banking activities increase sharply some time before a currency crisis. These activities may be induced by previous financial liberalization policies. Major financial deregulation preceded 71% of currency crises and 67% of banking crises.

5. THE ASIAN FINANCIAL CRISIS Our model may be applied to the 1997–1998 Asian crisis. In 1997, leading economic indicators gave a mixed signal about the economic prospects in East Asia. On the one hand, economic fundamentals were favorable. There were low inflation rates, balanced budgets, and high domestic savings. On the other hand, East Asian banks had a large percentage of non-performing bank loans. Mishkin (1999) documents that recognized non-performing loans were more than 10% of total bank loans in Thailand, Indonesia, and South Korea before the Asian crisis. Further, many newly constructed buildings were substantially less than fully utilized. The existence of many “see-through floors” did not bode well for the bank loans that were used to finance the construction, since these loans were likely to become non-performing as well. The state of the banking system made currencies in East Asia vulnerable to speculative attacks. Speculators could reasonably suspect that policy makers would be unlikely to defend their currencies. A currency defense would likely deplete a country’s foreign exchange reserves. Further, put options make it easier for speculators to take an indirect short position in a currency and thus place additional pressure against a currency peg. Alternatively, raising interest rates would likely induce a domestic inflation that would likely flood their banking systems, since bank deposits rates would rise above bank loan rates and induce even more uncertainty (Mishkin, 1999). Our model justifies the empirical results of Radelet and Sachs (1998), who attribute the Asian crisis to investor panics, and Kaminsky and Reinhart (1999), who document a strong correlation between banking crises and currency crises. Caprio and Honohan (1999), who document costly resolution of banking crises, and Hoggarth, Reis and Saporata (2002), who document the cost of banking system fragility, demonstrate the need to mitigate banking fragility. Chang and Valesco (2000b) and Bris and Koskinen (2002) also model leverage as a factor in currency crisis. Bris and Koskinen (2002) examine the Asian crisis

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ex post and argue that currency depreciation may be necessary to induce foreign investors to take an equity stake due to the debt overhang problem. Our model also demonstrates ex ante that more equity and long term debt investment will reduce but not eliminate financial fragility.

6. CONCLUSION Our modeling shows that a government policy of an exchange rate peg coupled with banking safety net guarantees is fragile. A domestic bank run or a cutback in foreign credit may compel the government to abandon its currency peg. This links a banking crisis with a currency crisis. Our model demonstrates that long term debt and more equity financing in the capital structure of banks and firms in developing countries will reduce but not eliminate financial fragility.

NOTES 1. Better corporate governance will allow firms to move away from bank loans and towards more long term debt and equity financing. Foreign creditors may be more willing to make long term commitments if they have better recourse to collateral in bankruptcy proceedings. Equity investors need more transparent accounting systems. Better accounting systems could facilitate performance measurement compensation schemes to better align the incentives of managers with those of shareholders. Shareholders value voting rights and minority shareholders need mechanisms (for instance, the threat of class action lawsuits) to protect them from managers or large blocks of shareholders who may expropriate their wealth. 2. Depositors who seek to withdraw their funds will be served on a first come, first served basis until funds have been exhausted (Bagehot, 1999). 3. Alternatively, we may use a fraction of a country’s exports as collateral. 4. We may regard a financial guarantee as a derivative contract. In banking, a financial institution derives a portion of its credit standing from the government that supplies a guarantee. If a guaranteed institution becomes illiquid or worse yet insolvent, then a government may have to honor its guarantee. 5. During this episode, one of the authors worked at Chase Manhattan Bank. Chase used the run as an early warning signal of the forthcoming currency crisis. When the branch manager from Hong Kong telephoned Chase’s managing director for global risk management, Roger Shields, that a large influx of domestic depositors were opening demand deposit accounts denominated in U.S. dollars, Chase moved its foreign exchange bid and ask quotes to induce net short positions in East Asian currencies in order to protect itself. 6. For simplicity, we do not consider domestic taxes that might give the central bank a larger budget constraint. Even so, the central bank would still face a budget constraint. 7. We do not allow the foreign creditor interest yield, r∗ , to decrease as it might as long term debt and equity capital increase. Thus, our modeling may understate all the benefits that additional equity financing might have on fragility. For instance, lenders may be willing

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to lend at better interest rates and be more willing to roll over existing loans if there is a larger equity cushion, all else equal. Since borrowing rates are complicated functions of many particulars such as: income potential, character, guarantees, net worth, collateral, economic conditions, and principal-agent conflict; we choose not to model interest rates in equilibrium to keep the modeling simple, otherwise we would have to substantially modify the social welfare problem and introduce unneeded complexity. 8. We do this for simplicity. The central bank financial support might make the government “invest” in the portfolio held by the domestic banks. Similar to the debt overhang problem (Jensen & Meckling, 1976), the upside benefits may go to the owners of domestic banks as well as foreign creditors of domestic projects while the domestic taxpayers bear the costs. Bris and Koskinen (2002) also model leverage as a factor in currency crisis. Their ex post analysis suggests that the government may need to break the fixed exchange rate to attract new foreign investment. 9. This assumption is made for simplicity. If we allow positive growth in the productive process, then issuing more equity will have a similar effective of reducing the proportion of debt in the capital structure. 10. Blodget and Kane (2003) propose an innovation that might allow American style corporate governance abroad, that is, executive stock options plans to compensate managers and class action litigation to protect minority shareholders from expropriation. Stock exchanges might establish and maintain a binding court of arbitration to settle corporate disputes between stakeholders with the companies that choose to list with them. Sovereigns could agree by treaty to enforce legal judgments of the court sponsored by the exchange. In this way, by choosing which stock exchange managers list their securities on, they would select a corporate governance infrastructure that might supersede national laws without having to change them. Since stock exchanges would sponsor arbitrage courts, they would have a strong incentive to foster ruling that would be investor friendly to attract business. Hence, stock exchange listings could serve as a loophole that would allow different corporate governance structures to compete with each other in the same industries and countries. Consequently, an investor friendly corporate governance system could evolve over time without having to harmonize the laws of individual countries. 11. See Dornbusch and Werner (1994) for the 1994–1995 Mexican crisis, Corsetti, Pesenti and Roubini (1998) and Radelet and Sachs (1998) for the 1997–1998 Asian crisis.

ACKNOWLEDGMENTS We thank Philip Dybvig, N’Deye Fall, Lin Guo, Tao Li, Mark Loewenstein, Morris McInnes, Anthony Santomero, and Benaiah Yongo-Bure for helpful comments. We are solely responsible for any errors.

REFERENCES Bagehot, W. (1999). Lombard Street: A description of the money market. New York: Wiley. Blodget, M. S., & Kane, S. A. (2003). Global corporate governance: Implications for a functionally harmonized legal infrastructure. Journal of Business & Economics Research, 2(7), 45–58.

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Bris, A., & Koskinen, Y. (2002). Corporate leverage and currency crisis. Journal of Financial Economics, 63(2), 275–310. Caprio, G., & Honohan, P. (1999). Restoring banking stability: Beyond supervised capital requirements. Journal of Economic Perspectives, 13, 43–64. Chang, R., & Valesco, A. (2000a). Financial fragility and the exchange rate regime. Journal of Economic Theory, 92, 1–34. Chang, R., & Valesco, A. (2000b). Banks, debt maturity and financial crises. Journal of International Economics, 51, 169–194. Chui, M., Gai, P., & Haldane, A. G. (2002). Sovereign liquidity crises: Analytics and implications for public policy. Journal of Banking and Finance, 26, 519–546. Coffee, J. (1999). The future is history: The prospects for a global convergence in corporate governance and its implications. Northwestern University Law Review (Spring), 641–707. Corsetti, G., Peseni, P., & Roubini, N. (1998). What caused the Asian currency and financial crisis? Working Paper, Stern School of Business, NYU, New York, NY. Diamond, D. W., & Dybvig, P. H. (1983). Bank runs, deposit insurance, and liquidity. Journal of Political Economy, 91, 401–419. Dornbusch, R., & Werner, A. (1994). Mexico: Stabilization, reform and no growth. Brookings Papers on Economic Activity, 2, 219–270. Goldfajn, I., & Valdes, R. O. (1997). Capital flows and the twin crises: The role of liquidity. IMF Working Paper. Hoggarth, G., Reis, R., & Saporta, V. (2002). Costs of banking system instability: Some empirical evidence. Journal of Banking and Finance, 26(5), 825–855. Jacklin, C. J. (1987). Demand deposits, trading restrictions, and risk sharing. In: E. C. Prescott & N. Wallace (Eds), Contractual Arrangements for Inter-Temporal Trade. Minneapolis: University of Minnesota Press. Jensen, M., & Meckling, W. (1976). Theory of the firm: Managerial behavior, agency costs, and ownership structure. Journal of Financial Economics, 3, 306–360. Kaminsky, G. L., & Reinhart, C. M. (1999). The twin crises: The causes of banking and balance of payment problems. American Economic Review, 89, 473–500. Kane, E. J. (2000). Capital movements, banking insolvency, and silent runs in the Asian financial crisis. Paciﬁc-Basin Finance Journal, 2, 153–175. Krugman, P. (1998). Bubble, boom, crash: Theoretical notes on Asia’s crisis. Mimeo. Cambridge, MA: MIT. Krugman, P. (1999). Balance sheets, the transfer problem, and financial crises. Working Paper. Cambridge, MA: MIT. Mishkin, F. S. (1999). Global financial instability: Framework, events, issues, the international lender of last resort: What are the issues? Journal of Economic Perspectives, 13, 3–20. Obstfeld, M., & Rogoff, K. (1995). The mirage of fixed exchange rate. Journal of Economic Perspectives, 9, 73–96. Radelet, S., & Sachs, J. D. (1998). The East Asian financial crisis: Diagnosis, remedies, prospects. Working Paper. Cambridge, MA: Harvard University. Rogoff, K. (1999). International institutions for reducing global financial instability. Journal of Economic Perspectives, 13, 21–42. Schmeidler, D. (1973). Equilibrium points of nonatomic games. Journal of Statistical Physics, 4, 295–300.

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APPENDIX Proof of Lemma 3: If depositors withdraw their bank deposits at date 1, their expected utility is E[u(w)] = u(ar1 /e − r ∗ b01 )

if f1 ≤ f m ( , e)

E[u(w)] = (f m ( , e)/f1 )u(ar1 /e − r ∗ b01 ) +(1 − f m ( , e)/f1 )u(0)

if f1 > f m ( , e)

(16)

m

where f ( , e)/f 1 is the fraction of depositors who get a positive amount of bank deposits and (1 − f m ( , e)) is the fraction of depositors who get nothing, because the bank becomes insolvent once the fraction f m ( , e) is reached. If depositors do not withdraw their bank deposits at date 1, their expected utility is E[u(w)] = qu(ar2 (f1 , e, vL )/e) + (1 − q)u(ar2 (f1 , e, vH )/e) E[u(w)] = u(0)

if f1 ≤ f m ( , e)

if f1 > f m ( , e)

(17)

where (1 − f 1 )r 2 ( f 1 , x) = ( f m ( , e) − f 1 )r 1 x/v. First, we seek pure strategy Equilibriums. The incentive compatibility condition (10) stipulates that late consumers have no incentive to pretend to be early consumers. Early consumers must consume at date 1, so f 1 = ␪ is an equilibrium outcome. If f 1 > f m ( , e), then bank run is an equilibrium. That is, f 1 = 1 is an equilibrium outcome. From Eqs (16) and (17), we get the condition u(0) < ( f m ( , e)/f 1 )u(ar 1 /e − r ∗ b 01 ) + (1 − f m ( , e)/f 1 )u(0). Thus, for f 1 > f m ( , e), it is optimal for late consumers to withdraw their bank deposits early. Thus, f 1 = 1 is an equilibrium outcome. We next examine mixed strategy Equilibriums. Suppose late consumers are indifferent between withdrawing and not withdrawing their bank deposits at date 1. If f 1 ≤ f m ( , e), then from (16) and (17) we obtain the equality u(ar 1 /e − r ∗ b 01 ) = (1 + ␳)−1 [qu(ar 2 ( f 1 , e, vL )/e) + (1 − q)u(ar 2 ( f 1 , e, vH )/e)].

(18)

Since r1 , a, r∗ , and b01 are constants, the left hand side of Eq. (18) is constant. For each value of x, the partial derivative of r2 (f1 , e, x) with respect to f1 is negative, because there are fewer funds to invest in the productive process. That is, for each value of x, r2 (f1 , e, x) is continuous, and is strictly decreasing with respect to f1 .

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This implies that qu(ar 2 ( f 1 , e, vL )/e) + (1 − q)u(ar 2 ( f 1 , e, vH )/e)) is continuous and strictly decreasing with respect to f1 . If f 1 = ␪, it follows from the incentive compatibility condition that the right hand side of the equation in (18) is greater than or equal to the corresponding left hand side. If f 1 = f m ( , e), the left hand side of the equation in (18) is greater than the corresponding right hand side, which is now equal to (1 + ␳)−1 u(0). Since the function in Eq. (18) is continuous, we employ the intermediate value theorem to assert the existence of h∗ ␧ (␪, f m ( , e)) which satisfies Eq. (18). Since this function is strictly monotonic, the fraction h∗ is unique. This completes the proof of Lemma 3. Example. We let the domestic investors’ preferences be represented by a logarithmic utility function, log(c). The amount of foreign equity investment is y. We assume that b 02 = 0 because there is indeterminacy in the amount of date 0 foreign borrowing b01 and b02 . The social optimum is given by date 0 foreign currency investment a = w + e(b 01 − y), where ␪c 1 + r ∗ (b 01 − y) = mw/e, date 1 foreign currency borrowing b 12 = mw/e, and per capita consumption c1 , where c1 is a solution to the quadratic equation Ac 21 − Bc 1 + C = 0

(19)

where the constants are defined by A = [e2 ␪(1 − ␪) + (1 + ␳)(e␪)2 r ∗−1 ]r ∗−1 vL vH B = e(1 − ␪)[qr ∗−1 ((m + r ∗ )wvH − r ∗2 mw)vL + (1 − q)r ∗−1 ((m + r ∗ )wvL − r ∗2 mw)vH ] + (1 + ␳)e␪[((m + r ∗ )wvL − r ∗2 mw)vH + ((m + r ∗ )wvH − r ∗2 mw)vL ]r ∗−2 C = (1 + ␳)((m + r ∗ )wvL − r ∗2 mw)((m + r ∗ )wvH − r ∗2 mw)r ∗−2 . Using the quadratic formula, we get the following roots of Eq. (19): c 1 = (B ± sqrt(B 2 − 4AC))/(2A). We choose the root c 1 = (B + sqrt(B 2−4 AC))/(2A) because the other root yields a counterintuitive result. That is, per capita consumption of early consumers would be negative.

LONG MEMORY IN CURRENCY FUTURES VOLATILITY Ching-Fan Chung, Mao-Wei Hung and Yu-Hong Liu ABSTRACT This study employs a new time series representation of persistence in conditional mean and variance to test for the existence of the long memory property in the currency futures market. Empirical results indicate that there exists a fractional exponent in the differencing process for foreign currency futures prices. The series of returns for these currencies displays long-term positive dependence. A hedging strategy for long memory in volatility is also discussed in this article to help the investors hedge for the exchange rate risk by using currency futures.

1. INTRODUCTION Currency futures began trading on the International Monetary Market (IMM) of the Chicago Mercantile Exchange in May 1972. Since such futures have played an important role in international business, trading volume has increased substantially over time. The main function of currency futures is in hedging to decrease exchange rate uncertainty. Without hedging via currency futures, companies expose themselves to the possibility of significant exchange losses when conducting international business. For example, when companies invest abroad, they must face the decision whether or not to hedge the risk of a depreciation of the foreign currency compared to the home currency. Without a proper hedging strategy, Research in Finance Research in Finance, Volume 20, 139–158 Copyright © 2003 by Elsevier Ltd. All rights of reproduction in any form reserved ISSN: 0196-3821/doi:10.1016/S0196-3821(03)20008-3

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any optimal portfolio allocation strategy is likely to fail. Before searching for a best hedging strategy when investing abroad, we must investigate the property of currencies. Smaller hedgers are attracted to the futures market to take advantage of standardized trading procedures and relatively small contract size. Furthermore, unlike in the forward market, speculation is encouraged in the futures market. Finally, increasing international operation of banks, pension funds, and insurance companies also helps stimulate trading in currency spot, forward and futures markets. Given the growing popularity of the futures market, it is worthwhile to investigate the time series property of currency futures contracts. This work studies whether or not currency futures display the long-memory property. Long memory is a special property of time series data that describes the correlation structure of a given series given long lags. Long memory in volatility occurs when the effects of volatility shocks decay slowly. The appearance of the long memory phenomenon in financial time series data indicates that the speculative efficiency hypothesis no longer adequately describes auction market price behavior, and that independent consecutive price changes no longer occur. Consequently, models based on this assumption require modification. For example, when the volatility in the famous Black-Scholes formula becomes stochastic, option prices would display both smile and term structure effects. Exact calculation of smile and term effect is only possible for special, short-memory volatility processes (Heston, 1993). When the volatility in the model displays long memory, Monte Carlo methods must be employed (Bollerslev & Mikkelsen, 1996, 1999). Numerous researchers have applied different models to investigate long memory and have found that it exists in most future contracts. For example, Barkoulas, Labys and Onochie (1999) applied the spectral regression method suggested by Geweke and Porter-Hudak (1983) to investigate long memory, and found that the returns series for commodities and currencies display long term positive dependence. The application of rescaled range (R/S) analysis to the foreign exchange market by Booth, Kaen and Koveos (1982b), to the gold market by Booth, Kaen and Koveos (1982a), and to stocks listed on the New York Stock exchange by Greene and Fielitz (1977) disproved the hypothesis that future price trends are not influenced by previous price trends. Furthermore, Stevenson and Bear (1965) performed a battery of tests on soybean futures and found that the random walk hypothesis does not satisfactorily explain the movement of those price series. Cheung (1993) found some evidence for long memory in the French franc/U.S. dollar rate and marginal evidence for U.K. pound/U.S. dollar rate. Sephton and Larsen (1991) find mixed evidence for the existence of a cointegrating relationship between this set of exchange rates. Baillie and Bollerslev (1994) find evidence that a linear combination of the same spot exchange rates displays long-range dependence.

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Previous studies, such as Booth and Tse (1995), Barkoulas, Labys and Onochie (1999), use the fractional integration test on a time series with mean (␮) to seek evidence of long memory. This study focuses on the second moment (the volatility, ␴2 ) to investigate the long memory. The present long memory stochastic volatility model differs from other econometric models by its incorporation of the ARFIMA (Fractionally Integrated Autoregressive Conditional Heteroskedastic and Moving Average) process into a standard stochastic volatility scheme. Strong persistence of volatility is widely accepted in many financial and macroeconomic time series. Notably, Baillie, Bollerslev and Mikkelsen (1996) and Bollerslev and Mikkelsen (1996) incorporated the idea of long memory fractional differencing into the GARCH (Generalized Autoregressive Conditional Heteroskedastic), thus establishing the FIGARCH (Fractionally Integrated Generalized Autoregressive Conditional Heteroskedastic) model. The conditional variance of the FIGARCH model has an important property rarely shared by other models, namely it displays not only short-run dynamics of the ARMA type, as in the standard GARCH model, but also the long-run persistence that decays slowly and hyperbolically rather than the usual exponential decay of the GARCH model. Combining the fractionally integrated ARMA and GARCH models produces an ARFIMA-FIGARCH model, in which both the conditional mean and conditional variance jointly share long memory. In a recent study, Chung (1998) found that Baillie, Bollerslev and Mikkelsen’s (1996) parameterization of the FIGARCH model might suffer a specification problem, and thus proposed a modified version of the ARFIMA-FIGARCH model while demonstrating the shortcomings of the old model through extensive simulations. Consequently, this study uses Chung’s version of the ARFIMA-FIGARCH model to check the long memory of futures contracts. For simplicity, the ARFIMA (0, 0, 0)-FIGARCH (0, d2 , 0) model is used to check for long memory. This econometric model differs from the traditional GARCH (1, 1) model, which is widely used to determine whether long memory exists. This study uses the ARFIMA (0, 0, 0)FIGARCH (0, d2 , 0) model to determine whether long memory exists in currency futures from 1994 to 1998. The model results demonstrate that the estimated parameters of our long memory model are significant. Generally, this study finds that the price behavior of currency futures contracts displays long memory. In addition to exploring the property of long memory in volatility of currency futures, we also propose a hedging strategy for this phenomenon. Conventional hedging models usually find hedging ratios by regressing the returns to holding the spot asset on the returns to holding the hedging instruments. However, because of two potential problems, these models cannot be employed when the target assets display long memory. First, conventional models do not consider the relationship of cointegration between the spot asset and the future asset, obscuring the long-run relationship between them. Second, the assumption that risk in spot and futures

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markets is constant over time of the conventional models is no longer suitable when trading assets display long memory. Therefore, a risk-minimizing hedging strategy must be established to hedge the exchange rate risk when currencies display long memory. Among the econometric models, which is used to capture the property of currencies, GARCH model is the most popular one because substantial empirical evidence proves that this model adequately characterizes the dynamics in second moments of currency prices. McCurdy and Morgan (1988) and Hsieh (1988, 1989) use GARCH (1, 1) to model the second moment of currency prices and find that it has better performance than ARCH models. Kroner and Sultan (1993) use a bivariate error correction GARCH model to find the risk-minimizing hedge ratio and find that their method leads to more effective hedges than the conventional methods and is superior to manage currency risk. Following the idea of Kroner and Sultan (1993) and using the FIGARCH (0, d2 , 0) in place of GARCH (1, 1) to capture the property of long memory, we construct the hedging strategy for currency futures. The remainder of the paper is organized as follows. Section 2 introduces the proposed ARFIMA-FIGARCH model. Section 3 then describes the methodology used for parameter estimation. Next, Section 4 reports the currency data used here, and the empirical results obtained using this data. Section 5 discusses the hedging strategy when the volatility in currency futures displays long memory. Finally, Section 6 summarizes the evidence, along with our conclusions, and suggestions for future research.

2. THE MODEL Numerous researchers interested in econometrics and empirical finance have focused on modeling temporal variations in market volatility. The most popular instrument used for such investigations is the Autoregressive Conditional Heteroskedastic (ARCH) class of models developed by Engle (1982). The ARCH model suffers from the drawback of simply postulating conditional variance to be a non-trivial function of the current information set, but economic theory provides little guidance regarding the variables that are important in determining the observed time variation in the conditional variances. Two of the most successful parameterizations for characterizing high-frequency financial market volatility are the Generalized ARCH (GARCH) model developed by Bollerslev (1986), and the Exponential GARCH (EGARCH) model proposed by Nelson (1991). The GARCH and the EGARCH models are as easy to interpret as: ARMA-type models for the conditional second-order moments and the conditional variance logarithm, respectively. A common finding with respect to these models in many empirical

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applications involves the apparent persistence of the estimated conditional variance processes; see Bollerslev, Chou and Kroner (1992). The IGARCH (Integrated GARCH) class of models was developed by Engle and Bollerslev (1986) to capture this effect. In the IGARCH model, a shock to the conditional variance continues to influence optimal variance forecasts for all future horizons. Consequently, from a forecasting perspective, the difference between the covariance-stationary GARCH formulation and the IGARCH model is that the latter provides a natural analog to the difference between I(0) and I(1) type processes for the conditional mean. I(0) means integrated of order 0, and when a macroeconomic time series is I(0), it is said to be stationary. Similarly, I(1) means integrated of order 1 and when a macroeconomic time series is I(0), it is said to be non-stationary. However, the distinction between the I(0) and I(1) time series for the conditional mean may be too narrow. Additional flexibility is obtained by allowing for fractional orders of integration, as in the I(d) class of models developed by Granger (1980), Granger and Joyeux (1980), Hosking (1981), and Mandelbort and Van Ness (1968). In contrast to an I(0) time series in which the influence of stocks reduces exponentially, or to an I(1) series in which no mean reversion exists, shocks to an I(d) time series with 0 < d < 1 dissipate slowly and hyperbolically. The importance of this generalization in modeling long-run economic phenomena has recently been illustrated by various studies, including Baillie and Bollerslev (1994), Baillie, Chung and Tieslau (1996), Cheung and Lai (1993), Diebold, Husted and Rush (1991), Lo (1991), and Sowell (1992). Just as the generalization of the standard ARIMA class of models to the fractionally integrated ARFIMA models has proven empirically important, a similar situation may also hold when modeling long-term dependence in conditional variances. The new class of Fractionally Integrated GARCH (FIGARCH) models developed by Baillie, Bollerslev and Mikkelsen (1996) allows for such added flexibility. Like the ARFIMA class of models for the conditional mean, a shock to the conditional variance in the FIGARCH model is transitory, in that the influence on forecast conditional variance decreases slowly and hyperbolically. This study presents some new results related to the theoretical properties and the importance of allowing for fractional unit roots in the conditional variance process. Baillie, Bollerslev and Mikkelsen (1996) and Bollerslev and Mikkelsen (1996), hereafter BBM and BM, respectively, incorporate the idea of long-memory fractional differences into the GARCH (Generalized Autoregressive Condition Heteroskedastic) model. The resulting model is termed the fractionally integrated GARCH model or the FIGARCH model. The FIGARCH model has different characteristics to the standard GARCH model. Specifically, the FIGARCH model displays not only the short-run dynamics of the ARMA type, but also the long-run persistence that decays

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slowly and hyperbolically (rather than the exponential decay of the GARCH model). Consequently, the fractionally integrated ARMA (ARFIMA) model can be used for the conditional mean, while the FIGARCH model can be used for the conditional variance. A combined model with the above form is called the ARFIMA-FIGARCH model. The ARFIMA-FIGARCH model is quite complex and difficult to estimate. The approximate maximum likelihood estimation (AMLE) approach is used here to estimate the data. This study also works out the analytic first-order derivatives of the log-likelihood function, allowing the AMLE to be calculated more efficiently. The following subsection presents a clear definition of the ARFIMA-FIGARCH model for the benefit of readers.

2.1. ARFIMA-FIGARCH Model A stochastic process yt is said to be a fractionally integrated ARMA process of the orders a and m in the lag operator L, or the ARFIMA (a, d1 , m) process, if it is denoted by ␾(L)(1 − L)d 1 (y t − ␮) = ␪(L)␧t

(1)

a

where ␾(L) = 1 − j=1 ␾j L j is the autoregressive operator with operator a, j ␪(L) = 1 + m j=1 ␪j L is the moving average with operator m, ␮ is the unconditional mean of yt and ␧t are white noises with the variance ␴2 . In this formula, the fractional differencing operator (1 − L)d 1 , of which d1 is a parameter, allows process yt to have long memory. The fractional differencing can be expressed as the following infinite polynomial: ∞ ∞ (j − d 1 ) (1 − L)d 1 = ␲j (d 1 )L j (2) Lj ≡ (j + 1)(−d 1 ) j=0

j=0

where ␲j (z) ≡ (j − z)/((j + 1)(−d 1 )) and (·) is the standard gamma function. Notably, d1 is allowed to assume any real value. The arbitrary restriction that d1 may only have integer values provides the basis for the standard autoregressive integrated moving average (ARIMA) model. For example, when d 1 = 0, the ARIMA model becomes y t = ␧t , and clearly the model is stationary. When d 1 = 1, the model becomes (1 − L)y t = ␧t , or y t = y t−1 + ␧t = ti=0 ␧i . Such a model is clearly non-stationary, as the effect of a shock never dies out. When 0 < d 1 < 1, the effect of the shock would die out, but the speed is slow, and long memory effect occurs. The stochastic process yt is both stationary and invertible if all roots of ␾(L) and ␪(L) lie outside the unit circle and |d 1 | < 0.5. Moreover,

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the process is non-stationary for |d 1 | > 0.5, since it has infinite variance – see Granger and Joyeux (1980). Assuming that −0.5 < d 1 < 0.5 and d 1 = 0, Hosking (1981) demonstrated that the correlation function, ␳(·), of an ARFIMA process is proportional to j 2d−1 as j → ∞. Consequently, the autocorrelations of the n ARFIMA process decay to a stationary ARMA process. When 0 < d 1 < 0.5, j=−n |␳(j)| diverges as n → ∞, and the ARFIMA process is said to possess long memory. The process possesses short memory given d 1 = 0 and intermediate memory given d 1 < 0. The ARFIMA model can be thought of as comprising an ARMA part, which has short memory and describes the short-term properties of the series, as well as having appropriate fractional differencing for explaining any persisting and long-term series behavior. The FIGARCH model is examined below. Suppose the conditional variance h t = Var(␧t | t−1 ), t−1 denotes the information set which contains information from time 0 to time t − 1. By applying the ARMA operators to the GARCH model, conditional variance ht can be expressed as follows: h t = ␻ + ␣(L)␧2t + ␤(L)h t

(3)

where ␣(L) =

q

␣j L j

(4)

␤j L j

(5)

j=1

␤(L) =

p j=1

␻ = ␴2 [1 − ␤(1) − ␣(1)]

(6)

␴2 denotes the unconditional variance of yt , and q and p represent the order of L, just as in the ARMA model. This GARCH (p, q) process can be written easily as an ARMA model for ␧2t : [1 − ␣(L) − ␤(L)]␧2t = ␻ + [1 − ␤(L)]␷t

(7)

where ␷t ≡ ␧2t − h t is the innovation with zero mean and constant variance. Replacing 1 − ␣(L) − ␤(L) with a polynomial that contains a fractional differencing term produces the following: (L)(1 − L)d 2 ␧2t = ␻ + [1 − ␤(L)]␷t

(8)

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where (L) ≡ 1 −

q

j L j

(9)

j=1

The formula (8) above is termed a FIGARCH (p, d2 , q) model. The corresponding conditional variance ht can be expressed more clearly as: [1 − ␤(L)]h t = ␻ + [1 − ␤(L)]␧2t − (L)(1 − L)d 2 ␧2t

(10)

2.2. Long Memory vs. Short Memory Brockwell and Davis (1991) define a weakly stationary process as having short memory when its autocorrelation function is geometrically bounded. This study assumes the following: |␳(h)| ≤ Cr |h|

for some C, 0 < r < 1

(11)

Unlike a short-memory process with a geometrically decaying autocorrelation function, a weakly stationary process has long memory if its autocorrelation function, ␳, decays hyperbolically: ␳(h) ∼ Ch 2d−1

as h → ∞, C = 0, d < 0.5

(12)

Brockwell and Davis (1991) go on to provide more details on the definition of short memory. Conversely, a process has long memory if its spectrum f(␭) decays asymptotically: f(␭) ∼ C|␭|−2d

as ␭ → 0

with d = 0

(13)

If, additionally, d > 0, then the autocorrelations are not absolutely summable. Furthermore |␳(h)| = 0, and the spectrum diverges at zero, f(␭) → ∞ as ␭ → 0. This study concludes that the process is persistent in this case.

2.3. Alternative Parameterization of the FIGARCH Model Chung (1998) found that the constant term ␻ in the above FIGARCH specification Eq. (8) differs structurally from ␮ in the ARFIMA model: that is, the fractional differencing operator (1 − L)d 1 applies to ␮ while (1 − L)d 2 does not apply to ␻. To avoid such a discrepancy in parameterization, Chung thus rewrote the GARCH (p, q) model as follows: [1 − ␣(L) − ␤(L)](␧2t − ␴2 ) = [1 − ␤(L)]υt

(14)

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and rewrote the FIGARCH model as (L)(1 − L)d 2 (␧2t − ␴2 ) = [1 − ␤(L)]␷t Thus, the relationship between ␻ and

␴2

(15)

is

␻ = (L)(1 − ␤(L))d 2 ␴2

(16)

However, Chung found that parameter ␻ in BBM/BM’s formulation is problematic in theory and difficult to estimate in practice. Accordingly, Chung developed the alternative parameterization of the FIGARCH model Eq. (17) to overcome this problem. This is also the reason why this study uses Chung’s ARFIMA-FIGARCH model instead of BBM/BM. [1 − ␤(L)]h t = [1 − ␤(L)]␧2t − (L)(1 − L)d 2 (␧2t − ␴2 )

(17)

The ARFIMA model defines in Eq. (1) for the condition mean and the FIGARCH model defines in Eq. (15) for the condition variance still have three structural differences. First, ARFIMA (a, 0, m) model can reduce to the ARMA (a, m) model while the FIGARCH (p, 0, q) model cannot reduce to the GARCH (p, q) model exactly. Second, the FIGARCH model, which is not weakly stationary, can be strictly stationary and ergodic for 0 ≤ d 2 < 1. Therefore, d1 and d2 are different and d2 is permitted to be greater than 0.5 while d1 is not. This implies the degree of persistence for conditional variances is greater than conditional means. Finally, the conditional mean in the ARFIMA model has no sign restriction, but the conditional variances in the FIGARCH model must all be non-negative.

3. ESTIMATION METHODOLOGY Following Chung (1998), this study uses the approximate maximum likelihood estimation to estimate the complicated ARFIMA-FIGARCH model. Suppose that y 1 , y 2 , . . . , y t follows the ARFIMA-FIGARCH model, and ␧t is normally distributed, then the approximate log-likelihood function is defined as: T T T 1 ␧2t 1 ln L(␩1 , ␩2 ) = − ln (2␲) − ln (h t ) − 2 2 2 ht t=1

(18)

t=1

␩1 ≡ [␴2 d 1 ␾ ␪] is the ARFIMA portion of the parameter. ␩2 ≡ [␴2 d 2 ␤ ␸] is the FIGARCH portion of the parameter. The parameter vectors ␾, ␪, ␤, ␸ have a, m, p, and q elements, respectively. The approximate log-likelihood function is then solved by solving the first

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order condition for ␩1 and ␩2 , that is, namely: (∂ln L/∂␩1 ) = (∂ln L/∂␩2 ) = 0. Moreover, the asymptotic variance-covariance matrix can be estimated using the inverse of the second-order derivative (the Hessian matrix) of the approximate log-likelihood function with a negative sign: 2 −1 ∂ ln L − (19) ∂␩∂␩ Another popular asymptotic variance-covariance matrix formula which can also be applied is −1 2 −1 2 T ∂ln L t ∂ln L t ∂ ln L ∂ ln L (20) ∂␩∂␩ ∂␩ ∂␩ ∂␩∂␩ t=1

where ln L t = −0.5 ln(2π) − 0.5 ln h t − 0.5(␧2t /h t ) and ln L = Tt=1 ln L t . Calculating the approximate log-likelihood functions and their first-order derivatives requires the values of innovations ␧t and the conditional variance ht , but this study observes only yt . Consequently, yt must first be transformed to ␧t and ht . The following four steps are used to derive ␧t and ht from yt : In the first two steps, ␧t is calculated for t = 1, 2, . . . , T from yt . Notably, ␰t is the intermediate variable in our calculation process. ␰t =

Step 1 :

t−1

␲j (d 1 )(y t−j − ␮)

(21)

j=0

␧t = ␰t =

Step 2 :

a

␾j ␰t−j −

j=1

m

␪j ␧t−j

(22)

j=1

After calculating the values of ␧1 , ␧2 , . . . , ␧T , the conditional variances ht for t = 1, 2, . . . , T can be easily calculated using formula (17) in the following two steps. Notably, ␵t is another intermediate variable. Step 3 :

␵t =

t−1

␲j (d 2 )(␧2t−j − ␴2 )

(23)

j=0

Step 4 :

ht =

p j=1

␤j h t−j −

p j=1

␤j ␧2t−j + ␧2t − ␵t +

q

␸j ␵t−j

(24)

j=1

The pre-sample values of ␵t and ␧t , for t = 0, −1, −2, . . . in Step 2 are all set to 0, while those of ␧2t and ht for t = 0, −1, −2, . . . in Step 4 are all set to ␴ˆ 2 ≡ T −1 Tt=1 ␧2t . Moreover, the pre-sample values of (y t − ␮) and (␧2t − ␴2 ) in Steps 1

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and 3 have all been replaced by 0. (The summation thus runs from 0 to t − 1, rather than ∞.) It is noted that in Step 1, for example, the exact relationship between ␰1 and yt should be ␰1 = (y 1 − ␮) + ␲1 (d 1 )(y 0 − ␮) + ␲2 (d 1 )(y −1 − ␮) + · · · ␰1 , calculated from Step 1, is simply (y 1 − ␮), and the remainder of the terms have all been truncated. The calculations of the other ␰2 , ␰3 , . . . all involve various degrees of “truncation error.” Importantly, concern exists that these zero pre-sample values may leave errors too large for the log-likelihood function and, thus, bias the resulting parameter estimates, especially given a small sample size. However, the simulation studies for the ARFIMA model by Chung and Baillie (1993) find that even given a sample size as small as 300, using the AMLE causes minimal bias provided the value of d1 is not close to 0.5. A possible reason for this simulation result is that given ␮ = E(y t ), (y t − ␮) can be expected to have a small absolute value and zero average. Consequently, assuming pre-sample values of zero for (y t − ␮) is not unreasonable. Next, letting ␴2 = E(␧2 ), then for the same reason as above the differences (␧2t − ␴2 ) are assumed to be small in absolute values and have a zero average. Consequently, this study proposes setting the pre-sample values of (␧2t − ␴2 ) as zero in Step 3.

3.1. Aspects in Which the Proposed Model is Superior to BBM/BM The difference between the proposed model Eq. (17) and BBM/BM lies in the parameterization of ␴2 and its fractional differencing transformation ␻ as indicated in the equity Eq. (16). The importance of this difference is clarified by the fact that given the unconditional variance ␴2 , parameter ␻ in BBM/BM is actually ␻ = ␴2 ␸(1)

∞

␲j (d 2 )

(25)

j=0

while the infinite sum of ␲j (d 2 ) equals 0. Restated, parameter ␻ should be zero regardless of the value of ␴2 . The question then follows that if estimates of ␻ continuously obtain small but definite non-zero values, as in BBM/BM, what do such non-zero estimates indicate other than the usual argument of random errors? The following attempts to answer this question after explaining how the estimation of the BBM/BM FIGARCH model works in practice. First, the estimation of BBM/BM’s formula (8) is slightly complicated compared with specification (15). Specifically, when the AMLE is implemented for models (8) or (10), the calculation of the conditional variances ht , for t = 1, 2, 3, . . . , T differs from that in Steps 3 and 4 in two instances: besides adding the constant ␻ to the right

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side of Step 4, a more serious change occurs in Step 3 where the value (1 − L)d 2 ␧2t is evaluated rather than (1 − L)d 2 (␧2t − ␴2 ). Since the fractional differencing operator is defined as an infinite sum Eq. (2) which involves pre-sample values, choosing suitable pre-sample values for ␧2t is essential. Unlike the differences (␧2t − ␴2 ), which can have either a sign or a zero average, the squared terms ␧2t are all positive and can never have a zero mean. Consequently, setting the pre-sample values of ␧2t to zero, as in the computation in Step 3, becomes much less convincing. BBM/BM and Teyssiere (1996) have proposed using ␴ 2 ≡ T −1 Tt=1 ␧2t as the pre-sample values of ␧2t , and then adding N more terms of such pre-sample values to at least partially account for the effects of those non-negative pre-sample values, while N is set as a sufficiently large integer, 1000. Following this argument, Step 3 can be revamped as follows: Step 3∗ :

␰t =

N+t−1

t−1

j=0

j=0

␲j (d 2 )␧2t−j =

␲j (d 2 )␧2t−j + ␴

N+t−1

␲j (d 2 )

j=t

Two issues call for immediate attention. First, it may be more convenient to define Step 3∗ alternatively as follows: ␰t =

N

␲j (d 2 )␧2t−j

(26)

j=0

where the summation runs from 0 to the fixed number N, rather than N + t − 1 which varies for different values of t. However, such a practice should be avoided since it causes inconsistent computation of the fractional differencing. Second, although in theory the extra N terms in Step 3∗ should help to improve the accuracy of the fractional differencing evaluation, we nevertheless argue that subjective choice of N will inevitably influence the estimate of ␻. To highlight the connection between the value of ␻ and the choice of N, BBM/BM’s definition of the conditional variance ht in the simplest FIGARCH (1, d2 , 1) model is considered here, namely: h t = ␻ + ␧2 − ␰ t = ␻ −

t−1 j=1

␲j (d 2 )␧2t−j − ␴ 2

N+t−1

␲j (d 2 )

(27)

j=t

Clearly, from the first and the last terms in the second line, for given values of ht , the estimate of ␻ is always related to the choice of N. Specifically, since the values of ␲j (d 2 ), j = 1, 2, . . . are all negative, ␻ decreases with increasing N. Consequently, although the theoretical value of ␻ is 0, any non-zero estimate of ␻ in a sense is produced by the subjective choices of a finite N as well as the pre-sample value ␴ˆ 2 .

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Finally, we emphasize that the problems discussed in this section only involve the parameterization used in BBM/BM Eq. (8), and do not occur in the present specification Eq. (15). The present analysis of the FIGARCH model also sheds some light on a similar issue in the ARFIMA modeling of the conditional means, for which most previous studies adopt the specification Eq. (1). Only very rarely is a formula like the following encountered, namely: ␾(L)(1 − L)d 1 y t = ␮∗ + ␪(L)␧t

(28)

where the parameter ␮∗ is clearly related to ␮ in Eq. (1) by the equality ∞ ∗ ␮ = ␮␾(1) j=0 ␲j (d 1 ) and always equals zero. Conceivably, the adoption of such a parameterization would cause the estimation of the parameter ␮∗ to encounter the same problems as that of ␻ in the formulation of the FIGARCH model in BBM/BM.

4. DATA AND EMPIRICAL RESULTS The currency futures price series used here is based on four major foreign currencies. Meanwhile, the price data are taken from daily closing prices of the contract nearest to expiration. The contract used for data is turned over and replaced with the succeeding contract at the beginning of the month in which the soon-to-expire contract matures. All data series are from March 1994 to March 1998 and are analyzed in the form of returns. The conditional mean of the futures returns series displays serial dependence. Significant variation in the second moment (conditional heteroskedasticity) is detected in all sample series. The foreign currency futures prices sampled here include: (1) the British pound; (2) Canadian dollar; (3) Deutsche mark; and (4) Swiss franc. The description of data of these four currency futures are summarized in Table 1. Table 1. Data Description and Sources. Futures Price Series

Exchange

Daily Data From

British Pound Canadian Dollar Deutsche Mark Swiss France

CME CME CME CME

March, 1994 March, 1994 March, 1994 March, 1994

Contract Months

Number of Observations

3, 6, 9, 12 3, 6, 9, 12 3, 6, 9, 12 3, 6, 9, 12

1187 1364 1250 1178

Note: Four currency futures contracts are used as our empirical data. These are British Pound, Canadian Dollar, Deutsche Mark, and Swiss France futures contracts, which are exchanged on the Chicago Mercantile Exchange (CME). The contract months are March, June, September, and December. A number of observations are shown in this table.

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Table 2. Sample Properties of CME Currency Futures Contracts. Currency British Pound Canadian Dollar Deutsche Mark Swiss France

1187 (1.5643) 1364 (0.7388) 1250 (0.6308) 1178 (0.7568)

Note: The reported numbers represent the total number of futures price observations from March 1994 to March 1998 for each currency respectively. The average futures prices are in parentheses.

Foreign currency futures returns series are covariance stationary since the estimated fractional differencing parameters fall between 0 and 0.5. The future contracts are those traded on the Chicago Mercantile Exchange. Notably, the well-known Samuelson effect cause volatility of futures prices to increase as a contract approaches expiration. This study examines a soon-to-expire one-year futures contract, and then switches over to follow the subsequent contract five days before its expiration date. Switchover times including both zero and ten days before maturity are used for the sample to investigate the robustness of the conclusions. However, since the results with different switchover times are essentially the same, this study concentrates only on the series constructed by switching five days before maturity. Some other features of data are shown in Tables 2 and 3. Table 2 shows the average futures price of the four currency futures. Table 3 shows that the autocorrelation of each data are high, even after six periods later, and such autocorrelation behavior is also consistent with that of fractionally integrated long-memory processes. Table 3. The Lag-6 Autocorrelation of Each Currency. The Lag-6 Autocorrelation of Currency Corr(a t, a t−6 ) British Pound Canadian Dollar Deutsche Mark Swiss Franc

0.945593 0.978032 0.982526 0.983154

4.1. British Pound Panel A in Table 4 displays the estimated parameters of the ARFIMA (0, 0, 0)FIGARCH (0, d2 , 0) model from the British Pound futures data. When the initial values of 0.30, 0.11 of parameters ␴2 , d2 are inputted into the proposed Gauss

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programs, they converge at the values 0.00008 and 0.16683, respectively. All tratio (4.69736, 6.78595) for ␴2 and (3.24116, 4.97148) for d2 are significant at the 5% level. Accordingly, the British Pound futures data clearly displays the property of long memory.

4.2. Canadian Dollar Panel B in Table 4 lists the estimated parameters of the ARFIMA (0, 0, 0)-FIGARCH (0, d2 , 0) model from the Canadian Dollar futures data. When the initial values of 0.30, 0.19 of parameters ␴2 , d2 are inputted into the proposed Gauss programs, they converge at the values 0.00001 and 0.19705, respectively. Moreover, all of their t-ratios (2.83754, 5.21043) for ␴2 and (2.83754, 5.09877) for d2 are also significant at the 5% level. Accordingly, the Canadian Dollar futures data also clearly displays the property of long memory. Table 4. The Estimation Results of the Currency Futures Volatility. Parameter

Estimate

Panel A: British Pound ␴2 0.00008 0.16683 d2

Standard Error

0.00002, 0.00001 0.05147, 0.03365

t-Ratio

4.69736; 6.78595 3.24116; 4.97148

The value of the likelihood function: 4044.565945 Panel B: Canadian Dollar ␴2 0.00001 0.19705 d2

0.00000, 0.00000 0.06944, 0.03865

2.83754; 5.21043 2.83754; 5.09887

The value of the likelihood function: 6347.762558 Panel C: Deutsche Mark ␴2 0.00002 0.15835 d2

0.00000, 0.00000 0.03725, 0.02771

6.37341; 7.98066 4.25117; 5.71363

The value of the likelihood function: 5092.507626 Panel D: Swiss Franc ␴2 d2

0.00003 0.14730

0.00001, 0.00000 0.04151, 0.02716

5.82980; 8.41483 3.54884; 5.42434

The value of the likelihood function: 4393.336667 Note: The estimation that results from our Gauss program shows whether or not the futures data of the British Pound (Panel A), Canadian Dollar (Panel B), Deutsche Mark (Panel C) and Swiss France (Panel D) between March 1994 and March 1998 fit the ARFIMA (0, 0, 0)-FIGARCH (0, d2 , 0). In the table below, we see that all t-ratios of the estimated parameters are greater than 1.96, i.e. they are significant at the 5% level.

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4.3. Deutsche Mark Panel C in Table 4 presents the estimated parameters of the ARFIMA (0, 0, 0)-FIGARCH (0, d2 , 0) model using the Deutsche Mark futures data. When the initial values of 0.30, 0.23 of parameters ␴2 , d2 are inputted into the proposed Gauss programs, they converge at the values 0.00002 and 0.15835, respectively. Moreover, all t-ratios (6.37341, 7.98066) for ␴2 and (4.25117, 5.71363) for d2 are significant at the 5% level. Accordingly, the Deutsche Mark futures data also clearly exhibits the property of long memory.

4.4. Swiss Franc Panel D in Table 4 shows the estimated parameters of the ARFIMA (0, 0, 0)-FIGARCH (0, d2 , 0) model for the Swiss France futures data. When the initial values of 0.30, 0.25 of parameters ␴2 , d2 are inputted into the proposed Gauss programs, they converge at the values 0.00003, 0.14730, respectively. All t-ratios (5.82980, 8.41483) for ␴2 and (3.54884, 5.42434) for d2 are significant at the 5% level. Therefore, the Swiss France futures data also displays the property of long memory. The above demonstrates that all of these futures contracts exhibit long memory, and their t-ratios are all under the 5% significance level.

5. HEDGING STRATEGY UNDER LONG MEMORY In the previous section, we find that all four currency futures have the long memory in volatility. Under such circumstance, how to hedge by using currency futures seem to be an interesting and important topic. In a conventional method, we usually find the hedging ratio by regressing the returns of the spot asset on the returns of the futures or other hedging instruments. For instance, if St were the price of a currency spot and Ht were the price of a currency futures contract, people who want to minimize their exposure to exchange rate risk would adopt the following hedging strategy. S t − S t−1 = a + b(H t − H t−1 ) + ␧t

(29)

Equation (29) means that one unit of exchange rate risk can be hedged by shorting bˆ unit of currency futures contracts (bˆ is the estimator of b). Finding the hedge portfolio just by regressing the returns of the currency spot asset on the returns of the currency futures cannot produce risk-minimizing hedge

Long Memory in Currency Futures Volatility

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ratios. We propose the following risk-minimizing hedge strategy to overcome this drawback. Let x be the random return of this hedging portfolio and the investor hold one unit of spot in the spot market and short −bt units of futures contracts in the futures market. The relationship of price change of the spot, st , price change of the future, ft , and the random return of hedging portfolio, xt , can be expressed as following: xt = st − bt ft

(30)

Suppose that investor face the mean-variance expected utility function EU(x t ) = E(x t ) − ␥Var(x t )

(31)

where ␥ is the risk aversion of the investor and the optimal hedging ratio can be obtained by solving the following maximization problem. maxEU(x t ) = max[E(s t ) + b t E(f t ) − ␥(␴2s t + b 2 ␴2f t − 2b t ␴s t ,f t )] b

b

(32)

The utility-maximizing hedge ratio at time t, which is obtained from solving Eq. (32) above, can be expressed as b ∗t =

E t (f t+1 ) + 2␥␴t (s t+1 , f t+1 ) 2␥␴2t (f t+1 )

.

(33)

The proposed hedging strategy is similar to that of Kroner and Sultan (1993) and this kind of method has the ability to find the risk-minimizing futures hedge ratio that conventional hedging strategy cannot do. This kind of method is superior to other hedging strategies, and it also provides the hedger an improved ability to manage foreign exchange risk. A difference between our hedging method and Kroner and Sultan (1993) is that theirs models the first moment with a bivariate error correction model (Engle & Granger, 1987) and the second moment with a bivariate constant correlation GARCH (1, 1) model (Bollerslev, 1990), but we model the first moment with a bivariate error correct model and the second moment with a bivariate FIGARCH (p, d2 , q) model (Brunetti & Gilbert, 2000). The variable d2 can be the value estimated as the one in Table 4. Some other methods, such as the one which considers the maturity effect of futures proposed by Chen, Duan and Hung (1999) can also be incorporated into our hedging strategy to improve the hedging effectiveness. We leave these interesting topics for future research work.

6. CONCLUSION This study has argued that currency futures are important because they display the property of long memory. Notably, this study examined existing econometric

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models in an attempt to find a model that is suitable for seeking this property. The mean-reverting fractionally integrated model is known to work effectively with long-run dependence time series data. Although previous researchers have used some fractionally integrated models such as ARFIMA, their models were only concerned with the mean (first-order moment). Therefore, this study developed a model which also incorporates long-memory volatility (second order moment). Specifically, this study used Chung’s revised version of the ARFIMA-FIGARCH model to test four futures contracts – (1) British Pound, CME; (2) Canadian Dollar, CME; (3) Deutsche Mark, CME; and (4) Swiss Franc, CME – to determine the effects of long memory. Evidence of long memory is found in all four currencies. The empirical results, thus, support the existence of long memory in futures contracts. The proposed ARFIMA-FIGARCH long memory model is an analytically tractable model of long memory in both conditional mean and variance, and it is easily fitted and analyzed using standard tools for weak stationary processes. Particularly, the ARFIMA-FIGARCH model is built using the widely used ARFIMA class of long memory time series models, and thus many of its properties are well understood. The above findings suggest some avenues to future research. For example, the proposed long-memory model could be used to investigate the phenomenon of long memory for other financial data. Still more intriguing would be to follow Duan (1995) in implementing an option-pricing formula that incorporates the long-memory properties of both mean and volatility. In fact, models that consider long memory will obtain more accurate results than those that use the Black-Scholes formula.

REFERENCES Baillie, R. T., & Bollerslev, T. (1994). Cointegration, fractional cointegration and exchange rate dynamics. The Journal of Finance, 737–745. Baillie, R. T., Bollerslev, T., & Mikkelsen, H. O. (1996). Fractionally integrated generalized auoregressive conditional heteroskedasticity. Journal of Econometrics, 3–30. Baillie, R. T., Chung, C.-F., & Tieslau, M. A. (1996). Analyzing inflation by the fractionally integrated ARFIMA-GARCH model. Journal of Applied Econometrics, 23–40. Barkoulas, J. T., Labys, W. C., & Onochie, J. I. (1999). Long memory in futures prices. The Financial Review, 91–100. Bollerslev, T. (1986). Generalized autoregressive conditional heteroskedasticity. Journal of Econometrics, 307–327. Bollerslev, T. (1990). Modeling the coherence in short-run nominal exchange rates: A multivariate generalized ARCH approach. Review of Economics and Statistics, 498–505. Bollerslev, T., Chou, T., & Kroner, K. (1992). ARCH modeling in finance: A selective review of theory and empirical evidence. Journal of Econometrics, 201–224.

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Bollerslev, T., & Mikkelsen, H. O. (1996). Modeling and pricing long memory in stock market volatility. Journal of Econometrics, 151–184. Bollerslev, T., & Mikkelsen, H. O. (1999). Long-term equity anticipation securities and stock market volatility dynamics. Journal of Econometrics, 75–99. Booth, G. G., Kaen, F. R., & Koveos, P. E. (1982a). Persistent dependence in gold prices. Journal of Financial Research, 85–93. Booth, G. G., Kaen, F. R., & Koveos, P. E. (1982b). R/S analysis of foreign exchange markets under two international monetary regimes. Journal of Monetary Economics, 407– 415. Booth, G., & Tse, Y. (1995). Long memory in interest rate futures market: A fractional cointegration analysis. Journal of Futures Markets, 15, 5. Brockwell, P. J., & Davis, R. A. (1991). Time series: Theory and methods (2nd ed.). New York: Springer. Brunetti, C., & Gilbert, C. L. (2000). Bivariate FIGARCH and fractional cointegration. Journal of Empirical Finance, 509–530. Chen, Y. J., Duan, J.-C., & Hung, M.-W. (1999). Volatility and Maturity effects in the Nikkei index futures. Journal of Futures Markets, 895–909. Cheung, Y. W. (1993). Long memory in foreign-exchange rates. Journal of Business and Economic Statistics, 93–101. Cheung, Y. W., & Lai, K. S. (1993). Do gold market returns have long memory? Financial Review, 181–202. Chung, C.-F. (1998). Estimating the fractionally integrated GARCH model. Working Paper. Chung, C.-F., & Baillie, R. T. (1993). Small sample bias in conditional sum of squares estimators of fractionally integrated ARMA models. Empirical Economics, 791–806. Diebold, F. X., Steven, H., & Rush, M. (1991). Real exchange rates under the gold standard. Journal of Political Economy, 1252–1271. Duan, J.-C. (1995). The GARCH option pricing model. Mathematical Finance, 13–32. Engle, R. F. (1982). Autoregressive conditional heteroscedasticity with estimates of the variance of U.K. inflation. Econometrica, 987–1008. Engle, R. F., & Bollerslev, T. (1986). Modeling the persistence of conditional variances. Econometric Reviews, 81–87. Engle, R. F., & Granger, C. W. (1987). Cointegration and error correction: Representation, estimation and testing. Econometrica, 251–276. Geweke, J., & Porter-Hudak, S. (1983). The estimation and application of long memory time series models. Journal of Time Series Analysis, 221–238. Granger, C. W. J. (1980). Long-memory relationships and the aggregation of dynamic models. Journal of Econometrics, 227–238. Granger, C. W. J., & Joyeux, R. (1980). An introduction to long-memory time series models and fractional differencing. Journal of Time Series Analysis, 15–39. Greene, M. T., & Fielitz, D. B. (1977). Long-term dependence in common stock returns. Journal of Financial Economics, 339–349. Heston, J. (1993). A closed-form solution for options with stochastic volatility with applications to bond and currency options. Review of Financial Studies, 327–343. Hosking, J. R. M. (1981). Fractional differencing. Biometrika, 165–176. Hsieh, D. A. (1988). The statistical properties of daily exchange rates: 1974–1983. Journal of International Economics, 129–145. Hsieh, D. A. (1989). Modeling heteroscedasticity in daily foreign-exchange rates. Journal of Business and Economic Statistics, 307–317.

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Kroner, K. F., & Sultan, J. (1993). Time-varying distributions and dynamic hedging with foreign currency futures. The Journal of Financial and Quantitative Analysis, 535–551. Lo, A. W. (1991). Long-term memory in stock market prices. Econometrica, 1279–1313. Mandelbort, B. B., & Van Ness, J. W. (1968). Fractal brownian motions, fractal noises and applications. Siam Review, 422–437. McCurdy, T., & Morgan, I. (1988). Testing the Martingale hypothesis in Deutsche mark futures with models specifying the form of the heteroscedasticity. Journal of Applied Econometrics, 187–202. Nelson, D. B. (1991). Conditional heteroskedasticity in asset returns: A new approach. Econometrica, 347–370. Sephton, P. S., & Larsen, H. K. (1991). Tests of exchange market efficiency: Fragile evidence from cointegration. Journal of International Money and Finance, 561–570. Sowell, F. (1992). Modeling long-run behavior with the fractional ARIMA model. Journal of Monetary Economics, 277–302. Stevenson, R., & Bear, R. (1965). Commodity prices: Trends or random walks. Journal of Finance (March).

VALUATION OF PENSION BENEFIT GUARANTEES AND TERMINATION CONDITIONS Jin-Ping Lee, Shih-Cheng Lee and Min-Teh Yu ABSTRACT We develop a model to estimate salary-based premiums for pension beneﬁt guarantees by simultaneously considering a stochastic interest rate and three practical pension plan termination conditions. We show the relationship among premium rates, a plan’s funding level, sponsoring ﬁrm’s capital position, early lapse, and a participant’s years of service. We also show how the regulatory intervention policy interacts with a plan’s funding level and a sponsor’s capital position and how it affects the pension insurance cost.

1. INTRODUCTION Under the defined benefit (DB) plan, an employee can receive a specified amount of benefits when he retires, but he may get less if the employer goes bankrupt and the pension is underfunded. In order to assure the timely and uninterrupted payment of pension benefits, the Pension Benefit Guaranty Corporation (PBGC) was established in 1974 by the Employee Retirement Income Security Act (ERISA) to protect retirement incomes. The PBGC receives no funds from general tax revenues and its operations are financed by insurance premiums. Until 1988, the insurance premiums charged by the PBGC were set at a flat rate Research in Finance Research in Finance, Volume 20, 159–180 Copyright © 2003 by Elsevier Ltd. All rights of reproduction in any form reserved ISSN: 0196-3821/doi:10.1016/S0196-3821(03)20009-5

159

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JIN-PING LEE, SHIH-CHENG LEE AND MIN-TEH YU

per plan participant. The PBGC was empowered by the 1987 Omnibus Budget Reconciliation Act to levy a variable rate premium, subject to a cap, based on the plan’s funding shortfall and the maximum premium limit was eventually completely eliminated in 1997. During this time, the PBGC’s deficit grew from $12 million in 1975 to $2.9 billion in 1993, then turned sharply around into a surplus in 1996 with the surplus increasing further to $5 billion in 1998. Even though this phenomenon may have resulted from the corresponding changes in economic environment, the premium rates’ setting remains the main concern of the PBGC, the plan participants, the sponsoring firms, and many academic studies. A number of studies have applied contingent-claim techniques to value pension insurance or to measure its impact on the sponsoring firm’s pension funding policy. Most of these studies, for instance, Sharpe (1976), Treynor (1977), Pesando (1982), Bicksler and Chen (1985), VanDerhei (1990) and Hsieh and Chen and Ferris (1994), assume that the term to maturity of a pension insurance guarantee is known. This is a convenient assumption since it allows pension insurance to be valued in a manner similar to that of a standard European put option written by the PBGC on the pension assets with a strike price equal to the pension benefit. Marcus (1987) notes the maturity’s uncertainty and values the pension insurance by linking the plan termination to both the financial condition of the pension fund and the sponsoring firm’s financial condition. Pennacchi and Lewis (1994) extend Marcus (1987) and provide a more realistic model of a contingent put option (rather than a contingent forward) for pension insurance with deterministic pension liabilities and a maturity date equal to the time of the sponsoring firm’s bankruptcy. In another line of pension research, Britt (1991) and Sherris (1995) value the retirement benefits by linking the benefits directly to the salary since an employee’s benefit usually relates to his wage or salary. Kalra and Jain (1997), in a salary-based pension insurance framework, obtain an active intervention policy for the PBGC to terminate a severely-underfunded pension plan so as to control the fund’s loss exposure. Boyce and Ippolito (2002) argue that pension insurance claims have an important market-risk component and suggest using contingent claim models in measuring pension insurance. Our study extends Marcus (1987) and Pennacchi and Lewis (1994) to a model with a stochastic interest rate and pension liabilities and incorporates the salary-based premiums of Britt (1991) and Sherris (1995). In estimating the pension insurance premiums, we also simultaneously consider three practical termination conditions: the sponsoring firm’s potential bankruptcy, the PBGC’s active intervention, and an employee’s early lapse. The remainder of this article is as follows. Section 2 develops the model, specifies the asset and liability dynamics of the pension fund and the sponsoring firm, constructs the insurance

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161

payoffs under three termination conditions, and identifies the premium formula. Section 3 provides the numerical analysis and results. Section 4 concludes the paper.

2. A MODEL OF PENSION BENEFIT GUARANTEES We develop a model that allows for three practical conditions of plan termination. First, the pension plan terminates when the sponsoring firm goes bankrupt. Second, the insurer or the PBGC is authorized to intervene and terminate a pension plan that is severely underfunded. Third, a decremental event such as an employee’s early retirement and/or disability is taken into account. In order to value the pension guarantees under alternative termination conditions, we specify the dynamics of the pension benefits, the pension assets, the sponsor’s assets and liabilities, and the termination conditions in the following subsections.

2.1. Pension Beneﬁt Dynamic We assume that the PBGC evaluates the single-employer DB pension plan at the employee level. When an employee retires, the pension plan pays a lump-sum benefit which is a fixed percentage of the average annual wage multiplied by the years of employment. We assume that the wage, denoted as St , follows a geometric Brownian motion: dS t = ␮s S t dt + ␴s S t dz s,t ,

(1)

where ␮s and ␴s are constant and denote the drift and volatility of the wage process respectively; and zs,t is a Weiner process. Following Kalra and Jain (1997), the risk-neutralized wage process can be described as follows: dS t = (r t + k)S t dt + ␴s S t dz ∗s,t ,

(2)

where dz ∗s,t = dz s,t +

␮s − r t − k dt, ␴s

and where k denotes the difference between the wage’s growth rate and the assets available in the market that can span the wage. Term rt is the instantaneous interest rate. In order to determine the dynamics of the average wage, we assume that the weight assigned to the wage increases exponentially with time. Consequently, we

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get the average wage dynamics as follows: dS¯ t = ␤(S t − S¯ t ) dt,

(3)

where S¯ t denotes the average wage and ␤ is the parameter of the exponential function that is used to account for the weights of the average wages.1 If an employee works for a company from time 0 to time t, then he has accrued a pension benefit equal to ␭S¯ t t payable at the time of retirement (denoted as T) and ␭ is a fixed ratio specified in the pension plan. The value of the accrued benefits at time t, Bt , can be written as follows: T

B t = e−

t

r s ds

␭S¯ t t,

(4)

where rs is the instantaneous interest rate. We adopt the square-root process of Cox et al. (1985) (CIR) to describe the interest rate dynamics. The CIR model has the mean-reverting property and can ensure positive interest rates. Following Cox et al. (1985), the instantaneous interest process in the risk-neutral world can be described as follows: √ dr t = a(b − r t ) dt + ␴r rt dz rt ,

(5)

where a is a positive constant measuring the magnitude of the mean-reverting force; b is the long-run mean of the interest rate; ␴r is the volatility parameter of the interest rate; and zr,t is a Weiner process. For derivative pricing, it is standard to use the device of risk-neutralization. The dynamic for the interest rate under the risk-neutralized pricing measure, denoted by Q, can be written as √ dr t = a ∗ (b ∗ − r t ) dt + ␴r rt dz ∗rt ,

(6)

where ␣∗ , m∗ , and Z ∗t are defined as a∗ = a + ␭ ab b∗ = a+␭ dz ∗r,t

= dz r,t

√ λ rt + dt. ␴r

Term ␭ is interpreted as the market price of interest rate risk and is a constant under the Cox et al. (1985) assumption and Z ∗t is a Wiener process under Q.

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2.2. Pension Asset Dynamic Following Sundaresan and Zapatero (1997) and Kalra and Jain (1997), the evolution of pension assets is assumed to be affected by both returns on investment performance and the sponsoring firm’s fund contributions. The sponsoring firm contributes to the fund according to a funding rate that can be categorized into two components: a normal funding rate, denoted by ␣t and a variable funding rate, denoted by ␥t . Kalra and Jain (1997) characterize the normal funding rate to ensure B0 PV0 [B t ] , = PV0 [A t ] A0 where PV0 stands for the present value at time 0 and At is the value of the pension asset at time t. This requirement yields ␣t =

S 0 ekt − PV0 [S¯ t ] 1 . +␤ t PV0 [S¯ t ]

(7)

Since the normal funding rate is independent of the financial situation of the sponsoring firm, the variable funding rate implicitly accounts for the financial condition of the sponsoring firm. They both implicitly assume that the level of pension funding increases with the firm’s financial condition. Thus, the variable funding rate, ␥t , can be described as follows: Bt , (8) ␥t = c 1 − c 2 ln At where c1 and c2 are constants such that c 1 > c 2 > 0. The values of c1 and c2 determine the extent to which PBGC can tolerate underfunding. The foregoing analysis produces the following process for the pension asset At in a continuoustime framework. dA t = (␮A + ␣t + ␥t )A t dt + ␴A A t dZ At ,

(9)

where ␥A and ␴A are respectively the drift and volatility of the pension assets and ZA,t is a Weiner process. The pension asset dynamic in the risk-neutral world can be written as follows: ∗ = (rt + ␣t + ␥t )At dt + ␴A At dZA,t ␮A − r t ∗ = dZ dZA,t dt. A,t + ␴A

dAt

(10)

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2.3. A Firm’s Asset Dynamic Following Marcus (1987) and Pennacchi and Lewis (1994), we assume that the asset value dynamic of the sponsoring firm Vt as follows: dV t = (␮V − c V )V t dt + ␴V V t dZ V,t ,

(11)

where ␥V and ␴V refer respectively to the drift and volatility of the return on the sponsor’s assets and cV is the dividend payment rate on the sponsor’s assets. In a risk-neutral world the asset value dynamic of the sponsoring firm can be written as follows: ∗ , dVt = (rt − cV )Vt dt + ␴V Vt dZV,t ␮v − r t ∗ = dZ dt. dZV,t V,t + ␴V

(12)

where term Z ∗V,t is a Weiner process under the risk-neutral measure.

2.4. A Firm’s Liability Dynamic We follow Marcus (1987) to set the dynamics of the sponsor’s liabilities denoted as Dt , which follow a geometric Brownian motion: dD t = ␮D D t dt + ␴D D t dZ D,t ,

(13)

where ␮D and ␴D refer respectively to the drift and volatility of the sponsor’s liabilities. In a risk-neutral world, the value of the sponsor’s liabilities can be written as follows: dD t = (r t − ␭D ␴D )D t dt + ␴D D t dZ ∗D,t , where term ␭D is the market risk price of the sponsor’s liability and Weiner process under the risk-neutral measure.

(14) Z ∗D,t

is a

2.5. Termination Conditions 2.5.1. Distress Termination The pension plan is terminated when the sponsoring firm declares bankruptcy. We assume that the firm goes bankrupt when the value of its assets falls to a specific level of the value of liabilities. The obligation of the PBGC in this termination condition depends on whether the pension assets are sufficient enough to pay the

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benefits guaranteed. The payments of PBGC can be described as follows: CtD = BtD − AtD 0

if AtD < BtD otherwise,

and

Vt ≤ ␦Dt , 0 < ␦ ≤ 1

(15)

where C t D denotes the amount that the PBGC needs to pay when the sponsor goes bankrupt. Term ␦ refers to the level of the sponsor’s negative net worth at which bankruptcy occurs and term tD represents the time that it takes for Vt to fall to ␦Dt . 2.5.2. Intervention Termination A pension plan may also be terminated by the intervention of the regulatory authority. Under the ERISA, the PBGC is authorized to terminate a plan irrespective of the plan sponsor’s wishes under certain circumstances. This authority protects the PBGC against unreasonable increases in its exposure to loss through continued operation of the plan, against continued accruals of benefit obligations and against any possible deterioration of the sponsor’s net worth. Kalra and Jain (1997) use option-pricing techniques to measure the optimal intervention policy for the PBGC to terminate the severely-underfunded pension plans. In contrast to Kalra and Jain’s study, we consider not only the effect of the funding level, but also the sponsoring firm’s capital position on the value of pension insurance. We do not expect that the optimal intervention point estimated by Kalra and Jain will still be satisfied for our model.2 In order to measure the effect of the PBGC’s early intervention on the cost of the pension insurance, we will specify different intervention points in the section of numerical analysis. In the U.S., by the Single Employer Pension Plan Amendments Act (SEPPA), under any case in which a single-employer plan is terminated due to a distress termination or when an intervention termination is instituted by the PBGC, the plan’s sponsor will incur a liability to the PBGC. This liability consists of the total amount of the unfunded benefit liabilities calculated from the termination date. Hence, the PBGC’s obligation in the case of intervention termination can be described as follows:

CtI =

 At  ≤ ␩ and (BtI − AtI ) > (VtI − DtI ) > 0  (BtI − AtI ) − (VtI − DtI ) if  Bt  B t I − A tI     0

At ≤ ␩ and Bt otherwise,

if

(BtI − AtI ) > 0 > (VtI − DtI )

(16) where ␩ is the intervention ratio specified by the PBGC and C t I is the PBGC’s payments when the intervention occurs at time tI .

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2.5.3. Early Lapse The PBGC insurance contract can also be considered as terminated for individual participants when early lapses occur. There are several types of early lapses, such as the participant’s early retirement, death, and/or disabilities. Sherris (1995) creates the annual decrement rate for workers with different ages and all the annual decrement rates are near 0.02. For simplicity, this study assumes that the annual decrement rate for plan participants is 0.02 and is uniformly distributed for a year. The probability distribution of the decrements can be written as follows: 1 Pr = 0.02 PtQ = 0 Pr = 0.98, where P t Q = 1 refers to the occurrence of the plan participant’s early lapse and P t Q = 0 refers to the participant who is still in the pension plan. The payments of PBGC at the time when the participant’s early lapse occurs can be described as follows:   BtQ − AtQ − (VtQ − DtQ ) if PtQ = 1 and BtQ − AtQ > VtQ − DtQ > 0 if PtQ = 1 and BtQ − AtQ > 0 > VtQ − DtQ C t Q = B tQ − A tQ  0 otherwise, (17) where C t Q denotes the PBGC’s obligation when the decremental events of participants occur at time tQ .

2.6. Premiums for PBGC Insurance Under the termination conditions and dynamics of assets, liabilities, and accrued benefits that are specified above, we can value the pension benefit guaranty insurance premium by using the risk-neutral pricing techniques. The fairly-priced premium for $1 of current wage can be written as follows: ti 1 Pt = E t ∗ [e−r i C tI ], (18) St {i=D,I,Q}

where 1 r¯t = ti − t

ti t

r s ds,

and Pt denotes the premium for the PBGC insurance and E ∗t [·] takes the expectation under the risk-neutral measure. The analytical framework is fully specified. We would not expect a closed-form solution for such a complex contract and will

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estimate the premium for the PBGC insurance using a numerical method in the next section.

3. NUMERICAL ANALYSIS The premium for the pension insurance contract is estimated by using the Monte Carlo method with 20,000 simulations paths. All the relevant values are generated monthly. That is, the financial conditions of the pension plan and sponsoring firm are evaluated monthly and we assume that these financial conditions are available to the PBGC and are based upon the PBGC terminating the plan according to its termination rules. 3.1. Simulation Method and Procedure Because the premium for the pension insurance contract depends on 4 state variables, we have to specify the stochastic processes for these state variables (Eqs (2), (10), (12) and (14)). Let Fi,t denote the value of state variable i and define ␴i and (r i + m i,t ) as the volatility and growth rate of XX in a risk-neutral world, respectively. Applying Ito’s lemma we have the following: dln(F i,t ) − (r t + m i,t − 21 ␴2i ) dt + ␴i dW ∗i,t ,

i = 1, 2, 3, 4.

Its solution is, for any q = 0, F i,t+q = F i,t exp(␴i (W ∗i,t+q − W ∗i,t ) + (m i,t − 21 ␴2i )q + i = 1, 2, 3, 4.

(19)

t+q t

r s ds), (20)

These solutions suggest a simple way of simulating asset values. First, we simulate the risk-neutralized interest rate process as in Eq. (6) to approximate the whole t+1 sample path. This in turn allows us to compute the quantity of interest: t r s ds. Second, we simulate W ∗i,t+1 − W ∗i,t using the fact that they are independent of the path of rt . Because these variables are correlated, the coefficient of correlation between W ∗i,t+1 − W ∗i,t and W ∗j,t+1 − W ∗j,t is ␳ij . We first sample four independent variables ␤1 , ␤2 , ␤3 , and ␤4 , from univariate standardized normal distributions. The required samples are W ∗i,t+1 − W ∗i,t , 1 = i = 4, where W ∗i,t+1 − W ∗i,t =

i k=1

␣ik ␤k .

(21)

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For W ∗i,t+1 − W ∗i,t to have the correct variance and the correct correlation with W ∗j,t+1 − W ∗j,t , 1 = j < i, we must have i

␣2ik = 1,

j

␣ik ␣jk = ␳ij , j < i. (22) k=1 k=1 The first sample, W ∗i,t+1 − W ∗i,t is set equal to ␤1 . These equations for the ␣s can be solved so that W ∗2,t+1 − W ∗2,t is calculated from ␤1 and ␤2 ; W ∗3,t+1 − W ∗3,t is calculated from ␤1 , ␤2 and ␤3 ; and so on. Combining W ∗i,t+1 − W ∗i,t , 1 = i = 4 with the t+1 simulated t r s ds. yields simulated values for F i,t+1 , 1 = i = 4, as described in and

Eq. (19). After simulating these four processes, the guarantee value as well as the total present value of all premium payments can be easily calculated. In short, we have devised a more practical way of computing the fairly-priced premium rate, P.

3.2. Parameter Values We establish a set of base values for the parameters and summarize them in Table 1. Deviations from the base values are set in order to assess the comparative effect of these parameters on the premiums of the PBGC insurance. We choose the parameter values according to those used by Marcus (1987), Pennacchi and Lewis (1994) and Kalra and Jain (1997). In addition, we assume that the employee starts working at age 25 and retires at age 65; thus, T = 40. The average annual wage of an employee at age 25 S0 is set to be $30,000, though any other values will not affect our premium estimates. We estimate the premiums for the workers at age 30 (i.e. t = 5), 35, 40, 45, 50, 55, and 60 to measure the effects of the worker’s years of service on the premiums. The initial level of pension funding (A/B) is set to be 0.6, 0.7, 0.8, 0.9, 1, 1.1, 1.2, and 1.3.3 The pension plan is fully funded when the ratio is 1 and is underfunded (overfunded) when the ratio is less (greater) than 1. The initial capital position (V/D) of sponsoring firms is set to be 1.1, 1.2, 1.3, and 1.4. The volatility of the return on the pension assets is assumed to be 15%; the average standard deviation of the wage growth is 10%. Other parameter values are all within the ranges typically used in the previous literature.

3.3. Fair Premiums and Results Table 2 reports the premiums under an alternative set of the sponsor’s capital positions (V/D), the funding levels (A/B), and the termination conditions, while fixing

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Table 1. Parameter Definition and Base Values. Wage parameters S0 S¯ t ␤ T ␭ k ␮s ␴s Bt

Wage at entry time 0 Average wage at time t Rate of exponential function Retirement time of the employee Ratio used to calculate the accrued benefit Difference between the growth rate of wages and assets available that span the wages Average growth rate of the wage Average standard deviation of the wage Accrued benefit at time t

Pension asset parameters A Value of the pension assets ␮A Average growth rate of pension assets ␴A Average standard deviation of pension assets Normal funding rate ␣t ␥t Variable funding rate Constants associated with the variable funding rate c1 , c 2

30,000 0.2 40 0.2 0

0.1

0.15

0.08, 0.04

Sponsoring firm’s parameters V Value of the firm’s assets ␮V Average growth rate of the firm’ assets Average standard deviation of the firm’s assets ␴V cV Dividend rate of the firm’s assets ␦ Level of the firm’s asset-liability ratio at which bankruptcy occurs Dt Value of the firm’s liabilities at time t Average growth rate of the firm’s liabilities ␮D ␴D Average standard deviation of the firm’s liabilities ␭D Market price of risk on the firm’s liabilities

0.1 0.1 0

Interest rate parameters Instantaneous interest rate at time t rt a Magnitude of mean reverting force b Long-run mean of interest rate ␴r Volatility parameter of interest rate

0.05 0.2 0.05 0.1

  ␳SS   ␳AS   ␳VS ␳DS

␳SA ␳AA ␳VA ␳DA

␳SV ␳AV ␳VV ␳DV

   ␳SD    1 0.1  ␳AD   =  0.1 1 ␳VD   0 0.5 ␳DD 0 0.2

Note: Correlation coefficients of related variables.

0 0.5 1 0.2

 0  0.2  0.2 1

0.1 0.2 0.03 0.8

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Table 2. Premiums for Participants with Five Years of Service. Vt /Dt = 1.1 Panel I: Distress termination 1.71875 At /Bt = 0.7 0.8 0.91385 0.9 0.33517 1.0 0.08186 1.1 0.01502 1.2 0.00378 1.3 0.00026

Vt /Dt = 1.2

Vt /Dt = 1.3

Vt /Dt = 1.4

1.15265 0.59143 0.22441 0.06154 0.01356 0.00171 0.00015

0.71725 0.36155 0.14055 0.03845 0.00766 0.00083 0.00014

0.42560 0.21979 0.07448 0.02256 0.00483 0.00077 0.00010

Panel II: Distress and involuntary termination (Intervention ratio = 0.45) At /Bt = 0.7 1.74358 1.15244 0.73346 0.8 0.92059 0.59231 0.36877 0.9 0.33961 0.23004 0.13734 1.0 0.09178 0.05958 0.03915 1.1 0.01649 0.01163 0.00714 1.2 0.00289 0.00128 0.00198 1.3 0.00049 0.00020 0.00017

0.41445 0.20915 0.07844 0.02365 0.00382 0.00061 0.00008

Panel III: Distress, involuntary termination, and early lapse (Intervention ratio = 0.45) At /Bt = 0.7 1.71815 1.12109 0.71055 0.40567 0.8 0.90496 0.58186 0.35836 0.21578 0.9 0.34270 0.21884 0.13865 0.07815 1.0 0.09099 0.05975 0.03388 0.02219 1.1 0.01639 0.01132 0.00698 0.00386 1.2 0.00241 0.00232 0.00114 0.00050 1.3 0.00066 0.00025 0.00030 0.00009 Note: Premiums are represented as a percentage of the participant’s wage. All estimates are computed using 20,000 simulation runs.

the participant’s years of service at 5, i.e. t = 5,4 and the intervention ratio is 0.45, i.e. ␩ = 0.45. We do observe that the premium decreases with the funding level and the sponsor’s capital position under all three scenarios of termination conditions. Comparing Panel I with Panel II, we observe that the PBGC terminates a plan early at a funding level of 0.45 and increases the cost of the PBGC’s insurance when the pension plans are underfunded or fullyfunded especially in the lower sponsoring firm’s capital position case. For instance, when the plan’s initial funding level equals 0.7 and the sponsoring firm’s capital position equals 1.1, the intervention increases the premium around 0.03%. We also observe that the PBGC’s early intervention decreases the insurance cost for overfunded pension plans especially for sponsoring firms with a higher capital position. In order to understand the effects of an early intervention further, we measure premiums under different intervention ratios in Section 3.4. Comparing

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Panel II with Panel III, the effect of the participant’s early lapse on the cost of pension guarantees is not clear. This is because the participant’s early lapse affects nothing but the maturity of the PBGC’s put liability and therefore its effect is indeterminate.5 Table 3 reports premiums for participants with different years of service under alternative termination conditions. Figure 1 shows the relationship among premiums, participants’ years of service, a plan’s initial funding levels while fixing the sponsoring firm’s capital position (V/D) to 1.2, and the intervention ratio at 0.45. We find that the premium generally increases with years of service, but the increase is more significant for plans which are underfunded and fullyfunded than overfunded. For example, premiums for underfunded plan participants with 35 years of service can be 25 times higher than those with 5 years of service. This is because the accrued benefits are based on a participant’s average wage and years of service, and participants with longer years of service accrue benefits faster than those with shorter years of service. Figure 1 also indicates that the premium decreases with the plan’s initial funding level. We observe that the decrement in premiums caused by increasing the plan’s initial funding level is substantial for deeply underfunded plans and for participants with many years of service. Figure 2 shows the relationship among premiums, participants’ years of service, a sponsoring firm’s capital position, while fixing the plan’s initial funding levels to 0.9 and the intervention ratio at 0.45. We observe that premiums increase with a participant’s years of service, but decrease with a sponsoring firm’s capital position. We also note that the decrement in premiums due to a sponsoring firm’s higher capital position rises with participant’s years of service. Our results show that years of service can affect the cost of pension insurance guarantee substantially under certain scenarios, which are inconsistent with the current pension insurance scheme that charges a flat rate on all participants without considering their years of service.6

3.4. Fair Premiums and the PBGC’s Intervention Policy In order to evaluate and measure how the PBGC’s intervention policy affects the cost of pension guarantees, we estimate fair premiums under different intervention ratios. Figure 3 shows the relationship among premium, intervention ratio, and the sponsoring firm’s capital position while fixing a participant’s years of service at 5 and the plan’s initial funding level at 0.9. We note that the premiums fall quickly when the intervention ratio is set to be close to the plan’s initial funding level. This finding agrees with our intuition since PBGC can always lower its cost by liquidating a plan immediately when the plan’s funding level falls below its initial

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Table 3. Premiums for Participants with Different Years of Service. Vt /Dt = 1.1 Funding level = 0.7 t=5 1.71815 10 3.74858 15 6.87381 20 11.85295 25 18.69755 30 28.50356 35 42.90747

Vt /Dt = 1.2

Vt /Dt = 1.3

Vt /Dt = 1.4

1.12109 2.50847 4.51325 7.58794 12.34375 18.32120 28.45085

0.71055 1.48546 2.81825 4.60416 7.56083 10.98136 16.41798

0.40567 0.91967 1.59110 2.80857 4.36274 6.90061 10.07051

Funding level = 0.9 5 10 15 20 25 30 35

0.34270 0.72050 1.29608 2.19621 3.45121 5.23980 8.06160

0.21884 0.45550 0.82578 1.40187 2.27804 3.45251 5.09221

0.13865 0.30294 0.47997 0.82914 1.33940 2.01480 3.07332

0.07815 0.17025 0.28380 0.49750 0.75402 1.17448 1.74974

Funding level = 1.0 5 10 15 20 25 30 35

0.09099 0.17069 0.32453 0.58633 0.82692 1.33924 1.91991

0.05975 0.11498 0.23375 0.36586 0.54951 0.82110 1.14093

0.03388 0.07191 0.14055 0.21337 0.33211 0.57058 0.89739

0.02219 0.04118 0.08139 0.13033 0.22068 0.33357 0.49521

Funding level = 1.2 5 10 15 20 25 30 35

0.00241 0.00441 0.00899 0.01394 0.02473 0.03903 0.03650

0.00232 0.00354 0.00724 0.01025 0.02228 0.02617 0.05541

0.00114 0.00133 0.00281 0.00529 0.00676 0.01570 0.01589

0.0050 0.00158 0.00235 0.00678 0.00644 0.01191 0.01093

Note: Distress Termination, Involuntary Termination, and Early Lapse are Simultaneously Considered Intervention Ratio = 0.45. Premiums are represented as a percentage of the participant’s wage. All estimates are computed using 20,000 simulation runs.

level. In reality, PBGC allows the funding level to change over time and does not terminate a plan as soon as its funding level begins to fall. Figure 3 does not show that an optimal intervention ratio exists over the range of the intervention ratio except for the corner optimal at the plan’s initial funding level.

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Fig. 1. Premiums for Participants with Different Years of Service.

We use the premiums estimated under the distress termination condition as the benchmark to measure the effect of an alternative termination condition on the cost of pension guarantees. Figures 4, 5 and 6 shows how the initial funding level interacts with the intervention ratio. These premiums are estimated with years of service equal to 5 and V/D = 1.1 or 1.4. We find that when the capital position of a sponsoring firm is high (V/D = 1.4%), the effect of early intervention

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Fig. 2. Premiums for Participants with Different Years of Service.

is ambiguous and does not change the pension insurance cost in any certain direction. When the capital position of a sponsoring firm is low (V/D = 1.1), early intervention can lower the pension insurance cost for overfunded plans, but will increase the cost for fullyfunded and underfunded plans.

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Fig. 3. Premiums under Different Intervention Ratio.

Our results indicate that, except for the range near the plan’s initial funding level, the PBGC’s early intervention can lower the cost of pension guarantees only for overfunded plans with a low capital position. This provides the policy implication that the optimal intervention rule should depend not only on the

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Fig. 4. Premiums under Different Intervention Ratios.

funding level (such as in Kalra & Jain, 1997), but also on the capital position and other risk factors of the sponsoring firm. It is as such incorrect to set a uniform intervention ratio of funding to all pension plans.

Valuation of Pension Beneﬁt Guarantees and Termination Conditions

Fig. 5. Premiums under Different Intervention Ratios.

177

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Fig. 6. Premiums under Different Intervention Ratios.

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179

4. CONCLUSION We develop a model to estimate salary-based premiums for pension benefit guarantees by simultaneously incorporating three practical pension plan termination conditions: corporate bankruptcy, regulatory intervention, and early lapse of participants. We also improve previous models by estimating the premiums in an economy with a stochastic interest rate and stochastic pension fund liabilities. Our model allows us to measure the impacts of the plan’s funding level, the sponsor’s capital position, and the participant’s years of service on the benefit guarantee premium. Our results show that the premium rates decrease with the sponsor’s capital position and the plan’s funding level, but increase with the participant’s years of service. The effect of years of service becomes more evident and significant for plans with a low initial funding level and a sponsor’s low capital position. This suggests that the PBGC needs to be alert about the loss exposure to underfunded plans that consist of participants with long years of service. We also note that the effect of early lapse is small and does not affect the premium in a clear way. Finally, we find that the PBGC’s intervention rule can be effective only for overfunded plans with a sponsor’s low capital position. The optimal intervention ratio may not exist and its determination should consider not only the funding level, but also the capital position and other risk factors of the sponsoring firm. It is therefore incorrect to set a uniform intervention ratio of funding to all pension plans.

NOTES 1. That is, we assume that the weight assigned to the salary increases exponentially with time to reflect the fact that more weight is usually given to the salary during the last few years, as compared to that in the earlier years. 2. According to Kalra and Jain’s numerical results, the optimal timing for the PBGC to intervene in a pension plan is when the ratio of the value of pension assets to the value of the accrued pension benefits reaches 0.45 or alternatively, A t /B t = 0.45. The optimal intervention point is derived by fixing S¯ t /S t = 1, and by some other parameter values that the authors specify. 3. The PBGC (1999) reports that the average funding ratios of underfunded and overfunded PBGC-insured plans for the single-employer program are 88% and 128% in 1997, respectively. 4. Premium estimates under other years of service have the same pattern, and therefore are not reported here. 5. Put options usually have negative thetas. However, deep-in-the-money European puts could have positive thetas.

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6. Currently, all single-employer pension plans pay a basic flat-rate premium of $19 per participant per year and underfunded plans pay an additional variable-rate charge of $9 per $1,000 of underfunded vested benefits. See U.S. GAO (1998).

ACKNOWLEDGMENTS We thank seminar participants at the 2002 FMA Annual Meeting and the 2002 Midwest Finance Association Annual Meeting for helpful comments.

REFERENCES Bicksler, J. L., & Chen, A. H. (1985). The integration of insurance and taxes in corporate pension strategy. Journal of Finance, 40, 943–955. Boyce, S., & Ippolito, R. (2002). The cost of pension insurance. Journal of Risk and Insurance, 69, 121–170. Britt, S. (1991). Greater of benefits: Member options in defined benefit superannuation plans. Transactions of the Institute of Actuaries of Australia, 77–118. Cox, J. C., Ingersoll, J. E., & Ross, S. A. (1985). A theory of the term structure of interest rates. Econometrica, 53, 385–407. Hsieh, S. J., Chen, A. H., & Ferris, K. R. (1994). The valuation of PBGC insurance using an option pricing model. Journal of Financial and Quantitative Analysis, 29, 89–99. Kalra, R., & Jain, G. (1997). A continuous-time model to determine the intervention policy for PBGC. Journal of Banking and Finance, 21, 1159–1177. Marcus, A. J. (1987). Corporate pensions policy and the value of PBGC insurance. In: Z. Bodie, J. Shoven & D. A. Wise (Eds), Issues in Pension Economics (pp. 49–79). University of Chicago Press. Pennacchi, G. G., & Lewis, C. M. (1994). The value of pension benefit guaranty corporation insurance. Journal of Money, Credit and Banking, 26, 735–756. Pension Benefit Guaranty Corporation (1999). The pension insurance data book. Pesando, J. E. (1982). Investment risk, bankruptcy risk, and pension reform in Canada. Journal of Finance, 37, 741–749. Sharpe, W. F. (1976). Corporate pension funding policy. Journal of Financial Economics, 3, 183–193. Sherris, M. (1995). The valuation of option features in retirement benefits. Journal of Risk and Insurance, 62, 509–534. Sundaresan, S. Z., & Zapatero, F. (1997). Valuation, optimal asset allocation and retirement incentives of pension plans. Review of Financial Studies, 10, 631–660. Treynor, J. L. (1977). The principles of corporate pension finance. Journal of Finance, 32, 627–638. U.S. General Accounting Office (1998). Pension benefit guaranty corporation: Final condition improving, but long-term risk remain, GAO/HEHS-99–5. VanDerhei, J. L. (1990). An empirical analysis of risk-related insurance premiums of the PBGC. Journal of Risk and Insurance, 57, 240–259.

ANNOUNCEMENT EFFECTS OF SPECIALLY DESIGNATED DIVIDENDS Ken Hung, Chang-Wen Duan and Gladson I. Nwanna ABSTRACT This paper explores dividend announcements based on information hypothesis. We explore in particular whether or not information signaling theory existed in Taiwan. We also explore the free cash ﬂow hypothesis. In order to eliminate affecting factors, we target companies with irregular dividends as research samples, just like those with specially designated dividends (SDD). We examine whether or not those proceeds may be deemed as future earnings prospection. In this paper we study mainly dividend announcements made during stockholder’s meetings of the companies listed in the Taiwan Stock Exchange (TSE) or R.O.C. Over-the-Counter Securities Exchange (ROSE). We apply event study as means of analyzing abnormal returns of the companies. In addition we use the GARCH model with traditional ordinary least square to estimate the market model. The results indicate that SDDs are considered positive signals by the national exchange, TSE. In addition, we also show that the ﬁrst-time SDD does transmit a positive signal to the market regarding the ﬁrm’s future cash ﬂow, and that the SDD of no payment in the previous three years is negative. Furthermore, we prove that low Q ﬁrms have greater market reaction than high Q ﬁrms in announcement period. The free cash ﬂow hypothesis and ﬁrm size effects could not be veriﬁed in Taiwan.

Research in Finance Research in Finance, Volume 20, 181–212 Copyright © 2003 by Elsevier Ltd. All rights of reproduction in any form reserved ISSN: 0196-3821/doi:10.1016/S0196-3821(03)20010-1

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1. INTRODUCTION Stock dividend is a payment of a company’s stocks to its shareholders in proportion to their share of ownership in the company. This takes two payment formats in Taiwan. The first is a sum of earnings distribution known as capital earnings appreciation, and the second is a capital distribution known as public capital appreciation. In Taiwan, stock market investors and listed companies are in the habit of calling both of the afore-mentioned formats stock dividends. For the company, stock dividend distribution is an accounting adjustment of equities that has no effect on existing company cash flow. For the shareholders, they stand to benefit in the form of extra assets through the distribution of stock dividends. This adjustment, however, does not change the percentage of their shareholdings. As the number of share-ownership increase, the total number of shares in circulation also rise as well, hence share prices decrease proportionally. This results in zero wealth change for shareholders after ex-righted. Generally, the majority of listed companies in Taiwan adopt stock dividends as means of earnings allocation. From an economic viewpoint stock dividends convey no essential economic profit for either the company or the stockholders. Yet the process of distributing stock dividends consumes much of company costs, such as the cost of applying and managing stock dividend payments, printing, public explanations of capital appreciation, and stock-related service costs i.e. notices and stock shares, etc. In Taiwan, listed companies annually engage in sizeable stock dividend payments. It is this anti-economic effect principle practiced by listed companies as well as the driving or motivating factors which is of interest to us. Research studies on stock market and stock dividends point mostly to a positive stock price effect response, i.e. Foster and Vickrey (1978), Woolridge (1983), Brickley (1983), Grinblatt, Masulis and Titman (1984), Foster and Scribner (1991), Forjan and McCorry (1998) and Gombola and Liu (1999), etc. From the investor’s viewpoint, stock dividends do not increase shareholder’s cash flow, but would sustain losses in shareholder’s rights instead, due to the increasing cost of dividend payment. Moreover, Taiwan levies taxes on the dividend payments. This means that shareholders not only do not generate cash flow from stock dividend payments, but also have to pay taxes. Therefore, the market would reflect negatively to information, when firm announces dividend, resulting in a dip in the firm’s stock price. Nonetheless, many studies have found that investors react positively to the announcement of dividends in the capital market. Many questions stated above couldn’t simply be the product of company/investor irrationality, hence many studies attempt to explain the situation via a theoretical framework. The most commonly used theory is the information signaling theory.

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The information signaling theory originated from information asymmetry theory. Ross (1977) first constructed his capital-structure signaling model based on the information asymmetry theory. Woolridge (1983) in his research experiment confirmed that dividends could convey the information of a prospective company’s future business outlook. Since then information signaling theory has become the most applied theory by researchers focusing on stock dividends or stock splits. Many companies in Taiwan when debating stock dividend payments would frequently take into consideration the likelihood of an increase in company stocks in circulation diluting future earnings per share. Furthermore, should the manager predict an increase in future company earnings, this could cause dividend yield to be lowered as a result. This type of pragmatic approach thus justifies the use of information signaling theory as a means of explaining why listed companies in Taiwan engage in massive stock dividend payments, as well as why investors view dividend announcements positively. In Taiwan, listed companies normally declare dividends once a year. The companies whose managers engage in this systematic distribution of dividends, according to the information signaling theory, are the ones that view dividend announcements as a way to convey future company earnings. However, should a company deem dividend allocation as a form of temporary or bonus payment, then investors would not anticipate the company is transmitting messages or reporting future earning’s prospects. They would thus consider this irregular dividend announcement as temporary, or a specially designated dividend (SDD) declared by the company. Nonetheless, Brickley (1983) in his research targeting SDD announcements concluded that a positive correlation existed between the announcements of SDDs and the behavior of share prices. In addition, to indirectly validate this type of information the effect was only short-lived and non-permanent. It is indicated that management uses the announcement of SDDs to convey information to market about future dividends and earnings. Gombola and Liu (1999) provide evidence of improved earning’s forecasts the year following an SDD announcement and a significant positive share price reaction to the announcement. Lang and Litzenberger (1989) applied the Tobin’s Q ratio on a group of overinvesting firms to distinguish between the prediction of the cash flow signaling hypothesis and the free cash flow hypothesis. They find an important factor – the free cash flow. Howe, He and Kao (1992) examined whether the market can explain SDDs as a vehicle for distributing free cash flow to shareholders. Their result was not found to be statistically significant when the sample was applied to Tobin’s Q ratio. Similarly, it could not be found significant when they separated their test into high-Q and low-Q clusters, to test whether or not SDD announcements would in fact produce different reactions through this form of

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categorization. The research by Gombola and Liu (1999) on cash flow hypothesis also could not support the hypothesis. Merton’s (1987) “investor recognition” hypothesis indicates that an increase in the number of investors holding a security should increase the company’s value. Therefore, the national exchange can enhance visibility and liquidity of a traded stock. The listed firms on organized exchange, like the Taiwan Stock Exchange (TSE), will have greater reaction on share price than the listed firms on Over-the-Counter (OTC) market for SDD’s announcement. To observe whether the firms listed on national exchange have greater reaction to stock price due to SDDs announcement, our research samples include TSE and R.O.C. Over-the-Counter Securities Exchange (ROSE). The purpose of this paper is to test the information content hypothesis for SDDs by analyzing the stock price reaction to SDD’s announcements of organized market and OTC market. We divide the samples into four groups: full sample, first-time stock dividend payment within TSE and the ROSE, and those without dividend in the previous three years, denoted 3-years. To test whether Tobin’s Q can explain abnormal phenomenon for SDD’s announcement, we divide our samples of TSE and ROSE into low Q (overinvesting) and high Q (value-maximizing) firms. Further, to observe whether low Q firms with greater free cash flow have greater announcement effect, we apply cross-sectional regression model in this analysis. Our results indicate that SDDs are considered positive signals by the national exchange in pre-SDD announcement. We show that SDD only has short-term effect in Taiwan. We also observe that low Q firms have greater market reaction in announcement period, and that the free cash flow with Jensen’s (1986) theory could not be verified in Taiwan. The announcement of first-time SDD has positive signal to market regarding the firm’s future cash flow. Since the announcement of 3-year SDD is a temporary phenomenon and will not be repeated from investor viewpoint, consequently, a 3-year SDD implied less positive information than a first-time SDD announcement. Our empirical study shows that the sample of 3-year has a negative abnormal return in event period. In Section 1 of this paper we explore the theories. Section 2 is a description of Taiwan’s stock market. In Section 3, we develop and state the research hypothesis. In Section 4, we describe the research samples and the methodology. The empirical results are reported in Section 5 and we conclude our findings in Section 6.

2. TAIWAN’S STOCK MARKET In over 35 years of its development, Taiwan’s economy experienced a rapid growth and a great deal of wealth was accumulated. To further develop Taiwan’s

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capital market, the OTC market was reopened, and on November 1, 1994, the government set up the R.O.C. Over-the-counter Security Exchange ROSE,. Under the new organizational structure, many procedures and clauses were modified and implemented to promote the less-seasoned public growth companies applying for listing. This move spurred the growth of this once-sluggish market. The ROSE, as differentiated from the TSE, assumed the responsibility of fostering a robust capital market for the less mature but perhaps faster growing small-size and mid-size firms in Taiwan. Public companies which desire to be listed on the exchange and to raise capital from the public through TSE or ROSE, must meet certain criteria in regard to their financial and operational conditions to qualify as listed companies. The TSE or ROSE staff screens the companies, applications according to the relevant listing criteria based on the Securities and Exchange Law. To be listed on the TSE or on the ROSE, the applicant company is required to meet the following, mainly different, listing criteria: (1) There shall have been over five years since its incorporation for listing on TSE. In the ROSE, listing companies must have at least three years corporate history; (2) The TSE listing companies’ amount of paid-in capital in its final accounts for the most recent two fiscal years shall be NT$300 million or more, the ROSE listing companies are required to have NT$50 million paid-in capital only; (3) both operating profits and before-tax net profits exceeding 6% of their paid-in-capital for the past two fiscal years to list on TSE, but to list on the ROSE firms only need 2%; and (4) In dispersion of share holdings, the number of name-bearing shareholders shall be 1,000 or more on TSE listing companies. Among them, the shareholders holding 1,000 to 50,000 shares shall not be less than 500, and the total number of shares they hold shall be 20%, or greater of the total issued shares.1 For ROSE listing companies, the total number of registered shareholders, with 1,000 to 50,000 shares in holding, shall be no less than 300. Also the total number of shares from the above shareholders category must exceed 10% of total number of shares issued or 5,000,000 shares. Similar to its counterparts in the other countries, the TSE has a more stringent listing threshold compared to those of ROSE. In addition to these different listing criteria, there are also other differences between the TSE and ROSE. Traders on the TSE can have short and long positions in the same stock on the same day, but this trading strategy is not allowed in the ROSE. The margin ratios for trading in stocks are different as well. The ROSE generally has a higher margin requirement regarding margin financing for purchases of securities, whereas the margin requirement for short selling is the same in both the TSE and ROSE markets. Furthermore, in the TSE, the disclosed bid-ask price is determined as the highest bid (lowest offer) price within the range of two up/down tick over and under the reference price, but the ROSE does not limit the price

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Table 1. The Characteristics of Taiwan Stock Market.

1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000

TSE

ROSE

Number of Firms

Trading Volume (100 Million Shares)

Trading Value (NT $100 Million)

Margin Volume (NT $100 Million)

Number of Firms

Trading Volume (Million Shares)

Trading Value (NT $100 Million)

Margin Volume (NT $100 Million)

181 199 221 256 285 313 347 382 404 437 462 531

2,205.6 2,323.1 1,759.4 1,075.9 2,046.8 3,512.4 2,673.0 3,507.4 6,542.0 6,120.1 6,780.6 6,308.7

254,079.6 190,312.9 96,827.4 59,170.8 90,567.2 188,121.1 101,515.4 129,075.6 372,411.5 296,189.7 292,915.2 305,265.7

21,478.7 56,589.4 49,914.5 37,839.2 80,417.8 145,915.4 92,070.8 118,149.8 315,824.0 271,696.0 260,109.6 247,084.3

1 4 9 11 11 14 41 79 114 176 264 300

0.0 7.5 13.9 20.0 20.0 19.4 171.0 16,958.7 43,115.0 30,680.7 49,052.0 88,392.7

0.0 11.8 4.6 6.7 6.5 5.7 27.9 4,535.1 23,106.6 11,981.6 18,999.0 44,783.6

0 0 0 0 0 0 0 0 0 0 6,161 16,546

Note: This table shows the number of listing firms in TSE and ROSE, the trading volume and margin trade in each exchange during the period of 1990 to 2000.

KEN HUNG, CHANG-WEN DUAN AND GLADSON I. NWANNA

Year

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fluctuation when executing two continuous orders. Therefore, the price movement of the ROSE seems to be able to more adequately reflect market conditions than does the TSE. Table 1 reports the descriptive statistics in these two markets from 1989 to 2000. Trading volume and dollar value of trading volume on the ROSE are only around 15% and 13% in 2,000, respectively, of those on the TSE. The margin trades are close to 80% of total trading volume on the TSE, but only close to 35% on the ROSE in 2,000. Margin trades were not allowed in the ROSE until 1999. So the market size of the ROSE either in terms of trading volume or trading value is much smaller than that of the TSE. Merton’s (1987) “investor recognition” theory provides a rationale for the effort of many investors to increase their stock holdings. Many researchers such as Barry and Brown (1986) and Arbel and Strebel (1982, 1983) show that neglected firms with lower visibility and limited information constitute a source of risk and thus investors demand a higher equilibrium expected rate of return. Amihud, Mendelson and Uno (1999) show that the stock prices appreciation are positively related to an increase in the number of shareholders. Therefore, by listing their share on organized exchange like TSE with larger number of shareholders, managers can not only achieve visibility gains but also expand a company’s investor base. Based on our discussion above, the TSE provides a better liquidity and visibility than the ROSE in stock transaction, since the listing criteria in TSE is more strict. Therefore, the national exchange will have greater reaction to share price, than for firms listed on Over-the-Counter (OTC) market by SDD’s announcement.

3. RESEARCH THEORY AND HYPOTHESIS Why do most investors in the capital market view dividend announcements favorably? Many researchers attempting to answer this question from a theoretical point-of-view often apply three different theories: (1) trading range theory; (2) tax option theory; and (3) signaling theory. Trading range theory is the oldest stock dividend theory, which advances that stock prices have appropriate trading ranges. As long as the share price falls between this range, its share liquidity would reach the highest top, while reflecting the true value of its stock shares. Hence companies would use the stock dividend payments and stock splits to maintain their share prices at the optimum range, and share price would in turn respond positively toward the company’s dividend announcements. For the Taiwanese stock market, however, the suitability of trading range theory is doubtful since considerations whether to give stock dividends must first pass both the Board of Directors and the shareholder meeting and then to be

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submitted to the Securities and Futures Exchange Commission for final approval. The duration involved until ex-righted would generally take several months. In other words, whether or not trading range theory can increase the number of shares in holding and share liquidity after ex-righted, or provide the highest stock value upon the declaration of dividends several months earlier is questionable. Tax option theory concept was first raised by Constantinides (1984). The theory pointed out that personal long-term investment capital gains and short-term capital losses under the special U.S. taxation code may be used to offset short-term capital gains, thus lowering individual tax brackets. This offset of capital gain with capital loss has a greater chance of realization when share price volatility is large. Constantinides (1984) called the afore-mentioned concept the tax option theory. He believed that investors would be willing to pay for this extra option and the value of this tax option would increase when share price volatility is increasing. Ohlson and Penman (1985) found the increasing of share price variation after the stock splits. Lamoureux and Poon (1987) advanced the abnormal returns prompted by the stock split announcement were in fact reflections of the increase of value as suggested in the tax option theory. Brennan and Copeland (1988) commented that tax option theory may explain market reactions toward dividend announcements, but would be unable to justify why companies engage in stock splits or stock dividend payments. The tax option theory however may not be appropriately applied to the Taiwanese stock market because Taiwan does not levy capital gains tax on stock transactions. Signaling theory originated from information asymmetry theory. The theory postulates that amongst the two transacting parties in the market, only one party has the complete information while the other party does not. Under this scenario, the transacting party lacking complete information would be unable to identify the advantage or shortcomings of the other party, hence inferior transacting parties would flood the market. This is called the adverse selection problem. In order to resolve the adverse selection problem, transacting parties would have to minimize or eliminate information asymmetrical situations. Spence (1973) proposes the information signaling model would explain how employees of the labor market with full information awareness on self-productivity transmit their true productivities to clueless bosses. Ross (1977) extended Spence’s information signaling theory into financial management. Leland and Pyle (1977) further extended the theory using holding ratios of portfolio managers as basis for the information signaling theory. Many researchers in other words, have applied the information signaling theory on corporate finance of various companies. After Ross and Leland and Pyle employed information signaling model in finance, others such as Bhattacharya (1979) applied Spence’s method, to create information signaling model on cash

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dividends. Brennan and Copeland (1988) used stock split as information signals to create the information signaling model on stock-splits. Vermaelen (1984) applied information signaling model on stock repurchases. Allen and Faulhaber (1989) used information signaling model to explain the undervaluation of initial public offerings new to the stock market. The information signaling theory assumes mangers to have more complete information of company performances and future developments than shareholders. Hence, under this information asymmetry situation, share prices could only reflect the market average value of the firms; saying in essence, that high-value firms could be undervalued while low-value firms could be overvalued. When signaling device exists, high-value firms must give appealing reasons so as to signal information to distinguish themselves from low-value firms. Because of the cost consumption of information signaling, low-value firms tend to shy away from engaging in identical activities as those of the high-value firms. Therefore, these information signaling activities would reduce information asymmetry or could even eliminate it completely, thus allowing share prices to reveal the true values of the companies. In order to allow high-value firms and low-value firms to each use disparaging signals, hence avoid copycat behaviors, one key criteria or component of information signaling must be recognized. That component is cost. Ippolito (1990) called this restrictive mechanism for signaling (cost) as a bonding mechanism. These mechanisms would discourage low-value firms from imitating high-value firms at will, thus preventing investors from jumping to the same financial decisions. Therefore, should the afore-mentioned theories be supported, then the information signaling hypothesis would be confirmed. In other words, positive abnormal returns would be present during announcement period, and the greater the dividend yield, the higher the abnormal return. Therefore, the first hypothesis of this research is: Hypothesis 1. The onset of positive abnormal returns during announcement period, and the greater the dividend yield, the higher the abnormal return generated. Merton (1987) proposes that an increase in the size of a company’s investor base will reduce investors’ expected return and therefore raise the market price of the firm’s stocks. Baker (1993) and Baker, Powell and Weaver (1999) provide some empirical support for the conventional notion that investors trade stock on a national exchange in part to increase their visibility. Thus, firms with fewer shareholders would have incentives to take activities with a desire to increase the investor base of the company’s stocks. This is the so-called “investor recognition” hypothesis. Therefore, our second hypothesis is:

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Hypothesis 2. The TSE have better visibility than the ROSE, the TSE’s listing firms have greater reaction to share price than the ROSE’s listing firms during dividend announcements. Grinblatt, Masulis and Titman (1984) indicated that small firms tend to generate greater investor attention than larger firms when disbursing stock dividends and stock splits, hence would produce greater reactions over share prices. Bajaj and Vijh (1995) in their research found that small firms receive greater positive abnormal returns than larger firms during announcement. Furthermore, those investors in the markets noticed small firms less, which was the reason why dividend announcements signal much more information for small firms than for larger firms, thus resulting in higher abnormal returns. The third hypothesis of this research is: Hypothesis 3. Small-size firms have greater positive abnormal returns than larger-size firms during dividend announcements. The Tobin’s Q ratio shows whether or not a company over-invests. Should the ratio be smaller than unity, under plausible conditions, implies overinvestment by company, i.e. that a company in order to fulfill its factory expansion project had taken on inferior investment opportunities thus lessened the company’s marginal efficiency of capital. However, when Tobin’s Q ratio is separated into high-Q and low-Q firms, high-Q firms and low-Q firms would respond differently in regard to the effect of dividend announcements, which means that when a company announced its dividends, the share prices of low-Q firms tend to generate a greater and more positive reaction than high-Q firms. Howe, He and Kao (1992) tested the Tobin’s Q into the two clusters, high and low but found the result to be insignificant. Lang and Litzenberger (1989), and Gombola and Liu (1999) however, did prove the existence of this effect. The fourth hypothesis of this research is: Hypothesis 4. When companies announce dividends, share prices of low-Q firms tend to generate a greater positive market reaction than high-Q firms. We compare company payment of stock dividends with earnings on reserve. Although neither would affect company’s cash flow, stock dividend payments would cause earnings on reserve to be reduced by an equal amount, thus allowing cash to stay inside the company permanently. This is greatly different from that of the earnings kept temporarily on reserve as a way of keeping cash in the company. In Taiwan, the stock dividend payment by a listed company generally is deemed as an act that the company takes to preserve cash within said company, thus giving it an opportunity for reinvestment. Hence for those companies that are prospecting for future investment opportunities and are somewhat short of cash flow, stock dividend payment would facilitate the permanent preservation of cash to stay inside

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the company. This information may be explained as ways for company to save their cash reserves for higher-return investments, in which investors would view as good news, thus share prices would appreciate. Nonetheless, for those companies lacking future investment opportunities while sitting on massive free cash flows, to distribute huge stock dividends in order to keep cash flow permanently within the respective company, chances are that managers are planning to get their hands on an even greater amount of cash flow to be used as perquisites. If this were the case, then managers disbursing stock dividends may be deemed as agency problem. And should investors share similar conclusions then share prices would decrease after stock dividend announcements. In other words, a negative correlation exists between free cash flow and abnormal return, in which we may use free cash flow as an explanation for the agency problem. Jensen (1986) defined free cash flow as the surplus cash flow after interest and taxes. At the notion of Jensen’s free cash flow theory lies the agency problem of managers and shareholders over the distribution of free cash flows generated by firms. As free cash flow increases, the manager of a firm may be more likely to engage in over-investment, which explains why the manager may accept negative net present value projects, or may accept inferior investment projects. One may say that greater free cash flow leads to poorer management performance. On the contrary, as the free cash flow decreases, the manager would not have surplus cash to engage in over-investment. Therefore, companies with less free cash flows enjoy better performance from their managers. In this paper, we examine whether or not the free cash flow hypothesis can be supported. This is our fifth hypothesis. Hypothesis 5. A negative correlation exists between free cash flow and abnormal return; hence a probable explanation for the agency problem.

4. SAMPLE AND METHODOLOGY This paper uses the event study methodology and employs samples from companies listed in the TSE and the ROSE.

4.1. Sample In order to examine the effects of stock dividend announcement and to directly test for share price reactions thus supporting the existence of information signaling theory, this paper used as samples, the first-time stock dividend announcement by listed companies and those companies that only pay stock dividends without

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distributing cash dividends in the previous three consecutive years. This type of SDD sampling can eliminate the influence cash dividend has on empirical results. We thus examine empirically whether stock dividends are in fact capable of transmitting future company cash flow and earnings information. We focus only on the event of stock dividend announcements happening within the TSE and the ROSE. We divide the samples into four groups: full sample, first-time stock dividend payment within TSE and the ROSE, and those without any stock dividend distribution announcements in the previous three consecutive years, denoted 3-year. Earlier researchers such as Brickley (1983), Jayaraman and Shastri (1988) and Gombola and Liu (1999) also adopted similar sample definitions. It is the habit of the Taiwanese stock market to deem the repayment of stocks as stock dividends, and according to accounting principle, a repayment of stocks may be divided into two types, the first includes a summary of a related sums of earnings allocations including capital earnings appreciation, legally defined capital earnings appreciation and a special capital earnings appreciation, while the second type is a non-earnings related distribution known as public capital appreciation, which is a capital appreciation-expanded stock dividend. However, looking from an accounting principle, only the earnings allocation may be deemed as a stock dividend and public capital appreciation is not. Nevertheless from an economic viewpoint, both formats are identical in the eyes of an investor. Therefore, based on the customary tradition of the Taiwanese stock market, this paper treated both the repayment of stocks and public capital appreciation as stock dividends. Our research period is from January 1 of 1989 to December 31 of 2000, and covers 261 announcements of SDD in the sample. These data are obtained from the TSE’s Monthly Market Bulletin, Securities and Futures Exchange Commission, R.O.C., Ministry of Education AREMOS database and Taiwan Economic Journal (TEJ) database.

4.2. Measures of Abnormal Return This paper uses event study to test whether or not dividend announcement effect induces abnormal returns. The explored market response variable is the rate of return, denoted Ri , while adopting a market model to calculate abnormal returns of event window periods. The market model assumed linear correlation between the share return and the market return, denoted Rm . Whereas market return from the information given by the TSE is based on the share prices of the weighted index, the OTC market follows the ROSE’s weighted index. The model is as follows: R it = ␣i + ␤i R mt + ␧it

(1)

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where the ␣i and ␤i contained are regression coefficients while ␧it represents tday’s error term. It stands as estimations of abnormal returns occurred during event periods. Bollerslev (1987) discovered that heteroscedasticity problem was present between the share returns, which means the assumption of equal variance in the market model was false. To overcome the heteroscedasticity problem, Engle (1982) derived the Autoregressive Conditionally Heteroscedasticity Estimation (ARCH), which allowed the conditional variance of error term to change over time. Thus, each observation has a different error variance. Bollerslev further introduced the lag-term of error conditional variance into the ARCH model, thus called the Generalized Autogressive Conditionally Heteroscedasticity Estimation (GARCH). The GARCH (p, q) model, where p refers, to the order of the autoregressive for variance and where q refers, to the order of the moving average for error term. According to the empirical research findings of Bollerslev (1987), Mohammad, Rahman and Yung (1992) and Lee and Ohk (1992), GARCH (1,1) model adequately capture the movement of stock price. In Taiwan stock markets, due to the short term investing behavior of investors, p and q terms do not appear to have an effect over several periods after. Furthermore, too many p and q terms would decrease the efficiency and accuracy of model parameter estimation. The variables we use are the rates of return of the data after taking logarithm. They are suitable for GARCH(1,1) model estimation. Therefore, in this paper when the stock price data of individual companies indicates that there is a heteroscedasticity characteristic during the estimative period, the GARCH (1,1) is used to estimate the coefficient of the market model. Otherwise, the traditional ordinary least squares estimation (OLS) method is used. The definition of GARCH (1,1) model is as follows: R it = ␣1 + ␤1 R mt + ␧it

(2)

˜ ␧it |t ∼N(0, h it )

(3)

h it =

␣2 + ␤2 ␧2it−1

+ ␤3 h it−1

(4)

where the hit indicates the conditional variance determinants of t for stock i on the date of transaction. Conditional on an information set at time t, denoted t , the distribution of the disturbance is assumed to be ␧t |t ∼N(0, h t ). As for whether or not the sequence is equipped with GARCH effect, we uses Box and Pierce’s (1970) Q and Lagrangian multiplier (LM) test. Table 2 contains sample statistics of annual stock dividend announcements made during the research period, 145 from the TSE, and 89 from the ROSE,2 for a total of 234 first-time stock dividend announcements. For the previous three consecutive years without stock dividend payments, there were 27 entries from the TSE. LM and Q testing statistics were used on the GARCH and OLS clusters

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Table 2. Describing the Sample of Classified as Taiwan Stock Market. Year

1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 TOTAL

TSE

ROSE

FULL

GAR

OLS

TOTAL

GAR

OLS

TOTAL

2 1 0 3 8 9 4 7 9 2 7 0

1 9 8 8 6 3 9 9 4 10 18 8

3 10 8 11 14 12 13 16 13 12 25 8

0 0 0 0 0 0 0 2 4 6 12 14

0 0 0 0 0 0 0 5 9 8 5 24

0 0 0 0 0 0 0 7 13 14 17 38

52

93

145

38

51

89

3-Year GAR

OLS

TOTAL

3 10 8 11 14 12 13 23 26 26 42 46

0 0 0 0 0 0 2 3 1 0 1 1

0 0 2 1 0 1 1 4 3 2 3 2

0 0 2 1 0 1 3 7 4 2 4 3

234

13

14

27

Note: This table shows the number of SDD announcement in TSE, ROSE and three-year, the estimative method of GARCH and OLS in each sample, and the number of SDD announcement during the period covering 1989–2000. GAR is GARCH (1, 1) and we use Box and Pierce’s Q and LM test statistic to test for GARCH. FULL is the sample of the TSE and ROSE for first announcement dividend event. The sample consists of 27 SDD events for the firms without any stock dividend distribution announcement for three consecutive year, denoted here as three-year.

to test whether or not the companies contained the GARCH effect. If the result was significant, said company is placed in the GARCH cluster; otherwise, it was placed in the OLS cluster. In regard to the event study on the effect of stock dividend announcement, event window was mostly based on 1 to 2 days before and after the announcement date. Researchers such as McNichols and Dravid (1990) and Gombola and Liu (1999) have all used the day before- and-after an event (−1, +1) as the event window, while Foster and Scribner (1991) used (−1, +2) as their event window, and Grinblatt, Masulis and Titman (1984) used (0, +1). However, the Taiwan stock market is affected by other factors such as the share price up/down3 daily fluctuation limit, poor market efficiency and insider information leaks. Therefore, we applied a greater event window for our observation. Our research uses (−1, +1), (−2, +2), (−3, +3), (−1, 0), (−1, +1), (−3, 0), (0, +1), (0, +2) and (0, +3) as event windows to observe the announcement effect of SDDs in the Taiwan stock market. Furthermore, we take into consideration the restrictions placed on the data of stock prices4 and the effects of new firm listings.5 Amongst the samples of first-time dividend allocations via stock dividend issuance, the model’s regression function for day t = A + 31to t = A + 150, day A is defined as the event day.

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Abnormal return is calculated over the event window between t = A − 30 and t = A + 30. For the samples in which dividend wasn’t paid in the previous three consecutive years, we use traditional method i.e. 31 to 150 days prior to announcement as the estimative period for the coefficient of the market model. Abnormal return is calculated the same way as first-time sample in the event period.

4.3. The Calculation of Tobin’s Q Ratio The original content for Tobin’s Q is defined as ratio of the market value of a company’s financial claims to the replacement value of its assets. Since the computation content was rather difficult and empty, the Lewellen and Badrinath (1997) calculation, which is more precise and definitive for the estimation of Tobin’s Q ratio was used. The calculation method is as follows: MV(CS) + MV(PS) + MV(LTD) + BV(STD) L–B q = (5) BV(TA) − BV(FA) − BV(INV) + RV(FA) + RV(INV) −[BV(TL) − BV(LTD) − BV(STD)] where MV(CS), MV(PS), MV(LTD) are the market value of common stock, preferred stock, and long-term debt, respectively; BV(STD), BV(TA), BV(FA), BV(INV), BV(TL) are the book values of short-term debt, total assets, fixed assets, inventory, and total liabilities, respectively; and RV(FA) and RV(INV) are the replacement values of fixed assets and inventory, respectively. Due to the difficulty with estimating replacement value (RV), we used Chung and Pruitt (1994) as an alternative because it does not require an estimate of the market value of debt and preferred stock. Their method is as follows: C–P q =

MV(CS) + BV(PS) + BV(LTD) + BV(INV) + BV(CL) − BV(CA) BV(TA) (6)

where CL and CA are current liabilities and current assets, respectively. We used the calculation method of C–P q model. Moreover, according to the findings by Lee and Tompkins (1999) the calculation efficiency of C–P q model is no less than that of L–B q model. It also shows better, the characteristic of the original Tobin’s Q ratio. Instead our calculation was based on the year-end financial report of the year previous to the announcement event. The market value of listed companies in Taiwan however, is usually much higher than reality, hence Tobin’s Q ratio tends to depict a higher ratio when calculating those listed companies. In addition to testing the different average cumulated abnormal returns (ACAR) for the two clusters each with Tobin’s Q ratio greater than one and smaller than one, we examined the two

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clusters simultaneously, one with a high mean score of Tobin’s Q ratio and the other with a low average. We denoted them as high-Q and low-Q, and tested both to verify whether their ACAR were different. 4.4. Free Cash Flow In order to support the hypothesis of the free cash flow, this paper used Lehn and Poulsen (1989)’s definition of free cash flow as shown in Eq. (7) below, denoted FCF. The objective of this method is to eliminate the diversity of firm-sizes amongst the samples. Calculation method is as follows: FCFi =

EBDITi − TAXi − I i − D pﬁ − D i EQUTYi

(7)

where EBDIT, TAX, I, Dpf , D and EQUTY are earnings before depletion, interest and taxes, preferred stock dividend and common stock cash dividend,6 respectively. The above formula expresses the surplus on the earnings of the unit-equity after the company takes off the dividends, interests and tax. Many researchers’ definition of the free cash flow is derived from this formula, such as Gombola and Liu (1999). Our sample is estimated based on the year-end financial report, before the year of the previous announcement date.

5. EMPIRICAL RESULT Table 3 presents the average cumulated abnormal returns (ACAR) on the event windows of our research. We noticed from TSE samples that significant positive abnormal returns exist in the event windows of (−2,0) and (−3,0) prior to the announcement date, while significant negative abnormal returns were present in post-announcement event windows of (0, +2) and (0, +3). In other words, the shift to negative impact happens immediately after the date of announcement. This fact illustrates a verifiable phenomenon that positive abnormal returns do exist prior to the date of SDD’s announcement in Taiwan, but it shifts into negative value immediately after the announcement date of SDD. It also proves that SDD only has a short and temporal effect in Taiwan. This conclusion confirms the findings of Brickley (1983). In Taiwan, the share price of a company tends to be bid up before the shareholder’s meetings, while the positive abnormal returns produced by the investors’ speculation drive the share prices even higher prior to the announcement dates. Thereafter, it shifts into negative soon after post-announcement dates. Apart from the significant (−1, −1) event window of the ROSE samples most of the remainder windows display insignificant positives. It is shown that the TSE has

Event Window

(−1, +1)

(−2, +2)

(−3, +3)

(−1, 0)

(−2, 0)

(−3, 0)

(0, +1)

(0, +2)

(0, +3)

Full

0.147 (0.95) −0.128 (−0.40) 0.596 (1.76)* −0.978 (−1.28)

0.121 (0.35) −0.136 (−0.33) 0.541 (0.89) −1.734 (−1.76)*

0.265 (0.65) 0.244 (0.50) 0.299 (0.42) −1.162 (−0.99)

−0.035 (−0.16) −0.119 (−0.47) 0.104 (0.27) −1.423 (−2.28)***

0.239 (1.65)* 0.349 (1.65)* 0.059 (0.13) −1.451 (−1.90)*

0.273 (0.89) 0.527 (1.75)* −0.139 (−0.26) −1.079 (−1.65)*

0.015 (0.07) −0.178 (−0.69) 0.331 (0.86) 0.029 (0.05)

−0.284 (−1.07) −0.656 (−2.07)** 0.321 (0.68) −0.699 (−0.91)

−0.175 (−0.57) −0.452 (−1.63)* 0.277 (0.51) −0.499 (−0.57)

TSE ROSE 3-Year

Note: The estimative method uses the ordinary least squares (OLS) and general autoregressive conditionally heteroscedasticity (GARCH) to calculate the market model. Abnormal return is calculated over the event window between t = A − 30 and t = A + 30, where A is the event day. The cumulative average abnormal return (ACAR) from date t1 to t2 for each SDD’s announcement i and it is calculated as ACARi = t2 t=t1 ARi,t /t 2 − t 1 + 1, which AR is defined as abnormal return. The table shows the sample of Full, TSE, ROSE and three-year, and the samples observed from 1989 to 2000. The event window (t1 , t2 ) period is between before t1 -day and after t2 -day of the announcement day for ith SDD. The “Full” shows the sample of TSE and ROSE. The “three-year” is used to describe three consecutive years without any stock dividend distribution announcement. In parentheses are T-test statistics. ∗ Significant at the 0.1 level. ∗∗ Significant at the 0.05 level. ∗∗∗ Significant at the 0.01 level.

Announcement Effects of Specially Designated Dividends

Table 3. Average Cumulated Abnormal Return for Event Window (t1 , t2 ).

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Fig. 1 The CAR of Full Sample Observed Event Day for SDD’s Announcement Day. (a) Plot of cumulative abnormal return for announcement date from event day −30 to event day +30. The sample consists of 234 SDD events for the TSE and ROSE. The CAR is calculated as CARi = t2 t=t1 ARi,t which AR is defined as abnormal return and calculated from the market model. Whereas market return (Rm ) from the information given by the TSE is based on the share prices of the weighted index, while the OTC

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199

better visibility than the ROSE, the TSE samples have greater positive (in preSDD) or negative (in post-SDD) abnormal returns than the ROSE. The empirical results of the full sample display somewhat similar findings as that of the TSE sample. Only the (−2, 0) window is an exception and shows a significant positive effect. Amongst those firms which did not pay any dividends in the previous three consecutive years, we discovered all event windows with significant abnormal returns to be negative. In fact, most of them occurred prior to the announcement date. The abnormal return of event window (−1, 0) was significant at the 0.01 level and the value of ACAR was −1.4234%. The result proved investors view the information, of the stock dividend announcement by companies with long-term unpaid dividends at shareholders meetings, as a bad or negative message. Figures 1–4 illustrates the cumulated abnormal returns (CAR). Apart from the slightly higher fluctuation of the OTC and the decreases in CAR of three-year samples, the TSE and Full samples depicted incremental increases of CARs prior to the date of announcement. This phenomenon implied support of the information signaling theory by announcement of SDD in TSE. We applied C–P q model7 to compute the Tobin’s Q ratio in Taiwan. However, as the value of locally listed companies are frequently undervalued and long-term market values are perceived to be high, Taiwanese Q ratio does appear to be overestimated. This makes the estimated value of Taiwan’s Q ratio departed from the original Tobin’s Q ratio. Therefore, we separated the estimated Q ratio by its mean into two clusters, high Q and low Q, and tested the Q ratio of these two clusters through the mean difference of the two population and the non-parametric Wilcoxon signed-rank and sign tests. As shown in Table 4, the separate clusters are tested to be significant. Thus, this type of classification is acceptable. In Table 5, we took the ACARs of both low-Q firm and high-Q firm clusters and applied with the T-test of mean difference, and the Wilcoxon test to see whether the two samples are different. The event windows of (−1, 0) and (−3, 0) from the full samples, and the event windows of (−3, 3), (−1, 0), (−2, 0) Fig. 1. (Caption Continued ) market follows the ROSE’s weighted index. (b) Plot of cumulative abnormal return for announcement date from event day −30 to event day +30. The sample consists of 234 SDD events for the TSE and ROSE. The CAR is calculated as CARi = t2 t=t1 ARi,t which AR is defined as abnormal return and calculated from the market model. The is the √ total cuCSAR t2 mulative standardized abnormal return and calculated as CSAR = CAR / V (CARi ) i i t1 ¯ m )2 / (R m − R ¯ m )2 . Whereas market return where V(CARi ) = ␴2 1 + 1/n + (R mi − R (Rm ) from the information given by the TSE is based on the share prices of the weighted index, while the OTC market follows the ROSE’s weighted index.

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Fig. 2 The CAR of TSE-Sample Observed Event Day for SDD’s Announcement Day. Note: Plot of cumulative abnormal return for announcement date from event day −30 to event day +30. The t2 sample consists of 145 SDD events for the TSE. The CAR is calculated as CARi = t=t1 ARi,t which AR is defined as abnormal return and calculated from the market model. The is the total cumulative standardized abnormal return and calculated t2 CSAR √ as CSARi 2= 2 ¯ m )2 / (R m − R ¯ m) . 1 + 1/n + (R mi − R t1 CARi / V (CARi ) where V(CARi ) = ␴ Whereas market return (Rm ) from the information given by the TSE is based on the share prices of the weighted index.

and (−3, 0) from the ROSE samples all showed significantly positive of the difference. The result shows that low Q firms have a greater positive reaction than high Q firms over share prices at announcement day. However, in empirical samples from TSE and those for firms that did not pay any dividends in the previous three consecutive years, a negative result was observed. The result of this finding contradicts the theoretical hypothesis. This result may be caused by the inappropriate classification based on the mean of the Tobin’s Q ratio applied. Tobin’s Q of one is used as the demarcation value. In Table 6, we also used Tobin’s Q equal to unity as grouping basis and separated the samples into two clusters, high-Q and low-Q. We found the high-Q firms were much higher than the low-Q firms, which meant that overestimation was present in Taiwan’s Q ratio. However, apart from the negative value (insignificant) in the ACAR difference between the low-Q and high-Q from TSE’s event window of (−3, +3) among the

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201

Fig. 3 The CAR of OTC-Sample Observed Event Day for SDD’s Announcement Day. Note: Plot of cumulative abnormal return for announcement date from event day −30 to event day +30. The t2 sample consists of 89 SDD events for the ROSE. The CAR is calculated as CARi = t=t1 ARi,t which AR is defined as abnormal return and calculated from the market model. The is the total cumulative standardized abnormal return and calculated t2 CSAR √ as CSARi 2= 2 ¯ m )2 / (R m − R ¯ m) . 1 + 1/n + (R mi − R t1 CARi / V (CARi ) where V(CARi ) = ␴ Whereas market return (Rm ) from the information given by the OTC is based on the ROSE’s weighted index.

first time dividend announcement event, all others matched the assumptions of this research. Moreover, the ACAR difference in the event windows of (−1, +1) and (−1, 0) from the full sample, also fell into the significant level of 0.01. This finding was identical to that of Lehn and Poulsen (1989), Denis, Denis and Sarin (1994), and Gombola and Liu (1999). Amongst the sample of those companies that had no dividend payments for the previous three consecutive years in the testing of ACAR difference, a negative value would be inconsistent with the theory. It would mean that high-Q firms generate a greater reaction for their positive abnormal returns produced by SDDs than the low-Q firms. This result implied that investors have a much lower valuation in low-Q firms which did not pay any dividends for the previous three years than the high-Q firms. Therefore, not all SDD’s announcements of three-year samples from a company might be deemed as a good message for an investor.

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Fig. 4 The CAR of Three-Year Sample Observed Event Day for SDD’s Announcement Day. Note: Plot of cumulative abnormal return for announcement date from event day −30 to event day +30. The sample consists of 27 SDD events for the forms without any stock dividend distribution announcement for three consecutive year, denoted here as 3-year. The CAR is calculated as CARi = t2 t=t1 ARi,t which AR is defined as abnormal return and calculated from the market model. The CSAR t2 is the√total cumulative standardized abnormal return and calculated as CSAR = i t1 CARi / V (CARi ) where V(CARi ) = ¯ m )2 / (R m − R ¯ m )2 . Whereas market return (Rm ) from the infor␴2 1 + 1/n + (R mi − R mation given by the TSE is based on the share prices of the weighted index, while the OTC market follows the ROSE’s weighted index.

Denis, Denis and Sarin (1994) generalized that the reasons for the differences between high-Q and low-Q firms was due to compounding effects associated with dividend yield or the size of dividend changes. To make sense of this effect, we used cross-sectional analysis to understand these mixtures of factors. Factors used in the regression model include SDD yield size (SDD divided by share price), free cash flow (free cash flow divided by total assets), firm size (market value of common equity), turnover (trading volume divided by share), and Tobin’s Q ratio. We then examine the relationship between these variables and the ACAR of event windows. Tables 7 and 8 shows the coefficients of the regression model for the full samples and those companies which did not pay any dividends in the

Sample Cluster N Means Difference Wilcoxon-Z

Full Low 157 1.174

High

TSE Total

Low

High

ROSE Total

Low

77 234 91 54 145 66 4.206 2.172 1.287 3.697 2.185 1.018 −3.032 −2.410 (–12.79)*** (−11.87)*** 10.04*** 12.42***

High

3-Year Total

Low

High

Total

23 89 19 8 27 5.403 2.151 1.015 2.465 1.498 −4.384 −1.451 (−8.20)*** (−4.76)*** 7.11*** 4.14***

Note: The table separated the estimated Q ratio by its mean into two clusters, high Q and low Q, and tested the Q ratio of these two clusters through the mean difference of two population and the non-parametric of Wilcoxon signed-rank and sign tests. The difference is low Q minus high Q. In parentheses are T-test statistics for means difference. The N is the number of sample. ∗∗∗ Significant at the 0.01 level.

Announcement Effects of Specially Designated Dividends

Table 4. Testing for Means of Tobin’s Q as Grouping Basis.

203

204

Table 5. Testing for the Difference Between the Low Q’s CAR and High Q’s ACAR with Means of Tobin’s Q as Grouping Basis. (−1, +1)

(−2, +2)

(−3, +3)

(−1, 0)

(−2, 0)

(−3, 0)

(0, 1)

(0, 2)

(0, 3)

Full

Differ

TSE

p-Value Differ

ROSE

p-Value Differ

3-Year

p-Value Differ

0.055 (0.09) 0.286 −0.38 (−0.61) 0.242 0.655 (0.54) 0.376 0.035 (0.02) 0.312

−0.516 (−0.76) 0.113 −1.463 (−1.9)** 0.031** 1.094 (0.82) 0.494 −3.508 (−1.36)* 0.227

−0.63 (−0.74) 0.117 −2.241 (−2.29)** 0.027** 2.523 (1.6)* 0.314 −6.882 (−2.85)*** 0.005***

0.646 (1.35) 0.138 0.293 (0.57) 0.224 1.292 (1.3)* 0.266 −0.762 (−0.59) 0.184

0.511 (0.93) −0.237 −0.076 (−0.13) 0.389 1.806 (1.61)* 0.216 −2.435 (−1.6)* 0.145

0.819 (1.34)* 0.087* −0.158 (−0.21) 0.367 3.039 (2.38)*** 0.029** −3.620 (−2.71)*** 0.011**

0.039 (0.08) 0.345 −0.480 (−0.87) 0.316 0.881 (0.94) 0.17 −0.447 (−0.28) 0.369

−0.399 (−0.68) 0.342 −1.195 (−1.76)** 0.058** 0.807 (0.75) 0.154 −2.316 (−1.35)* 0.277

−0.821 (−1.41)* 0.141 −1.891 (−2.39)*** 0.018** 1.002 (0.79) 0.239 −4.506 (−2.25)** 0.038**

p-Value

Note: In this table, day 0 is the SDD day. ACAR (t1 , t2 ) is the means of cumulated abnormal return from date t1 to date t2 . To test the differences between the low Q sample and high Q sample, we use T-test and the Wilcoxon rank-sum test. The Differ is the ACAR of low Q minus high Q. In the parentheses are T-test statistics. The p-Value is the probability value of Wilcoxon rank-sum test for two-sample data. ∗ Significant at the 0.1 level. ∗∗ Significant at the 0.05 level. ∗∗∗ Significant at the 0.01 level.

KEN HUNG, CHANG-WEN DUAN AND GLADSON I. NWANNA

Event Window

Event Window Full

Differ

TSE

p-Value Differ

ROSE

p-Value Differ

3-year

p-Value Differ p-Value

(−1, +1)

(−2, +2)

(–3, +3)

(−1, 0)

(−2, 0)

(−3, 0)

(0, +1)

(0, +2)

(0, +3)

1.628 (2.56)*** 0.024** 1.405 (1.68)** 0.088* 1.615 (1.47) 0.185 −1.717 (−0.91) 0.227

0.726 (0.95) 0.187 0.614 (0.59) 0.2856 0.534 (0.44) 0.477 −4.418 (−1.64)* 0.042**

0.551 (0.58) 0.277 −0.142 (−0.11) 0.431 1.214 (0.84) 0.342 −5.539 (−2.17)** 0.052**

1.262 (2.39)*** 0.011** 1.003 (1.47)* 0.088* 1.52 (1.69)** 0.074* 0.138 (0.11) 0.408

0.661 (1.08) 0.228 0.740 (0.94) 0.192 0.827 (0.8) 0.46 −0.583 (−0.37) 0.369

0.485 (0.66) 0.252 0.182 (0.18) 0.487 1.188 (0.99) 0.273 −1.788 (−1.31)* 0.294

1.02 (1.93)** 0.014** 1.311 (1.79)** 0.016** 0.608 (0.71) 0.217 −1.689 (−1.06) 0.294

0.730 (1.12) 0.089* 0.783 (0.85) 0.109 0.22 (0.22) 0.374 −3.399 (−1.74)** 0.17

0.729 (0.96) 0.132 0.584 (0.54) 0.129 0.539 (0.47) 0.41 −3.584 (−1.73)** 0.26

Announcement Effects of Specially Designated Dividends

Table 6. Testing for the Difference Between the Low Q’s ACAR and High Q’s ACAR with Tobin’s Q Equal One as Grouping Basis.

Note: In this table, day 0 is the SDD day. ACAR (t1 , t2 ) is the means of cumulated abnormal return from date t1 to date t2 . To test the differences between the low Q sample and high Q sample, we use T-test and the Wilcoxon rank-sum test. The Differ is the ACAR of low Q minus high Q. In the parentheses are T-test statistics. The p-Value is the probability value of Wilcoxon rank-sum test for two-sample data. ∗ Significant at the 0.1 level. ∗∗ Significant at the 0.05 level. ∗∗∗ Significant at the 0.01 level.

205

206

Table 7. Cross-Section Regressive Analysis for ACAR (t1 , t2 ) of Full Sample. Independent Variable

MV Tobin’s Q FCF Div/price R-square F-statistic

(−2, +2)

(−3, +3)

(−1, 0)

(−2, 0)

(−3, 0)

(0, +1)

(0, +2)

(0, +3)

−0.121 (−0.59) −0.026 (−0.09) −0.117 (−0.76) −1.162 (−1.69)* 17.394 (1.66)* 0.027 0.289

−0.041 (−0.17) 0.247 (0.73) −0.320 (−1.80)* 3.970 (1.15) 14.142 (0.95) 0.033 0.171

−0.007 (−0.02) 0.449 (1.09) −0.521 (−2.38)** 7.203 (1.70)* 19.635 (1.08) 0.053 0.028

0.021 (0.12) −0.033 (−0.14) −0.087 (−0.70) −2.523 (−1.74)* 12.442 (1.19) 0.024 0.345

−0.087 (−0.46) 0.294 (1.09) −0.238 (−1.67)* −0.289 (−0.10) 15.423 (1.30) 0.039 0.093

−0.071 (−0.31) 0.401 (1.24) −0.357 (−2.09)** −0.576 (−0.17) 15.326 (1.07) 0.045 0.062

−0.115 (−0.68) 0.056 (0.24) −0.106 (−0.85) −0.093 (−1.04) 17.956 (1.71)* 0.033 0.170

0.073 (0.36) 0.002 (0.01) −0.159 (−1.65)* 2.805 (0.94) 11.724 (0.92) 0.016 0.602

0.092 (0.39) 0.097 (0.29) −0.240 (−1.66)* 6.324 (1.84)* 17.314 (1.17) 0.033 0.174

Note: Estimating from OLS regression of the relative cumulated average abnormal return on Turnover, MV, Tobin’s Q and Div/price at event windows of our study. The Turnover is trading volume divided by share. MV is the firm size and is calculated from market value of common equity. The independent variables Tobin’s Q and FCF are described in sample section. The Div/price variable is the SDD yield size, and it is calculated as SDD divided by share price. ∗ Significant at the 0.1 level. ∗∗ Significant at the 0.05 level.

KEN HUNG, CHANG-WEN DUAN AND GLADSON I. NWANNA

Turnover

Event Window (t1 , t2 ) (−1, +1)

Independent Variable

Turn-over MV Tobin’s Q FCF Div/price R-square F-statistic

Event Window (t1 , t2 ) (−1, +1)

(−2, +2)

(−3, +3)

(−1, 0)

(−2, 0)

(−3, 0)

(0, +1)

(0, +2)

(0, +3)

0.202 (0.18) 1.487 (1.05) −1.343 (−1.19) 6.918 (0.61) −36.212 (−0.88) 0.144 0.624

1.275 (0.75) 0.431 (0.20) 0.896 (0.54) −10.024 (−0.60) −29.256 (−0.48) 0.138 0.650

0.164 (0.10) −1.999 (−1.01) 3.259 (2.08)** −9.344 (−0.59) −53.782 (−0.94) 0.305 0.048

1.286 (1.71)* 1.012 (1.09) −0.857 (−1.16) 13.728 (1.85)** 1.597 (0.06) 0.290 0.074

1.529 (1.65)* 0.103 (0.08) 0.762 (0.77) 1.944 (0.19) 26.139 (0.72) 0.146 0.616

0.454 (0.51) −1.080 (−0.98) 2.123 (2.43)** −2.789 (−0.32) 4.317 (0.14) 0.274 0.028

−0.331 (−0.31) 1.279 (0.97) −0.764 (−0.73) −0.977 (−0.09) −37.926 (−1.00) 0.093 0.824

0.498 (0.38) 1.132 (0.70) −0.144 (−0.11) −6.135 (−0.48) −55.512 (−1.19) 0.159 0.563

0.462 (0.34) −0.114 (−0.07) 0.859 (0.65) −0.722 (−0.05) −58.216 (−1.20) 0.194 0.436

Announcement Effects of Specially Designated Dividends

Table 8. Cross-Section Regressive Analysis for ACAR (t1 , t2 ) of Three-Year Sample.

Note: Estimating from OLS regression of the relative cumulated average abnormal return on Turnover, MV, Tobin’s Q and Div/price at event windows of our study. The Turnover is trading volume divided by share. MV is the firm size and is calculated from market value of common equity. The independent variables Tobin’s Q and FCF are described in sample section. The Div/price variable is the SDD yield size, and it is calculated as SDD divided by share price. ∗ Significant at the 0.1 level. ∗∗ Significant at the 0.05 level.

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previous three years. From Table 7, we found the coefficient of Tobin’s Q ratio for all event windows of the full sample group to be negative; except that the coefficients of event windows (+1, 1), (−1, 0) and (0, +1) were found significant. It means that Tobin’s Q is in inverse proportion to the cumulated abnormal return, and indicates the smaller the Q ratio a company has, the greater or more positive its SDD announcement would be. This finding is consistent with the empirical results of the U.S. by Gombola and Liu (1999). FCF’s estimated coefficients were inconsistent; but as the table shows, all coefficients were negative in pre-announcement of SDD date, and the event window (−1, 0) was also significant. But the coefficient of FCF turned positive immediately after the date of announcement, and event window (0, +3) was also significant. This result implied that event windows prior to the announcement day do support the hypothesis of free cash flow; however, there were inconsistencies pre- and post- the announcement date, so the free cash flow hypothesis is not supported in Taiwan. This situation is identical to that reported by Howe, He and Kao (1992). Furthermore, the results from dividend yield coefficient verification were all positive, meaning that the higher the dividend yields, the higher the abnormal return. However, only the coefficient of event window (−1, +1) and (0, +1) were significant. In the empirical findings produced by the 3-year samples, the results were inconsistent. Tobin’s Q coefficient changed from the negative of short-term event windows into positive for long-term event windows. Only the long-term event windows of (−3, 0) and (−3, +3) demonstrated significant positive. FCF coefficient only showed a significant positive in event window (−1, 0), while the remainder were mostly insignificant. Hence a completely different situation was produced between the empirical results for coefficient of Tobin’s Q and FCF and the conclusion reached from the first-time announcement of SDD event. As for the coefficient estimator of the turnover, the entire first-time dividend announcement event was not statistically significant; however, empirical results from three-year samples, event windows (−1, 0) and (−2, 0), were positive and significant. It indicates that the turnover has a positive contribution in ACAR. Although dividend yield results were different for the three-year samples and the first-time SDD samples, they did show a positive effect in pre-announcement date; and then turned negative in post-announcement date. This shows that prior to the date of announcement, investors believed that the greater the dividend yield, the higher the confidence they have for that company, and thus the effect is positive. The empirical findings are consistent with that of Woolridge (1983), and McNichols and Dravid (1990). However, this type of announcement effect was short-lived and did not continue beyond the announcement date.

Announcement Effects of Specially Designated Dividends

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Firm size effect amongst all empirical samples were statistically insignificant. This conclusion was consistent with the investor behavior of being less likely to refer to firm size during sell/buy of a company’s stocks. Although the R-square of some regressive models was not high, the test of model suitability for partial-models was found to be significant.

6. SUMMARY This research employed a form of SDD to test the existence of information hypothesis. We found that in Taiwan, the information hypothesis was in fact supported prior to the announcement of SDD amongst TSE samples, and it means there were positive abnormal returns. However, this type of conveyable information is short-lived. Due to its limitation on trading conditions,8 the ROSE usually received less attention by local investors; hence the conveyed effect of dividend announcement during shareholders meetings were different than those of the TSE samples. Therefore, the information hypothesis of SDDs weren’t supported in the ROSE. It is consistent with Merton’s hypothesis. Nevertheless, in the empirical findings of announcement events from companies without dividend payment for three years, three-year samples, abnormal returns were negative. This result implied that investors had the impression for a long time of these companies with poor business performances; hence, the messages of dividend announcement were perceived as bad by investors. Secondly, we discovered that Tobin’s Q ratio in empirical result was supported in Taiwan. This result illustrated that SDD announcements from low-Q firms generate a greater response of abnormal return than that from high-Q firms. This is particularly supportive when categorized under the original definition of the Tobin’s Q ratio. The free cash flow hypothesis could not be supported from Taiwanese SDD announcement testing. Findings from firm size and turnover analysis, shows no significant relationship, which indicated firm size and turnover are unrelated to abnormal returns. This type of result is in line with the way Taiwanese investors select their stocks. However, in the examination of dividend yield, although not all of the regressive coefficients were significant, their symbols did express the expectations investors have for the future earnings of a company.

NOTES 1. At least 10 million. 2. Since the ROSE was established in 1995.

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3. Since opening, the Taiwan’s stock market has always slapped a maximum up/down limitation; it now stands at 7%. 4. Should the method of the traditional estimation be used during estimative period, then a lack of days in the estimative period would be present between initial listing day of companies and dividend announcement day. 5. In Taiwan, because of the government limit daily fluctuation in the stock market, a grace period allowing for reasonable stock price adjustments of newly listed companies is expected, in order to reflect market information. 6. This research’s cash dividend is zero. 7. See Chung and Pruitt (1994). 8. The transaction conditions at the ROSE are far less than the TSE, such as the financing ratio or margin ratio, paid-in capital, the tick of trading share price, etc.

ACKNOWLEDGMENTS We acknowledge the financial support from National Science Council of R. O. C. (Grant No: 89-2416-H-259-0023).

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