JOURNAL OF MONETARY ECONOMICS Aims and Scope: The Journal of Monetary Economics publishes important research contributions to a wide range of modern macroeconomic topics including work along empirical, methodological and theoretical lines. In recent years, these topics have been: asset pricing; banking, credit and financial markets; behavioral macroeconomics; business cycle analysis; consumption, labor supply, and saving; dynamic equilibria (theory and computational methods); economic growth and development; expectation formation, information and aggregate economic activity; fiscal shocks and fiscal policies; expectation formation; forecasting, macroeconometrics, and time series analysis; information and aggregate economic activity; international trade, exchange rates, and open economy macroeconomics; labor markets; macroeconomic data and history; monetary policy; monetary theory; money demand and money supply behavior; optimal contracting and economic activity; productivity measurement and theory; pricing in product markets and labor markets; and real investment (inventories, fixed, human capital). The Journal has eight regular issues per year, with the Carnegie-Rochester Conference Series on Public Policy as the January and July issues. Founding Editors: KARL BRUNNER and CHARLES I. PLOSSER Editor: ROBERT G. KING, Department of Economics, Boston University, 270 Bay State Road, Boston, MA 02215, USA Co-Editors: Urban Jermann, University of Pennsylvania; Ricardo Reis, Columbia University Senior Associate Editors: MARIANNE BAXTER, Boston University; JANICE EBERLY, Northwestern University; SERGIO REBELO, Northwestern University; STEPHEN WILLIAMSON, University of Washington Associate Editors: KLAUS ADAM, University of Mannheim; GEORGE ALESSANDRIA, Research department of Federal Reserve Bank, Philadelphia; YONGSUNG CHANG, University of Rochester; MARIO CRUCINI, Vanderbilt University; HUBERTO ENNIS, Federal Reserve Bank of Richmond; KRISTOPHER GERARDI, Federal Reserve Bank of Atlanta; FRANCOIS GOURIO, Boston University; REFET GURKAYNAK, Bilkent University, Turkey; JONATHAN HEATHCOTE, Federal Reserve Bank of Minneapolis; ERIK HURST, University of Chicago; RICARDO LAGOS, New York University; EDWARD NELSON, Federal Reserve Board; GIORGIO PRIMICERI, Northwestern University; ESTEBAN ROSSI-HANSBERG, Princeton University; PIERRE-DANIEL SARTE, Federal Reserve Bank of Richmond; FRANK SCHORFHEIDE, University of Pennsylvania; CHRISTOPHER SLEET, Carnegie-Mellon University; SILVANA TENREYRO, London School of Economics; ANTONELLA TRIGARI, Università Bocconi; ADRIEN VERDELHAN, Massachusetts Institute of Technology; ALEXANDER WOLMAN, Federal Reserve Bank of Richmond; JONATHAN WRIGHT, Johns Hopkins University, Baltimore CRC Editors: THOMAS F. COOLEY, New York University; MARVIN GOODFRIEND, Carnegie Mellon University CRC Advisory Board: ANDREW ABEL, University of Pennsylvania; MARK AGUIAR, University of Rochester; MARK BILS, University of Rochester; YONGSUNG CHANG, University of Rochester; HAROLD COLE, University of Pennsylvania; JANICE EBERLY, Northwestern University; BURTON HOLLIFIELD, Carnegie Mellon University; BENNETT T. McCALLUM, Carnegie Mellon University; THOMAS PHILIPPON, New York University; CHARLES I. PLOSSER, Federal Reserve Bank of Philadelphia; CHRISTOPHER SLEET, Carnegie Mellon University; GIANLUCA VIOLANTE, New York University; TONI WHITED, University of Rochester; STANLEY E. ZIN, New York University Submission fee: There is a submission fee of US$250 for all unsolicited manuscripts submitted for publication. There is a reduced fee for full-time students (US$150). To encourage quicker response referees will be paid a nominal fee and the submission fee will be used to cover these refereeing expenses. There are no page charges. Cheques should be made payable to the Journal of Monetary Economics. When a paper is accepted the fee will be reimbursed. Publication information: Journal of Monetary Economics (ISSN 0304-3932). For 2011, volume 58 (8issues) is scheduled for publication by Elsevier (Radarweg 29, 1043 NX Amsterdam, the Netherlands). Further information on this journal is available from the Publisher or from the Elsevier Customer Service Department nearest you or from this journal’s website (http://www.elsevier.com/locate/jme). Information on other Elsevier products is available through Elsevier’s website (http://www.elsevier.com). Periodicals Postage Paid at Rahway, NJ, and at additional mailing offices. USA mailing notice: Journal of Monetary Economics (ISSN 0304-3932) is published 8 times per year by Elsevier (Radarweg 29, 1043 NX Amsterdam, The Netherlands). Periodical postage rate paid at Rahway NJ and additional mailing offices. USA Postmaster: Send change of address to Journal of Monetary Economics, Elsevier Customer Service Department, 3251 Riverport Lane, Maryland Heights, MO 63043, USA. Airfreight and mailing in USA by Mercury International Limited, 365 Blair Road, Avenel, NJ 07001.
The paper used in this publication meets the requirements of ANSI/NISO Z39.48-1992 (Permanence of Paper).
Printed by Henry Ling Ltd., The Dorset Press, Dorchester, UK
Journal of Monetary Economics 58 (2011) 191–205
Contents lists available at ScienceDirect
Journal of Monetary Economics journal homepage: www.elsevier.com/locate/jme
Payments and liquidity under adverse selection Guillaume Rocheteau a,b, a b
University of California, Irvine, United States Federal Reserve Bank of Cleveland, United States
a r t i c l e i n f o
abstract
Article history: Received 27 November 2010 Received in revised form 18 June 2011 Accepted 22 June 2011 Available online 5 July 2011
Informational asymmetries regarding the future value of assets affect their role in exchange. I construct a random-matching economy composed of two assets: a risk-free bond and a Lucas tree whose terminal value is privately known to its holder. No restrictions are imposed on payment arrangements. The main finding supports a pecking-order theory of payments: Agents use their risk-free bonds first in order to finance their spending shocks, and they use their information-sensitive assets only if their holdings of bonds are depleted. The theory has implications for the optimal provision of risk-free bonds, the structure of asset returns, and liquidity. & 2011 Elsevier B.V. All rights reserved.
1. Introduction Liquidity considerations matter for macroeconomics. They help explain asset pricing anomalies, the codetermination of asset prices and macroeconomic conditions, and the transmission mechanism of monetary policy. Liquid assets have an essential role in economies where unsecured credit arrangements that would allow households and firms to finance spending shocks (e.g., consumption or investment opportunities) are not feasible. A critical observation from Kiyotaki and Moore (2005) and Lagos (2010a) is that not all assets are equally suitable for helping agents handle these shocks: some assets are more liquid than others. In Kiyotaki and Moore, agents who hold land and capital can use only a fraction of their capital stock to finance investment opportunities. In Lagos, agents hold risk-free bonds and equity, but equity shares can only be used to finance a fraction of their consumption opportunities. While these liquidity differences among assets help to explain several macroeconomic phenomena, the differences in liquidity themselves are left unexplained by the proposed theories. The objective of this paper is to investigate how informational asymmetries regarding the future value of assets affect their role in exchange, and the implications those asymmetries have for liquidity and the structure of asset yields. History is marked by episodes where the imperfect recognizability of some assets has impaired their ability to serve as media of exchange. In the Antebellum United States thousands of different notes issued by hundreds of banks circulated, and a fraction of these notes were worthless, since they were either counterfeits or the floating issue of insolvent banks. More recently, during the financial market turmoil of 2007–2008, the recognizability problem with asset-backed securities arising from their complexity and heterogeneity has contributed to a major liquidity crunch by reducing investors’ ability to use them as collateral for loans.1 I construct an environment that features pairwise meetings, a meaningful role for means of payment (or collateral), and two types of assets that differ in terms of their exposure to private-information problems: risk-free bonds and risky
Correspondence address: University of California, Irvine, United States.
E-mail address:
[email protected] For a description of the circulation of banknotes during the U.S. 19th century, see Mihm (2007). The drying-up of liquidity in the market for assetbacked commercial paper during the financial crisis of 2007–2008 is described in Brunnermeier (2009). 1
0304-3932/$ - see front matter & 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.jmoneco.2011.06.005
192
G. Rocheteau / Journal of Monetary Economics 58 (2011) 191–205
Lucas (1978) trees. Agents holding a Lucas tree are better informed about its future performance than agents who receive it. The Lucas tree, which is information sensitive, can be thought of as private equity, a corporate bond, or an asset-backed security.2 Beside being a realistic description of the way many assets are traded, having pairwise meetings allows the model to provide explicit game-theoretic foundations for the exchange of goods and assets, as well as for the transfer of information that takes place in a match. The intricate part is determining the terms of trade in matches where the two parties are asymmetrically informed. Most of the recent literature in monetary theory neglects this issue. (See Section 1.1 for a review of the relevant literature.) In contrast, the transfer of goods and assets in this model will be the outcome of an explicit bargaining game, and it will be shown that asset holders can select offers that signal the quality of their assets. The possibility of such signaling generates new insights for payment arrangements in pairwise meetings. The main insight is that payment arrangements exhibit a pecking-order property. Agents have a strict preference for risk-free bonds as means of payment (or, equivalently, as collateral): they spend their risk-free bonds first in order to finance their consumption, and they use their information-sensitive assets as means of payment only if their holdings of risk-free bonds are depleted. Moreover, information-sensitive assets are (partially) illiquid in the sense that agents sell only a fraction of their asset holdings even when their consumption is inefficiently low. Intuitively, by retaining a fraction of their information-sensitive assets, agents are able to credibly reveal their private information regarding the future value of their assets. In contrast, if an agent attempts to sell too large a quantity of information-sensitive assets, then his offer will get rejected because it will be attributed to someone holding low-value assets. This result captures the notion that large trades of information-sensitive assets involve sizeable transaction costs—a standard notion of asset illiquidity. A major insight of Kiyotaki and Wright (1989) was to show that the acceptability of a good depends on its storage cost as well as other fundamentals (e.g., the pattern of specialization) and beliefs. In the same vein, the liquidity of the informationsensitive asset depends on the stochastic process that drives its fundamental value. The asset becomes more illiquid as the dispersion of its future values across states increases. The methodology in this paper could be applied to Kiyotaki and Moore (2005) or Lagos (2010a) models in order to relate the partial illiquidity of some assets to their risk characteristics. In the limiting case where the asset has no value in some states, it becomes fully illiquid and, in the absence of risk-free assets, trade shuts down. While it is well understood that adverse-selection problems can cause markets to cease to function, here it occurs in the context of a market with bilateral trades and bargaining – the two main characteristics of an over-the-counter market – despite agents’ private information being revealed in equilibrium through signaling. The model has implications for asset prices and the liquidity structure of asset yields. Risk-free bonds exhibit a liquidity premium – the difference between the market price and the discounted terminal value of the asset – if there is a shortage of information-insensitive assets.3 Moreover, the rate of return of the risk-free bonds is less than the rate of return of the information-sensitive assets even though agents are endowed with quasilinear preferences. This rate-of-return difference occurs because risk-free bonds are preferred means of payment. This finding is consistent with the observed convenience yield of Treasury securities relative to corporate bonds (Krishnamurthy and Vissing-Jorgensen, 2008). Finally, the model provides a channel through which policy – described as a change in the supply of the risk-free bonds – affects asset prices, the structure of asset returns, and output. If the quantity of bonds is below a threshold, an increase in the supply of bonds raises the risk-free rate, output, and welfare. A policy that would consist of issuing risk-free bonds in order to substitute them for information-sensitive assets would be welfare improving. The optimal policy is such that the demand for risk-free bonds is satiated. In that case, asset prices are driven down to their fundamental values, and the information-sensitive asset is illiquid, i.e., its transaction velocity (in some states) is zero. The paper is organized as follows. Section 1.1 provides a review of the relevant literature. The environment is described in Section 2. Section 3 analyzes the bargaining game under incomplete information. Section 4 embeds the bargaining game into a general equilibrium structure and studies the effects of policy and fundamentals on asset liquidity. The proofs of lemmas and propositions are in an online appendix. 1.1. Related literature There is a related literature that studies adverse selection in decentralized asset markets with pairwise meetings.4 This includes Cuadras-Morato´ (1994) on the emergence of a commodity money, Velde et al. (1999), and Burdett et al. (2001) on Gresham’s law, and Hopenhayn and Werner (1996) on the liquidity structure of asset returns. These papers differ from this one in that they avoid the thorny issue of the determination of the terms of trade under asymmetric information by restricting asset holdings to f0,1g and by assuming that agents cannot hold multiple assets. Even when consumption goods are divisible, such restrictions reduce agents’ ability to signal their private information, and they prevent the emergence of separating equilibria. Aiyagari (1989) circumvents the difficulty of analyzing strategic interactions within 2 An asset is information sensitive if its future value is random and if it is subject to a private-information problem. According to this definition, a risk-free asset is information insensitive. If agents are symmetrically informed about the future value of a risky asset, the asset is also information insensitive. The notion of information sensitivity is related to Jevons’s (1875) notion of cognizability defined as the capability of a substance for being easily recognized and distinguished from all other substances. 3 The idea that the available supply of liquid assets is relatively scarce is empirically relevant. See, e.g., Caballero (2006). 4 There is a recent literature on liquidity in decentralized asset markets. See, e.g., Duffie et al. (2005) and Lagos and Rocheteau (2009). These papers, however, do not incorporate informational asymmetries.
G. Rocheteau / Journal of Monetary Economics 58 (2011) 191–205
193
bilateral matches, and the possibility of information transmission through signaling or screening, by assuming competitive trades in overlapping generations economies with privately informed agents.5 Huggett and Krasa (1996) adopt a mechanism design approach – instead of an equilibrium approach – to show the essentiality of fiat money in a model with alternating endowments, a storage technology with positive returns, and differential information. While my paper focuses on an adverse-selection problem, there is a related literature that studies the role of money in the presence of moral hazard problems regarding the quality of goods. Williamson and Wright (1994), Trejos (1997, 1999), and Berentsen and Rocheteau (2004) consider an economy with pairwise trades, where consumption goods can be counterfeited and fiat money is the only asset. Li (1995) studies an environment with multiple commodity monies but where terms of trade are exogenous. In these models, the possibility of signaling, which underlies my pecking-order theory of payments, is shut down, because money holdings are restricted to {0,1} or allocations are restricted to those that are pooling. Banarjee and Maskin (1996) do not restrict asset holdings, but they study the emergence of commodity monies in an environment with Walrasian trading posts, where agents can allocate their labor to the production of low- or high-quality goods. The assumption of price-taking agents rules out the strategic considerations in the pairwise meetings that are the focus of this paper. Lester et al. (2007) also extend the Lagos and Wright (2005) model to include multiple divisible assets, fiat money, and capital. The recognizability problem takes the form of claims on capital that can be costlessly counterfeited and can only be authenticated in an endogenous fraction of meetings.6 However, they simply assume that uninformed sellers do not accept claims on capital. Li and Rocheteau (2009) solve the bargaining game under incomplete information in the case where counterfeits are produced at a positive cost. Li and Rocheteau’s paper complements my analysis by showing the different implications of moral hazard and adverse selection for payment arrangements. Papers in the search-theoretic literature concerned with liquidity and asset pricing include Lagos (2010a), Geromichalos et al. (2007), Lagos and Rocheteau (2008), and Ravikumar and Shao (2010). Finally, my model provides a foundation for the trading restrictions that have been imposed in some recent models that have fiat money coexisting with other assets, e.g., Aruoba and Wright (2003), Aruoba et al. (2011), Kiyotaki and Moore (2005), Lagos (2010a), and Telyukova and Wright (2008).7
2. Environment The environment is similar to the one in Lagos and Wright (2005) and Rocheteau and Wright (2005). Time is discrete, starts at t ¼0, and continues forever.8 Each period has two subperiods: a morning, where trades occur in a decentralized market (DM), followed by an afternoon, where trades take place in a competitive market (CM). There is a unit measure of infinitely lived households and a unit measure of firms. There are two perishable consumption goods, one produced in the DM and the other in the CM (Fig. 1). The lifetime expected utility of a household from date 0 onward is
E
1 X
bt Uðyt ,xt ,nt Þ,
ð1Þ
t¼0
where xt is the CM consumption of period t, nt is the hours of work in the CM, yt is the DM consumption, and b 2 ð0,1Þ is a discount factor. For tractability, the period utility is separable across stages and linear in the CM, i.e., Uðyt ,xt ,nt Þ ¼ uðyt Þ þxt nt . The utility function u(y) is twice continuously differentiable, uð0Þ ¼ 0, u0 ð0Þ ¼ 1, u0 ðyÞ 40, and u00 ðyÞ o0. The production technology in the CM is linear, with labor as the only input, xt ¼ nt . The DM output is produced by firms.9 Each firm invests k 4 0 units of the CM good at t1. This allows it to generate at t any amount y 2 ½0,Y of the DM good, plus x ¼ f ðYyÞ of the CM good, where Y 40, f is twice continuously differentiable, strictly increasing and concave, f 0 ð0Þ ¼ 1, and f 0 ðYÞ ¼ 0. This makes cðyÞ f ðYÞf ðYyÞ the opportunity cost of selling y in the DM, where cð0Þ ¼ 0, c0 ð0Þ ¼ 0, and c0 ðYÞ ¼ 1. Let yn ¼ arg maxy ½uðyÞcðyÞ. Assume ko bf ðYÞ, so that it is always profitable to participate in the market. The profits of the firms (defined as income net of investment cost) are redistributed in a lump-sum fashion to the households. At the beginning of the CM, each household is endowed with A4 0 units of one-period-lived, divisible Lucas trees that can be interpreted as private equity, corporate bonds, or asset-backed securities. Trees are subject to an idiosyncratic shock, k 2 fk‘ , kh g, at the beginning of the DM, which is privately known to the holder of the trees. With probability ph 2 ð0,1Þ, the terminal output of a tree is k ¼ kh , and with complement probability p‘ , k ¼ k‘ , where 0 o k‘ o kh and 5 Smith (1989), in an overlapping generations model, and Jafarey and Rupert (2001) in a model with alternating endowments explain the usefulness of fiat money when credit is available by a private-information friction regarding individuals’ abilities to repay their debts. 6 There is a related literature on counterfeiting, which includes Green and Weber (1996), Williamson (2002), and Nosal and Wallace (2007). 7 Aruoba and Wright (2003) and Aruoba et al. (2011) also refer to the lack of portability of capital goods to justify the assumption that capital cannot be used as a means of payment in decentralized markets. Telyukova and Wright (2008, Section 4) lay down an extension of their model with Lucas trees, in which agents pay a fixed cost if they use their real assets as means of payment. 8 The assumption of an infinite time horizon is not necessary but it makes the model comparable to standard monetary models. It can be readily extended to have long-lived assets or fiat money. See Rocheteau (2008, 2009). 9 The description of firms is borrowed from Berentsen et al. (2011).
194
G. Rocheteau / Journal of Monetary Economics 58 (2011) 191–205
Fig. 1. Timing. Each representative period is composed of two stages. In the first stage, agents trade in competitive markets (CM). In the second stage, they trade in decentralized markets (DM) with bilateral matching and bargaining.
ph kh þ p‘ k‘ ¼ 1.10 (With no loss in generality, the expected income of each asset is normalized to one.) The realizations of the productivity shocks are common to all the trees held by a household, but they are independent across households. The government supplies a constant quantity, Z, of one-period-lived, risk-free bonds. The safety of bonds is backed by the unrestricted ability of the government to tax households in the CM. Bonds are perfectly divisible, and each unit pays one unit of output in the CM. The interest payments are financed by lump-sum taxes in the CM. In the CM, households can trade consumption goods, bonds, and trees competitively. In the DM, each firm is matched bilaterally and at random with a household. The household makes an offer that the firm accepts or rejects. If the offer is accepted, the trade is implemented.11 Unsecured credit arrangements are not incentive-feasible since households are anonymous and cannot commit. In this case, DM trade is either quid pro quo, or equivalently, for the purpose of this paper, collateralized debt.12 Matched agents can transfer any nonnegative quantity of DM output and any quantity of their asset holdings. 3. Payments under private information Consider the bargaining game between a household holding a portfolio composed of a trees and z bonds, and a firm. The analysis of the bargaining game is simplified by assuming that the household’s portfolio is common knowledge in the match.13 3.1. Description of the bargaining game In order to define the payoffs in the bargaining game, it is useful to derive first some properties of the value functions in the CM. Let Wðz,a, kÞ denote the value function of a household holding z bonds and a trees before the CM opens, when the terminal value of a tree is k 2 fk‘ , kh g. fxn þ bEVðz0 ,a0 , k0 Þg Wðz,a, kÞ ¼ max 0 0 x,n,z ,a
s:t:
x þqz z0 þ qa a0 þ T ¼ n þ ka þ z þqa A þ P,
ð2Þ ð3Þ
where Vðz,a, kÞ is the value function of the household at the beginning of the DM, qz is the price of bonds (expressed in CM output), qa is the price of trees, T Zð1qz Þ is the lump-sum tax by the government, and P are the profits paid by the firms (revenue net of the investment cost). The expectation is taken with respect to the terminal value k0 . According to (2), each household chooses its net consumption, xn, and its portfolio, z0 and a0 , in order to maximize its expected lifetime utility subject to the budget constraint (3). According to (3), the value of the household’s initial portfolio in terms of CM output is ka þz. In order to hold a portfolio ðz0 ,a0 Þ in the next CM, the household must invest qz z0 of current output in bonds and qa a0 in trees. It must also pay some lump-sum taxes T, and it receives an endowment of trees worth qa A and the profits of the firms. Substitute xn ¼ ka þ zqz z0 þqa ðAa0 ÞT þ P from (3) into (2) to obtain fqz z0 qa a0 þ b½ph V b ðz0 ,a0 , kh Þ þ p‘ V b ðz0 ,a0 , k‘ Þg: W b ðz,a, kÞ ¼ ka þz þ qa AT þ P þ max 0 0 z ,a
ð4Þ
The household’s value function in the CM is linear in its wealth. Moreover, a household’s portfolio choice is independent of its initial portfolio when it entered the period. Both properties greatly simplify the model. The bargaining game between the household and the firm has the structure of a signaling game.14 A strategy for the household specifies an offer ðy,d, tÞ 2 F R þ ½0,a ½0,z, where y is the output produced by the firm, d is the transfer of trees by the household, and t is the transfer of bonds, as a function of the household’s type (i.e., its private information about 10 Plantin (2009) justifies the ‘‘learning-by-holding’’ assumption for securitized pools of loans. Rocheteau (2008, Appendix D) shows that the model can be generalized to allow for more than two terminal values. 11 I chose a bargaining protocol in which the household makes a take-it-or-leave-it offer because it has been extensively used in monetary theory, and it remains tractable under private information. See Section 5.2 for more details. 12 The above-mentioned equivalence between the use of the asset as a means of payment or as collateral for a loan is described by Lagos (2010b). 13 This assumption is made in order to avoid having to specify firms’ beliefs regarding the portfolio held by households in the pairwise meetings. It will be shown in the following that the surplus functions in the DM are weakly monotonically increasing in the household’s asset holdings. Hence, if households had the possibility of showing their portfolios in a pre-stage of the bargaining game, there would be an equilibrium in which they would do so truthfully. 14 See Appendix B in Rocheteau (2009) for a more detailed presentation of signaling games.
G. Rocheteau / Journal of Monetary Economics 58 (2011) 191–205
195
the future value of the trees). The transfers of assets are constrained by the household’s portfolio. A strategy for the firm is an acceptance rule that specifies a set A D F of acceptable offers. The household’s payoff in the state k is ½uðyÞ þ Wðzt,ad, kÞIA ðy,d, tÞ þWðz,a, kÞ½1IA ðy,d, tÞ,
ð5Þ
where IA ðy,d, tÞ is an indicator function that is equal to one if ðy,d, tÞ 2 A. If an offer is accepted, then the household enjoys its utility of consumption in the DM, u(y), but it forgoes d trees and t bonds. Using the linearity of the household’s value function, and omitting the constant terms, the household’s payoff can be expressed as its surplus, ½uðyÞkdtIA ðy,d, tÞ. The firm’s payoff function is ½f ðYyÞ þ t þ kdIA ðy,d, tÞ þ f ðYÞ½1IA ðy,d, tÞ ¼ ½cðyÞ þ t þ kdIA ðy,d, tÞ þ f ðYÞ:
ð6Þ
In order to accept or reject an offer, the firm will have to form expectations about the terminal value of the household’s trees. Let lðy,d, tÞ 2 ½0,1 represent the updated belief of a firm that the household holds high-value trees (k ¼ kh ), conditional on the offer ðy,d, tÞ being made. Then, El ½k ¼ lðy,d, tÞkh þ½1lðy,d, tÞk‘ . For a given belief system, the set of acceptable offers for a firm is AðlÞ ¼ fðy,d, tÞ 2 F : cðyÞ þ flðy,d, tÞkh þ ½1lðy,d, tÞk‘ gd þ t Z 0g:
ð7Þ
For an offer to be acceptable, the firm’s cost of production in the DM, cðyÞ, must be compensated for by its expected revenue in the next CM, El ½kd þ t. Assuming a tie-breaking rule according to which a firm agrees to any offer that makes it indifferent between accepting or rejecting a trade,15 the problem of a household holding trees of quality k is then max½uðyÞkdtIA ðy,d, tÞ y,d, t
s:t:
ðy,d, tÞ 2 R þ ½0,a ½0,z:
ð8Þ
3.2. Equilibrium of the bargaining game The equilibrium concept is perfect Bayesian equilibrium (PBE). An equilibrium of the bargaining game is a profile of strategies for the household and the firm, and a belief system, l. If ðy,d, tÞ is an offer made in equilibrium, then lðy,d, tÞ is derived from the firm’s prior belief according to Bayes’s rule. Since there is no discipline for out-of-equilibrium beliefs, b the equilibrium concept is refined by using the Intuitive Criterion of Cho and Kreps (1987).16 Denote Uh the surplus of an h-type household and U‘b the surplus of an ‘-type household in a proposed equilibrium of the bargaining game. (The superscript b stands for buyer.) The proposed equilibrium fails the Intuitive Criterion if there is an out-of-equilibrium ~ t~ Þ 2 F , and a household’s type w 2 f‘,hg, such that the following is true: ~ d, offer, ðy, ~ t~ 4 U b , ~ kw d uðyÞ w
ð9Þ
~ t~ o U b , ~ kw d uðyÞ w
ð10Þ
~ þ kw d~ þ t~ Z 0, cðyÞ
ð11Þ
~ t~ Þ would make a w-type household strictly better off if it were ~ d, where fwg ¼ f‘,hg\fwg. According to (9), the offer ðy, ~ t~ Þ would make the w-type household strictly worse off. According to (11), the ~ d, accepted. According to (10), the offer ðy, offer is acceptable provided that the firm believes it comes from a w-type. Definition 1. An equilibrium of the bargaining game is a pair of strategies and a belief system, /½yðkÞ,dðkÞ, tðkÞ, A, lS, such that ½yðkÞ,dðkÞ, tðkÞ is a solution to (8), with k 2 fk‘ , kh g; A is given by (7); l : F -½0,1 satisfies Bayes’s rule whenever possible and the Intuitive Criterion. Equilibria of the bargaining game are characterized in three steps. First, the Intuitive Criterion is used to eliminate all PBE with a pooling offer (Lemma 2). Second, it is shown that among separating PBE, all but the Pareto-efficient (or least-costly separating) one can be dismissed by the Intuitive Criterion (Lemma 3). Third, a system of beliefs is constructed that supports the Pareto-efficient separating PBE that complies with the Intuitive Criterion, and the firm’s acceptance rule is derived. Lemma 2. In equilibrium, there is no pooling offer with d 4 0. 15 A similar tie-breaking assumption is used in Rubinstein (1985, Assumption B-3). It is made so that the set of acceptable offers is closed, and the household’s problem has a solution. 16 The Intuitive Criterion is a refinement supported by much of the signaling literature. An equilibrium that fails the Intuitive Criterion gives an outcome that is not strategically stable in the sense of Kohlberg and Mertens (1986). See Riley (2001) for a survey of the applications of the Intuitive Criterion (and other refinements) in various contexts. It has been used in monetary theory by Nosal and Wallace (2007); in the corporate finance literature by DeMarzo and Duffie (1999); in bargaining theory by Rubinstein (1985, Assumption B-1). In the context of this paper, the Intuitive Criterion has the additional advantage of preserving the tractability of the model once the bargaining game is embodied in the general equilibrium structure in Section 4. For the sake of completeness, the model is also analyzed under the alternative refinement from Mailath et al. (1993) in Appendix C of Rocheteau (2009). See Section 5.
196
G. Rocheteau / Journal of Monetary Economics 58 (2011) 191–205
Any equilibrium in which there are transfers of trees between households and firms is separating. The logic of the argument goes as follows. Suppose there is a pooling offer such that d 40. The ask price of the h-type household for a tree in terms of the DM good is defined as the minimum quantity of DM output the household would accept in exchange for an additional tree. It is equal to kh =u0 ðyÞ, which is larger than the ask price of the ‘-type household, k‘ =u0 ðyÞ. The household in the high state has, therefore, the possibility of signaling its state by reducing the transfer of its trees by a small amount, e 4 0, and its consumption by a quantity between k‘ e=u0 ðyÞ and kh e=u0 ðyÞ. Such an offer would raise its payoff relative to the proposed equilibrium, but it would hurt households in the low state. Consequently, the firm should attribute this offer to an h -type household and should be willing to accept it given that it was willing to accept the pooling offer in the first place. (See Section 3.4 for a graphical illustration of this argument.) The next lemma shows that among separating PBE, only the Pareto-efficient one survives the Intuitive Criterion. Lemma 3. An optimal offer by a household in the low-value state is ðy‘ ,d‘ , t‘ Þ 2 arg max½uðyÞk‘ dt, y, t,d
s:t:
cðyÞ þ k‘ d þ t Z 0,
0 r t rz,
ð12Þ ð13Þ
0 r d ra:
ð14Þ
An optimal offer by a household in the high-value state is ðyh ,dh , th Þ 2 arg max½uðyÞkh dt, y, t,d
s:t:
cðyÞ þ kh d þ t Z0,
ð15Þ ð16Þ
uðyÞk‘ dt r uðy‘ Þcðy‘ Þ,
ð17Þ
0 r t rz,
ð18Þ
0 r d ra:
The only way an ‘-type household can achieve a higher payoff than the one it would get in a game with complete-information is by making an offer with d‘ 4 0, which a firm would attribute to an h-type household with positive probability, but this has been ruled out by Lemma 2. Hence, households in the low-value state make their complete-information offer (which is always acceptable irrespective of firms’ beliefs). The solution to (12)–(14) is y‘ ¼ yn ,
ð19Þ
k‘ d‘ þ t‘ ¼ cðyn Þ,
ð20Þ
if k‘ a þz Z cðy Þ. If k‘ a þ z ocðy Þ, then n
n
t‘ ¼ z,
ð21Þ
d‘ ¼ a,
ð22Þ
y‘ ¼ c1 ðk‘ a þ zÞ:
ð23Þ
The only possible offer an h-type household can make in equilibrium is the one that maximizes its payoff in the class of all offers that are incentive-compatible and that satisfy the participation constraint of the firm, where the firm has the correct belief that it faces an h-type household. This offer is called the least-costly separating offer. The proof is by contradiction. Suppose there is a separating equilibrium where the h-type household makes an offer that is not the solution to (15)–(18). Then, the h-type household could make an offer arbitrarily close to the least-costly separating offer that would raise its payoff and lower the payoff of an ‘-type household. Hence, according to the Intuitive Criterion, such an offer should provide a profitable deviation to h-type households for reasonable systems of beliefs. The last step in characterizing an equilibrium is to construct a belief system that generates an acceptance rule for firms that is consistent with the households’ offers in Lemma 3 and that satisfies the Intuitive Criterion. Beliefs regarding equilibrium offers are determined from Bayes’s rule. All out-of-equilibrium offers that would raise the payoff of households in the low state relative to their complete-information payoff are attributed to ‘-type households, and all other out-of-equilibrium offers are attributed to h-type households. By construction, this system of beliefs satisfies the Intuitive Criterion.17 Formally,
17
lðy,d, tÞ ¼ 0, 8ðy,d, tÞ= 2O s:t: uðyÞk‘ dt 4 uðy‘ Þcðy‘ Þ,
ð24Þ
lðy,d, tÞ ¼ 1, 8ðy,d, tÞ= 2O s:t: uðyÞk‘ dt ruðy‘ Þcðy‘ Þ,
ð25Þ
The belief system is not uniquely determined, but the output levels and agents’ payoffs are unique.
G. Rocheteau / Journal of Monetary Economics 58 (2011) 191–205
197
where O is the set of equilibrium offers. Under this belief system, the set of acceptable offers is A ¼ fðy,d, tÞ 2 F : uðyÞk‘ dt r uðy‘ Þcðy‘ Þ
and
cðyÞ þ kh d þ t Z0g:
ð26Þ
Feasible offers that violate the incentive-compatibility constraint (17) are attributed to ‘-type households. Consequently, they violate the firm’s participation constraint (13), and they are rejected. All the offers that satisfy uðyÞk‘ dt ruðy‘ Þcðy‘ Þ are attributed to h-type households, except ðy‘ ,d‘ , t‘ Þ. In order for such offers to be accepted, they must also satisfy (16). Proposition 4 (A pecking-order theory of payments). Consider a match between a household holding a portfolio (z,a) and a firm. There is a solution ðyh ,dh , th Þ to (15)–(18), and it has the following properties: If z Z cðyn Þ, then yh ¼ yn ,
ð27Þ
th þ kh dh ¼ cðyn Þ,
ð28Þ
dh ¼ 0:
ð29Þ
If z o cðyn Þ, then th ¼ z and ðyh ,dh Þ 2 ½0,y‘ ½0,a is the unique solution to:
kh dh ¼ cðyh Þz,
ð30Þ
k‘ ½cðyh Þz ¼ uðy‘ Þcðy‘ Þ, uðyh Þcðyh Þ þ 1
ð31Þ
kh
where y‘ ¼ min½yn ,c1 ðz þ k‘ aÞ. Moreover, if a 4 0, then yh oy‘ and dh 2 ð0,aÞ. Proposition 4 offers a pecking-order theory of payment choices: households with a consumption opportunity finance it with risk-free bonds first, and they use their risky, information-sensitive assets as a last resort.18 If households hold enough risk-free bonds to buy yn (z Z cðyn Þ), then they do not transfer any tree to the firms. In this sense, the risk-free bond is a preferred means of payment. Even when households do not have enough wealth to buy the surplus-maximizing level of output, they choose not to spend all their trees (i.e., they only use a fraction of their holdings of trees as collateral). By retaining a fraction of their trees, households signal the high future value of their assets, and hence they secure better terms of trade.19 The partial illiquidity of trees can also be explained by using the more familiar notions of bid and ask prices. Consider a household that does not hold enough bonds to consume yn . If it spends slightly less than dh tree, where dh is defined in Eq. (30), then a tree is sold at the bid price of the firm, i.e., the maximum it is willing to pay in terms of DM output, given that it believes trees will have a high terminal value, kh =c0 ðyh Þ. If the household offers to spend slightly more than dh, then the firm is not willing to pay more than the ask price of an ‘-type household, i.e., the minimum quantity of DM output an ‘-type household would accept in exchange for an additional tree, k‘ =u0 ðyh Þ. Indeed, an attempt by a household to obtain a better price for a transfer of trees above dh would be attributed to an ‘-type household and it would be rejected. Since k‘ =u0 ðyh Þ o kh =c0 ðyh Þ, the household faces a steep decline of the price at which it can sell trees if it spends more than dh. It is this greater discount for large trades – a standard notion of asset illiquidity – that prevents households in h-type matches from spending more than dh even though their consumption is inefficiently low and they have not exhausted all their wealth. 3.3. Determinants of asset liquidity The fraction yh dh =a of its holdings of trees that a household spends in the DM is a function of its portfolio and the process pffiffiffi that drives the terminal value of trees. For the functional forms uðyÞ ¼ 2 y and cðyÞ ¼ y the closed-form solution for yh is 2 " sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi #2 kh k‘ pffiffiffiffiffi k‘ 1 1 2 y‘ y‘ þ 1 z z
yh ðkh ,z,aÞ ¼
k‘
yh ðkh ,z,aÞ ¼ 0 otherwise,
kh
kh
kh a
ifz r yn ,
ð32Þ ð33Þ
where y‘ ¼ minð1, k‘ a þ zÞ and k‘ ¼ ð1ph kh Þ=p‘ . This expression points to the differences between the approach in this paper and the approaches of Kiyotaki and Moore (2005) and Lagos (2010a). In Kiyotaki and Moore (2005), agents can only sell a fraction, y 2 ð0,1Þ, of their illiquid asset (capital) to raise funds; in Lagos (2010a), agents can use their illiquid asset (Lucas trees) in a fraction, y, of the matches. In both cases, the parameter y is exogenous. In contrast, in this model households spend 18 The term ‘‘pecking order’’ was coined by Myers (1984, p. 581). It describes the predictions of models of capital structure choices under private information. According to the pecking-order theory, firms with an investment opportunity prefer internal finance (nondistributed dividends). If external finance is required, then they issue the safest security first, and they use equity as a last resort. 19 This result is reminiscent of some of the findings of the liquidity-based model of security design from DeMarzo and Duffie (1999). They consider the problem faced by a firm that needs to raise funds by issuing a security backed by real assets. The issuer has private information regarding the distribution of cash flows of the underlying assets. Using the Intuitive Criterion, they show that a signaling equilibrium exists in which the seller receives a high price for the security by retaining some fraction of the issue.
198
G. Rocheteau / Journal of Monetary Economics 58 (2011) 191–205
a fraction, yh , of their holdings of trees when their terminal value is high, where yh is a function of the intrinsic characteristics of the asset (k‘ and kh ) and the composition of the portfolio held by the household (z and a). Hence, the (il)liquidity of the trees depends on their intrinsic characteristics, as well as policy, as captured by the supply of risk-free bonds. Proposition 5 (Asset liquidity and riskiness). Assume z ocðyn Þ and a 40. Then: dyh o 0: dkh ph kh þ k‘ p‘ ¼ 1
ð34Þ
The liquidity of trees decreases as the spread of the distribution of their terminal values increases. To understand this result, notice from (17) that, in order to separate themselves from ‘-type households, h-type households incur a signaling cost – the difference between the household’s surplus in the low state and the household’s surplus in the high state – equal to ðkh k‘ Þdh 4 0. As k‘ gets closer to kh , this signaling cost decreases, and the incentive-compatibility constraint is relaxed, which improves the liquidity of trees in the high state. Conversely, as kh k‘ increases, the informational asymmetries become more severe, which makes the incentive-compatibility condition more binding. Proposition 6 (Market breakdowns). Assume z ocðyn Þ and a 40. As k‘ tends to0, then yh approaches0. In the case where k‘ approaches 0, the adverse-selection problem is so severe that trees cease to be traded, and bonds become the only means of payment.20 There is a drying-up of liquidity in the market for trees when they become valueless in the worst state. The proof of this result goes as follows. From Lemma 2, an equilibrium of the bargaining game cannot be pooling, since, otherwise, h-type households would have a profitable deviation to signal the quality of their assets. If a tree in the low state is worthless, this immediately implies that ‘-type households cannot sell their trees at any positive price. But incentive-compatibility also implies that h-type households cannot sell their own trees. Proposition 7 (Payments and portfolio composition). If z o cðyn Þ and a 4 0, then @ðkh dh Þ u0 ðy‘ Þ=c0 ðy‘ Þu0 ðyh Þ=c0 ðyh Þ ¼ o 0: k‘ @z u0 ðy Þ=c0 ðy Þ h
h
ð35Þ
kh
If k‘ a þ z ocðyn Þ, then @dh u0 ðy‘ Þ=c0 ðy‘ Þ1 ¼k 2 ð0,1Þ: h 0 @a u ðyh Þ=c0 ðyh Þ1
ð36Þ
k‘
As the household accumulates a larger quantity of risk-free bonds, its use of trees (expressed in CM output) as means of payments (or collateral) decreases. An h-type household reduces its signaling cost by substituting information-insensitive bonds for information-sensitive trees, thereby relaxing the incentive-compatibility constraint (17). This dependence of yh on z offers a channel through which the supply of bonds affects the liquidity of trees. According to (36), the marginal propensity of a household to spend its trees in the high state is less than one. Provided that k‘ a þ z o cðyn Þ, an additional tree raises the surplus that the household can obtain in the low state. As a consequence, the household in the high state that receives an additional tree can spend a fraction of it without giving ‘-type households incentives to imitate its offer. If k‘ a þ z 4 cðyn Þ, then y‘ ¼ yn and @dh =@a ¼ 0. In this case, the liquidity needs in the low state are satiated and, as a result, an additional tree does not affect the incentive-compatibility constraint, and hence the terms of trade, in the high state. 3.4. A benchmark In the following, I describe an economy with no risk-free bonds, z ¼0. This special case lends itself to simple graphical representations of the results in Lemmas 2 and 3 and Proposition 4. In Fig. 2 the participation constraint of a firm that believes it is facing an h-type (respectively, ‘-type) household is represented by the frontier Uhs fðy,dÞ : cðyÞ þ kh d ¼ 0g (respectively, U‘s fðy,dÞ : cðyÞ þ k‘ d ¼ 0g). (The superscript s stands for seller.) The Intuitive Criterion selects a unique equilibrium among multiple PBE. As shown in Lemma 2, there is no equilibrium of the bargaining game with a pooling offer. The proof is illustrated in the left panel of Fig. 2. Consider an equilibrium with a pooling offer ðy,dÞ with d 4 0. 20 Strictly speaking, the ‘-type households can still use trees in payments, but because k‘ tends to 0, the amount of output they buy with them approaches 0. Also, a well-known property of the equilibrium selected by the Intuitive Criterion is that the outcome is independent of the distribution of types ðph , p‘ Þ, which can make the adverse-selection problem look very severe when the occurrence of the low state is infrequent. Rocheteau (2009, n ^ Appendix C) checks the robustness of the result to the notion of undefeated equilibrium proposed by Mailath et al. (1993). If z 2 ½cðyÞ,cðy ÞÞ, where y^ is the solution to u0 ðyÞ ¼ kh Þc0 ðyÞ, then the unique undefeated equilibrium corresponds to the one selected by the Intuitive Criterion.
G. Rocheteau / Journal of Monetary Economics 58 (2011) 191–205
199
Fig. 2. Pooling vs separating equilibria. The equilibrium of the bargaining game cannot be pooling since otherwise one could find offers that violate the Intuitive Criterion. See left panel. The equilibrium is separating. The ‘-type household makes the complete-information offer and the h-type household makes the least-costly separating offer. See the right panel.
The surpluses of the two types of households at the proposed equilibrium are denoted U‘b uðyÞk‘ d and Uhb uðyÞkh d. b (The superscript b stands for buyer.) The indifference curves U‘b and Uh in Fig. 2 exhibit a single-crossing property, which is s key to obtaining a separating equilibrium. The offer ðy,dÞ is located above Uh since it is accepted when l o 1. The shaded b area indicates the set of offers that raise the utility of an h-type household (offers to the right of Uh), but reduce the utility s b of an ‘-type household (offers to the left of U‘ ), and are acceptable by firms provided that l ¼ 1 (offers above Uh). These offers satisfy (9)–(11) with w ¼ h, so that the proposed equilibrium with a pooling offer ðy,dÞ violates the Intuitive Criterion. In order to separate itself, an h-type household reduces its DM consumption, Dy o0, as well as its transfer of assets to the b firm, Dd o0. Provided that Dd=Dy is between the slopes of U‘b and Uh, u0 ðyÞ=k‘ and u0 ðyÞ=kh , respectively, an h-type household would gain from such an offer while an ‘-type household would be made worse off. Among the separating PBE, only one satisfies the Intuitive Criterion, the one that maximizes the utility of h-type households, and the associated offer s is at the intersection of U‘b and Uh. See the right panel of Fig. 2. The last component of an equilibrium is a system of beliefs, l, and the associated acceptance rule for firms, A. From (24) to (25) firms attribute all offers to the right of U‘b to ‘-type households. See the shaded area in the right panel of Fig. 2. Such offers are also located to the right of U‘s , and therefore they are rejected. Offers to the left of U‘b are attributed to h-type s households. Among these offers, only the ones above Uh are acceptable. The acceptance rule, A, is represented by a striped area in the right panel of Fig. 2. It shows clearly that there are offers with a larger transfer of trees than the one made in equilibrium, which are rejected even though they would raise the utility of h-type households and would be acceptable to b s firms under optimistic beliefs about the quality of the asset—such offers are located above dh and between Uh and Uh. n As shown in the figure, and proved in Proposition 4, yh oy‘ r y . Households always consume less in the high state than in the low state. Despite this inefficiently low consumption, households retain a fraction of their asset holdings, dh od‘ r a (Proposition 4).
4. Asset prices and liquidity This section incorporates the bargaining game studied in Section 3 into the general equilibrium structure described in Section 2 in order to determine the conditions under which the price of each asset exhibits a liquidity premium, and the structure of asset returns. The sequence of events is as follows. Households make a portfolio choice in the CM. At the beginning of the subsequent period, households receive a private and fully informative signal about the terminal value of their trees. Then, households get matched with firms. An implication of this timing is that the household’s portfolio does not convey any information about its private information. From Proposition 4, the terms of trade, ½yðz,a, kÞ, tðz,a, kÞ,dðz,a, kÞ, are functions of the household’s portfolio and its private signal.21
4.1. Portfolio choices and asset prices The missing element of the model so far is the determination of households’ portfolio choices. These choices depend on the benefits that a household expects to receive from holding assets in the DM. The expected lifetime utility of a household entering the DM with z units of bonds, a trees, and a private signal k, is Vðz,a, kÞ ¼ u½yðz,a, kÞ þW½ztðz,a, kÞ,adðz,a, kÞ, k:
21
The solutions to (12)–(14) and (15)–(18) might not be unique, e.g., if z 4 cðyn Þ, but agents’ surpluses are unique.
ð37Þ
200
G. Rocheteau / Journal of Monetary Economics 58 (2011) 191–205
Using the linearity of W, (37) becomes Vðz,a, kw Þ ¼ Sw ðz,aÞ þ z þ kw a þ Wð0,0, kw Þ, where
Sw ðz,aÞ
w 2 f‘,hg,
ð38Þ
is the household’s surplus in the DM when the type of the trees is w, i.e.,
Sw ðz,aÞ u½yðz,a, kw Þkw dðz,a, kw Þtðz,a, kw Þ for w 2 f‘,hg: Substituting V by its expression given by (38) into (4), the household’s portfolio problem reduces to qz b qa b ½zðjÞ,aðjÞ 2 arg max z a þ ph Sh ðz,aÞ þ p‘ S‘ ðz,aÞ , 8j 2 H,
b
ðz,aÞ2R2 þ
b
ð39Þ
ð40Þ
where qz =b1 is the cost of holding bonds, qa =b1 is the cost of investing in trees, and H is the set of households. The cost of holding an asset is approximately equal to the difference between the price of the asset and its fundamental value, b. According to (40), households choose their portfolios in order to maximize their expected surplus in the DM, net of the cost of holding the assets. Finally, the clearing of the asset market implies Z aðjÞ dj ¼ A, ð41Þ j2H
Z
zðjÞ dj ¼ Z:
ð42Þ
j2H
Definition 8. An equilibrium is a list of portfolios, terms of trade in the DM, and the prices of trees and bonds, /½zðjÞ, aðjÞj2H ,½yðÞ,dðÞ, tðÞ,qa ,qz S, such that ½zðjÞ,aðjÞ is solution to (40) for all j 2 H; For all ðz,aÞ 2 R2 þ , ½yðz,a, kÞ, dðz,a, kÞ, tðz,a, kÞ is a solution to (12)–(14) if k ¼ k‘ and to (15)–(18) if k ¼ kh ; ðqa ,qz Þ solves (41) and (42). The characterization of the set of equilibria is done in two steps. The first step provides necessary and sufficient conditions for an optimal portfolio (Lemma 9). The second step uses the market-clearing conditions, (41) and (42), to determine asset prices and the DM allocations (Proposition 10). In order to characterize the household’s choice of asset w w holdings, let Sz and Sa denote the partial derivatives of the household’s surplus function for w 2 f‘,hg. They represent the transactional benefits to a household that bonds and trees provide at the margin in the DM in the state w. Lemma 9 (Households’ portfolio choices). If qz Z b and qa Z b, then (z,a) is a solution to the household’s portfolio problem, (40), if and only if
qz b
b qa b
b
þ ph Shz ðz,aÞ þ p‘ S‘z ðz,aÞ r 0
‘‘ ¼ ’’ if z 40,
ð43Þ
þ ph Sha ðz,aÞ þ p‘ S‘a ðz,aÞ r 0
‘‘ ¼ ’’ if a 4 0,
ð44Þ
where S‘z ¼ Shz ¼
Sha
S‘a
k‘
¼
u0 ðy‘ Þ 1, c0 ðy‘ Þ
ð45Þ
0 0 u ðyh Þ u ðy‘ Þ=c0 ðy‘ Þk‘ =kh 1 , c0 ðyh Þ u0 ðyh Þ=c0 ðyh Þk‘ =kh
2 3 0 u ðyh Þ k‘ 6 u0 ðy‘ Þ=c0 ðy‘ Þ1 7 1 ¼ kh 0 4 5: c ðyh Þ kh u0 ðy Þ=c0 ðy Þ k‘ h
h
ð46Þ
ð47Þ
kh
If qz 4 b and qa 4 b, then (z,a) is unique. If qz ¼ b, then z Z cðyn Þ. If qa ¼ b, then z þ k‘ a Z cðyn Þ. From (43) and (44), for an asset to be held, its cost must be equal to the expected marginal benefit that the asset confers in the DM. According to (45), a marginal unit of the risk-free bond allows an ‘-type household to purchase 1=c0 ðy‘ Þ units of DM output; this additional output is valued according to the marginal surplus of the match, u0 ðy‘ Þc0 ðy‘ Þ. The first term in brackets on the right side of (46) has a similar interpretation for the high state. This term is multiplied by 1 þ@ðkh dh Þ=@z o1 because a household that accumulates one additional unit of the bond can cut down on its transfer of trees in order to reduce its signaling cost. Similarly, the first two terms on the right side of (47) correspond to the liquidity value of trees in the high state if households and firms are symmetrically informed. This liquidity component is multiplied by the marginal propensity to spend trees, @dh =@a 2 ½0,1Þ, which is less than one in the private-information economy.
G. Rocheteau / Journal of Monetary Economics 58 (2011) 191–205
201
Proposition 10 (Equilibrium allocations and prices). An equilibrium exists, and it is such that ðqa ,qz ,y‘ ,yh Þ is uniquely determined. Asset prices are qz ¼ bð1 þ Lz Þ,
ð48Þ
qa ¼ bð1 þLa Þ,
ð49Þ
with Lz ¼ p‘
0 0 u ðy‘ Þ u ðy Þ kh u0 ðy‘ Þ=c0 ðy‘ Þk‘ 1 þ ph 0 h 1 , 0 0 0 c ðy‘ Þ c ðyh Þ kh u ðyh Þ=c ðyh Þk‘
La ¼ p‘ k‘
ð50Þ
0 0 u ðy‘ Þ u ðyh Þ k‘ u0 ðy‘ Þ=c0 ðy‘ Þk‘ 1 þ 1 p k , h h c0 ðy‘ Þ c0 ðyh Þ kh u0 ðyh Þ=c0 ðyh Þk‘
ð51Þ
where y‘ ¼ min½yn ,c1 ðZ þ k‘ AÞ, and yh solves (31), with z ¼Z. An equilibrium exists, and it is essentially unique.22 The price of each asset is composed of its fundamental value, b, times a liquidity premium. 4.2. Liquidity premia and asset returns The next proposition determines the condition under which the liquidity premia, Lz and La , are positive. Let rz 1=qz denote the (gross) rate of return of risk-free bonds and ra 1=qa the (gross) rate of return of information-sensitive trees. 1
Proposition 11 (Liquidity premia). Lz 40 and rz o b 1 La 40 and ra o b if and only if Z o Z cðyn Þk‘ A.
if and only if Z oZ n cðyn Þ.
The rate of return of risk-free bonds is below the rate of time preference whenever the supply of bonds, Z, is too low relative to the liquidity needs of the economy, as measured by cðyn Þ. This low rate of return does not account for the liquidity services that bonds provide in the DM by reducing the signaling costs incurred by h-type households to reveal the terminal value of their trees. Information-sensitive trees can also provide liquidity services if households do not hold enough wealth to maximize the total surplus in ‘-type matches, Z þ k‘ A o cðyn Þ. Finally, when Z 2 ðZ ,Z n Þ, ‘-type households have enough wealth to purchase yn , while the h-type households consume yo yn . In this case trees do not pay a liquidity premium because ‘-type households do not wish to buy additional output in the DM, and h-type households cannot spend more than dh o A because of a binding resalability constraint. Bonds pay a liquidity premium because they relax the liquidity constraint faced by h-type households. Proposition 12 (Liquidity structure of asset returns). If Z o Z n , then Lz 4La Z 0 and b
1
Z ra 4 rz .
The liquidity value of bonds is greater than the liquidity value of trees, so the rate-of-return differential between bonds and trees is positive. This finding addresses the rate-of-return dominance puzzle, according to which individuals hold monetary assets despite those assets being dominated in their rate of return by other assets. In my model, households hold some assets that are dominated in their rate of return because such assets are less sensitive to private-information problems and hence they provide greater liquidity services in the DM. Fig. 3 represents the conditions on Z and A under which the liquidity factors Lz and La are positive for both the complete-information and the private-information economies. In the complete-information economy (right panel of Fig. 3) either all asset prices exhibit a liquidity component, or none of them does. Provided that there is enough wealth in the economy, k‘ Aþ Z Z cðyn Þ, assets are priced according to their fundamental values. In contrast, in the private-information economy (left panel of Fig. 3) bonds can be priced above their fundamental value even if the total wealth in the economy is very large. Consequently, a liquidity differential between trees and bonds (the gray areas in Fig. 3) is more likely to exist in the presence of an informational asymmetry. The next proposition examines how the supply of bonds affects liquidity premia and assets’ rates of return. Proposition 13 (Liquidity premia and the supply of risk-free bonds). If Z o Z n , then dLz =dZ o0 and dr z =dZ 4 0. If Z o Z , then dLa =dZ o 0 and dr a =dZ 40. If Z o Z n , then @ðLz La Þ=@Z o 0 and @½ðra rz Þ=rz ra =@Z o0. As the supply of bonds increases, liquidity premia fall, while the rate-of-return differential between assets narrows. If households hold a larger quantity of bonds, then they can trade larger quantities in the DM, irrespective of their private information, and the marginal benefit from holding an additional unit of any asset is reduced. This result is consistent with the negative relationship found by Krishnamurthy and Vissing-Jorgensen (2008) between the convenience yield of Treasury securities and the supply of treasuries. 22
Any indeterminacy, such as the composition of the payments in terms of bonds and trees in the low state when Z þ k‘ A 4 cðyn Þ, is payoff irrelevant.
202
G. Rocheteau / Journal of Monetary Economics 58 (2011) 191–205
Fig. 3. Liquidity and asset prices. In the private-information economy the price of risk-free bonds exhibits a liquidity premium (Lz 4 0) whenever the supply of bonds (Z) is smaller than households’ liquidity needs. This liquidity premium is larger than the one of information-sensitive assets (Lz 4 La ). In the complete-information economy, liquidity premia emerge if the total supply of assets (Z þ k‘ A) is too low.
Proposition 14 (Open-market purchases of information-sensitive assets). Assume Z oZ n . A policy that consists in issuing A units of risk-free bonds in order to substitute them for the information-sensitive assets is welfare improving. An obvious remedy to the private-information problem consists of replacing information-sensitive assets with information insensitive ones. Since households hold A þ Z units of risk-free bonds, the quantity of DM output they consume is at least as large as what they would consume in an ‘-type match in the presence of Z units of risk-free bonds and A units of informationsensitive assets (since A þ Z 4 k‘ A þ Z). Moreover, from Proposition 4, the output in h-type matches is less than the output in ‘-type matches if Z oZ n . Therefore, by taking the information-sensitive assets out of circulation early enough that the privateinformation problem does not materialize, and by replacing them with risk-free bonds, the government raises the quantities traded in all matches, and hence social welfare. Moreover, from Proposition 12, qz Z qa , so that the government raises enough revenue from the sale of its bonds to purchase all the information-sensitive assets, and the output generated by the trees in the following period covers the repayment of the bonds. Proposition 15 (Optimal provision of risk-free bonds). For all Z Z Z n , y‘ ¼ yh ¼ yn and rz ¼ ra ¼ b
1
.
The supply of risk-free bonds is optimal for all Z Z Z n . In this case, the quantities traded in the DM maximize the match surpluses, y‘ ¼ yh ¼ yn . In the high state, households trade only bonds (dh ¼ 0), while in the low state households are indifferent between using bonds and trees to finance their consumption. The prices of the two assets are equal to their fundamental values (qa ¼ qz ¼ b). This condition for the optimal provision of bonds is reminiscent of the Friedman rule for the optimum quantity of money.23 The optimal quantity of monetary assets is such that the demand for liquidity services is satiated, i.e., the liquidity premia are zero, and all assets exhibit the same (risk-adjusted) rate of return. 5. Sensitivity analysis The role played by two assumptions is succinctly reviewed: the use of the Cho-Kreps refinement; the assumption that the terms of trade are set by households. 5.1. An alternative refinement Mailath et al. (1993) proposed an alternative to the Intuitive Criterion called the undefeated equilibrium. Rocheteau (2009) shows that the (separating) equilibrium of the bargaining game that satisfies the Intuitive Criterion is the only undefeated equilibrium if the household’s payoff at the Pareto-efficient separating equilibrium is greater than the one the household would enjoy at its preferred pooling equilibrium, i.e., b
U h uðqp Þkh dp tp oUhb uðqh Þkh dh th ,
ð52Þ
where ðqh ,dh , th Þ is the solution to (15)–(18) and ðqp ,dp , tp Þ ¼ arg maxfuðqÞkh dtg, q,d, t
ð53Þ
23 Rocheteau (2008) considers a version of the model with fiat money in which the optimum quantity of money requires the money growth rate to approach agents’ discount factor.
G. Rocheteau / Journal of Monetary Economics 58 (2011) 191–205
s:t:
203
cðqÞ þðph kh þ p‘ k‘ Þd þ t Z0,
ð54Þ
uðqÞk‘ dt Z uðq‘ Þcðq‘ Þ,
ð55Þ
ðd, tÞ 2 ½0,a ½0,z,
ð56Þ b U h 4Uhb
b Uh
¼ Uhb
where q‘ ¼ min½q ,c ðk‘ a þzÞ. If then there is an undefeated equilibrium and it is pooling. If then there is both a pooling and a separating undefeated equilibrium. It can be shown that for all matches where a 40 and n ^ z 2 ½cðqÞ,cðq ÞÞ, where q^ is the solution to u0 ðqÞ ¼ ðkh =k c0 ðqÞ, the unique undefeated equilibrium of the bargaining game is separating. This result suggests that the separating outcome predicted by the Intuitive Criterion is consistent with other refinements for signaling games, provided that the supply of bonds is not too small. n
1
5.2. Signaling vs screening Instead of households making take-it-or-leave-it offers in pairwise meetings, suppose that firms are the ones to make offers.24 Firms choose a menu of contracts, fðyh ,dh , th Þ,ðy‘ ,d‘ , t‘ Þg, to maximize their expected profits subject to incentive-compatibility and individual rationality constraints. It is shown in an appendix that an optimal menu is such that the participation constraint of a household in the high state and the incentive-compatibility constraint of a household in the low state are binding, i.e., uðyh Þth kh dh ¼ 0,
ð57Þ
uðy‘ Þt‘ k‘ d‘ ¼ uðyh Þth k‘ dh ¼ ðkh k‘ Þdh :
ð58Þ
According to (57), firms leave no surplus to households in the high state, whereas, according to (58), households in the low state can extract a surplus proportional to the transfer of trees in the high state, ðkh k‘ Þdh . Moreover, households in the high state transfer fewer trees than households in the low state, dh r d‘ . It can also be shown that the equilibrium of the screening game exhibits a pecking-order property: if the household holds enough bonds, then the firm asks to be paid with bonds only; if the quantity of bonds held by the household is small, then the firm will ask for all of the bonds of the household and some of its trees. The payment in trees decreases with the quantity of bonds held by the household. Since the household’s surplus in the DM is equal to ðkh k‘ Þdh , and dh is decreasing with z, households have no incentive to hold bonds. Suppose, for instance, that households do not have to bring their bonds in bilateral matches in the DM: they can keep them at home. Then, bonds are not used as means of payment in the DM, i.e., trees are the only means of payment, and therefore bonds have no liquidity value. This result is analogous to the nonexistence of a monetary equilibrium in economies where firms set the terms of trade unilaterally.25 6. Conclusion A model has been proposed where multiple assets are traded in pairwise meetings, no restrictions are placed on the transfer of goods, assets, or information, and assets differ in terms of their information sensitivity. This simple model has delivered new insights for payment arrangements, asset liquidity, and the distribution of asset returns. In the model, an asset’s sensitivity to informational asymmetries reduces its usefulness as a means of payment or collateral. This description is consistent with several historical episodes, including the circulation of coins in medieval Europe or the coexistence of numerous banknotes in the 19th century United States. Some predictions of the model are also relevant to interpreting the drying-up of liquidity during the financial crisis of 2007–2008. For instance, the model predicts that the market for information-sensitive assets breaks down when some of these assets are valueless. The model also showed that there is an optimal provision of risk-free assets that can overcome the illiquidity of information-sensitive assets. The findings in terms of liquidity premia are consistent with the evidence from Krishnamurthy and Vissing-Jorgensen (2008) regarding the convenience yield of Treasury securities relative to corporate bonds. Half of the convenience yield of Treasury securities relative to corporate bonds can be explained by a surety motive, where surety is the ‘‘value investors place on a sure cash-flow above and beyond what would be implied by the pricing kernel’’. To get an idea of the quantitative importance of this convenience yield, Krishnamurthy and Vissing-Jorgensen value the liquidity services provided by the current level of treasuries at about 0.95% of GDP per year. From a methodological viewpoint, my approach can be viewed as providing tractable microfoundations for some of the trading restrictions that have been imposed in recent monetary models. A natural next step is to construct a calibrated 24 Ennis (2008) studies a related trading mechanism in a model with fiat money where buyers have some private information about their marginal utility of consumption. 25 In order to allow households to capture some of the surplus that their recognizable assets generate, one could adopt the notion of competitive search, according to which firms post contracts and compete in order to attract households. See Guerrieri et al. (2010) for an application where agents trade a single indivisible asset available in two different qualities. As in this model, the contract is separating, and the low-quality asset has a higher velocity than the high-quality one.
204
G. Rocheteau / Journal of Monetary Economics 58 (2011) 191–205
version of the model incorporating more realistic features, such as risk aversion, infinitely lived assets, and a richer information structure.
Acknowledgments This paper has circulated under the title ‘‘A monetary approach to asset liquidity.’’ It has benefited from discussions with Ricardo Lagos and Pierre-Olivier Weill. I also thank an anonymous referee for her/his comments and suggestions. I also thank for their comments and suggestions of anonymous referees, Murali Agastya, Aditya Goenka, Steve LeRoy, Yiting Li, Ed Nosal, Peter Rupert, Neil Wallace, Asher Wolinsky, Tao Zhu, and seminar participants at the Federal Reserve Bank of Cleveland, Federal Reserve Bank of Chicago, Hong Kong University of Science and Technology, National Taiwan University, National University of Singapore, Rice University, Singapore Management University, the Southern Workshop in Macroeconomics (Auckland), the University of California at Irvine, the University of California at San Diego, the University of Missouri, the University of Southern California, the University of Tokyo, the University of Wisconsin, the workshop on ‘‘Networks and Payments’’ at the University of California at Santa Barbara, and the 2008 meeting of the Society of Economic Dynamics in Cambridge. I thank Monica Crabtree-Reusser for editorial assistance. Appendix A. Supplementary data Supplementary data associated with this article can be found in the online version at doi:10.1016/j.jmoneco.2011.06.005.
References Aiyagari, S.R., 1989. Gresham’s law in a lemons market for assets. Canadian Journal of Economics 22, 686–697. Aruoba, S.B., Wright, R., 2003. Search, money and capital: a neoclassical dichotomy. Journal of Money, Credit and Banking 35, 1086–1105. Aruoba, S.B., Waller, C., Wright, R., 2011. Money and capital: a quantitative analysis. Journal of Monetary Economics 58, 98–116. Banarjee, A., Maskin, E., 1996. A Walrasian theory of money and barter. Quarterly Journal of Economics 111, 955–1005. Berentsen, A., Rocheteau, G., 2004. Money and information. Review of Economic Studies 71, 915–944. Berentsen, A., Menzio, G., Wright, R., 2011. Inflation and unemployment in the long-run. American Economic Review 101, 371–398. Brunnermeier, M., 2009. Deciphering the liquidity and credit crunch 2007–2008. Journal of Economic Perspectives 23, 77–100. Burdett, K., Trejos, A., Wright, R., 2001. Cigarette money. Journal of Economic Theory 99, 117–142. Caballero, R., 2006. On the macroeconomics of asset shortages. NBER Working Paper 12753. Cho, I., Kreps, D., 1987. Signaling games and stable equilibria. Quarterly Journal of Economics 102, 179–221. Cuadras-Morato´, X., 1994. Commodity money in the presence of goods of heterogenous quality. Economic Theory 4, 579–591. DeMarzo, P., Duffie, D., 1999. A liquidity-based model of security design. Econometrica 67, 65–99. Duffie, D., Gˆarleanu, N., Pedersen, L., 2005. Over-the-counter markets. Econometrica 73, 1815–1847. Ennis, H., 2008. Search, money, and inflation under private information. Journal of Economic Theory 138. Geromichalos, A., Licari, J., Suarez-Lledo, J., 2007. Monetary policy and asset prices. Review of Economic Dynamics 10, 761–779. Green, E., Weber, W., 1996. Will the new $100 bill decrease counterfeiting? Federal Reserve Bank of Minneapolis Quarterly Review 20, 3–10 Guerrieri, V., Shimer, R., Wright, R., 2010. Adverse selection in competitive search equilibrium. Econometrica 78, 1823–1862. Hopenhayn, H., Werner, I., 1996. Information, liquidity, and asset trading in a random matching game. Journal of Economic Theory 68, 349–379. Huggett, M., Krasa, S., 1996. Money and storage in a differential information economy. Economic Theory 8, 191–209. Jafarey, S., Rupert, P., 2001. Limited commitment, money, and credit. Journal of Economic Theory 99, 22–58. Jevons, W., 1875. Money and the Mechanism of Exchange. D. Appleton and Co., New York. Kiyotaki, N., Moore, J., 2005. Liquidity and asset prices. International Economic Review 46, 317–349. Kiyotaki, N., Wright, R., 1989. On money as a medium of exchange. Journal of Political Economy 97, 927–954. Kohlberg, E., Mertens, J., 1986. On the strategic stability of equilibria. Econometrica 54, 1003–1037. Krishnamurthy, A., Vissing-Jorgensen, A., 2008. The aggregate demand for Treasury debt. Mimeo. Lagos, R., 2010a. Asset prices and liquidity in an exchange economy. Journal of Monetary Economics 57, 913–930. Lagos, R., 2010b. Asset prices, liquidity, and monetary policy in the search theory of money. Federal Reserve Bank of St. Louis Review 92, 303–309. Lagos, R., Rocheteau, G., 2008. Money and capital as competing media of exchange. Journal of Economic Theory 142, 247–258. Lagos, R., Rocheteau, G., 2009. Liquidity in asset markets with search frictions. Econometrica 77, 403–426. Lagos, R., Wright, R., 2005. A unified framework for monetary theory and policy analysis. Journal of Political Economy 113, 463–484. Lester, B., Postlewaite, A., Wright, R., 2007. Information and liquidity. University of Pennsylvania Working Paper. Li, Y., 1995. Commodity money under private information. Journal of Monetary Economics 36, 573–592. Li, Y., Rocheteau, G., 2009. Liquidity constraints under moral hazard. Working Paper. Lucas, R., 1978. Asset prices in an exchange economy. Econometrica 46, 1429–1445. Mailath, G., Okuno-Fujiwara, M., Postlewaite, A., 1993. Belief-based refinements in signaling games. Journal of Economic Theory 60, 241–276. Mihm, S., 2007. A Nation of Counterfeiters: Capitalists, Con Men, and The Making of The United States. Harvard University Press, Cambridge. Myers, S., 1984. The capital structure puzzle. Journal of Finance 39, 575–592. Nosal, E., Wallace, N., 2007. A model of (the threat of counterfeiting). Journal of Monetary Economics 54, 229–246. Plantin, G., 2009. Learning by holding and liquidity. Review of Economic Studies 76, 395–412. Ravikumar, B., Shao, E., 2010. Search frictions and asset price volatility. Working Paper. Riley, J., 2001. Silver signals: twenty-five years of screening and signaling. Journal of Economic Literature 39, 432–478. Rocheteau, G., 2008. Money and competing assets under private information. Working Paper of the Federal Reserve Bank of Cleveland 08-02. Rocheteau, G., 2009. A monetary approach to asset liquidity. Working Paper of the Federal Reserve Bank of Cleveland 09-01. Rocheteau, G., Wright, R., 2005. Money in search equilibrium, in competitive equilibrium, and in competitive search equilibrium. Econometrica 73, 175–202. Rubinstein, A., 1985. A bargaining model with incomplete information about time preference. Econometrica 53, 1151–1172. Smith, B., 1989. Limited information, money, and competitive equilibrium. Canadian Journal of Economics 19, 780–797.
G. Rocheteau / Journal of Monetary Economics 58 (2011) 191–205
205
Trejos, A., 1997. Incentives to produce quality and the liquidity of money. Economic Theory 9, 355–365. Trejos, A., 1999. Search, bargaining, money and prices under private information. International Economic Review 40, 679–695. Telyukova, I., Wright, R., 2008. A model of money and credit with an application to the credit card debt puzzle. Review of Economic Studies 75, 629–647. Velde, F., Weber, W., Wright, R., 1999. A model of commodity money, with applications to Gresham’s law and the debasement puzzle. Review of Economic Dynamics 2, 291–323. Williamson, S., 2002. Private money and counterfeiting. Federal Reserve Bank of Richmond, Economic Quarterly 88, 37–57. Williamson, S., Wright, R., 1994. Barter and monetary exchange under private information. American Economic Review 84, 104–123.
Journal of Monetary Economics 58 (2011) 206–219
Contents lists available at ScienceDirect
Journal of Monetary Economics journal homepage: www.elsevier.com/locate/jme
Customer markets and the welfare effects of monetary policy ¨ Johan Soderberg Department of Economics, Uppsala University, Box 513, SE-751 20 Uppsala, Sweden
a r t i c l e in f o
abstract
Article history: Received 17 February 2010 Received in revised form 26 May 2011 Accepted 31 May 2011 Available online 30 June 2011
A customer market model in which firms and customers form long-term relations is developed and integrated into the canonical New Keynesian framework. This leads to two important differences compared to the standard model. First, the purely forwardlooking Phillips curve is replaced by a hybrid variant where current inflation also depends on past inflation. Second, the welfare cost of inflation is much lower, which leads to an optimal monetary policy where relatively more weight is put on output gap stabilization than previously found in the literature. & 2011 Elsevier B.V. All rights reserved.
1. Introduction Survey evidence consistently ranks implicit contracts and other forms of customer relations as important factors that firms consider when setting prices. For instance, price raises are often refrained from for fear of adverse customer reactions that may damage long-term relations. The importance of these factors for pricing has been documented in numerous studies for different countries; for recent studies, see Apel et al. (2005), Amirault et al. (2005), and Fabiani et al. (2007). In recent years, narrative evidence that documents the importance of implicit contracts has also emerged. Young and Levy (2006) provide evidence for implicit contracts in the marketing of Coca-Cola, while Nakamura and Steinsson (in press) survey the media and find numerous examples of firms communicating their intentions not to raise their prices. The customer market model, first proposed by Phelps and Winter (1970), formalizes the idea that firms and customers form long-term relations. In their model, a firm’s customer base is a valuable asset that only gradually adjusts to price changes. It is now well established in the literature that the dynamic interaction between prices and demand arising in the customer market model has important implications for price-setting behavior. Early contributions include Bils (1989) and Gottfries (1991), who use customer market models to explain why short-run variations in demand have weak effects on prices. In order to expand their customer base, firms refrain from increasing their prices in times of high demand. More recent examples on this theme are Ravn et al. (2006) and Kleshchelski and Vincent (2009), who construct general equilibrium customer market models that predict countercyclical markups, providing a source of real rigidity. The idea that firms fear adverse customer reactions is formalized in the customer anger model in Rotemberg (2005), where it is assumed that consumers react negatively to prices they perceive as unfair. This fear of antagonizing consumers makes firms scrupulous about price changes, which has the potential of generating nominal price rigidity. Nakamura and Steinsson (in press) analyze a model with forward-looking customer markets and find that nominal price rigidity is sustainable as an equilibrium outcome. This paper investigates how customer markets affect inflation dynamics and the optimal conduct of monetary policy in the context of the New Keynesian framework. The economic environment I have in mind is one where there are costs associated with the acquisition and processing of information about prices, so that households only occasionally Tel.: þ46 18 471 11 00.
E-mail address:
[email protected] 0304-3932/$ - see front matter & 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.jmoneco.2011.05.012
J. S¨ oderberg / Journal of Monetary Economics 58 (2011) 206–219
207
reoptimize their allocation of consumption among different goods. For instance, if different goods are sold at different physical locations, households may choose to only infrequently compare price quotes across stores. This means that information about better shopping opportunities diffuses slowly through the economy. This interpretation is in the spirit of the original customer market model proposed by Phelps and Winter (1970). But even if households are fully informed about prices, there may be costs associated with the time and cognitive effort required to optimally allocate consumption between goods. Such frictions, as well as uncertainty about other product attributes, are factors known to give rise to repeat purchase behavior; see Solomon et al. (2006, Chapter 8) and references therein. Explicit modeling of information frictions is technically complicated, and I therefore resort to a variant of the signaling mechanism proposed by Calvo (1983). It is assumed that a household allocates consumption among different goods by choosing the relative consumption of each good, i.e., the quantity consumed of the good relative to the total basket consumed. But in each period, the household is only allowed to reoptimize for a randomly chosen subset of all goods. By applying the restriction of infrequent reoptimization across goods, as opposed to across households, the representative household construct is preserved, which fundamentally simplifies aggregation and solution of the model. The result is a model where a firm’s market share depends on its lagged market share as well as on current and expected future prices. Because demand is a function of expected future prices, there is a problem of time inconsistency in price setting. Firms would like to promise low future prices, but renege on these promises when the future arrives. The time inconsistency problem is resolved by assuming that firms commit to state contingent price plans. This assumption is unrealistic if taken literately, but it captures the idea that firms can, to a considerable extent, make promises to their customers. The ability of firms to commit should be interpreted as a stylized way of modeling implicit contracts between firms and their customers. Nakamura and Steinsson (in press) obtain a similar demand formulation by assuming internal deep habits, i.e., households form habits in the consumption of individual goods. They analyze a partial equilibrium model where firms are unable to commit to price policies and show that nominal price rigidity is sustainable in a reputational equilibrium under imperfect information. In their model, a firm compensates for the lack of commitment by setting a price cap above which it will not raise its price. In this paper, in contrast, it is assumed that firms can commit to a price policy. Taking price stickiness as given, the general equilibrium implications for aggregate dynamics and monetary policy are analyzed. A central difference compared to Ravn et al. (2006) and Nakamura and Steinsson (in press) is that customer markets in this paper are the result of frictions that do not alter households’ preferences for different goods. As a consequence, the consumption Euler equation is unaffected by the introduction of customer markets. This has the advantage of allowing me to study the implications of customer markets without having to account for simultaneous changes in preferences and aggregate demand. The customer market framework is integrated in an otherwise standard New Keynesian staggered price-setting model. The resulting model differs from the standard one in two important respects. First, the Phillips curve is no longer purely forward-looking but also depends on lagged inflation, leading to endogenous inflation persistence. This is a consequence of the forward-looking nature of demand. A firm that desires a higher price, but is constrained by price-setting frictions, will, as a second best option, commit to raising the price in the future. This results in firms continuing to raise their prices even after the factor that initially led them to desire higher prices has dissipated. Second, the welfare criterion places a much lower weight on inflation stabilization. The main lesson emerging from the utility-based analysis in the canonical New Keynesian model is the importance of inflation stabilization over output gap stabilization. Inflation leads to price dispersion, which distorts the allocation of consumption among the different goods in the economy. Customer markets reduce this distortion by slowing down the reallocation of consumption when relative prices are dispersed. This makes price dispersion less distortionary, which reduces the welfare cost of inflation and leads to an optimal monetary policy that involves a substantially higher volatility of inflation and a lower volatility of the output gap. The remainder of this paper is organized as follows. Section 2 describes the model and Section 3 presents the welfare criterion. Section 4 describes the calibration and Section 5 shows the results from the numerical simulations. Section 6 concludes. 2. The model In this section, the decisions of households and firms are analyzed, and a log-linear approximation to the model is derived. 2.1. Households The economy is populated by a large number of households, indexed by h 2 ½0,1. A household h derives utility from the consumption of a large number of different goods, indexed i 2 ½0,1, according to the aggregator: "Z #Z=ðZ1Þ Cth ¼
1
0
ðCith ÞðZ1Þ=Z di
,
ð1Þ
208
J. S¨ oderberg / Journal of Monetary Economics 58 (2011) 206–219
where Cith denotes the household’s consumption of good i. The household’s utility is 1 X 1 1 E0 bt ðCth Þ1sC ðNth Þ1 þ sN , 1sC 1þ sN t¼0
ð2Þ
where b 2 ð0,1Þ is the subjective discount factor, and Nth is the number of working hours supplied. The household’s budget constraint is Z 1 Bht þ Pit Cith di ¼ Rt1 Bht1 þ Wt Nth þ Ft , ð3Þ 0
where Bht denotes bond holdings from t to t þ1, Pit is the price of good i, Rt is the gross nominal interest rate paid off in t þ1, Wt is the nominal wage, and Ft is dividends from firm ownership. The household solves the intertemporal problem of maximizing (2), subject to (1) and (3). However, I impose the additional restriction that the allocation of consumption among different goods is subject to Calvo (1983) style frictions. In each period, the household draws a random subset of measure 1y of all goods. For each of these goods, the household is allowed to reoptimize the relative consumption of the good, i.e., the quantity consumed of the good relative to the total basket consumed. For the remaining goods, the household is not allowed to adjust its relative consumption.1 The draw is assumed to be uncorrelated both in time and across households. R1 h h Let Pt 0 Pit C~ it di be an aggregate ‘‘price index’’, where C~ it ¼ Cith =Cth denotes the relative consumption of good i. Because the subset of goods for which a household reoptimizes is chosen at random, the law of large numbers implies that Pt is identical across households. This fundamentally simplifies aggregation and ensures that all households choose the same allocations of aggregate consumption, labor supply, and bond holdings. The first-order conditions for consumption and bond holdings yield the familiar consumption Euler equation: CtsC ¼ bEt Rt
Pt C s C , Pt þ 1 t þ 1
ð4Þ
and the first-order condition for labor supply yields NtsN Wt ¼ : Pt CtsC
ð5Þ
The optimal relative consumption of good i is given by Z n Git , C~ it ¼
ð6Þ
Gt
P1
k
k
where Git ¼ Et k ¼ 0 ðybÞk Dt,t þ k Ct þ k Pit þ k is the expectation of a weighted sum of future prices for good i, b Dt,t þ k ¼ b R 1 1Z ðCt þ k =Ct ÞsC ðPt =Pt þ k Þ is the nominal stochastic discount factor between periods t and t þk, and Gt ¼ ½ 0 Git di1=ð1ZÞ is an 2 average across firms of expected future prices. When a household decides how much to consume of a particular good, it realizes that in each future period it will not be able to reoptimize with probability y. Therefore, the household takes expected future prices of the good into account, discounted at a rate that incorporates the probability that reoptimization has not occurred. Integrating consumption over households yields the market share of good i, Y~ it Yit =Ct , given by Z Git Y~ it ¼ yY~ it1 þ ð1yÞ : ð7Þ
Gt
A fraction y of the market share remains from the previous period because some of the households have not been given the opportunity to reoptimize their relative consumption of the good in this period. The remaining fraction 1y of the market share, consisting of demand from households who reoptimize, depends on the current price and expected future prices, relative to the current and expected future price levels in the economy. 2.2. Firms Good i is produced by a monopolist with technology: Yit ¼ Nit :
ð8Þ
The time inconsistency problem in price setting, arising as a result of demand being a function of future prices, is resolved by assuming that the firm commits to a state contingent price plan. It is also assumed that the plan was set up an infinitely 1 It is not possible for a household to end up in a situation where it cannot adjust its relative consumption for the subset of goods for which it is allowed to reoptimize without adjusting its relative consumption for the remaining goods. It follows from (1) and the law of large numbers that the exponential sum of relative consumption for the subset of goods for which the household is not allowed to reoptimize must be unity. But this also implies that the exponential sum of relative consumption for the subset of goods for which the household is allowed to reoptimize must be unity, i.e., the adjustments of relative consumption of different goods cancel each other out. 2 See web Appendix A for details of the household’s problem.
J. S¨ oderberg / Journal of Monetary Economics 58 (2011) 206–219
209
long time ago, so as to prevent the firm from exploiting the fact that expectations are fixed when the plan is announced. As discussed in Introduction, this is as a stylized way of modeling the existence of implicit contracts. Price-setting frictions are introduced by assuming that prices are set according to the mechanism in Calvo (1983). In each period, the firm is allowed to reoptimize its price with probability 1a. Given this restriction, the firm’s problem is to maximize its discounted profit stream: E0
1 X
bt D0,t ½Pit Yit Wt Nit ,
ð9Þ
t¼0
subject to (7) and (8). The firm’s Lagrangian, written in terms of the market share, is L ¼ E0
1 X
(
bt D0,t ðPit Wt ÞY~ it Ct þ nit yY~ it1 þ ð1yÞ
t¼0
Git Gt
Z
" #) 1 X Y~ it þ rit Git ðybÞk Dt,t þ k Ct þ k Pit þ k :
ð10Þ
k¼0
Differentiating (10) with respect to Y~ it and Git yields
nit ¼ ðPit Wt ÞCt þ ybEt Dt,t þ 1 nit þ 1
ð11Þ
and
rit ¼ Zð1yÞ
Git Gt
Z1
1
Gt
nit ,
ð12Þ
The multiplier nit is the shadow value of a marginal increase in the firm’s market share. Eq. (11) says that the value of a marginal increase in the firm’s market share is the profits generated by the additional customers today plus the present value of future profits from these customers, given by ybEt Dt,t þ 1 nit þ 1 . The multiplier rit is the shadow cost of a marginal increase in Git , the discounted sum of expected future prices. Eq. (12) says that the cost of a marginal increase in Git is the resulting decrease in the firm’s market share, given by Zð1yÞðGit =Gt ÞZ1 =Gt , multiplied by the value of the lost customers nit . The firm’s price must satisfy the optimality condition: Et
1 X
ðabÞk Dt,t þ k Ct þ k ½Y~ it þ kjt Cit þ kjt ¼ 0,
ð13Þ
k¼0
P j ~ where Cit ¼ 1 j ¼ 0 y ritj . Under flexible prices ða ¼ 0Þ, the additional revenue generated by a marginal price increase, Y it , must equal the shadow cost of the price increase, Cit , resulting from the corresponding reduction in the firm’s market share.3 When setting up its price plan, at the beginning of time, the firm considers how a price change affects its market share at time t, captured by rit . But since households that reoptimize take expectations about future prices into account, the firm must also consider how the price change affects its market share in periods before t, which is why Cit depends on rit1 , rit2 , . . . The notation t þ kjt denotes the value of a variable at time t þk, conditional on the firm’s price last being reoptimized at time t. When prices are sticky, the optimality condition under flexible prices holds only as an expected discounted average over the expected duration of the price. Traditionally, customer markets have been analyzed under the assumption that demand is independent of expected future prices.4 Under that formulation, the price at time t has no effect on demand before t, so the last first-order condition would, ignoring price-setting frictions, correspond to Y~ it ¼ rit . In such a model, a firm faces a trade-off between investing in its customer base or capitalizing on it. By raising its price, the firm reaps a higher revenue from its existing customers, but at the cost of a smaller market share, which reduces revenue in future periods. This mechanism is also present in the model developed in this paper. But when firms commit to price plans, the insight that a price increase at time t also reduces demand before t adds another intertemporal aspect to price setting. This counteracts the incentive for firms to exploit their customers. The parameter y can be viewed as a measure of the degree of customer markets. Increasing the value of y has two opposing effects on the pricing decision. On the one hand, a price increase generates more revenue from existing customers because fewer households are able to reoptimize. On the other hand, a price increase in period t has a bigger negative effect on sales in the past and the loss of market shares will be more persistent. If prices are flexible, it turns out that the optimal price is set with a fixed markup of ðZ1Þ1 over marginal cost, which is identical to the optimal price obtained without customer markets. The two effects of increasing y cancel each other out when prices are flexible.5 3 The problem in (10) is not recursive, since it involves expected values of future prices, but can be transformed into a recursive saddle point problem, by applying the methods in Marcet and Marimon (1998), where Cit1 acts as an additional state variable. 4 Ravn et al. (2006) show that such a specification can be derived from microfoundations by assuming external deep habits, i.e., that households form habits in the consumption of individual goods, but the habitual component depends on aggregate consumption of that particular good. 5 This result also holds with internal deep habits under commitment, as shown by Nakamura and Steinsson (in press).
210
J. S¨ oderberg / Journal of Monetary Economics 58 (2011) 206–219
2.3. Log-linearization and equilibrium The model is solved by taking a first-order log-linear approximation of the equilibrium conditions around a steady state with zero inflation. Note that a firm’s optimal price depends both on its market share and on the shadow cost of a price increase Cit . These, in turn, depend on the whole history of previous prices. This implies that different firms, which reoptimize their prices at the same time, will in general not set the same price, making the state space of the model infinite dimensional. Still, it is possible to derive a solution to the log-linearized model using the method of undetermined coefficients, applying the same logic as in Woodford (2005).6 Log-linearization of the Euler equation in (4) yields the IS curve: e xt ¼ Et xt þ 1 s1 C ðrt Et pt þ 1 rt Þ,
ð14Þ
7
where xt denotes the output gap, rt ¼ log Rt is the nominal interest rate, pt ¼ logðPt =Pt1 Þ is the inflation rate between t 1 and t, and rte is an exogenously introduced disturbance. The disturbance rte is the real interest rate consistent with the efficient level of output and will henceforth be referred to as the efficient interest rate. The IS curve derived here is identical to that obtained in standard New Keynesian model. Aggregate demand, up to a first-order approximation, is not affected by the presence of customer markets. Shocks emanating from preferences and technology are modeled by e assuming that the efficient interest rate follows the AR(1) process rte ¼ ð1rr Þr þ rr rt1 þ ert , where r ¼ log b is the steady r 2 state value of the efficient interest rate, and et is i.i.d. N ð0, sr Þ. As shown in web Appendix B, inflation dynamics in the model is determined by a modified Phillips curve of the form: ½ðpt ypt1 ÞbEt ðpt þ 1 yEt1 pt Þ ¼ os^ t þ ybEt ½ðpt þ 1 ypt Þbðpt þ 2 ypt þ 1 Þ,
ð15Þ
where o ¼ ðð1aÞð1abÞ=aÞz, and s^ t ¼ ðsC þ sN Þxt is the log deviation of aggregate real marginal cost from its steady state value. Inflation dynamics is more complex with customer markets. The Phillips curve includes various leads and lags of inflation and also the previous period’s expectation of current inflation. The Phillips curve can be written on a more familiar form by solving (15) forward to obtain:
pt ¼ ypt1 þ oEt
1 X
bk
k¼0
k X
yj s^ t þ k þ ybet ,
ð16Þ
j¼0
where et ¼ pt Et1 pt is the inflation forecast error between t 1 and t. This Phillips curve differs from that obtained in the standard New Keynesian model in several respects. First, inflation depends on past inflation—with the coefficient on the backward-looking component of inflation coinciding with the backward-looking component of the firms’ market share equation—and on the inflation forecast error. Second, the slope of the Phillips curve o is lower, as z is a decreasing function of y.8 Third, the rate at which future marginal costs are discounted is affected. To make the policy problem non-trivial, an inefficient time-varying disturbance to marginal cost is introduced in the form of a cost-push shock. This captures shocks unrelated to preferences and technology, e.g., markup shocks or timevarying tax wedges. Written in terms of the output gap, the relation in (15) then reads ½ðpt ypt1 ÞbEt ðpt þ 1 yEt1 pt Þ ¼ oðsC þ sN Þxt þ ybEt ½ðpt þ 1 ypt Þbðpt þ 2 ypt þ 1 Þ þ out , u t,
where the cost-push ut follows the AR(1) process ut ¼ ru ut1 þ e
u t
ð17Þ
2 u Þ.
and e is i.i.d. N ð0, s
2.4. Price setting and inflation dynamics To get some intuition for how customer markets affect inflation dynamics, it is instructive to log-linearize the pricesetting condition in (13), which yields Et
1 X
ðabÞk zit þ kjt ¼ 0,
ð18Þ
k¼0
where zit ¼ log Y~ it log Cit . One can think of zit as a measure of a firm’s incentive to change its price if unconstrained by price rigidities; if zit is positive, the firm desires a higher price, and vice versa. Eq. (18) thus implies that firms set their prices so that the incentive to adjust the price over the expected duration of the price is zero on average. Log-linearization of (11) and (12) yield that the law of motion for zit is given by ( ) 1 X k zit ¼ yzit1 þð1yÞ ðZ1Þð1ybÞEt ðybÞ ½logðPit þ k =Pt þ k Þs^ t þ k : ð19Þ k¼0
If profit margins are expected to be high, the term inside the curly bracket is negative. Then, customers are more valuable and this gives the firm an incentive to lower its price in order to attract more customers. But (19) indicates that the incentive to 6 7 8
The details of this derivation can be found in web Appendix B. The output gap is defined as the log deviation of the actual level of output from the efficient level of output. The negative relation between y and z has not been proved analytically, but has been confirmed for all numerical values used in this paper.
J. S¨ oderberg / Journal of Monetary Economics 58 (2011) 206–219
211
change the price also depends on what that incentive was in the previous period. This is without consequence for price setting when prices are flexible, as zit will be equalized to zero at all times, but has important implications when prices are sticky. Consider a firm that experiences a temporary one-time reduction in its marginal cost. It would like to temporarily lower its price in order to expand its customer base. But if it is unable to adjust the price, it will instead, as a second best option, commit to lower prices in the future, which, because of the forward-looking aspect of demand, is already something that attracts customers today. This commitment is encoded in the evolution of zit: when the firm fails to adjust its price, zit becomes negative, which gives the firm an incentive to lower its price in the next period. This implication is in contrast to the standard New Keynesian model, where a firm that fails to adjust its price in response to a temporary reduction in marginal cost will have no incentive to change its price in the future. By averaging (19) across firms, we obtain a measure for the aggregate ‘‘price pressure’’ in the economy, given by zt ¼ yzt1 þð1yÞðZ1Þð1ybÞEt
1 X
ðybÞk s^ t þ k :
ð20Þ
k¼0
If real marginal costs are expected to be high, this means that profit margins are depressed on average and that firms on average desire to raise prices. When constrained by infrequent price adjustment, firms commit to raising their prices in the future instead. As shown in web appendix B, zt is negatively correlated with the quasi-rate of inflation acceleration 1 Et pt þ 1 b pt .9 The dependence of zt1 in (20) implies that if the expected rate of inflation acceleration in the previous 1 period, Et1 pt b pt1 , was negative, as would be the case if inflation was expected to return to steady state, this puts upward pressure on prices in the current period. As seen in (16), this translates into inflation today depending positively on both inflation in the previous period and the inflation forecast error. Intuitively, inflation is persistent because price pressure in the economy accumulates over time and only gradually dissipates, leading firms on average to continue to raise their prices even after the rise in marginal cost has receded. An implication of (19) is that if a firm is allowed to adjust and raises its price, so that zit is lowered, this reduces the firm’s incentive to raise the price in the future because future values of zit will also be lower. The price increase erodes the firm’s customer base, which alleviates the desire to raise the price in coming periods. Because firms set their prices so that the incentive to adjust them over the expected duration of the price is on average zero, this counteracts the firm’s incentive to raise the price following an increase in marginal cost. This explains the lower value of o in the model with customer markets. Because zit depends on a sum of discounted future profit margins, this means that future marginal costs will, compared to the standard New Keynesian model, have a higher weight in the firm’s price-setting decision. This period’s marginal cost only enters in zit, but next period’s marginal cost enters in both zit and abzit þ 1 , and so on. As seen in (16), this affects the discounting of future marginal costs in the Phillips curve. This period’s marginal cost is discounted by 1, next period’s by bð1 þ yÞ, and so on. If y is sufficiently high, future marginal costs may be more important for inflation dynamics than the current marginal cost. 3. Welfare Welfare is evaluated by taking a second-order approximation to the ‘‘representative household’s’’ expected utility.10 Assuming that a subsidy is in place that neutralizes the distortion from monopolistic competition, so that the steady state is efficient, this yields an expression for welfare, expressed as a fraction of steady state consumption, given by 1 1 X bt fðsC þ sN Þx2t þ Z1 var i log Cith g, E0 2 t¼0
ð21Þ
ignoring terms independent of policy and higher-order terms. This welfare criterion is identical to that obtained in the standard New Keynesian model. Optimality requires both that aggregate output is at its efficient level and that the same amount is consumed of all goods. The welfare criterion can be written in terms of the output gap and inflation: 1 1 X E0 bt ½lx x2t þ lp p2t , 2 t¼0
ð22Þ
where lx ¼ sC þ sN and lp ¼ a=ðð1aÞð1abÞÞZe. Inflation reduces welfare because it leads to price dispersion, which distorts the allocation of consumption among the different goods in the economy. The parameter e, which takes on a value of one in the standard New Keynesian model, is a decreasing function of y.11 Customer markets reduce the welfare cost of inflation by slowing down the reallocation of consumption when relative prices are dispersed. 9 Price pressure is also negatively correlated with the quasi-rate of inflation acceleration in the standard New Keynesian model, but without customer markets, price pressure in the economy only arises from variations in current period real marginal cost. 10 The details of the derivation can be found in web Appendix C. 11 The same proviso as in footnote 8 applies for the negative relation between y and e. The relation between inflation and the dispersion of consumption across goods is significantly more complicated with customer markets. This is a result of the ‘‘mechanical’’ inertial behavior of market shares, but also of households taking both current and expected future prices into account when allocating consumption among goods.
212
J. S¨ oderberg / Journal of Monetary Economics 58 (2011) 206–219
One might wonder how preventing households from reoptimizing their allocation of consumption for some goods can increase their welfare. Should not households be able to increase their utility, when relative prices are dispersed, by adjusting their consumption to the changes in relative prices? While this conjecture is correct in itself, observe that households prefer a balanced consumption basket, so the increase in consumption utility can only be achieved if the reallocation of consumption leads to an increase in the household’s total consumption of goods. For a given budget, households buy more of the goods that are cheap and less of those that are expensive, so total consumption increases. But in general equilibrium, this increase in consumption must be accompanied by a corresponding increase in economy-wide labor supply. Because different goods are imperfect substitutes, utility from consumption will increase less than the disutility from increased labor supply in the economy, and this is why there will be a decrease in welfare when consumption becomes more dispersed.
4. Calibration Table 1 summarizes the benchmark calibration, where one period corresponds to one quarter. The value of b implies a steady state annual interest rate of about 4%. Nakamura and Steinsson (2008) report a monthly median frequency of price adjustment for consumer goods—excluding sales and product substitutions—of about 9%.12 Converted to a quarterly frequency, this corresponds to a value of a of 0.75, implying that prices on average remain fixed for four quarters.13 The novelty is the calibration of y. Observing this parameter directly from households’ behavior is hardly a viable option. But it can be inferred from the model’s structural relations: the backward-looking component of the firms’ market share equation is equal to y, and so is the backward-looking component of inflation in (16). Unfortunately, empirical studies that estimate market share equations are scarce. An exception is Gottfries (2002), who uses time-series data to estimate a customer market equation in which a firm’s market share depends on its relative price and its lagged market share. In his full sample estimate, the backward-looking component of the market share equation is found to be 0.92. There is an abundance of empirical literature estimating the backward-looking behavior of inflation. While most studies find that lagged inflation is statistically significant in estimates of hybrid New Keynesian Phillips curves, there is little consensus regarding the importance of backward-looking behavior in explaining inflation dynamics. Galı´ and Gertler (1999) and Galı´ et al. (2001) argue that the purely forward-looking New Keynesian Phillips curve provides a good fit for inflation dynamics in both the US and Europe. In contrast, the estimates in Rudd and Whelan (2005) and Linde (2005) indicate that the backward-looking behavior of inflation is more important than the forward-looking. For instance, the baseline estimates in Rudd and Whelan (2005) of the backward-looking component of inflation are in the range of 0.79–0.91; the lower estimates are obtained when a measure of marginal cost is used instead of the output gap.14 I set y ¼ 0:875 as a benchmark value, indicating a substantial degree of inflation persistence, but I also consider lower values as a sensitivity check. This value implies that a household on average reoptimizes the relative consumption of a good every eight quarters. The elasticity of substitution between goods, Z, is calibrated to imply a 10% steady state markup, consistent with the estimates in Basu and Fernald (1995). The long-run price elasticity is Z; a permanent price change will over time have the same effect on demand as in an economy without customer markets. The short-run price elasticity depends on households’ expectations about future prices. To get a sense of the magnitude of this parameter, I calculate the implied price elasticity for two special cases: when a price change is perceived to be completely transitory and when it is expected to be permanent. In the former case, the short-run price elasticity is Zð1yÞð1ybÞ, and in the latter case it is Zð1yÞ. For the value of y assumed here, these two cases correspond to a short-run price elasticity of 0.18 and 1.38 respectively. As a comparison, Gottfries (2002) and Lundin et al. (2009) estimate a short-run (within-quarter) price elasticity of 0.27 and 0.13, respectively. The elasticity of intertemporal substitution is set following Rotemberg and Woodford (1998). The value of sC may appear to imply an implausibly high intertemporal elasticity of substitution but, as discussed by Woodford (2003), this parameter should not be calibrated, in a model that abstracts from capital, from estimates of consumer expenditure. Instead it should be interpreted as the intertemporal elasticity of overall private spending, including interest rate sensitive investment spending. The elasticity of the real wage with respect to output in the model is sC þ sN . The labor supply elasticity is set to match the estimate in Solon et al. (1994) of a real wage elasticity with respect to output of 0.62. The standard deviations of the shocks are calibrated so that the responses to shocks are of reasonable magnitudes (cf. Smets and Wouters, 2007).
12 The mean frequency is higher, but Nakamura and Steinsson (2010) recommend using the median frequency when calibrating a single-sector model, on grounds that this yields a similar degree of monetary non-neutrality as in a multi-sector model calibrated to account for the heterogeneity in frequency of price change between sectors. 13 The durations reported in Nakamura and Steinsson (2008) are somewhat lower because they calculate durations using the continuous time formula 1=ðlog aÞ, whereas I calculate the duration using the discrete time formula 1=ð1aÞ. 14 It should be noted, however, that these estimates are not directly transferable to the model in this paper because their specification is different from (16).
J. S¨ oderberg / Journal of Monetary Economics 58 (2011) 206–219
213
Table 1 Calibration. Parameter
Value
Description
b
0.99 0.75 0.875 11 0.46 0.16 0.8 0.8 0.001 0.01
Households’ subjective discount factor Calvo parameter firms Calvo parameter households Elasticity of substitution between goods Inverse of (Frisch) labor supply elasticity Inverse of intertemporal elasticity of substitution Persistence of shock to the efficient interest rate Persistence of cost-push shock Standard deviation of shock to the efficient interest rate Standard deviation of cost-push shock
a y
Z sN sC rr ru sr su
Note: This table shows the benchmark calibration used in the numerical simulations.
Output gap
Annualized pp
1 0.5 0 −0.5
0.4 0.2 0
0.3 0.2 0.1
−0.2 0
6 Quarters Output gap
12
Annualized pp
0 pp
−0.2 −0.4 −0.6
0 0
0.2
6 Quarters Inflation
12
0.8
0.4
0.6
0.3
0.4 0.2
0
6 Quarters
12
0
6 Quarters Nominal rate
12
0
6 Quarters
12
0.2 0.1
0
−0.8
Nominal rate
0.4
Annualized pp
pp
Inflation
0.6
Annualized pp
1.5
0 0
6 Quarters Customer markets
12
Standard
Fig. 1. Impulse responses of the output gap, inflation, and the nominal interest rate under the Taylor rule. The top row shows the responses to a one standard deviation shock to the efficient interest rate. The bottom row shows the responses to a one standard deviation cost-push shock. The response of the output gap is expressed in percentage points (pp); the responses of inflation and the nominal interest rate are expressed in annualized percentage points.
5. Results In this section, aggregate dynamics is first analyzed by assuming an interest rule and then an analysis is made of how optimal monetary policy and welfare are affected by the introduction of customer markets. 5.1. Monetary policy under a Taylor rule Suppose that monetary policy follows a Taylor rule of the form: rt ¼ ð10:8Þðr þ1:5pt þ 0:1xt Þ þ 0:8rt1 ,
ð23Þ
These coefficients are roughly consistent with empirical evidence for the Greenspan era; see, e.g., Taylor (1999) and Clarida et al. (2000). The top row of Fig. 1 shows the effects of a shock to the efficient interest rate. The central bank could in principle completely offset the shock by letting the nominal interest rate perfectly track the rise in the efficient rate. However, the
214
J. S¨ oderberg / Journal of Monetary Economics 58 (2011) 206–219
k=1
k=2 0.4
0.3
0.3
0.3
0.2
0.2
0.2
0.1
0.1
0.1
%
0.4
%
%
Flexible prices 0.4
0
0
0
−0.1
−0.1
−0.1
−0.2
−0.2 0
6 Quarters
12
−0.2 0
12
0
k=8 0.4
0.3
0.3
0.3
0.2
0.2
0.2
0.1
0.1
0.1
%
0.4
0
0
0
−0.1
−0.1
−0.1
−0.2
−0.2 0
6 Quarters
12
Price
6 Quarters
12
k=12
0.4
%
%
k=4
6 Quarters
−0.2 0
Market share
6 Quarters
12
Price New Keynesian
0
6 Quarters
12
Price Level
Fig. 2. Price and market share responses in the model economy with customer markets following a one standard deviation shock to the efficient interest rate. A firm reoptimizes its price for the first time k 1 periods after the shock and thereafter every four quarters. All responses are expressed in percentages.
equilibrium interest rate response implied by the Taylor rule is too small to attain this, so the shock will trigger a boom.15 The bottom row of Fig. 1 shows the effects of a cost-push shock. In this case, the central bank is unable to simultaneously stabilize the output gap and inflation. Since the Taylor rule prescribes a heavy weight on inflation stabilization, the central bank drives down the output gap to stabilize inflation, leaning strongly against the wind. As expected, the model economy with customer markets exhibits a greater degree of inflation persistence. After a shock to the efficient interest rate, inflation returns to steady state several quarters later than in the standard model. In a simulated business cycle, driven by both shocks to the efficient interest rate and cost-push shocks, the first-order autocorrelation of inflation increased from 0.61 to 0.78, while remaining virtually unchanged for the output gap and the nominal interest rate.
5.2. Price and market share dynamics To gain further insights into price and inflation dynamics, it is instructive to look at the evolution of prices and market shares at the firm level. Fig. 2 plots the price and market share, following a shock to the efficient interest rate in the model economy with customer markets, for firms with different ex post realizations of the Calvo signal. This includes firms that reoptimize their prices for the first time k 1 periods after the shock and thereafter, corresponding to the average duration of prices, every four quarters. Also plotted is the price that would have been set by a firm that follows the price-setting rule implied by the standard New Keynesian model, i.e., sets its price as a discounted average of expected future marginal costs. Consider first a firm that is allowed to adjust its price in the period that the shock occurs. The New Keynesian firm, anticipating that marginal costs will fall in the future, sets its price lower than the flexible price. Customer markets have no effect on prices when they are flexible, yet they call for a smaller initial price response when prices are sticky. As discussed in Section 2.4, a firm that is about to reoptimize realizes that a price increase will have a negative effect on its market share, which reduces the incentive to raise the price. Perhaps the most salient characteristic of Fig. 2 is the observation that price changes are typically larger in size and that price decreases are more common with customer markets. A firm that is unable to adjust its price for some time will typically see its market share either rise or fall, affecting both the direction and the size of the eventual price adjustment. 15
For all simulations, Dynare software, available at http://www.dynare.org/, was used.
J. S¨ oderberg / Journal of Monetary Economics 58 (2011) 206–219
Output gap
Inflation 0.6
0
0.4
0.4
−0.4 −0.6 −0.8
Annualized pp
0.6 Annualized pp
pp
Nominal rate
0.2
−0.2
0.2 0 −0.2 −0.4
−1 0
6 Quarters
12
0.2 0 −0.2 −0.4
0
Output gap
6 Quarters
12
0
Inflation
0
0.4
0.4
−0.6 −0.8
Annualized pp
0.6
Annualized pp
0.6
−0.4
0.2 0 −0.2 −0.4
−1 0
6 Quarters
12
6 Quarters
12
Nominal rate
0.2
−0.2 pp
215
0.2 0 −0.2 −0.4
0
6 Quarters
Customer markets
12
0
6 Quarters
12
Standard
Fig. 3. Impulses responses of the output gap, inflation, and the nominal interest rate to a one standard deviation cost-push shock under optimal policy. The top row is policy based on the value of l implied by the respective model. The bottom row is policy when the value of l obtained without customer markets is imposed in both models. The response of the output gap is expressed in percentage points (pp); the responses of inflation and the nominal interest rate are expressed in annualized percentage points.
As illustrated in the figure, firms that are late to adjust after the shock have gained market shares and therefore have big incentives to raise their prices. Still, the price level adjusts slowly because market share movements cancel each other out in the aggregate. Arguably, this pattern of price adjustment is more in line with empirical evidence of price-setting behavior that typically finds quite a lot of flexibility in prices at the microeconomic level, even though there is considerable inertia in the aggregate price level (see, e.g., Klenow and Kryvtsov, 2008 and Nakamura and Steinsson, 2008). A detailed analysis of price dynamics is beyond the scope of this paper. I note, however, that in order to match the size of price changes found in the data, one must reasonably add idiosyncratic shocks at the firm level, in order to amplify the size of price changes.16 5.3. Optimal monetary policy It was shown above that for a given monetary policy, the main consequence of customer markets pertains to the dynamic response of inflation. I now turn to the question of how customer markets affect the conduct of optimal monetary policy. The central bank’s problem is to choose a sequence fxt , pt g1 t ¼ 0 to minimize the discounted sum of normalized period loss functions: L ¼ p2t þ lx2t ,
ð24Þ
where l ¼ lx =lp is the relative weight on output gap stabilization, subject to the model’s equilibrium relations given by (14) and (17). The policy problem is solved under the assumption that the central bank is able to make state contingent commitments about future policy actions. The baseline calibration implies that the annualized value of l is 0.948, making output gap stabilization about as important as inflation stabilization.17 The corresponding value without customer markets is 0.0774, giving the central bank a much stronger motive to stabilize inflation. The top row of Fig. 3 shows the response of the model economy to a cost-push shock. The hump-shaped decline in the output gap engineered by the central bank is more gradual with customer markets, resulting in a less intense, but more 16 Klenow and Kryvtsov (2008) and Nakamura and Steinsson (2008) both find that for consumer prices excluding sales, the median absolute size of price changes is about 10%. 17 Since the model is calibrated to a quarterly periodicity, the value of l is annualized by multiplying it by 42.
216
J. S¨ oderberg / Journal of Monetary Economics 58 (2011) 206–219
5 4.5 4
Variance output gap
3.5 3 2.5 2 1.5 1 0.5 0 0
0.1
0.2
0.3 0.4 Variance inflation
0.5
0.6
0.7
Fig. 4. Trade-off between inflation and output gap stabilization when the business cycle is driven by both shocks to the efficient interest rate and costpush shocks. The solid line shows the efficient policy frontier for the baseline calibration of y ¼ 0:875. The circles show optimal points for different degrees of customer markets. The variance of the output gap is expressed in percentage points; the variance of inflation is expressed in annualized percentage points.
prolonged, downturn. The central bank finds it optimal to accommodate some of the inflationary pressure arising due to the cost-push shock. It is well known from the literature that the central bank, in this class of models, anchors inflation expectations by committing to reverting the price level back to its pre-shock level. This result carries over to the customer market model. After the initial rise in inflation, the central bank therefore keeps inflation negative for some time. Both the degree of accommodation and the subsequent drop in inflation are larger and more persistent with customer markets. We see that the optimal monetary policy response is substantially affected by the introduction of customer markets. A question that follows is how much of the difference in policy is due to the new hybrid Phillips curve, and how much is due to the higher relative weight on output gap stabilization. To separate these two effects, I also consider the experiment of imposing the value of l obtained without customer markets in both models; this comparison is plotted in the bottom row of Fig. 3. The impulse responses are very similar, suggesting that the main difference in policy is due to the higher relative weight on output gap stabilization with customer markets. The central bank’s trade-off between inflation and output gap stabilization can be illustrated by means of Fig. 4, which shows the variance of inflation and the output gap for a simulated business cycle driven by both shocks to the efficient interest rate and cost-push shocks. The solid line is the efficient policy frontier for the baseline calibration; the filled circle indicates the optimal point based on the value of l implied by the welfare criterion. Instead, imposing the value of l obtained without customer markets leads to the point on the efficient frontier indicated by the asterisk. Comparing these two points, it is evident that the higher relative weight on output gap stabilization obtained with customer markets involves an optimal policy with substantially higher volatility of inflation and lower volatility of the output gap. The unfilled circles in Fig. 4 show optimal points for model economies with different degrees of customer markets (with l based on the value implied by the welfare criterion in each model). The values of y correspond to households reoptimizing every quarter and every two, four, and six quarters. In the baseline case, when households reoptimize every eight quarters, the introduction of customer markets leads to a decrease in the volatility of the output gap of almost 40%, but there is a more than sevenfold increase in the volatility of inflation. If, instead, households reoptimize every four or six quarters, the change in policy implied by the introduction of customer markets is smaller compared to the baseline calibration. Yet, it is not trivial; for instance, setting y ¼ 0:75 still leads to a reduction in the volatility of the output gap of 21%, but a more than two and half times increase in the volatility of inflation. Thus, even relatively modest degrees of customer markets imply an optimal policy that, compared to the standard New Keynesian model, involves substantially higher volatility of inflation.
J. S¨ oderberg / Journal of Monetary Economics 58 (2011) 206–219
217
0.12 Optimal policy Baseline rule Alternative rule I Alternative rule II
0.1
Welfare loss
0.08
0.06
0.04
0.02
0 0
0.2
0.4
0.6
0.8
1
θ Fig. 5. Average welfare loss per period, expressed as a percentage of steady state consumption, for different values of y under alternative policies, with the business cycle driven by both shocks to the efficient interest rate and cost-push shocks. The baseline rule corresponds to (23). Alternative rule I sets the reaction coefficient with respect to inflation to 5. Alternative rule II sets the reaction coefficient with respect to the output gap to 0.3.
5.4. Welfare In this section, the implications for the welfare of different policies are evaluated. Welfare is measured by calculating the average welfare loss per period, given by 1 2½lx varðxt Þ þ lp varð t Þ:
p
ð25Þ
Fig. 5 shows the welfare loss for different values of y under optimal policy, the baseline Taylor rule, and two alternative Taylor rules. Keeping the other coefficients at their baseline values, alternative rule I sets the reaction coefficient with respect to inflation to 5, while alternative rule II sets the reaction coefficient with respect to the output gap to 0.3. For all policies, the welfare loss is decreasing in y. When this parameter approaches unity, the welfare cost associated with inflation vanishes, as price dispersion no longer distorts the allocation of consumption among the different goods. In this case, optimal policy involves complete stabilization of the output gap. Of the Taylor rules, alternative rule I, with a strong reaction to inflation, performs the best without customer markets when the gain from inflation stabilization is large. Alternative rule II, which puts a high weight on output gap stabilization, leads to the largest welfare losses in this case. The more balanced baseline Taylor rule lies in-between the two alternative rules. Without customer markets, alternative rule I is relatively close to optimal policy, while the other rules lead to substantially higher welfare losses. For high values of y, when the loss associated with inflation volatility is small and the gain from stabilizing the output gap is large, the situation is reversed. Alternative rule II performs the best, while alternative rule I, as a result of its focus on inflation stabilization, performs the worst. In this case, however, the difference between the different rules are much smaller. 5.5. Commitment versus discretion An important question is how the results would change if firms were unable to commit to future prices. In a strict interpretation, commitment requires firms to write binding contracts specifying prices in all future states of the world. Even if firms are scrupulous about not antagonizing their customers, such contracts are, at least for consumer goods, inconceivable. Unfortunately, the fact that the firm’s market share and its price are state variables in the optimization makes even the Markov perfect equilibrium intractable when firms act with discretion. A full analysis is therefore beyond the scope of this paper. Suppose, however, that one is able to obtain a solution to the Markov perfect equilibrium under discretion. How would the results be likely to change? First, as discussed in Section 2.4, we should consider that the backward-looking nature of inflation is a result of firms’ ability to commit. Under discretion, one would therefore expect the return of a purely
218
J. S¨ oderberg / Journal of Monetary Economics 58 (2011) 206–219
forward-looking Phillips curve. Markup dynamics would also be different. Under commitment, a firm’s incentive to raise its price when profit margins erode is counteracted by concerns of its customer base in past periods. Under discretion, the firm has no such concerns and will want to raise its price more than is necessary to restore its markup. Hence, optimal markups will plausibly be time-varying, as has traditionally been found in the customer market literature. Moreover, markups will be higher on average when firms cannot commit to low prices in order to improve their market share positions. The characterization of optimal monetary policy will also be different. For one thing, the time-varying markups introduce an inefficient disturbance to the natural level of output that generally makes it impossible for the central bank to simultaneously stabilize the output gap and inflation, even in the absence of exogenously imposed cost-push shocks. Preferences are not affected, so given a subsidy that makes the steady state efficient, the expression in (21) is still the relevant welfare criterion. The relation between inflation and the dispersion of consumption across goods will be different however, as prices are set differently. One may hypothesize that, when unconstrained by past commitments, firms will react more strongly to market share movements. This would likely increase the dispersion of prices in the economy and counteract the reduction in the welfare cost of inflation. Reasonably, customer markets reduce the welfare cost of inflation, and lead to an optimal monetary policy that assigns a higher relative weight to output gap stabilization, also under discretion, but the quantitative effects may be smaller. 6. Conclusion Two salient characteristics of the canonical New Keynesian model are the purely forward-looking nature of inflation and the utility-based welfare criterion’s emphasis on inflation stabilization over output gap stabilization. In this paper, a customer market model in which firms and customers form long-term relations is developed and integrated in the standard New Keynesian model. This leads to a Phillips curve of the hybrid variant, where current inflation depends on past inflation. In the literature, inflation persistence is usually generated by imposing generalized price indexation schemes. Besides the ad hoc nature of such schemes, they also have the counterfactual implication that all prices are adjusted at all times, albeit not optimally. The customer market model developed in this paper, in contrast, displays endogenous inflation persistence, arising as a consequence of the forward-looking nature of demand and firms’ ability to commit to future prices. The model has important implications for monetary policy. When customers respond sluggishly to relative price changes, price dispersion is a significantly less distortionary phenomena, leading to lower welfare costs of inflation and an optimal monetary policy that assigns relatively more weight to output gap stabilization. There are also implications of the model that merit further investigation. It is important to determine the exact role of firms’ ability to credibly commit to price plans, and how the result would change under discretion. Furthermore, it would be interesting to investigate how price adjustment at the microeconomic level, reasonably combined with some kind of firm-specific shocks, fits the empirical facts.
Acknowledgments ¨ ¨ I would like to thank Nils Gottfries, Mikael Carlsson, Ulf Soderstr om, Morten Ravn, and participants at various seminars for helpful comments and suggestions. Part of the research was conducted while visiting Sveriges Riksbank. Financial support from Handelsbanken forskningsstiftelser is gratefully acknowledged. Appendix A. Supplementary data Supplementary data associated with this article can be found in the online version at doi:10.1016/j.jmoneco.2011.05.012.
References Amirault, D., Kwan, C., Wilkinson, G., 2005. A survey of the price-setting behaviour of Canadian companies. Bank of Canada Review 2004, 29–40. Apel, M., Friberg, R., Hallsten, K., 2005. Microfoundations of macroeconomic price adjustment: Survey evidence from Swedish firms. Journal of Money, Credit and Banking 37, 313–338. Basu, S., Fernald, J.G., 1995. Are apparent productive spillovers a figment of specification error? Journal of Monetary Economics 36, 165–188. Bils, M., 1989. Pricing in a customer market. The Quarterly Journal of Economics 104, 699–718. Calvo, G.A., 1983. Staggered prices in a utility-maximizing framework. Journal of Monetary Economics 12, 383–398. Clarida, R., Galı´, J., Gertler, M., 2000. Monetary policy rules and macroeconomic stability: Evidence and some theory. The Quarterly Journal of Economics 115, 147–180. Fabiani, S., Loupias, C.S., Martins, F.M.M., Sabbatini, R., 2007. In: Pricing Decisions in the Euro Area—How Firms Set Prices and Why. Oxford University Press, New York. Galı´, J., Gertler, M., 1999. Inflation dynamics: A structural econometric analysis. Journal of Monetary Economics 44, 195–222. Galı´, J., Gertler, M., Lopez-Salido, J.D., 2001. European inflation dynamics. European Economic Review 45, 1237–1270.
J. S¨ oderberg / Journal of Monetary Economics 58 (2011) 206–219
219
Gottfries, N., 1991. Customer markets, credit market, imperfections and real price rigidity. Economica 58, 317–323. Gottfries, N., 2002. Market shares, financial constraints and pricing behaviour in the export market. Economica 69, 583–607. Klenow, P.J., Kryvtsov, O., 2008. State-dependent or time-dependent pricing: Does it matter for recent us inflation? The Quarterly Journal of Economics 123, 863–904. Kleshchelski, I., Vincent, N., 2009. Market share and price rigidity. Journal of Monetary Economics 56, 344–352. Linde, J., 2005. Estimating New-Keynesian Phillips curves: A full information maximum likelihood approach. Journal of Monetary Economics 52, 1135–1149. ¨ Lundin, M., Gottfries, N., Bucht, C., Lindstrom, T., 2009. Price and investment dynamics: Theory and plant-level data. Journal of Money, Credit and Banking 41, 907–934. Marcet, A., Marimon, R., 1998. Recursive Contracts. Economics Working Papers eco98/37. European University Institute. Nakamura, E., Steinsson, J., 2008. Five facts about prices: A reevaluation of menu cost models. The Quarterly Journal of Economics 123, 1415–1464. Nakamura, E., Steinsson, J., 2010. Monetary non-neutrality in a multisector menu cost model. The Quarterly Journal of Economics 125, 961–1013. Nakamura, E., Steinsson, J. Price setting in forward-looking customer markets. Journal of Monetary Economics, in press. doi:10.1016/j.jmoneco.2011. 06.004. Phelps, E., Winter, S., 1970. Optimal price policy under atomistic competition. In: Phelps, E. (Ed.), Microeconomic Foundations of Employment and Inflation Theory. Norton, New York. Ravn, M., Schmitt-Grohe, S., Uribe, M., 2006. Deep habits. Review of Economic Studies 73, 195–218. Rotemberg, J.J., 2005. Customer anger at price increases, changes in the frequency of price adjustment and monetary policy. Journal of Monetary Economics 52, 829–852. Rotemberg, J.J., Woodford, M., 1998. An Optimization-Based Econometric Framework for the Evaluation of Monetary Policy: Expanded Version. Working Paper 233. National Bureau of Economic Research. Rudd, J., Whelan, K., 2005. New tests of the New-Keynesian Phillips curve. Journal of Monetary Economics 52, 1167–1181. Smets, F., Wouters, R., 2007. Shocks and frictions in US business cycles: A Bayesian DSGE approach. American Economic Review 97, 586–606. Solomon, M., Bamossy, G., Bamossy, S., Hogg, M.K., 2006. In: Consumer Behaviour: A European Perspective third ed. Financial Times/Prentice Hall. Solon, G., Barsky, R., Parker, J.A., 1994. Measuring the cyclicality of real wages: How important is composition bias. The Quarterly Journal of Economics 109, 1–25. Taylor, J.B., 1999. A historical analysis of monetary policy rules. In: Monetary Policy Rules. National Bureau of Economic Research Inc, pp. 319–348 (NBER Chapters). Woodford, M., 2003. In: Interest and Prices: Foundations of A Theory of Monetary Policy. Princeton University Press, Princeton. Woodford, M., 2005. Firm-specific capital and the New Keynesian Phillips curve. International Journal of Central Banking 1. Young, A., Levy, D., 2006. Explicit Evidence on an Implicit Contract. MPRA Paper 926. University Library of Munich, Germany.
Journal of Monetary Economics 58 (2011) 220–233
Contents lists available at ScienceDirect
Journal of Monetary Economics journal homepage: www.elsevier.com/locate/jme
Price setting in forward-looking customer markets Emi Nakamura a,b,c, Jo´n Steinsson a,b,c, a
Columbia University, United States NBER, United States c CEPR, United Kingdom b
a r t i c l e in f o
abstract
Article history: Received 23 April 2010 Received in revised form 6 June 2011 Accepted 13 June 2011 Available online 5 July 2011
If consumers form habits in individual goods, firms face a time-inconsistency problem. Low prices in the future help attract customers in the present. Firms, therefore, have an incentive to promise low prices in the future, but price gouge when the future arrives. In this setting, firms benefit from ‘‘committing to a sticky price.’’ If consumers have incomplete information about costs and demand, the firm-preferred equilibrium has the firm price at or below a ‘‘price cap.’’ The model therefore provides an explanation for the simultaneous existence of a rigid regular price and frequent ‘‘sales’’. & 2011 Elsevier B.V. All rights reserved.
1. Introduction A consumer’s past purchases of a particular product often exert a strong positive influence on his current demand for this product. Such time non-separability of preferences arises for many different reasons. Some goods are addictive while consumers develop a sense of ‘‘brand-loyalty’’ to others. Consumers favor some products that they have used in the past because of compatibility with other equipment while they favor other products because the quality of competing products is unknown to them. And consumers continue using some products simply because of the large transaction costs associated with switching to a competitor (e.g., another bank or another internet service provider). For all these reasons, it is common for consumers to be partially locked into purchasing a particular product once they have begun purchasing it. Similar lock-in effects are common when firms purchase from suppliers (Shapiro and Varian, 1999). This paper analyzes the implications of such lock-in effects for firm price setting. It is well known that consumer lock-in implies that firms face a time-inconsistency problem. This was first shown in models with consumer switching costs (Klemperer, 1995).1 More recently, Ravn et al. (2006) have shown that the same is true when consumers form goodspecific habits. The fact that consumers are partially locked-in—by switching costs and habits—implies that consumer demand is forward-looking; consumer demand depends negatively not only on the current price of the product but also on the consumer’s expectations about the good’s future prices. This implies that firms would like to promise that they will keep their prices low in the future. However, when the future arrives, the firms have an incentive to renege on their earlier promises and price gouge locked-in consumers. The consumers understand these incentives and do not take the firms’ promises at face value unless the firms are able to make credible commitments.
Corresponding author. Department of Economics, Columbia University, 420 W 118th St., NY 10027, United States. Tel.: þ1 212 854 3690.
E-mail address:
[email protected] (J. Steinsson). In an important early contribution, Diamond (1971) provides a particularly dramatic example where even an infinitesimally small switching cost yields monopoly pricing unless firms are able to make credible commitments about future prices. 1
0304-3932/$ - see front matter & 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.jmoneco.2011.06.004
E. Nakamura, J. Steinsson / Journal of Monetary Economics 58 (2011) 220–233
221
Using the good-specific habit model of Ravn et al. (2006), the paper explores how the firm’s time-inconsistency problem gives rise to various forms of price rigidity.2 If firms are not able to make credible commitments, the timeinconsistency problem leads them to set prices that are sub-optimally high both from a profit perspective and from the perspective of overall welfare. When firms and consumers interact repeatedly, they can improve on this discretionary outcome by entering into ‘‘implicit contracts’’. This idea is formalized by studying sustainable plans of the infinitely repeated game played by a firm and its consumers (Chari and Kehoe, 1990). In this good-specific habit model, implicit contracts involving price rigidity can be sustained as equilibria. In standard models without consumer lock-in, price rigidity is simply a constraint on firms’ ability to set the price they would like to set. In these models, implicit contracts involving price rigidity yield lower profits than the discretionary outcome and thus cannot be sustained as equilibria. However, in models with consumer lock-in, implicit contracts involving price rigidity serve as a partial commitment device and therefore help firms overcome their time-inconsistency problem. To see this, consider an implicit contract in which firms promise to change their price only every other period. Such a contract leads firms to set a lower price and earn higher profits than in the discretionary equilibrium since their incentive to price gouge already locked-in consumers is tempered by a desire not to negatively affect next period’s demand. Firms are induced not to deviate from the terms of such implicit contracts by the threat that a deviation would trigger an adverse shift in customer beliefs about future prices. Many components of a typical firm’s marginal costs and demand are either unobservable or very costly for a consumer to observe. In the standard no-habit model, this is irrelevant for firm price setting. However, in the habit model, asymmetric information limits the variables that it is possible, even in principle, for the firm and customers to make use of implicit contracts. Building on the results of Athey et al. (2005), we show that the most desirable sustainable price path from the firm’s perspective under this kind of asymmetric information takes the form of an implicit contract that limits the firms discretion by setting a ‘‘price cap’’ above which the firm cannot set its price. Under this policy, the firm acts with discretion when its marginal costs and demand are relatively low; but sets its price equal to the price cap when marginal costs and demand are high. The price cap has the beneficial effect that it lowers the customers’ expectations about future prices and thereby increases demand. Given plausible assumptions about the process followed by the firm’s desired price and the extent of informational asymmetries, the firm’s price will be ‘‘stuck’’ at the price cap a significant fraction of the time. It will, however, frequently drop below the price cap and exhibit much more flexibility when it is not at the price cap. Our asymmetric information model implies that the price cap should be a function of observable variables. It should therefore trend upward with the aggregate price level, since the aggregate price level is observable. And even if observing the price level on a regular basis is too costly to be worthwhile for consumers, the price cap should trend upward because of expected movements in the price level. Empirically, nominal price rigidity is pervasive (e.g., Nakamura and Steinsson, 2008). From the viewpoint of our model, this implies that the equilibrium in most markets is not the one that is strictly most preferred by firms. One possible explanation for this is that firms may find it easier to convincingly communicate a fixed price cap rather than a trending price cap. In other words, fixed nominal prices may be a focal point in the efforts of firms and consumers to avoid the discretionary outcome. Hall (2005) has recently emphasized how a similar equilibrium selection issue is fundamental to labor market models with wage bargaining.3 This issue of equilibrium selection—coordination of firms and consumers on an equilibrium that is superior to a discretionary outcome—does not arise at all in price setting models without consumer lock-in. In price setting models without consumer lock-in, there is a unique equilibrium and nominal rigidities only arise as a consequence of real frictions such as menu costs.4 The asymmetric information version of the model implies that: (1) goods prices should spend a significant portion of their time at a rigid upper bound; (2) below this upper bound, they should be much more flexible. The model therefore endogenously generates both rigid ‘‘regular’’ prices and frequent ‘‘sales.’’ The salience of rigid regular prices and frequent sales is well documented (Hosken and Reiffen, 2004; Pesendorfer, 2002). The paper adds to this evidence by showing that sales prices are about eight times more flexible than regular prices. In our model, the consumers’ habit implies that they are partially locked into purchasing certain goods. Several recent papers study related issues. Kleshchelski and Vincent (2009) consider a model of customer lock-in in which consumers must incur costs to switch sellers/brands. They focus on the Markov perfect equilibrium of the model and show that firms adjust prices less than one-for-one in percentage terms to a given change in
2 The primary focus of Ravn et al. (2006) is on a model with good-specific external habits—‘‘keeping up the Jonses’’ at the good level—in which no time-inconsistency problem arises. However, in Section 4.3 of their paper, they discuss a model with good-specific internal habits in which the timeinconsistency problem discussed above arises. This good-specific internal habit model is the model studied in this paper. 3 Hall’s results follow from the fact that once workers and firms have been matched (which is costly) they face a bilateral bargaining problem regarding the wage with a wide set of candidate wage outcomes that are acceptable to both parties in that they improve on their outside options. For this reason, the wage is indeterminate in such a model. Hall (2005) argues that social norms cause fixed wages to be a focal point within the bargaining set. An important difference between our setting and Hall’s is that wage rigidities do not lead to allocative inefficiencies in Hall’s setting because wages do not affect labor supply conditional on a match. See also MacLeod and Malcomson (1993). 4 In the context of explicit contracts, the costs of writing complicated contracts are often cited as a reason why observed contracts are extremely incomplete. Perhaps it is similarly ‘‘more costly’’ to coordinate on and enforce a complicated state-contingent implicit contract than simple fixed-price rules. More generally, explaining why observed contracts are incomplete is an important topic in contract theory (see, e.g., Hart and Moore, 1999).
222
E. Nakamura, J. Steinsson / Journal of Monetary Economics 58 (2011) 220–233
prices.5 Motivated by costs of attention, Soderberg (forthcoming) captures consumer lock-in by assuming that consumers can only adjust their relative demand for a fraction of the products they purchase. This yields a similar consumer demand specification as our model. Soderberg focuses on the commitment equilibrium and assumes nominal rigidity. He shows that the consumer lock-in affects the aggregate dynamics of the economy and the welfare effects of monetary policy.6 A number of other recent papers also study adverse reactions by consumers as a source of price rigidity. L’Huillier (2010) studies a setting in which firms avoid price increases to avoid incurring negative reactions from uninformed consumers, who do not realize that the aggregate price level has risen. Rotemberg (forthcoming) presents a model in which consumers become angry if they perceive firm pricing to be unfair. Heidhues and Koszegi (2010) study a model in which loss aversion of consumers generates a motive for sticky regular prices and sales. The paper proceeds as follows. Section 2 discusses evidence supporting the customer market view of price rigidity developed in this paper. Section 3 analyzes the basic time-inconsistency problem that arises in the good-specific habit model and present results about the sustainability of implicit contracts that entail nominal rigidity. Section 4 considers the case in which firms have private information about their marginal costs and demand and show the optimality of a price cap rule in this setting. Section 5 presents empirical evidence on the flexibility of prices during sales. Section 6 concludes. Proofs are available in an online appendix on the authors’ and the journal’s websites.
2. Evidence for the customer markets view of price rigidity The model studied here is a model of ‘‘customer markets’’. The seminal paper on customer markets is Phelps and Winter (1970).7 Explaining price rigidity was a major motivation for the original development of customer markets models. According to Okun’s (1981) ‘‘invisible handshake’’ version of the customer markets idea, firms have implicit agreements with their customers not to take advantage of tight market conditions by raising their price in exchange for stable prices in weak markets. This view of price rigidity finds strong support in the views of firm managers. In Blinder et al. (1998), 64.5% of firms report that they have implicit contracts with their consumers and an overwhelming majority of these firms (79%) indicate that these implicit contracts are an important source of price rigidity. When asked why they did not change their prices more often, by far the most frequent answer given by firm managers was that they feared that this would ‘‘antagonize’’ their customers. Similar surveys in a host of other countries have since confirmed that the most important reason cited by firm managers for price rigidity is that they are loathe to ‘‘damage customer relations’’ by changing their prices.8 The customer markets view of price rigidity suggests that prices should be more rigid in markets in which customers and firms interact repeatedly. There is a direct experimental evidence to this effect. In an experiment on price setting in a market with search costs, Cason and Friedman (2002) show that higher search costs lead customers to remain with sellers for longer periods. Sellers respond to this increase in loyalty with significantly more rigid prices. Renner and Tyran (2004) study a setting in which buyers are uncertain about the quality of competing products. They show that the price rigidity is more pronounced in a customer market than a market without repeat customers following an increase in costs, and that price rigidity is more pronounced if the increase in costs is unobservable than if it is public information. The latter finding lines up well with the implications of the model presented in this paper (Section 4). Survey evidence also suggests that the link between customer markets and price rigidity may be important. In a survey of British firms, Hall et al. (1997) find that companies with over 75% of their customer relationships lasting for longer than five years rated fixed-price contracts as more important than firms with a smaller fraction of long-term customers. Small and Yates (1999) find that customer turnover seems to have a significant effect on the responsiveness of prices to changes in cost, but not to changes in demand. Carlton (1986) finds no evidence for a relationship between price rigidity and the importance of long-term contracts in a cross-industry study of the Stigler–Kindahl data set. However, the number of observations in Carlton’s study is small and the result may be confounded by other differences across industries. One problem with the invisible handshake story of Okun (1981) has been that in the context of the standard model without customer lock-in, it is difficult to rationalize why firms would enter into implicit contracts that impose restrictions on their future prices. In the context of the habit model considered below, firms make such commitments as part of their efforts to manage the expectations of their customers about their future prices. The firms’ price commitments are part of their efforts to convince their customers that they will not take advantage of them in 5 In our model, prices adjust proportionately to costs in the Markov perfect equilibrium, making the time-inconsistency problem the sole source of price rigidity. 6 This contrasts with our focus on the time-inconsistency problem and its implications micro-pricing behavior in the absence of physical costs of price adjustment. 7 Other contributions include Okun (1981), Bils (1989), Rotemberg and Woodford (1991, 1995), Bagwell (2004) and Ravn et al. (2006). 8 See Apel et al. (2005) for a survey of Swedish firms; Hall et al. (1997) for U.K. firms; Amirault et al. (2004) for Canadian firms; and Fabiani et al. (2004) for a meta-study of surveys of firms in Belgium, Germany, Spain, France, Italy, Luxembourg, the Netherlands, Austria and Portugal. A consistent finding across these surveys is that firms rate implicit and explicit contracts as the most important (or, in a few cases, among the most important) sources of price rigidity. In contrast, menu-costs and information costs typically rank rather low among the reasons for price rigidity. Fabiani et al. (2004) is particularly noteworthy due to its size (over 10,000 respondents) and scope (nine countries and many different sectors).
E. Nakamura, J. Steinsson / Journal of Monetary Economics 58 (2011) 220–233
223
future periods. Models with customer lock-in therefore provide one way of explaining why firms enter into implicit contracts regarding their prices.9 A brief survey of the media yields numerous examples of firms’ efforts to convince customers that they do not plan on raising their prices. For example, On May 23, 2002, Marvel CEO Bill Jemas began a pricing conference with the statement: ‘‘Read my lips, we will not raise prices.’’ On October 9, 2000, Revlon Inc. announced as part of its new terms of trade a ‘‘commitment not to raise prices for its retail partners in 2001’’. On December 1, 2004, Apple Computer ‘‘flatly denied a report thaty[it] was planning to raise prices for songs bought on the popular iTunes online music storey‘These rumors aren’t true,’ said Apple spokeswoman Natalie Sequerira. ‘We have multiyear agreements with the labels and our prices remain 99c a track.’ The webhosting company Tech Trade Internet Services states on its website ‘‘Price Freeze Guarantee. Same Price. Forever.’’10 In some cases, an explanation is provided. The large fence manufacturer Sarel states: Sarel yhas had no price increases for more than five years and no price changes are expected in the foreseeable future. yWhen [customers have] made their choice, the exceptional stability of our prices means that they know not only that they are getting superb value for their money today, but also that they will continue to do so in the future. A small photofinishing company ‘‘Color Express’’ states: Once we publish our price list, our track record proves that we commit to those prices: it’s not uncommon to maintain prices for one or two years barring significant increases in the paper industry. Take a look at other published prices, and you will find revisions sometimes as frequently as every 3–6 months. Even if the competitions prices are ‘‘slashed’’, doesn’t it make you wonder? Though far from conclusive, these anecdotes provide concrete examples of firms seeking to ‘‘commit to a sticky price’’, sometimes for the stated purpose of affecting consumers’ future price expectations.11 A notable feature of these price commitments is that they are often asymmetric. The firms announce that they will not raise their prices rather than committing that they will not change their prices. 3. The model with complete information This section considers the interactions of a monopolistic firm and a continuum of consumers that form habits in particular goods in a setting of complete information. The section considers both a case in which the firm can make credible commitments about future prices and also explore two types of equilibria when firms cannot make such commitments. In all three cases, consumer choice must satisfy the same demand function. Let us begin the section by deriving consumer demand. 3.1. Consumer demand Consider a continuum of consumers who purchase a continuum of differentiated products.12 Consumers’ preferences over the consumption of these products are given by E0
1 X
bt UðCt Þ,
ð1Þ
t¼0
where Ct ¼
"Z
1
#yt =ðyt 1Þ ðct ðzÞgct1 ðzÞÞðyt 1Þ=yt dz
,
ð2Þ
0
cj(z) denotes the consumption of good z at time j, yt determines the elasticity of substitution between goods, b is the consumer’s subjective discount factor and E0 denotes an expectations operator conditional on information at time t. This utility function implies that consumers’ utility from the consumption of a particular good is not time separable. Rather, the utility a consumer derives from good z in a particular period depends not only on his level of consumption in that period but also on how much he consumed of this good in the previous period. In other words, the consumer has a habit in each of the differentiated goods. The parameter g is a measure of the degree of this good-specific habit, 0 r g r 1. The time variation in yt should be viewed as a stand-in for all time varying features of demand that affect the firm’s optimal price 9 Zbaracki et al. (2004) document large costs associated with convincing customers of the logic of a price change to prevent price changes from antagonizing customers. 10 These examples were collected from news articles and company webpages on the internet. A number of similar examples for various industrial and consumer goods industries are presented in an online appendix to this paper. It is important to note that in many of these examples, the firms’ consumers are other firms rather than households. As discussed in Shapiro and Varian (1999), lock-in effects are prevalent in many ongoing firm-to-firm purchasing relationships. 11 Another potential explanation for firms pre-announcing their prices is collusion. 12 The analysis in this section follows that in Section 4.3 of Ravn et al. (2006).
224
E. Nakamura, J. Steinsson / Journal of Monetary Economics 58 (2011) 220–233
and that are not explicitly modeled. Our approach to ensuring that the model has an equilibrium is to follow SchmittGrohe and Uribe (2007) in assuming that consumers will drop a firm’s product from their consumption bundle unless they archive a given level of utility from that product. Without this assumption, firms have an incentive to raise their prices to infinity in the discretionary equilibrium since consumer demand has an inelastic term (see Eq. (4) below).13 Consumers face two types of decisions about consumption. They must decide how much to spend on consumption at each point in time and how to allocate their spending at each point between the different goods. These two problems may be analyzed separately. The focus here is on the allocation of spending across goods at a particular point in time. Given a state-contingent path for total consumption fCt þ j g1 j ¼ 0 , the consumers seek to minimize their expenditures. Formally, the consumers choose ct ðzÞ 4 0 to minimize Z 1 1 X Et Mt,t þ j pt þ j ðzÞct þ j ðzÞ dz ð3Þ j¼0
0
subject to fCt þ j g1 j ¼ 0 , where Mt,t þ j denotes the stochastic discount factor that the consumers use to value future cash flows. The solution to this optimization problem implies that consumer demand for good z is !yt P j Et 1 j ¼ 0 g Mt,t þ j pt þ j ðzÞ , ð4Þ ct ðzÞ ¼ gct1 ðzÞ þCt Pt where Pt denotes the price level in period t.14 Notice that when g ¼ 0 this demand curve reduces to an iso-elastic Dixit– Stiglitz demand curve. When ga0, consumer demand differs from this simple benchmark in two ways. First, current demand depends on consumption in the previous period. Second, demand in period t is negatively influenced not only by pt(z) but also by Et pt þ j ðzÞ. The intuition for these two effects is straightforward. When the consumers have a habit, their flow utility at a given point in time depends directly on their consumption in the previous period. Their demand today therefore depends on their consumption in the previous period. However, the consumers also understand that by consuming a particular good today, they are increasing their habit in this good, thereby increasing their future demand for it. As a consequence, the consumers’ demand today is affected by how costly it will be to feed their habit in the future, i.e., their demand today depends negatively on the future price of the good. 3.2. The firm’s problem Our primary interest is in the pricing decision of a monopolist producer of product z. Firm z chooses the price of its product pt ðzÞ 4 0 to maximize its value E0
1 X
M0,t ½pt ðzÞct ðzÞSt ct ðzÞ
ð5Þ
t¼0
subject to the demand for its product, given by Eq. (4) taking aggregate demand Ct, the aggregate price level Pt and its marginal cost St as given. A key focus of our paper is comparing equilibria under commitment with equilibria under discretion. Solving analytically for equilibria when firms optimize under discretion is intractable in general. One solution to this problem is to adopt approximation methods of the sort that are widely used in monetary economics (see, e.g., Woodford, 2003 and Benigno and Woodford, 2005). Below, the firm’s problem is approximated around its steady state solution with commitment and it is assumed that exogenous shocks and the habit coefficient, g, are small.15 In addition, it is assumed that the exogenous shocks St and yt are i.i.d. Allowing for persistent shocks would, of course, be highly desirable for macroeconomic applications, but renders the model intractable in the asymmetric information case, as is discussed in Section 4. Given these assumptions, the online appendix shows that a second-order approximation of the firm’s value is 1 X 1 1 1 y1 ^ t ^ 0,t þ 1 c^ t ðzÞM ^ 0,t , pðzÞcðzÞb ð6Þ E0 p^ t ðzÞ þ p^ t ðzÞ2 þ c^ t ðzÞ þ c^ t ðzÞ2 þ p^ t ðzÞc^ t ðzÞ S t c^ t ðzÞ þ p^ t ðzÞM 2 2 y y y t¼0 where c^ ðzÞ ¼ logðct ðzÞ=cðzÞÞ, hatted versions of other variables are defined analogously. A second-order approximation of the consumer demand curve is 1 1þy 1 y e c^ t ðzÞ þ c^ t ðzÞ2 gc^ t1 ðzÞ c^ t ðzÞ2 yP^ t C^ t þ P^ t c^ t ðzÞ þ C^ t c^ t ðzÞ þ ðy1Þc^ t ðzÞU^ t ¼ yð1ggbÞp^ t ðzÞ p^ t ðzÞ2 ygbp^ t þ 1 ðzÞ, 2yð1gÞ y 2 2
ð7Þ
13
See Schmitt-Grohe and Uribe (2007) for a detailed description of the assumptions needed to guarantee that an equilibrium exists in this model. Pt is the Lagrange multiplier in the consumer’s constrained expenditure minimization problem. It therefore measures the shadow cost of attaining an extra unit of Ct. 15 More precisely, the equilibrium of the original non-linear model is characterized up to a residual of order OðJx, gJ2 Þ, where x denotes a vector of the exogenous shocks and Jx, gJ denotes the standard Euclidean distance norm in ðx, gÞ space. See Woodford (2003, pp. 383–392 and 630–635) for a detailed discussion of the validity of this approximation method. 14
E. Nakamura, J. Steinsson / Journal of Monetary Economics 58 (2011) 220–233
225
where U^ t ¼ y^ t =ðy1Þ. Exogenous second-order terms have been dropped, since they do not affect the analysis below and e p^ t þ 1 ðzÞ denotes consumers’ expectations at time t of the price firm z will charge at time t þ1. The last term in the demand e function is denoted as p^ t þ 1 ðzÞ to emphasize that this is a choice variable of the households in each period. Rational e expectations requires p^ t þ 1 ðzÞ ¼ Et p^ t þ 1 ðzÞ. As noted above, our goal is to characterize a first-order approximation of the solution of the model. Since, up to a first order, the model has no endogenous state variables and the exogenous shocks are e assumed to be i.i.d., p^ t þ 1 ðzÞ is a constant in equilibrium. 3.3. Commitment Let us begin by analyzing a situation in which the firm is able to make commitments about future prices. More precisely, assume that at the beginning of period 0 the firm chooses a state-contingent path for its price for all future periods. After the firm announces this state-contingent path for prices, consumers choose how much to demand in each state of the world. Assume that the firm has access to a commitment device that prevents it from reneging on these choices in future periods. Here, attention is limited to symmetric equilibria in which all firms set the same price and all consumers demand the same quantity. An equilibrium given these assumptions is a state-contingent path for prices and demand that satisfies two conditions: (1) for any path for pt(z), the path for consumer demand ct(z) satisfies Eq. (4); (2) the path for firm z’s price pt(z) maximizes expression (5) subject to Eq. (4). This is defined as the commitment equilibrium. Using the demand curve—Eq. (7)—to eliminate c^ t ðzÞ from the firm’s objective function—Eq. (6)—yields the following expression for the value of the firm: 1 X t 1y p^ t ðzÞ2 þðy1ÞU^ t p^ t ðzÞ þðy1ÞS^ t p^ t ðzÞ þpðzÞcðzÞgp^ 0 ðzÞ, pðzÞcðzÞb ð8Þ E0 2 t¼0 ignoring irrelevant terms and terms of third and higher order (see online appendix for details). The firm’s optimal pricing policy in a commitment equilibrium can then be characterized as follows. Proposition 1. In a commitment equilibrium, the price set by firm z in period t Z 1 is c p^ t ðzÞ ¼ S^ t þ U^ t ,
ð9Þ 2
up to an error of order OðJx, gJ Þ. Proof. See online appendix. Recall that U^ t is meant to be a stand-in for demand-side features that affect the firm’s optimal price but are not modeled explicitly. It is possible to show that this proposition holds exactly—i.e., without approximation—in the case of no markup shocks (constant yt ).16 This result contrasts the results of earlier customer market models based on demand specifications that introduced customer markets in a reduced form way such as those in Phelps and Winter (1970) and Rotemberg and Woodford (1991, 1995). In Phelps and Winter (1970) firms optimally vary their price less than one-for-one with marginal costs. Thus, markups vary countercyclically. In Rotemberg and Woodford (1991, 1995) the cyclicality of markups is in general ambiguous but they vary procyclically in the case the authors focus on. The idea that motivates the demand specifications assumed in these papers is that consumers respond sluggishly to changes in prices—due to switching costs and habits. Firms can invest in their ‘‘customer base’’ by lowering their current price. Likewise, by raising their price, firms not only lower current demand but also erode their customer base thereby negatively affecting future demand. The crucial difference between our model and earlier customer markets models is that in our model consumers realize that their demand in future periods depends on their actions in the current period. Consumers therefore decide to become customers of a particular firm not only based on the current price of the firm’s product but also based on their expectations about its future prices. In contrast, the earlier customer market literature assumes that changes in a firm’s market share are a function only of the firm’s current price. This assumption is not consistent with the interpretation that consumer’s sluggish responses are due to switching costs. Surely consumers realize that if they become customers of a particular firm they will become partially locked into that relationship in the future. Eq. (9) shows that, given the functional form assumptions embedded in consumption aggregator (2), it is optimal for a firm facing forward-looking consumers to let its price vary one-for-one in percentage terms with marginal costs. Furthermore, in this case, the price set by the firm under commitment is independent of the degree of habit g. These results simplify our analysis and help focus attention on the sources of price rigidity that arise because of the firm’s inability to make commitments. 16 Proposition 1 describes the pricing policy of the firm in the period after the commitment is made and in subsequent periods. This is analogous to the common approach in monetary economics of analyzing the commitment case from the ‘‘timeless perspective’’ (Woodford, 2003). If consumers start off with a habit in the period in which the commitment is made, the firm has an incentive to price gouge in this initial period and promise never to do so again.
226
E. Nakamura, J. Steinsson / Journal of Monetary Economics 58 (2011) 220–233
3.4. Discretion Now consider the case of ‘‘optimization under discretion.’’ At the beginning of period t, the exogenous shocks yt and St are realized. Then the firm sets a price for period t. Finally, consumers update their expectations about future prices and choose how much to purchase of each good. Since firms are not able to commit to a future price policy, consumer expectations reflect the incentives firms will have in the future when they set future prices. In general, consumers and the firm can vary their decisions depending on the history of exogenous variables, the history of the distribution of prices set by firms in earlier periods and the history of the distribution of consumption choices made by consumers. Let us again limit attention to symmetric equilibria in which all firms set the same price and all consumers demand the same quantity. In this section, let us, furthermore, restrict attention to equilibria in which firm z’s price in period t is a function only of the current exogenous shocks. These equilibria are referred to as Markov perfect equilibria (Maskin and Tirole, 2001).17 Section 3.5 considers the more general case in which firm z’s pricing decision may vary with the history of its own price. Formally, a Markov perfect equilibrium is a path for pt(z), ct(z) and pet þ 1 ðzÞ, where these three variables are functions only of pay-off relevant variables in each period and they satisfy the following three conditions in each period t: (1) e e consumers’ expectations are formed such that p^ t þ 1 ðzÞ ¼ Et p^ t þ 1 ðzÞ, (2) given pt(z) and p^ t þ 1 ðzÞ, consumers choose ct(z) to satisfy their demand curve—Eq. (7), (3) firms maximize their value—Eq. (6)—subject to consumer demand— e Eq. (7)—taking p^ t þ 1 ðzÞ as given. This yields the following result about the firm’s optimal pricing policy under discretion: Proposition 2. In the Markov perfect equilibrium of the model, firm z sets its price equal to m p^ t ðzÞ ¼
g y1
þ S^ t þ U^ t :
ð10Þ
Proof. See online appendix. The positive constant term in Eq. (10) implies that in the discretionary equilibrium the firm sets a higher price than it does when it can make commitments.18 The higher price implies a lower demand and lower profits for the firm. The higher price, of course, also hurts consumers. Social welfare is therefore lower in the discretionary equilibrium than when the firm can make state-contingent commitments. Proposition 2 shows that when consumers form habits the firm faces a time-inconsistency problem which leads it to set a price that is ‘‘too high’’. Each period, the firm takes advantage of its customers’ habits and ‘‘price gouges’’. It knows that customer’s expectations about future price gouging negatively affects its profits. But its inability to honor commitments prevents it from setting lower prices and experiencing higher profits. In the model, all consumers are infinitely lived. The model therefore abstracts from customer turnover. If firms can price discriminate between different cohorts of consumers, the model with customer turnover is a straightforward extension of our model. In the absence of commitment, firms offer an ‘‘introductory low price’’ to new consumers but set sub-optimally high prices for existing consumers. The pricing policy for existing consumers is, therefore, similar to the overall pricing policy in a model without customer turnover.19 Introducing customer turnover is more difficult if firms cannot price discriminate between new and old consumers. In this case, the fact that new consumers are not born with habit decreases the incentive of firms to price gouge. However, an offsetting effect applies to consumers nearing the end of their lives as customers. Firms have a greater incentive to price gouge these customers since they have a habit but do not care as much about the future as younger customers. Analyzing the model with customer turnover in the absence of price discrimination is beyond the scope of the present paper. Eq. (4) assumes that consumers form habits in individual goods. For some products, it may be more realistic to assume that consumers form habits in product varieties. For example, consumers may form a habit in coffee rather than Folgers coffee. In this case, while the formal structure of the model would not apply, the intuition for the ‘‘commitment problem’’ would go through as long as an increase in a given firm’s price leads to an increase in the price index of the product category: that is, a rise in the price of Folgers coffee leads to a rise in the price of the consumer’s ‘‘coffee habit’’. In this case, Folgers would face a time-inconsistency problem. Raising the price of its coffee would lead to a short-term increase in profits due to locked-in coffee consumers, but a long-run decrease in demand for coffee. 17 The model analyzed here has no lagged endogenous variables as state variables given our approximation. The only pay-off relevant state variables of the model are thus the current exogenous shocks. 18 Eq. (10) is calculated using an approximation around the steady state under commitment rather than the steady state under discretion. For this to yield a solution that is accurate up to a residual of order OðJx, gJ2 Þ, it is important that it is assumed that g is small (formally that g ¼ OðJx, gJÞ). The steady states under commitment and discretion differ merely by g=ðy1Þ. The fact that g ¼ OðJx, gJÞ implies that the approximation error that occurs due to the difference in the steady state that the model is linearized around and the steady state under discretion is of order OðJx, gJ2 Þ. This guarantees the desired accuracy for the overall approximation. See Woodford (2003, pp. 385) for a detailed discussion of this approach. 19 As in the model without price discrimination, the efficient outcome cannot be attained in the absence of commitment. Farrell and Shapiro (1989) show that an efficient outcome can be obtained in the case of inelastic demand and non-linear pricing. MacLeod and Malcomson (1993) show that in the case of inelastic demand, price rigidity can be efficient.
E. Nakamura, J. Steinsson / Journal of Monetary Economics 58 (2011) 220–233
227
3.5. Implicit contracts as a substitute for commitment When consumers and firms interact repeatedly, the firm may be able to overcome its time-inconsistency problem even if it is unable to make commitments by what is often referred to as reputation formation but in this context might be called an implicit contract with its consumers (Okun, 1981). These implicit contracts sustain equilibria in which the firm is induced not to take advantage of its customers’ habits by the threat that doing so would trigger an adverse shift in customer beliefs about its future behavior. As in Section 3.4, assume that the firm and consumers act sequentially and the firm is not endowed with any ability to make commitments. Also, again limit attention to symmetric equilibria in which all firms set the same price and all consumers demand the same quantity. However, in this section, consider equilibria in which the firm’s price may be contingent on its own past actions as well as current and past exogenous shocks. Refer to such equilibria as sustainable equilibria (Chari and Kehoe, 1990) and the path for prices in such an equilibrium as a sustainable price plan. Formally, a sustainable equilibrium is a path for pt(z), ct(z) and pet þ 1 ðzÞ, where these three variables may be functions of current and past exogenous shocks as well as the history of past prices and they satisfy the following three conditions in e e each period t: (1) consumers’ expectations are formed such that p^ t þ 1 ðzÞ ¼ Et p^ t þ 1 ðzÞ, (2) given pt(z) and p^ t þ 1 ðzÞ, consumers choose ct(z) to satisfy their demand curve—Eq. (7), (3) firms maximize their value—Eq. (6)—subject to consumer e demand—Eq. (7)—taking p^ t þ 1 ðzÞ as given. Many sustainable price plans exist. In particular, if the firm is sufficiently patient the pricing policy chosen by the firm under commitment can be sustained by an implicit contract. Proposition 3 formalizes this idea. c c Proposition 3. If b 4 b , the following price path is a sustainable price plan: at time 1, p^ 1 ðzÞ ¼ p^ 1 ðzÞ, where p^ 1 ðzÞ is the c c m commitment price of Proposition 1. At time t 4 1, p^ t ðzÞ ¼ p^ t ðzÞ if p^ t ðzÞ ¼ p^ t ðzÞ for all 0 o t ot. Otherwise p^ t ðzÞ ¼ p^ t ðzÞ, where m p^ t ðzÞ is the price set in the Markov perfect equilibrium of Proposition 2.
Proof. See online appendix. This implicit contract involves a trigger strategy. If the firm deviates from pct ðzÞ, consumers believe that the firm will set its price as in the discretionary equilibrium from then on. This adverse shift in consumer beliefs induces the firm not to deviate from pct ðzÞ. A prominent stylized fact about most goods prices is that they exhibit nominal rigidity. In the standard no-habit model, nominal rigidity does not arise as an equilibrium outcome. In contrast, when consumers form habits in specific goods, nominal rigidity can arise as an equilibrium outcome. Proposition 4 characterizes a simple sustainable price plan with two period nominal rigidity. Proposition 4. Assume that b 4 b and 2
g2 4 ðy1Þ2
1 þ bb
2
2b þ b
varðS^ t þ U^ t Þ:
ð11Þ
The following price path is a sustainable price plan. Set p^ t ðzÞ ¼
g ðy1Þð1 þ bÞ
þ
1 ^ ðS t þ U^ t Þ 1þb
ð12Þ
in periods t 2 f1,3,5, . . .g and do not change the price in the even numbered periods as long as all past prices have been set in this m way. Otherwise, set p^ t ðzÞ ¼ p^ t ðzÞ. Proof. See online appendix. This price path may be viewed as an implicit contract between the firm and its consumers which stipulates: (1) the firm’s prices should remain fixed for two periods at a time; and (2) if the firm ever deviates from this, consumers expect the firm to set its price as in the discretionary equilibrium from then on. Given this type of trigger strategy by the consumers, Eq. (12) is the firm-preferred price path.20 Proposition 4 can easily be extended to the case of n-period price rigidity. The firm can be induced not to deviate from this implicit contract because the price rigidity it entails helps the firm partially overcome its incentive to price gouge. Notice that the constant term in Eq. (12) is smaller than the constant term in Eq. (10). The firm sets a lower average price in this case because a high price in period t raises consumer’s expectations about the firm’s price in period t þ 1 and therefore raises the consumer’s cost of forming a habit in the good. Against this benefit, the firm must weigh the cost of price inflexibility. Since the firm can only change its price every other period, it is not able to respond optimally to fluctuations in marginal costs and demand. Instead of responding one-for-one in percentage terms to variations in marginal costs and demand as in Eq. (10), the firm only changes its price by 1=ð1 þ bÞ percent for each percentage point deviation in marginal costs or demand. Condition (11) determines how strong the consumers’ habit must be for the commitment benefit to outweigh the costs of inflexibility. 20
This is shown in the proof to Proposition 4.
228
E. Nakamura, J. Steinsson / Journal of Monetary Economics 58 (2011) 220–233
3.6. Discussion Our model suggests that price rigidity may be due to implicit contracts between firms and consumers. The punishment phase of such implicit contracts provides an interpretation for consumers’ adverse reactions to price increases that are not justified by observable increases in costs. Consumers often perceive such price increases as ‘‘unfair’’ (see, e.g., Kahneman et al., 1986; Rotemberg, 2005, forthcoming). If firms and consumers enter into implicit contracts, it is exactly these types of price increases that lead to adverse reactions by customers. Many other implicit contracts yield sustainable price paths in the model. Some entail price rigidities and others do not. Whether equilibria with price rigidity occur is therefore a matter of equilibrium selection. In a market with a large number of atomistic buyers, a firm with market power may disproportionately be able to influence equilibrium selection. All else equal, the firm would prefer the equilibrium described in Proposition 3, which does not involve price rigidity. One motivation for the asymmetric information model presented in Section 4 is that, in that setting, firms respond incompletely to some shocks, even in the firm-preferred equilibrium. In the complete information case, the firm could potentially prefer an equilibrium with price rigidity because it is easier to coordinate on. It may be easier for the firm to communicate a policy in which prices remain unchanged for several periods than a more complicated state-dependent pricing rule. It is important to note, however, that firms and consumers must also coordinate on off-equilibrium play to sustain the trigger strategy equilibria considered in Propositions 3 and 4. The multiplicity of equilibria embedded in our model may help explain some of the huge sectoral variation in the frequency of price change documented in the recent literature (see, e.g., Bils and Klenow, 2004)—perhaps equilibria with nominal rigidity become norms in some industries but not others. The idea that firms face menu costs and other barriers to price changes is arguably the most important idea used by macroeconomists to explain price rigidity. The standard view in the literature is that the existence of menu costs hurt firms. Firms therefore have an incentive to adopt technologies that eliminate menu costs. The existence of a timeinconsistency problem in the habit model discussed above suggests a dramatically different view of menu costs. In the habit model, menu costs can be beneficial to a firm since they can help the firm overcome its incentive to price gouge. 4. Asymmetric information Many components of a typical firm’s marginal costs and demand are either unobservable or very costly for a consumer to observe. Section 3 shows that in a complete-information setting the most favorable sustainable price path from the firm’s perspective is one in which the price is a function of the firm’s marginal costs and its demand. If marginal costs and demand are unobservable to the consumers, such price paths are unsustainable since there is no way for consumers to verify whether the firm deviates from them or not. This observation raises the question: What is the most favorable sustainable price path from the firm’s perspective when it has private information about its marginal costs and demand? It turns out that this question is formally related to the problem studied by Athey et al. (2005). They study the timeinconsistency problem of a central bank that has private information about the state of the economy. Using methods developed by Abreu et al. (1990), they are able to show that under relatively mild restrictions this type of problem has a surprisingly simple solution. Proposition 5 states a similarly simple result about the most favorable sustainable price path from the firms perspective when marginal costs and demand are unobservable.21 Proposition 5. Assume that S^ t and U^ t are unobservable to the consumers but that their probability distributions are known and ^ t ¼ S^ t þ U^ t is bounded on the interval ½ F ^ ,F ^ and satisfies a monotone hazard condition. Assume the probability distribution of F also that b 4 b . The sustainable price plan that maximizes the value of the firm at time 0 in this case has the firm do one of two things from t ¼ 1 on: ^ , the firm sets a constant price p^ ðzÞ ¼ Ep^ c ðF ^ t ,zÞ ¼ 0. (I) If g 4F t ^ , the firm sets (II) If g oF ( m ^ t ; zÞ if F ^ t 2 ½F ^ ,F ^ n , p^ ðF p^ t ðzÞ ¼ m ^n ^ t 2 ½F ^ n,F ^ :: ; zÞ if F p^ ðF
ð13Þ
If the firm deviates from this, it sets pt ðzÞ ¼ pm t ðzÞ forever after. Proof. See online appendix. The firm-preferred price path takes the form of an implicit contract that limits the firms discretion by setting a ‘‘price ^ t is relatively low, the firm acts with discretion—i.e., sets cap’’ above which the firm cannot set its price. When F 21 For simplicity, the unobservability of demand is modeled by assuming that U^ t is unobservable to the consumers. One way to motivate the unobservability of U^ t is to suppose that the population is made up of two groups: Group 1 has no habit and a low U^ . Group 2 has habits and a higher U^ . Unobservable variation in the relative size of these two groups then causes unobservable variation in the market U^ t .
E. Nakamura, J. Steinsson / Journal of Monetary Economics 58 (2011) 220–233
229
m ^ t 4F ^ n , the firm sets its price equal to the price cap (which is equal to the discretionary p^ t ðzÞ ¼ p^ t ðzÞ. However, when F n ^ ^ price for F t ¼ F ). Athey et al. (2005) refer to this as bounded discretion. The level of the price cap depends on the severity of the time-inconsistency problem, which in turn depends on the strength of the habit that consumers develop in the ^ n is decreasing in g. Thus, the firm’s desire to limit its discretion increases with the firm’s good. In other words, the cutoff F ^ n oF ^ . Thus, the price distribution over time for the firm will have a severity of the time-inconsistency problem. For g 4 0, F
mass-point at its upper bound so long as consumers have a habit. Conditional on the firm choosing a static pricing policy, the intuition for the price cap result is fairly straightforward. The time-inconsistency problem leads to sub-optimal profits because consumers anticipate that firms will price gouge in the future, leading them to demand less of the habit-forming good today. To improve on the Markov perfect equilibrium, a pricing policy must lower consumers’ expectations of future prices, implying that the pricing policy should constrain prices from above rather than below. Given that the pricing policy cannot be contingent on any relevant variable (which are assumed to be private information) a price cap policy is the best the firm can do. Unfortunately, the intuition for why the pricing policy must be static is much more complex and we are not aware of a simple intuition. The results above apply to the simple case in which the consumer cannot observe any of the variables that the firm would like to make its price depend on. They can, however, be extended to a setting in which the consumer observes some such variables but not others. In this case, the variables that the consumer observes are state variables and the price cap would be a function of these variables. Since the aggregate price level is trending upward, firms’ price caps should trend upward. The fact that the regular price of most goods in the U.S. economy are fixed in nominal terms for considerable periods is thus a deviation from the equilibrium that is strictly most preferred by firms in the model. Another limitation of our result in this section is that it holds only for i.i.d. shocks.22 5. Dynamic pricing implications Proposition 5 shows that in the model the firm’s optimal pricing policy when it has private information about its desired price is one in which its price is upward-rigid at a price cap. Below this cap the firm’s price is flexible. A substantial amount of empirical evidence supports the view that many products have a rigid regular price and that temporary sales are common. Hosken and Reiffen (2004) and Nakamura and Steinsson (2008) provide extensive evidence for the presence of this type of pricing behavior using data on a wide variety of consumer goods from the U.S. Bureau of Labor Statistics.23 Hosken and Reiffen (2004) document a clear asymmetry between price increases and decreases. ‘‘Reverse sales’’—i.e., brief periods during which the price of a good rises above its regular price and then returns back to the regular price—are extremely uncommon. This is one empirical implication of our dynamic pricing model. Another implication of the model is that prices should be substantially more flexible during sales than during other periods. By definition, price changes occur at the beginning and end of a sale. But multi-week sales account for somewhat less than half of all sales in many grocery products categories. The model suggests that prices should be more flexible over the course of these multi-week sales. In addition, the model implies that there is likely to be a great deal of price flexibility across different sale spells. In other words, the sale prices that arises in one sale spell are likely to differ from the sale prices that arise in the subsequent sale spells. 5.1. Evidence from supermarket data Weekly data from Dominick’s Finer Foods (DFF) are used to investigate these predictions of the model.24 Sales periods are identified using the filter described in Nakamura and Steinsson (2008) with the parameters J ¼ 8, K ¼ 3 and L ¼ 3.25 To give the reader a feel for the data and the procedure used to identify sales, Fig. 1 shows the original and ‘‘regular price’’ series for a popular item, Nabisco Premium Saltines 16 oz. The figure shows that the regular price series generated by this procedure corresponds well with our intuition about how to define a sale. The price series has infrequent adjustments in regular prices and frequent sales. When no recurring regular price can be identified from the data, the sales filter simply sets the regular price equal to the observed price. According to this sales filter, sales occur about 13% of the time in the Dominick’s data set. The regular price often remains fixed for significant periods of time—the frequency of price adjustment of regular prices is 6.1% or less in more 22 It is notoriously difficult to characterize dynamic incentive problems with private information and persistent shocks (see, e.g., Fernandes and Phelan, 2000; Athey and Bagwell, 2008). 23 Pesendorfer (2002) and Kehoe and Midrigan (2010) present similar evidence for scanner data. 24 DFF is the second-largest supermarket chain in the Chicago metropolitan area with approximately 100 stores and a 25% market share. DFF provided the University of Chicago Graduate School of Business (GSB) with weekly store-level scanner data, available at http://gsbwww.uchicago.edu/ kilts/research/db/dominicks/. See Chevalier et al. (2003) for a more detailed description of this data set. Data from store number 126 is used since the data from this store has the least missing data points. 25 Our qualitative findings are not sensitive to the exact parameters used in the sales filter. Related approaches to identifying sales based on the time series behavior of prices have been suggested by Kehoe and Midrigan (2010) and Hosken and Reiffen (2004). An alternative approach would be to use data on the timing of promotions. The labeling of promotions in the Dominick’s data set is, however, undependable. According to the University of Chicago GSB website describing the data, ‘‘if the variable is set it indicates a promotion, if it is not set, there might still be a promotion that week’’.
230
E. Nakamura, J. Steinsson / Journal of Monetary Economics 58 (2011) 220–233
$ 3.5 3.0 2.5 2.0 1.5 1.0 0.5
Price Regular Price + $1
0.0 Sep-89 Sep-90 Sep-91 Sep-92 Sep-93 Sep-94 Sep-95 Sep-96 Fig. 1. Nabisco Premium Saltines 16 oz. The solid line is the price of Nabisco Premium Saltines. The dotted line is the regular price of Nabisco Premium Saltines shifted up by $1.
than half of the categories included in the Dominick’s data. It is important to note that the answers to the questions investigated here regarding the flexibility of prices during sales are not guaranteed by the definition of sales. One might think of prices as oscillating between two distinct values: a regular price and a sale price, each of which exhibits substantial price rigidity. In this case, one would not expect to see a substantial difference in the flexibility of sale prices as compared to regular prices. Columns 1 and 2 of Table 1 compare the frequency of price adjustment for regular prices versus sale prices during multi-week sales, not including the price changes at the start and end of the sale. The frequency of price adjustment during sales is about eight times as high as the frequency of adjustment of the regular price.26 Existing menu cost models of price rigidity do not provide any reason why the price of a good should be more flexible when it is on sale. This pricing pattern is, however, a natural implication of our model.27 From the perspective of the customer markets model presented in this paper, this pattern of pricing reflects the fact that the firm optimally chooses to commit to a sticky price cap. Column 4 of Table 1 reports our measure of the flexibility of prices during sales. The table reports the number of unique sale values as a fraction of the total number of weeks spent on sale. This statistic would be equal to one if there were a unique sale price in every sale period and would approach zero if only one sale price was ever visited. Column 3 of the table reports an analogous statistic for regular prices. Sale prices are considerably more variable than regular prices. The median value of this fraction across categories for sale prices is 43%. In contrast, the same statistic for regular prices is 4.5%, about 10 times smaller.28 The data are not, therefore, consistent with the idea that the price always returns to a particular sale price when the product goes on sale.
5.2. Discussion In conjunction with the earlier evidence discussed above, Table 1 shows that the data support the presence of a rigid upper bound in prices with much more price flexibility below the upper bound. These features of the data are consistent with our model of the regular price as a commitment mechanism. These features of the data do not, however, arise naturally in standard models of price adjustment. Menu costs and other barriers to price changes are the dominant paradigm for explaining price rigidity in macroeconomics. Yet, it is difficult to reconcile menu cost models with the large amount of price flexibility that arises during temporary sales. Kehoe and Midrigan (2010) consider a model in which a different menu cost applies to sale price changes than to other types of price adjustments. A complete model of pricing behavior must, however, explain why the barriers to price adjustment are greater for some types of price adjustments than others. In the industrial organization literature, there are several important models of temporary sales in retail stores. Varian (1980) considers a model in which the presence of uninformed consumers supports a mixed strategy equilibrium in prices. The price variation associated with this mixed strategy equilibrium may be interpreted as representing temporary sales. Sobel (1984) presents an alternative model in which temporary sales arise when low-valuation, low discount-factor consumers build up in the market. As the stock of potential consumers varies over time, the firm has an incentive to vary 26 Levy et al. (2005) find an even greater difference in the flexibility of regular prices and sales prices in the DFF data set. Using a different algorithm to identify sales they estimate that sales prices are 64 times more likely to change than regular prices. 27 Again, these empirical facts do not arise from the particular approach used to identify sales, since our algorithm does not in any way affect the dynamics of prices during a sale. 28 An even higher fraction of sale prices are unique if the prices are defined in terms of percent off the regular price, or an absolute amount off the regular price.
E. Nakamura, J. Steinsson / Journal of Monetary Economics 58 (2011) 220–233
Table 1 Adjustment of regular versus sale prices. Product
Analgesics Bath soap Bathroom tissues Beer Bottled juices Canned soup Canned tuna Cereals Cheeses Cigarettes Cookies Crackers Dish detergent Fabric softeners Front-end-candies Frozen dinners Frozen entrees Frozen juices Grooming products Laundry detergents Oatmeal Paper towels Refrigerated juices Shampoos Snack crackers Soaps Soft drinks Toothbrushes Toothpastes Median
Frequency of price change
Number of unique prices as a fraction of total weeks
Regular prices
Sale prices
Regular prices
Sales prices
0.036 (0.001) 0.026 (0.002) 0.110 (0.003) 0.063 (0.001) 0.084 (0.001) 0.058 (0.001) 0.069 (0.002) 0.069 (0.001) 0.111 (0.001) 0.036 (0.001) 0.046 (0.001) 0.065 (0.001) 0.054 (0.001) 0.057 (0.001) 0.028 (0.001) 0.066 (0.002) 0.054 (0.001) 0.081 (0.002) 0.034 (0.001) 0.061 (0.001) 0.071 (0.002) 0.086 (0.003) 0.133 (0.002) 0.043 (0.001) 0.073 (0.001) 0.051 (0.002) 0.076 (0.001) 0.049 (0.001) 0.056 (0.001)
0.411 (0.013) 0.354 (0.025) 0.491 (0.014) 0.200 (0.006) 0.454 (0.006) 0.418 (0.007) 0.304 (0.008) 0.528 (0.010) 0.530 (0.005) – 0.500 (0.005) 0.445 (0.008) 0.453 (0.011) 0.404 (0.011) 0.344 (0.008) 0.551 (0.011) 0.495 (0.006) 0.522 (0.009) 0.497 (0.007) 0.425 (0.009) 0.530 (0.019) 0.482 (0.015) 0.635 (0.008) 0.443 (0.010) 0.529 (0.007) 0.510 (0.011) 0.652 (0.004) 0.406 (0.011) 0.492 (0.009)
0.035 (0.001) 0.031 (0.002) 0.064 (0.004) 0.040 (0.002) 0.053 (0.002) 0.042 (0.001) 0.046 (0.003) 0.061 (0.001) 0.080 (0.007) 0.053 (0.001) 0.034 (0.001) 0.044 (0.002) 0.047 (0.002) 0.045 (0.003) 0.024 (0.001) 0.040 (0.003) 0.039 (0.001) 0.051 (0.002) 0.036 (0.001) 0.049 (0.003) 0.062 (0.004) 0.045 (0.004) 0.089 (0.005) 0.038 (0.001) 0.051 (0.002) 0.039 (0.003) 0.042 (0.001) 0.045 (0.002) 0.048 (0.001)
0.578 (0.019) 0.531 (0.047) 0.359 (0.029) 0.195 (0.016) 0.404 (0.014) 0.464 (0.016) 0.331 (0.013) 0.668 (0.014) 0.395 (0.010) 0.580 (0.037) 0.426 (0.009) 0.349 (0.013) 0.434 (0.018) 0.495 (0.023) 0.338 (0.016) 0.432 (0.022) 0.446 (0.007) 0.344 (0.011) 0.442 (0.011) 0.538 (0.027) 0.607 (0.029) 0.301 (0.023) 0.447 (0.016) 0.443 (0.013) 0.428 (0.013) 0.449 (0.026) 0.309 (0.006) 0.403 (0.016) 0.443 (0.013)
0.061
0.487
0.045
0.434
Note: Standard errors are in parentheses. The total number of observations is 985,022. The regular price and sale prices of a good are identified using the sales filter that is described in Nakamura and Steinsson (2008). The frequency of price change is calculated by dividing the total number of price changes by the total number of weeks. The statistics in columns three and four are calculated by first dividing the number of unique regular or sale prices observed for a product by the total number of weeks at the regular price or on sale and then averaging within categories.
231
232
E. Nakamura, J. Steinsson / Journal of Monetary Economics 58 (2011) 220–233
its prices. These cyclical variations in prices may be interpreted as temporary sales. Aguirregabiria (1999) presents a motive for temporary sales based on store inventories. In this model, temporary sales arise when firms wish to rid themselves of excess inventories. This model generates cyclical movements in prices due to movements in the shadow value of inventory that can be interpreted as temporary sales. It is not clear, however, that these models present a convincing explanation for the presence of a rigid upper bound in retail prices. In Sobel’s (1984) model, a fixed ‘‘regular’’ price only arises if the discount factor of the low-valuation consumers is exactly zero and the distribution of consumer valuations is bounded from above. Pesendorfer (2002) considers a model similar to Sobel’s (1984) model in which the presence of consumers with high- and low-valuations leads prices to oscillate between two values. However, it is not clear that this motive for rigidity survives in a model with a continuous distribution of consumer types. The model also fails to generate an asymmetry in the flexibility of sale versus regular prices. Finally, the fixed ordering costs considered in Aguirregabiria (1999) lead to continual cyclical movements in prices since the shadow cost of store inventories is continually adjusting. The sticky upper bound in retail prices is an important feature for models of temporary sales to explain, since one of the most salient features of temporary sales is the tendency of prices to return to the original price following the sale. A fuller quantitative analysis of our model would evaluate its predictions for other features of the pricing distribution, such as the size of sale price changes and the fraction of time prices spend at the price cap. Rearranging equation (15) in the appendix yields a relationship between the habit parameter, the distribution of prices below the cap, the fraction of time spent at the price cap, and the price elasticity of demand that could be studied empirically.29 For example, a back-ofthe-envelope calculation suggests that a high value of the habit parameter is be required to rationalize the observed price rigidity if the distribution of desired prices is uniform, whereas a smaller value is required if the distribution is bimodal. Recent work suggests that a bimodel of distribution of desired prices could arise from a structural model of price discrimination (Guimaraes and Sheedy, 2011). This type of quantitative analysis is, however, beyond the scope of the present paper. 6. Concluding remarks In an environment in which consumers are partially locked-in to purchase particular goods, firms face a timeinconsistency problem when they set prices. They would like to promise low prices in the future. But when the future arrives they have an incentive to take advantage of the locked-in consumers and price gouge. Various forms of price rigidity arise as equilibrium outcomes in this environment. The reason equilibria involving price rigidity can be sustained is that price rigidity serves as a partial commitment device that helps firms overcome their desire to price gouge locked-in consumers. If firms have private information about their desired prices, the firm-preferred equilibrium involves the firm committing to set its price equal to or below a price cap. Our model, therefore, implies that prices should spend a significant portion of their time at a rigid upper bound. Below this upper bound, prices should be much more flexible. As is shown in Section 5, the behavior of retail prices bears a striking resemblance to this price cap policy. In contrast, the combination of a rigid regular price and frequent sales is difficult to explain within standard models in which price rigidity arises from menu costs alone. Our model also helps explain why firms fear adverse reactions to price changes, why sales prices are more flexible than regular prices and why firms make explicit promises not to change prices. The results derived are for the simple case in which the consumer cannot observe any of the variables that the firm would like to make its price depend on. If the consumer observes some such variables but not others, the variables that the consumer observes are state variables and the price cap would be a function of these variables. One interesting extension of the model is to consider a model incorporating small costs of coordinating on complex equilibria. Such a model might, in principle, yield simple pricing strategies (such as those with fixed prices) as equilibria even in the presence of common state variables.
Acknowledgments We would like to thank Alberto Alesina, Roc Armenter, Susanto Basu, Daniel Benjamin, Michael Katz, David Laibson, Greg Mankiw, Alice Nakamura, Ariel Pakes, Morten Ravn, Ricardo Reis, Kenneth Rogoff, Julio Rotemberg, Stephanie Schmitt-Grohe, Martin Uribe, Michael Woodford, anonymous referees and seminar participants at Harvard, Columbia, MIT and NYU for valuable comments and discussions. This research has been supported by the National Science Foundation Grant SES 0922011. Appendix A. Supplementary data Supplementary data associated with this article can be found in the online version at doi:10.1016/j.jmoneco.2011.06.004. 29
We thank an anonymous referee for suggesting this line of argument.
E. Nakamura, J. Steinsson / Journal of Monetary Economics 58 (2011) 220–233
233
References Abreu, D., Pearce, D., Stacchetti, E., 1990. Toward a theory of discounted repeated games with imperfect monitoring. Econometrica 58 (5), 1041–1063. Aguirregabiria, V., 1999. The dynamics of markups and inventories in retail firms. Review of Economic Studies 66, 275–308. Amirault, D., Kwan, C., Wilkinson, G., 2004. A survey of the price-setting behavior of Canadian companies. Bank of Canada Review Winter 2004–2005, 29–40. Apel, M., Friberg, R., Hallsten, K., 2005. Micro foundations of macroeconomic price adjustment: survey evidence from Swedish firms. Journal of Money, Credit and Banking 37 (2), 313–338. Athey, S., Atkeson, A., Kehoe, P.J., 2005. The optimal degree of discretion in monetary policy. Econometrica 73 (5), 1431–1475. Athey, S., Bagwell, K., 2008. Collusion with persistent cost shocks. Econometrica 76 (3), 493–540. Bagwell, K., 2004. Countercyclical pricing in customer markets. Economica 71 (284), 519–542. Benigno, P., Woodford, M., 2005. Inflation stabilization and welfare: the case of a distorted steady state. Journal of the European Economic Association 3, 1185–1236. Bils, M., 1989. Pricing in a customer market. Quarterly Journal of Economics 104 (4), 699–718. Bils, M., Klenow, P.J., 2004. Some evidence on the importance of sticky prices. Journal of Political Economy 112 (5), 947–985. Blinder, A.S., Canetti, E.R.D., Lebow, D.E., Rudd, J.B., 1998. Asking About Prices. Russell Sage Foundation, New York. Carlton, D.W., 1986. The rigidity of prices. American Economic Review 76, 637–658. Cason, T.N., Friedman, D., 2002. A laboratory study of customer markets. Advances in Economic Analysis and Policy 2 (1) Article 1. Chari, V., Kehoe, P.J., 1990. Sustainable plans. Journal of Political Economy 98 (4), 783–802. Chevalier, J.A., Kashyap, A.K., Rossi, P.E., 2003. Why don’t prices rise during peak demand periods? Evidence from scanner data. American Economic Review 93 (1), 15–37. Diamond, P.A., 1971. A model of price adjustment. Journal of Economic Theory 3, 156–168. Fabiani, S., Druant, M., Hernando, I., Kwapil, C., Landau, B., Loupias, C., Martins, F., Matha, T., Sabbatini, R., Stahl, H., Stokman, A., 2004. The pricing behavior of firms in the euro area: new survey evidence. In: Paper Presented at Conference on ‘‘Inflation Persistence in the Euro Area’’ at the European Central Bank. Farrell, J., Shapiro, C., 1989. Optimal contracts with lock-in. American Economic Review 79, 51–68. Fernandes, A., Phelan, C., 2000. A recursive formulation for repeated agency with history dependence. Journal of Economic Theory 91, 223–247. Guimaraes, B., Sheedy, K., 2011. Sales and monetary policy. American Economic Review 101, 844–876. Hall, R.E., 2005. Employment fluctuations with equilibrium wage stickiness. American Economic Review 95 (1), 50–65. Hall, S., Walsh, M., Yates, T., 1997. How do uk companies set prices? Bank of England Quarterly Bulletin, 180–192 Hart, O., Moore, J., 1999. Foundations of incomplete contracts. Review of Economic Studies 66 (1), 115–138. Heidhues, P., Koszegi, B., 2010. Regular prices and sales. Working paper, University of California at Berkeley. Hosken, D., Reiffen, D., 2004. Patterns of retail price variation. Rand Journal of Economics 35 (1), 128–146. Kahneman, D., Knetsch, J.L., Thaler, R., 1986. Fairness as a constraint on profit seeking: entitlements in the market. American Economic Review 76 (4), 728–741. Kehoe, P., Midrigan, V., 2010. Prices are sticky after all. Working paper, New York University. Klemperer, P., 1995. Competition when consumers have switching costs: an overview with applications to industrial organization, macroeconomics, and international trade. Review of Economic Studies 62, 515–539. Kleshchelski, I., Vincent, N., 2009. Market share and price rigidity. Journal of Monetary Economics 56, 344–352. Levy, D., Lee, D., Chen, H., Kauffman, R.J., Bergen, M., 2005. Making sense of ignoring cents: price points and price rigidity under rational inattention. Working paper, Bal-Ilan University. L’Huillier, J.-P., 2010. Consumer’ imperfect information and nominal rigidities. Working paper, Einaudi Institute for Economics and Finance. MacLeod, W.B., Malcomson, J.M., 1993. Investments, holdup, and the form of market contracts. American Economic Review 83 (4), 811–837. Maskin, E., Tirole, J., 2001. Markov perfect equilibrium. Journal of Economic Theory 100, 191–219. Nakamura, E., Steinsson, J., 2008. Five facts about prices: a reevaluation of menu cost models. Quarterly Journal of Economics 123 (4), 961–1013. Okun, A.M., 1981. Prices and Quantities: A Macroeconomic Analysis. Brookings Institution, Washington, DC. Pesendorfer, M., 2002. Retail sales: a study of pricing behavior in supermarkets. Journal of Business 75 (1), 33–66. Phelps, E.S., Winter, S.G., 1970. Optimal price policy under atomistic competition. In: Phelps, E.S. (Ed.), Microeconomic Foundations of Employment and Inflation Theory. W.W. Norton, New York. Ravn, M., Schmitt-Grohe´, S., Uribe, M., 2006. Deep habits. Review of Economic Studies 73 (1), 195–218. Renner, E., Tyran, J.-R., 2004. Price rigidity in customer markets: an empirical study. Journal of Economic Behavior and Organization 55 (4), 575–593. Rotemberg, J.J., 2005. Customer anger at price increases, changes in the frequency of price changes and monetary policy. Journal of Monetary Economics 52 (4), 829–852. Rotemberg, J.J. Fair pricing. Journal of the European Economic Association, forthcoming. hhttp://www.people.hbs.edu/jrotemberg/workcurr/fairpri6b.pdfi. Rotemberg, J.J., Woodford, M., 1991. Markups and the business cycle. In: Blanchard, O.J., Fischer, S. (Eds.), NBER Macroeconomics Annual. MIT Press, Cambridge, Mass. Rotemberg, J.J., Woodford, M., 1995. Oligopolistic pricing and the effects of aggregate demand on economic activity. In: Cooley, T.F. (Ed.), Frontiers of Business Cycle Research. Princeton University Press, Princeton, NJ. Schmitt-Grohe, S., Uribe, M., 2007. Why the monopolist does not deviate from the symmetric equilibrium in a model with good-specific subsistence points. Working paper. Shapiro, C., Varian, H.R., 1999. Information Rules. Harvard Business School Press, Boston, MA. Small, I., Yates, T., 1999. What makes prices sticky? Some survey evidence for the United Kingdom. Bank of England Quarterly Bulletin, 262–271. Sobel, J., 1984. The timing of sales. Review of Economic Studies 51, 353–368. Soderberg, J. Customer markets and the welfare effects of monetary policy. Journal of Monetary Economics, forthcoming. hhttp://www.nek.uu.se/ StaffPages/Publ/P1437.pdfi. Varian, H.R., 1980. A model of sales. American Economic Review 70, 651–659. Woodford, M., 2003. Interest and Prices. Princeton University Press, Princeton, NJ. Zbaracki, M.J., Ritson, M., Levy, D., Dutta, S., Bergin, M., 2004. Managerial and customer costs of price adjustment: direct evidence from industry markets. Review of Economics and Statistics 86 (2), 514–533.
Journal of Monetary Economics 58 (2011) 234–247
Contents lists available at ScienceDirect
Journal of Monetary Economics journal homepage: www.elsevier.com/locate/jme
Dynamic monetary–fiscal interactions and the role of monetary conservatism Stefan Niemann Department of Economics, University of Essex, Wivenhoe Park, Colchester CO4 3SQ, Essex, United Kingdom
a r t i c l e in f o
abstract
Article history: Received 28 April 2009 Received in revised form 27 March 2011 Accepted 30 March 2011 Available online 12 April 2011
Assuming that macroeconomic policies are directed by distinct monetary and fiscal policy makers who cannot commit to future actions, we reassess the implications of monetary conservatism and fiscal impatience in a setting with nominal government debt. For environments where a non-negative steady state level of government debt (assets) emerges in the absence of conservatism and impatience, monetary conservatism induces accumulation of a higher stock of liabilities (assets) and has adverse (positive) welfare implications. This result obtains irrespectively of the degree of fiscal impatience and questions the unambiguous desirability of monetary conservatism traditionally found in the literature. & 2011 Elsevier B.V. All rights reserved.
1. Introduction In the context of monetary time-consistency problems, the implications of central bank inflation aversion (‘conservatism’) have been extensively studied. The predominant view is that delegation to a weight-conservative central banker has positive welfare effects (Rogoff, 1985; Adam and Billi, 2008, 2010). However, it has not yet been investigated whether central bank conservatism remains desirable in an environment with endogenous fiscal policy and an explicit role for the dynamics of government debt. The present paper examines this question within the deterministic framework of a flexible price economy with nominal government debt. The model assumes that macroeconomic policies are implemented sequentially and without intertemporal commitment. In contrast to most of the existing literature, however, it presumes that monetary and fiscal instruments are directed by separate policy authorities whose objectives may not be perfectly aligned. This is in line with the institutional setup in most developed economies, where monetary and fiscal policies are determined by independent policy authorities with their own respective mandates. The model allows for two deviations from the purely benevolent benchmark where both policy authorities share the representative household’s objective function. In particular, it considers ‘fiscal myopia’ and ‘monetary conservatism’. Monetary conservatism is modelled in terms of an explicitly inflation-averse central bank a la Rogoff (1985). Fiscal myopia is modelled by assuming that the fiscal authority discounts the future at a higher rate and fails to fully internalize the consequences of current profligacy. While fiscal myopia is taken as a given primitive of the model, it is important to recognize that such myopia can arise endogenously in a politico-economic context (electoral concerns among politicians, fiscal institutions which disperse decision power over public expenditures, etc.). The present paper’s focus is on the implications of such fiscal myopia for the interaction with monetary policy and the desirability of monetary conservatism.
Tel.: þ44 1206 87 3351; fax: þ44 1206 87 2724.
E-mail address:
[email protected] 0304-3932/$ - see front matter & 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.jmoneco.2011.03.008
S. Niemann / Journal of Monetary Economics 58 (2011) 234–247
235
In the face of their diverging objectives, monetary and fiscal policies are chosen in a non-cooperative fashion. Since it is possible to issue government debt, the ensuing monetary-fiscal interaction is dynamic, with the level of real debt taking the role of an endogenous state variable. Under the maintained assumption of no commitment, attention is restricted to Markov-perfect equilibria. Hence, at any point of time, monetary and fiscal policy choices may depend on the past only via the inherited endogenous state variable. The mechanics of the intertemporal government budget constraint require that the stock of government debt must be covered by future revenues; such revenues can only be generated by distortionary activity. Therefore, outstanding liabilities have adverse welfare effects.1 Taking the stock of inherited debt as given, the current authorities choose their respective policies such as to balance current and future distortions (as perceived by them). This, in turn, introduces a motive for manipulating the future state of the economy and thus the policies implemented by future authorities. Our analysis investigates the role of fiscal myopia and monetary conservatism as determinants of the economy’s steady state and the associated welfare implications. The central findings are as follows. The policies implemented in the Markovperfect equilibrium by the monetary and fiscal authority, respectively, can be characterized by two distinct generalized Euler equations (Klein et al., 2008). Accordingly, the steady state level of real debt must balance both authorities’ accumulation and decumulation incentives. In the special case where both authorities pursue the same purely benevolent objective, the Markov-perfect equilibrium allocation coincides with the one implemented by a single benevolent authority. In this case, steady state debt is positive (negative) when the agents’ elasticity of intertemporal substitution is smaller (larger) than one. Starting from a benevolent benchmark with non-negative steady state debt, the introduction of monetary conservatism and/or fiscal impatience makes the two authorities pursue non-aligned objectives and generally leads to higher steady state debt. By contrast, starting from a benchmark with government assets, the same perturbation works to augment the government’s asset position against the private sector. Both endogenous fiscal policy and monetary conservatism are needed to generate these results. However, the effects of monetary conservatism unfold independently of fiscal impatience; and fiscal impatience can amplify or contain the implications of monetary conservatism for the accumulation of debt. The key mechanism behind these findings is the interaction of the monetary time-consistency problem with the consolidated government budget constraint, which implies that the steady state level of debt is endogenous with respect to the degree of monetary conservatism. Specifically, increased monetary conservatism induces an increase in debt but has ambiguous effects on inflation. The direct effect of increased conservatism is that any given level of real liabilities can be sustained at a lower rate of inflation. However, since this is internalized, the indirect effect is that the Markov-perfect equilibrium generates a steady state with higher indebtedness. Consequently, the welfare gains during the transition to the steady state must be weighed against the costs of inducing a steady state with higher accumulation of real liabilities (assets). For a calibrated economy, the indirect effect dominates such that increased monetary conservatism has adverse (positive) welfare implications if the elasticity of intertemporal substitution is smaller (larger) than one. This is in contrast to findings in the previous literature, which neglects the endogeneity of government debt. The dynamic inconsistency of optimal plans is a pervasive phenomenon in models of macroeconomic policy making (Kydland and Prescott, 1977). The literature has investigated a number of potential solutions to address the distortions caused by the lack of monetary commitment (Rogoff, 1985; Walsh, 1995; Svensson, 1997). However, all these approaches abstract from fiscal policy or take it as exogenously given. On the other hand, there is a growing literature analyzing timeconsistent fiscal policies in dynamic general equilibrium models without money (Chari and Kehoe, 1990; Klein et al., 2008; Ortigueira and Pereira, 2009). Given that the intertemporal government budget constraint is an important source of monetary–fiscal interactions (Sargent and Wallace, 1981; Lucas and Stokey, 1983; Leeper, 1991), this dichotomy in the analysis of the monetary and fiscal aspects of macroeconomic time-consistency problems is a shortcoming. Only recently, a number of papers have investigated optimal time-consistent policies in settings with a meaningful role for both monetary and fiscal instruments (Dı´az-Gime´nez et al., 2008; Martin, 2009; Niemann et al., 2008). However, these papers proceed under the assumption of a single policy authority deciding about the complete set of monetary and fiscal policy instruments. Hence, they provide only little information on the strategic interaction between monetary and fiscal policy makers in general and the role of monetary conservatism in particular. The work by Adam and Billi (2008, 2010), who consider separate policy authorities, constitutes a notable exception. Specifically, they find that monetary conservatism can help to eliminate the inflation and spending biases arising from monetary and fiscal commitment problems. However, their analysis is cast in terms of a stabilization problem in the spirit of Barro and Gordon (1983) and invokes either lump-sum taxes or alternatively a periodically balanced budget. By contrast, in allowing for endogenous fiscal policy with non-balanced budgets, the present paper advises caution with respect to the welfare implications of monetary conservatism derived by Adam and Billi (2008, 2010) as well as the earlier literature which abstracts from fiscal policy altogether. The rest of the paper is organized as follows. The next section sets up the model economy and introduces the objectives pursued by fiscal and monetary policy makers. Section 3 lays out the structure of the policy game and defines an
1 Since the economy under consideration is deterministic, there is no role for stabilization policies in general, or for debt as a shock absorber in particular.
236
S. Niemann / Journal of Monetary Economics 58 (2011) 234–247
equilibrium in time-consistent policies. Section 4 first characterizes the equilibrium outcomes analytically and then presents key results from quantitative experiments for a calibrated economy. Finally, Section 5 concludes.2 2. The model We consider a dynamic monetary general equilibrium economy whose basic structure is identical to the one in Dı´azGime´nez et al. (2008). The economy is made up of a private sector and a government. There is no capital, and in each period labor nt can be transformed into private consumption ct or public consumption gt at a constant, unitary rate. Consequently, in each period t Z 0 aggregate feasibility is reflected by the following linear resource constraint: ct þ gt r nt :
ð1Þ
The economy is inhabited by a continuum of measure one of identical, infinitely lived households whose preferences over sequences of consumption ct and labor nt can be represented by the following additively separable expression: 1 X
bt fuðct Þvðnt Þg,
ð2Þ
t¼0
where the discount factor b satisfies 0 o b o1. Government expenditure gt yields no utility.3 In each period t, each household faces the following budget constraint: Mt þ 1 þBt þ 1 rMt Pt ð1þ tct Þct þ Bt ð1 þ Rt Þ þ Wt nt ,
ð3Þ
where Pt and Wt are the price level and the nominal wage prevailing at time t; Bt þ 1 and Mt þ 1 are nominal government debt and nominal money balances carried from period t to period t þ1; Rt is the nominal interest rate on government debt held from period t 1 to period t. A demand for money arises due to the assumption that the gross-of-tax consumption expenditure in period t must be financed using currency carried over from period t 1. This gives rise to the following cash-in-advance constraint: Mt Z Pt ð1þ tct Þct :
ð4Þ
The timing protocol underlying this cash constraint follows Svensson (1985) and implies that the goods market operates and closes before the asset market opens. Consequently, household purchases of goods have to be undertaken before nominal balances can be reshuffled optimally. Hence, the effects of inflationary money expansions are twofold: First, expected inflation leads to a distortion via its effect on the nominal interest rate. Second, surprise inflation is distortionary since the households are constrained in their consumption decisions by the value of the money balances taken over from the previous period. Finally, each consumer faces a no-Ponzi condition that prevents him from running explosive consumption/debt schemes: lim b
T
T-1
BT þ 1 Z 0: PT
The government sector consists of a monetary authority and a fiscal authority who take their decisions independently. a The policy instrument controlled by the monetary authority is the supply of money Mt þ 1. (Throughout, the superscript a is used to distinguish an aggregate variable from an individual variable.) The fiscal authority collects consumption taxes tct in order to finance an exogenously given stream of public expenditures gt. For simplicity, public spending is deterministic and constant over time such that gt ¼g for all t Z0. The two authorities interact via the consolidated budget constraint of the government sector. Seignorage revenues from money creation by the monetary authority accrue to the consolidated government budget. Thus, our focus is on the public finance role of monetary policy and the implications of decentralized decision power among the two independent authorities. Finally, it is assumed that the fiscal authority, besides its tax a policy, issues nominal one-period bonds Bt þ 1, whereby the quantity of bonds issued must satisfy the following sequence of budget constraints for the government sector for all t Z 0: Mtaþ 1 þBatþ 1 þPt tct ct ZMta þBat ð1 þRt Þ þ Pt g:
ð5Þ
Moreover, the consolidated government sector faces the following no-Ponzi condition: lim b
T-1
T
BaT þ 1 r 0: PT a
A government policy is represented by a sequence ftct ,Mtaþ 1 ,Batþ 1 g1 t ¼ 0 , whereby the initial stock of money M0 and the initial a debt liabilities B0(1 þ R0) are given. Given the government policy, the private sector equilibrium is determined via the government budget constraint (5), the aggregate resource constraint (1) and the following conditions that must hold 2 3
Technical details and derivations are relegated to a supplementary web-appendix. Since gt is exogenous, it could also enter the utility function in an additively separable fashion without changing results.
S. Niemann / Journal of Monetary Economics 58 (2011) 234–247
237
for all t Z04: Mt ¼ Pt ð1þ tct Þct ,
ð6Þ
u0 ðct Þ ¼ ð1þ Rt Þð1þ tct Þ, v0 ðnt Þ
ð7Þ
ð1 þ Rt þ 1 Þ ¼
v0 ðnt Þ
Pt þ 1
bv0 ðnt þ 1 Þ Pt
:
ð8Þ
2.1. Fiscal authority The fiscal authority is assumed to be myopic, which encompasses two aspects. First, the fiscal authority is impatient insofar as it evaluates the sequence of the household’s period utilities with a discount factor d r b. The second important implication of fiscal myopia is the failure to internalize the systematic response of future policies to variations in the future state of the economy. The fiscal objective function is 1 X
dt fuðct Þvðnt Þg:
ð9Þ
t¼0
This payoff function is a shortcut for introducing politico-economic frictions into the model; examples include electoral concerns, dynamic common pool problems or fiscal institutions which disperse the decision power over debt and deficits. Notice that a rationale for fiscal myopia can be explicitly derived in a politico-economic context.5 For the purposes of this paper, though, fiscal myopia is simply taken as a primitive of the model. A divergence in the discount factors of the form d o b then reflects the systematic tendency towards policy choices that shift distortions into the future. Moreover, since a myopic fiscal authority fails to take into account the effects of its current choices on future policy makers’ decisions, it does not recognize the true dimension of such future distortions. 2.2. Monetary authority As regards the monetary authority, our starting point are the statutes of many independent central banks which ascribe importance to the task of stabilizing the inflation rate pt ¼ Pt =Pt1 1 at a low level, but at the same time also refer to further indicators for general economic performance. This is parameterized by defining the monetary authority’s objective function as follows: 1 X
bt fgðpt p~ Þ2 þ ð1gÞ½uðct Þvðnt Þg,
ð10Þ
t¼0
where p~ is an exogenously given inflation target and g 2 ½0,1Þ is a weight which balances the relative impacts on the monetary authority’s payoff of the inflationary loss term and general welfare (as measured by the representative household’s lifetime utility). Hence, the specification in (10) introduces a weight-conservative central banker (Rogoff, 1985), where g measures the degree of monetary conservatism. 3. Equilibrium We presume that the authorities’ policy choices are the outcome of a dynamic game between the monetary and the fiscal authority in which they do not have access to an intertemporal commitment technology. Hence, implemented policies must be sequentially optimal. Our interest here is in time-consistent policy rules, and the analysis is limited to (differentiable) Markov-stationary policy rules mapping the current aggregate state, zat Bat ð1 þRt Þ=Mta , into policy choices. Switching to recursive notation, fiscal policy in each period is denoted by a function jf ðza Þ that delivers the current tax rate tc 4 1 as a function of the aggregate state za. Similarly, monetary policy is described by a function jm ðza Þ that delivers the current rate of money growth m ðM a 0 =M a Þ14 1 as a function of the aggregate state za. To summarize: za ¼
Ba ð1þ RÞ , Ma
tc ¼ jf ðza Þ, m ¼ jm ðza Þ:
4 The cash constraint (4) is binding whenever Rt 40. Furthermore, the private sector equilibrium must obey the following transversality condition: T limT-1 b ððMT þ 1 þ BT þ 1 Þ=PT Þ ¼ 0. 5 For example, Malley et al. (2007) argue that fiscal incumbents with uncertain prospects of reelection find it optimal to follow shortsighted fiscal policies. Using U.S. data from 1947 to 2004, they find a statistically and economically significant link between electoral uncertainty and macroeconomic policy outcomes, whereby the mechanism at work is that increased electoral uncertainty maps into decreased discount factors. See Persson and Tabellini (2000) for a discussion of other politico-economic mechanisms shaping the conduct of fiscal policy.
238
S. Niemann / Journal of Monetary Economics 58 (2011) 234–247
At each point in time, the two authorities choose their current policy instruments simultaneously. Following Klein et al. (2005), the model’s Markov-perfect equilibrium (MPE) is solved for in three steps. The first step computes the private sector equilibrium for given arbitrary policy rules. The second step determines the optimal equilibrium policy instruments tc and m for the current period when future policies are determined by arbitrary rules; that is, it solves for the optimal current rules given future rules. Finally, the time-consistent equilibrium is obtained by the requirement that the current optimal rules must coincide with the future rules (policy fixed point).6 A MPE of the policy game is a profile of timeconsistent Markov strategies for the two authorities that yields a Nash equilibrium at every point in time. It is these timeconsistent policies jðza Þ ¼ fjf ðza Þ, jm ðza Þg and the associated equilibrium outcomes that we are interested in. 4. Equilibrium outcomes In what follows, we assume uðcÞ ¼ ðc1s 1Þ=ð1sÞ and vðnÞ ¼ an. Based on this specification, the economy’s aggregate resource constraint (1) and the competitive equilibrium conditions (6) to (8) can be used to substitute in the government budget constraint (5) to obtain two distinct implementability constraints faced by the fiscal and monetary authority, respectively. The authorities’ policy problems can then be reformulated in terms of the primal choice variables c and z0 .7 Accordingly, the current fiscal authority’s problem is 1s f c 1 aðc þ gÞ þ dV f ðz0 ; jÞ V^ ðz; m, jÞ ¼ max c,z0 1s b b z g ¼ 0 , ð11Þ s:t: cðz0 Þ1s þ bz0 ð1 þ tc ðz0 ÞÞcðz0 Þc cðz0 Þ1s ð1 þ mðzÞÞ a a whereby the fiscal authority’s myopia implies that it fails to recognize the dependence of m on z. Similarly, the current monetary authority’s problem becomes: 8 !2 1s b s < m c 1 ac ~ ð1 þ g p Þ þ ð1gÞ aðc þ gÞ þ bV m ðz0 ; jÞ V^ ðz; tc , jÞ ¼ max c 0 c,z : 1s ð1 þ t ðzÞÞ b s:t: cðz0 Þ1s þ bz0 ð1 þ tc ðz0 ÞÞcðz0 Þczð1þ tc ðzÞÞcg ¼ 0 , ð12Þ
a
where the expression ðb=aÞcs =ð1þ tc ðzÞÞ in the inflationary loss term denotes gross inflation ð1 þ pÞ in the current period. 4.1. Generalized Euler equations Concentrating on differentiable Markov-stationary policy rules, the first order conditions with respect to the primal choice variables c and z0 can be condensed into two distinct generalized Euler equations (GEEs) for the interacting authorities. These GEEs, together with the respective implementability constraints in (11) and (12), are necessary f conditions characterizing any differentiable MPE.8 Let l ¼ ðcs aÞ denote the marginal utility from increased consumption as perceived by the fiscal authority (and private households). Moreover, let ex ðz0 Þ ¼ ð@xðz0 Þ=@z0 Þ=ðxðz0 Þ=z0 Þ denote the elasticity of a generic variable xðz0 Þ in response to a change in the future aggregate state z0 . The GEE for the myopic fiscal authority then reads: cðz0 Þs z d f 0 1 ¼ lf 1 þ eð1 þ tc Þ ðz0 Þ þ ec ðz0 Þ 1 þ ð1sÞ 0 ð13Þ l , ð1 þ mðzÞÞ az ð1þ tc ðz0 ÞÞ b where
Gf ðz,z0 Þ 1 þ eð1 þ tc Þ ðz0 Þ þ ec ðz0 Þ 1 þð1sÞ
cðz0 Þs z 1 : ð1 þ mðzÞÞ az0 ð1 þ tc ðz0 ÞÞ
Eq. (13) indicates that the fiscal authority seeks to equate marginal utilities over time, but subject to two frictions. First, due to the fiscal authority’s relative impatience, the future marginal utility is discounted by the factor d=b r 1. Second, the term Gf ðz,z0 Þ captures the additional costs of current consumption due to future policy makers’ commitment problem and the associated private sector anticipation effects. These extra costs can be traced back to the implementability constraint in (11): Higher current consumption c leads to increased accumulation of future debt z0 and thus affects the authorities’ continuation play jðz0 Þ. This is internalized by the private sector and reduces its willingness to carry debt and money into the next period. Importantly, this mechanism is taken into account even by a myopic policy authority; this is because private agents’ foresight feeds into intertemporal prices and thus constrains current policy choices via the implementability constraint. 6
Supplementary web-appendix A provides further details on each of these steps and formally defines the equilibrium in time-consistent policy rules. In a symmetric private sector equilibrium individual variables correspond to economy-wide aggregates (z ¼za); hence, in what follows, the superscript a for the aggregate state is dropped. 8 The GEEs are formally derived in supplementary web-appendix B. 7
S. Niemann / Journal of Monetary Economics 58 (2011) 234–247
239
f
Recall that l ¼ ðcs aÞ is the marginal utility from increased consumption. From the monetary authority’s perspective, m f the corresponding expression is l ¼ ðgwm þ ð1gÞl Þ=½1 þ zð1þ tc ðzÞÞ, where
wm 2s
b s c
a
c ðzÞÞ
ð1þ t
! ð1þ p~ Þ
b s1 c
a
ð1 þ tc ðzÞÞ m
denotes the marginal effect of increased consumption on the deviation of inflation from the target p~ . Accordingly, l , which governs the monetary authority’s assessment of a marginal increase of consumption, involves three components. f The numerator is a weighted sum of l , the direct effect via current household utility, and wm ; the latter captures the fact that, given some fiscal policy, higher consumption necessitates lower inflation and hence affects the inflationary loss term. These benefits from increased consumption are weighted according to g and discounted by the denominator, which is larger (smaller) than one for z 4 0 (z o0). The GEE for the monetary authority, which takes these considerations into account, reads: 2 0 13 1 1 ðwm Þ0 g 1þ 0 0 s s c 0 B C7 cðz Þ z ð1 þ t ðz ÞÞ m 6 0 B C7: ¼ ðl Þ0 6 ð14Þ lm 1 þ eð1 þ tc Þ ðz0 Þ þ ec ðz0 Þ 1 þð1sÞ 0 41 þ eð1 þ tc Þ ðz Þ@1 A5 az ð1 þ tc ðz0 ÞÞ gðwm Þ0 þ ð1gÞðlf Þ0 Again, the GEE has an interpretation in terms of intertemporal equalization of marginal utilities subject to distortions. m As in the fiscal GEE (13), the cofactor for l on the LHS captures the additional costs of current consumption due to expectational effects in the face of future policy makers’ commitment problem; as explained above, these additional costs are consumption distortions due to increased nominal interest rates. On the RHS, an additional term appears, which was not present for the myopic fiscal authority. It reflects an anticipation effect that works independently from private sector expectations, namely the monetary authority’s internalization of the systematic response of future policies to variations in the future aggregate state z0 .9
4.2. Steady state It is useful to begin the discussion of steady states by drawing on a benchmark result established in Dı´az-Gime´nez et al. (2008) for the case of a monetary policy maker who does not interact with a separate fiscal authority. These authors study MPE and explain the steady state level of debt by two effects. On the one hand, nominal debt is a source of timeinconsistency in that a sequential policy maker faces an incentive to inflate when debt is positive or to deflate when debt is negative (i.e., when the government holds claims against the private sector); this is the nominal debt effect. On the other hand, the intertemporal elasticity effect dictates that, if the elasticity of intertemporal substitution is higher than one (s o1), then a sequentially optimal policy should tax current consumption more than future consumption. Conversely, if the elasticity of intertemporal substitution is lower than one (s 4 1), future consumption should be taxed more heavily.10 Depending on s and the current level of debt z, the two effects can tend to reinforce or offset each other. A steady state emerges at the level of debt that balances the potentially conflicting incentives until the policy maker does not benefit from manipulating the allocation any further.
4.2.1. Unperturbed game The following proposition extends the results from Dı´az-Gime´nez et al. (2008) to the case of interacting policy makers. It establishes that decentralized decision power among interacting policy makers per se does not change the nature of MPE outcomes and formalizes the importance of the elasticity of intertemporal substitution, 1=s, for shaping them. Proposition 1. Suppose s o 1=ð1bÞ. For d ¼ b and g ¼ 0, there are two steady states in differentiable policy rules. Consumption and real debt at these steady states are identical to the steady state allocations implemented under a single monetary authority and can be characterized as follows: c1 ðz1 Þs
a
¼ 1,
z1 ¼ 1
g o1: ð1bÞc1 ðz1 Þ
9 A final important aspect embodied in (14) is the term gð1=sÞð1 þ 1=z0 ð1 þ tc ðz0 ÞÞÞðwm Þ0 . Inspection of this term reveals that the monetary authority evaluates future deviations of inflation from the target p~ with an endogenous weight. The endogenous component, ð1 þ 1=z0 ð1 þ tc ðz0 ÞÞÞ, is decreasing in z0 ð1 þ tc ðz0 ÞÞ, which indicates that an increased fiscal burden induces the monetary authority to increasingly compromise its inflation target. 10 For s ¼ 1, when the elasticity of intertemporal substitution coincides with the elasticity implicit in the household’s cash constraint, the intertemporal elasticity effect vanishes. See Nicolini (1998) for further details.
240
S. Niemann / Journal of Monetary Economics 58 (2011) 234–247
At z1 , the government sector’s net assets are sufficient to finance expenditures, and the allocation is undistorted; this is an isolated steady state. c2 ðz2 Þ1s
a At
z2 ,
½1ð1bÞs ¼ c2 ðz2 Þ þ g,
z2 ¼ ð1sÞ
c2 ðz2 Þs : að1 þ tc ðz2 ÞÞ
the allocation is distorted; z2 4 0 ( o 0) if s 4 1 ( o 1); and the elasticities of taxes and money growth are 1
1
b
b
eð1 þ tc Þ ðz2 Þ ¼ ð1sÞ ec ðz2 Þ, eð1 þ mÞ ðz2 Þ ¼ ½1ð1bÞs ec ðz2 Þ, where ec ðz2 Þ o0ð 4 0Þ if s 41ð o1Þ. In the neighborhood of z2 , if s 41, taxes and money growth are increasing in z; if s o 1, taxes are decreasing and money growth is increasing in z. The steady state allocations ðz ð1 þ tc ðz ÞÞ,cðz ÞÞ for the unperturbed game (d ¼ b, g ¼ 0), where both authorities share the same benevolent objective function, coincide with the steady state outcomes when there is a monolithic authority deciding about both fiscal and monetary policies.11 Indeed, it is immediate that a MPE for the single-authority economy also constitutes a MPE with interacting authorities. This is because an optimal policy outcome under single-authority must have been decentralized by strategies for the fiscal and monetary policy instruments which are mutual best responses. If this was not the case, there would be an incentive to revise the policies. 4.2.2. Perturbed game Turning to the steady state outcomes of the perturbed game (d r b, 0 r g o 1), the following proposition highlights the role of the institutional parameters d, p~ and g as well as the importance of endogenous fiscal policy implemented by a separate authority. Proposition 2. Let the absence of endogenous fiscal policy be defined in terms of a (globally) constant tax rate, tc ðzÞ ¼ t c , such that eð1 þ tc Þ ðzÞ ¼ 0 for all z. (i) Absent endogenous fiscal policy, the pair ðz1 ,cðz1 ÞÞ is a steady state provided taxes are consistent with the inflation target: t c ¼ bð1=ð1 þ p~ ÞÞ1. The pair ðz2 ,cðz2 ÞÞ is a steady state irrespective of the specification of the parameters d, g and p~ . (ii) Under endogenous fiscal policy, for d r b and g ¼ 0, both the pair ðz1 ,cðz1 ÞÞ and the pair ðz2 ,cðz2 ÞÞ are steady states. At z2 , the elasticities of taxes and money growth are 1 bd 1 bd eð1 þ tc Þ ðz2 Þ ¼ ð1sÞ ec ðz2 Þ , eð1 þ mÞ ðz2 Þ ¼ ½1ð1bÞs ec ðz2 Þ þ :
b
b
b
b
(iii) Under endogenous fiscal policy, for d r b, g 2 ð0,1Þ and some given inflation target p~ , the pair ðz1 ,cðz1 ÞÞ is a steady state. By contrast, the pair ðz2 ,cðz2 ÞÞ is only a steady state if d ¼ b and s ¼ 1. The first part of Proposition 2 reveals that endogenous fiscal policy is critical for engineering a deviation from the unperturbed benchmark described in Proposition 1. In particular, absent endogenous fiscal policy monetary institutions are irrelevant for the determination of steady state outcomes. This is because monetary expansions are the only variable instrument to generate government revenue. There is no substitutability between m and tc , and therefore the magnitude of the nominal debt effect described above is not affected by p~ or g. By contrast, under endogenous fiscal policy a given allocation can be implemented via multiple combinations of m and tc . As a consequence, monetary conservatism affects the monetary authority’s trade-off of whether to inflate the economy or not. Specifically, for g 4 0, an inflation target of p~ ¼ 0 means that the nominal debt effect is less pronounced. For z 4 0 (z o 0), this implies that the intertemporal elasticity effect is met by a smaller incentive to generate surprise inflation (deflation). Hence, at z2 the intertemporal elasticity effect dominates the nominal debt effect. Instead, if s 41 (s o1), the two effects will be balanced at a steady state with a higher level of government debt (assets). Finally, for s ¼ 1, the intertemporal elasticity effect vanishes, and there continues to be a steady state at z2 , provided d ¼ b. However, with fiscal impatience (d o b), the steady state at z2 is eliminated even for s ¼ 1 because of the fiscal authority’s desire to increase current consumption at the expense of accumulating debt. Unlike this last result, however, the second part of Proposition 2 reveals that the steady states from the unperturbed benchmark remain intact even with fiscal impatience (d o b) as long as g ¼ 0. Accordingly, a purely benevolent monetary authority can fully control the economy’s steady state allocation ðz2 ,cðz2 ÞÞ; fiscal institutions pin down only the extent to which monetary and fiscal instruments respond to variations of real debt around the steady state. But for g 2 ð0,1Þ the monetary authority has preferences over how to decentralize a given allocation via the available policy instruments. Due to its aversion to use the inflation tax to control the level of real debt z, there is then scope for the fiscal policy maker to shift tax distortions into the future by accumulating public debt. 11
In both cases, taxes and interest rates are individually indeterminate, but z^ ¼ z ð1 þ tc ðz ÞÞ is determinate.
S. Niemann / Journal of Monetary Economics 58 (2011) 234–247
241
In summary, under endogenous fiscal policy and monetary conservatism, fiscal and monetary institutions jointly determine the economy’s steady state. Since the undistorted steady state at z1 is isolated, the subsequent analysis will concentrate on the steady state of the perturbed game that replaces the distorted steady state at z2 . A distorted allocation is characterized in terms of a marginal utility from consumption which exceeds the marginal disutility from labor effort f (l 4 0). In such a situation, government expenditures and debt service need to be financed via taxation or seignorage. This implies that private consumption is crowded out by government debt such that the function c(z) is decreasing, and outstanding government liabilities have adverse welfare implications. f Formally, given that l 40 and c(z) decreasing, (13) reveals that the fiscal authority prefers to accumulate debt as long as Gf ðz,zÞ 4 d=b. On the other hand, the same argument implies that there is a limit to the economy’s tendency to accumulate debt. Indeed, for Gf ðz,zÞ o d=b the fiscal GEE (13) dictates decumulation of debt. The model’s long-run prediction therefore is that the economy converges to a stationary level of debt z implicitly characterized by Gf ðz ,z Þ ¼ d=b. Similarly, according to the monetary GEE (14), it must be the case that, at z , the marginal losses incurred due to inflation and the marginal benefits from stabilizing the level of debt by monetizing fiscal deficits via the inflation tax are equal from the monetary authority’s perspective. In other words, the steady state level z of public liabilities must be such that the motives for debt accumulation and decumulation exactly balance each other from both authorities’ perspectives. 4.3. Calibration We now parameterize the model in order to assess its quantitative implications. The elasticity of intertemporal substitution is initially fixed at s ¼ 1. This allows to concentrate on the role of nominal debt as a source of timeinconsistency and to abstract from the additional effects due to seignorage on the private holdings of nominal money balances (Nicolini, 1998). This focus is consistent with the situation in most developed economies where government debt is arguably more important than money holdings as a source of dynamically inconsistent incentives. The period length is set to be a year. For the U.S., the average annualized nominal interest rate for three-year constant maturity Treasury Bills during 1962–2006 was 6.7%.12 Annual inflation (based on the consumption deflator) over the same period averaged at 3.9%. By the Fisher equation (8), these two statistics imply an average real interest rate of 2.8%, consistent with a household discount factor of b ¼ 0:97. The fraction of time devoted to labor is set to 0.3. Accordingly, from (1), GDP is c þg ¼n¼ 0.3. Average government outlays over 1962–2006 amounted to 20.4% of GDP. This implies a value of g ¼0.0612. Federal revenue (which does not include loans or seignorage) over the sample period amounted to a fraction of 18.2% of GDP on average; this is consistent with a tax rate of tc ¼ 22:9%. From (7), one can then infer a ¼ 3:19. Given the normative nature of our analysis, the institutional parameters d, g and p~ are not calibrated. Instead, the focus is on investigating the implications of the following parameter variations. We allow d to vary in the set {0.97, 0.965, 0.96}, thus encompassing the case without fiscal impatience as well as scenarios where the fiscal authority discounts the future at an annual rate of 3.6% or 4.2%, respectively (compared to the real interest rate of 2.8%). Similarly, apart from the benchmark where g ¼ 0, results are reported for variations of the degree of monetary conservatism in the set {0.9, 0.7, 0.5}. This focus on relatively large values is motivated by findings in Adam and Billi (2008) according to which the welfare losses due to lack of commitment are basically eliminated if the monetary authority is sufficiently conservative (corresponding to a weight g close to but slightly below one). Finally, the inflation target is initially fixed at p~ ¼ 0. 4.4. Comparative statics This section examines the quantitative implications of parameter changes for the properties of MPE outcomes. The parameter s plays a crucial role in shaping MPE policy choices, reflecting the interaction of the nominal debt effect and the intertemporal elasticity effect discussed above. It is therefore convenient to distinguish three cases: s ¼ 1, s 4 1 and s o 1. 4.4.1. Unitary elasticity of intertemporal substitution Starting with the case of s ¼ 1, Table 1 presents steady state outcomes for both the unperturbed benchmark (first row) and the perturbed game discussed in Propositions 1 and 2, respectively. Consistent with Proposition 2, if s ¼ 1, variations in g are inconsequential for the determination of the steady state (and local welfare) as long as d ¼ b. However, monetary institutions matter for the way the equilibrium allocation is decentralized via monetary and fiscal instruments. Specifically, at the steady state at z2 , money growth is decreasing in g, while taxes are increasing. The remaining panels of Table 1 are concerned with the implications of fiscal impatience (d o b). As expected, the benchmark steady state at z2 breaks down under fiscal impatience. Instead, as a consequence of the fiscal authority’s preference for frontloading consumption at the cost of accumulating debt, a new steady state with higher—positive—debt emerges. An increase in monetary conservatism actually amplifies this effect in that a higher g is associated with higher steady state debt. The direct effect of a higher g 2 ð0,1Þ is to make the monetary authority more averse against inflationary deviations from the target p~ . Hence, since the monetary authority’s incentive to monetize outstanding liabilities (the nominal debt effect) 12
Empirical data are obtained from Council of Economic Advisers (2008).
242
S. Niemann / Journal of Monetary Economics 58 (2011) 234–247
Table 1 Steady state implications of variations in g and d: s ¼ 1. c
z
m
tc
b
b cþg
s ¼ 1, d r b g¼0
0.2429
z^¼ 0:0000
–
–
0.0000
0.0000
0.0000
s ¼ 1, d ¼ 0:97 g ¼ 0:9 g ¼ 0:7 g ¼ 0:5
0.2429 0.2429 0.2429
0.0000 0.0000 0.0000
0.0080 0.0342 0.1071
0.2420 0.2106 0.1309
0.0000 0.0000 0.0000
0.0000 0.0000 0.0000
0.0000 0.0000 0.0000
s ¼ 1, d ¼ 0:965 g ¼ 0:9 g ¼ 0:7 g ¼ 0:5
0.2402 0.2420 0.2424
0.2950 0.0983 0.0554
0.0065 0.0232 0.1122
0.2578 0.2280 0.1278
0.0865 0.0283 0.0147
0.2869 0.0935 0.0484
0.0477 0.0146 0.0046
s ¼ 1, d ¼ 0:96 g ¼ 0:9 g ¼ 0:7 g ¼ 0:5
0.2387 0.2413 0.2421
0.4627 0.1757 0.0842
0.0108 0.0302 0.0745
0.2602 0.2231 0.1680
0.1350 0.0503 0.0231
0.4502 0.1663 0.0762
0.0745 0.0249 0.0108
D welfare
The model’s aggregate state is z ¼ Bð1þ RÞ=M. The empirical counterpart is end-of-period real debt, b0 ¼ B0 =P. The conversion between the two variables is b ¼ bzð1 þ tc Þc. If g ¼ 0, taxes and interest rates are indeterminate, but z^ ¼ zð1 þ tc Þ is determinate. Welfare losses are converted into consumption equivalents and calculated in percentage terms relative to consumption in the distorted steady state at ðz2 ,c2 ðz2 ÞÞ of the unperturbed benchmark with purely benevolent policy makers (d ¼ b, g ¼ 0).
is reduced, increased monetary conservatism implies that the value for eð1 þ mÞ ðzÞ and thus the indirect liability costs of sustaining any given level of real government debt z decrease. Importantly, however, an additional indirect effect kicks in. Specifically, because the nominal debt effect and the intertemporal elasticity effect now balance at a higher level of z, the economy’s endogenous response is to accumulate more debt. Therefore, while the adverse welfare consequences of any given amount of real debt diminish, z , the steady state level of real government debt, increases. Throughout, the debt accumulation induced by an increase in g is associated with a decrease in consumption. Whereas the effects on consumption are moderate, the change in real debt is quantitatively substantial. For example, if d ¼ 0:965 and g ¼ 0:9, the benchmark steady state with zero debt is replaced by a steady state with a debt-to-GDP ratio of 28.7%; a further decrease in the fiscal discount factor to d ¼ 0:96 gives rise to a debt-to-GDP ratio of 45.0%. Steady state taxes increase along with the debt position, but inflation reacts in a non-monotonic fashion. The latter finding reflects the interplay between the direct commitment effect of a higher g and the increased incentives to monetize outstanding liabilities as more debt is accumulated. However, the overall distortions induced by monetary and fiscal policies, as measured by the wedge ð1þ RÞð1 þ tc Þ, are necessarily increasing in z. Thus, increased debt crowds out consumption and leads to lower welfare. Nevertheless, a meaningful normative assessment of monetary conservatism must weigh the costs of inducing a steady state with higher debt (the indirect effect) against the benefits of reduced distortions during the transition to the steady state (the direct effect). Accordingly, the last column of Table 1 calculates the welfare effects associated with moving from an unperturbed situation (d ¼ b, g ¼ 0) to the perturbed situation parameterized as described in the relevant row (d r b, g 4 0). The welfare effects are calculated locally at the steady state z of the relevant perturbed game, but take transitory effects fully into account. We find that, for s ¼ 1, monetary conservatism does not have any welfare implications when d ¼ b, but has adverse welfare implications when d o b. These welfare losses relative to the unperturbed benchmark are decreasing in d and increasing in g. 4.4.2. Low elasticity of intertemporal substitution The findings for s ¼ 1 highlight that the welfare implications of monetary and fiscal institutions are closely tied to their effects on the determination of steady state debt. Next, Table 2 examines the case of s 41, where already the unperturbed game predicts positive steady state debt. There are two main lessons. First, inspection of the relevant panels for d ¼ b reveals that monetary conservatism eliminates the benchmark steady state at z2 even without fiscal impatience. Indeed, no matter whether there is fiscal impatience or not, increased monetary conservatism leads to higher steady state debt. Accordingly, there emerge negative welfare implications of monetary conservatism even when d ¼ b. The second important aspect concerns the effect of variations in s. Comparing the panels for s ¼ 1:1 and s ¼ 1:25, it is evident that, irrespective of the degree of fiscal impatience, an increase in s reduces the effects of monetary conservatism on debt accumulation and welfare losses relative to the unperturbed benchmark. The reason behind this is that an increase f m in s generates more curvature in l and l , thus mitigating the economy’s willingness to accumulate debt at the expense of lower consumption. For s ¼ 1:1, increased fiscal impatience has the expected effect of exacerbating debt accumulation and the associated distortions. By contrast, for s ¼ 1:25, when coupled with monetary conservatism, fiscal impatience actually acts as a brake on the accumulation of debt. This is because fiscal impatience now forces increased monetary
S. Niemann / Journal of Monetary Economics 58 (2011) 234–247
243
Table 2 Steady state implications of variations in g and d: s 4 1
s ¼ 1:1, d r b g¼0
c
z
m
tc
b
b cþg
0.2808
z^¼ 0:1258
–
–
0.0345
0.1003
0.0000
D welfare
s ¼ 1:1, d ¼ 0:97 g ¼ 0:9 0.2799 g ¼ 0:7 0.2818 g ¼ 0:5 0.2824
0.4131 0.2075 0.1389
0.0092 0.0129 0.0090
0.2226 0.2090 0.2108
0.1371 0.0686 0.0461
0.4020 0.1999 0.1341
0.0464 0.0234 0.0160
s ¼ 1:1, d ¼ 0:965 g ¼ 0:9 0.2785 g ¼ 0:7 0.2814 g ¼ 0:5 0.2823
0.5722 0.2561 0.1515
0.0178 0.0342 0.0673
0.2189 0.1860 0.1445
0.1884 0.0829 0.0475
0.5546 0.2420 0.1382
0.0597 0.0252 0.0153
s ¼ 1:1, d ¼ 0:96 g ¼ 0:9 0.2776 g ¼ 0:7 0.2813 g ¼ 0:5 0.2817
0.6754 0.2732 0.2327
0.0258 0.0623 0.0717
0.2137 0.1551 0.1421
0.2208 0.0861 0.0726
0.6515 0.2514 0.2118
0.0669 0.0220 0.0177
–
–
0.0999
0.2519
0.0000
s ¼ 1:25, d r b g¼0
0.3353
z^¼ 0:3071
s ¼ 1:25, d ¼ 0:97 g ¼ 0:9 0.3343 g ¼ 0:7 0.3347 g ¼ 0:5 0.3350
0.3930 0.3421 0.3019
0.0584 0.0513 0.0288
0.1304 0.1363 0.1597
0.1440 0.1262 0.1137
0.3642 0.3188 0.2871
0.0217 0.0199 0.0206
s ¼ 1:25, d ¼ 0:965 g ¼ 0:9 0.3346 g ¼ 0:7 0.3349 g ¼ 0:5 0.3351
0.3634 0.3323 0.3036
0.0951 0.0890 0.0695
0.0910 0.0961 0.1153
0.1287 0.1183 0.1100
0.3251 0.2987 0.2777
0.0140 0.0137 0.0150
s ¼ 1:25, d ¼ 0:96 g ¼ 0:9 0.3352 g ¼ 0:7 0.3352 g ¼ 0:5 0.3353
0.3137 0.3049 0.2946
0.1584 0.1474 0.1229
0.0293 0.0390 0.0615
0.1050 0.1030 0.1017
0.2648 0.2598 0.2565
0.0039 0.0051 0.0077
The model’s aggregate state is z ¼ Bð1 þ RÞ=M. The empirical counterpart is end-of-period real debt, b0 ¼ B0 =P. The conversion between the two variables is b ¼ bzð1 þ tc Þc. If g ¼ 0, taxes and interest rates are indeterminate, but z^ ¼ zð1 þ tc Þ is determinate. Welfare losses are converted into consumption equivalents and calculated in percentage terms relative to consumption in the distorted steady state at ðz2 ,c2 ðz2 ÞÞ of the unperturbed benchmark with purely benevolent policy makers (d ¼ b, g ¼ 0).
responsiveness to variations in the stock of debt (as measured by eð1 þ mÞ ðzÞ) and thus accentuates the indirect liability costs of government debt. For sufficiently high s, this countervailing effect overcompensates the direct effect of fiscal impatience, and the MPE outcome is a steady state with a lower stock of liabilities. 4.4.3. High elasticity of intertemporal substitution Finally, Table 3 displays results for the case of s o 1 when steady state debt z2 in the unperturbed benchmark game is negative. As seen, the steady state allocation of the perturbed game with g 2 ð0,1Þ has negative debt in excess of the unperturbed benchmark, but is also characterized by substantial inflation rates. Throughout, increases of g 2 ð0,1Þ reduce the government’s asset position against the private sector13 and result in higher inflation and lower taxes. This can be understood as follows. At z o 0, the nominal debt effect provides incentives for the monetary authority to generate surprise deflation. But starting from inflation rates that exceed the inflation target p~ , such surprise deflation would reduce the losses incurred due to the monetary authority’s inflation aversion. This benefit works to augment the nominal debt effect and is perceived with a weight that is increasing in g. Thus, an increase in g implies that the nominal debt effect is stronger for any given level of z o 0. Since the steady state level z o 0 of government assets just balances the incentives for surprise inflation (intertemporal elasticity effect) and surprise deflation (nominal debt effect), and since the magnitude of the nominal debt effect is increasing in the absolute value of z, an increase in g therefore induces a reduction in government assets. As expected, a similar asset decumulation is triggered also by an increase in fiscal impatience. As before, also for s o1 the welfare assessment of monetary conservatism can be traced back to the respective effects on the government’s net asset position against the private sector. Irrespective of whether there is fiscal impatience or not, equilibrium allocations under g 2 ð0,1Þ now dominate those of the unperturbed benchmark. However, the relative welfare 13
s o 1.
The entries for end-of-period debt/assets b reveal this result most cleanly. Notice also that qualitatively similar findings obtain for other values of
244
S. Niemann / Journal of Monetary Economics 58 (2011) 234–247
Table 3 Steady state implications of variations in g and d: s o 1.
s ¼ 0:75, d r b g¼0
c
z
m
tc
b
b cþg
D welfare
0.1186
z^¼ 0:3877
–
–
0.0446
0.2481
0.0000
s ¼ 0:75, d ¼ 0:97 g ¼ 0:9 0.1199 g ¼ 0:8 0.1199 g ¼ 0:7 0.1203
0.4570 0.4573 0.4732
0.1469 0.1194 0.0575
0.3016 0.3328 0.4079
0.0692 0.0709 0.0777
0.3820 0.3915 0.4283
0.2375 0.2624 0.3321
s ¼ 0:75, d ¼ 0:965 g ¼ 0:9 0.1197 g ¼ 0:8 0.1198 g ¼ 0:7 0.1201
0.4425 0.4421 0.4570
0.1506 0.1229 0.0602
0.2984 0.3297 0.4055
0.0667 0.0683 0.0748
0.3688 0.3774 0.4128
0.2282 0.2519 0.3196
s ¼ 0:75, d ¼ 0:96 g ¼ 0:9 0.1196 g ¼ 0:8 0.1197 g ¼ 0:7 0.1200
0.4271 0.4258 0.4388
0.1547 0.1270 0.0635
0.2948 0.3260 0.4025
0.0642 0.0655 0.0716
0.3548 0.3624 0.3953
0.2180 0.2405 0.3055
The model’s aggregate state is z ¼ Bð1þ RÞ=M. The empirical counterpart is end-of-period real debt, b0 ¼ B0 =P. The conversion between the two variables is b ¼ bzð1 þ tc Þc. If g ¼ 0, taxes and interest rates are indeterminate, but z^ ¼ zð1 þ tc Þ is determinate. Welfare losses are converted into consumption equivalents and calculated in percentage terms relative to consumption in the distorted steady state at ðz2 ,c2 ðz2 ÞÞ of the unperturbed benchmark with purely benevolent policy makers (d ¼ b, g ¼ 0).
gains are decreasing in g. This pattern actually points at a discontinuity of the welfare effects of monetary conservatism at g ¼ 0. As the following subsection reveals, this discontinuity at g ¼ 0 is potentially relevant also for s 4 1.
4.4.4. Global welfare effects and inflation targets The findings for the case s o1 indicate that monetary conservatism may have positive welfare effects even under endogenous fiscal policy. But these results relate to environments with negative government debt. By contrast, empirically and from a policy perspective, environments characterized by positive government debt and potential incentives for monetary policy makers to monetize outstanding liabilities are arguably of key interest.14 For these environments, the previous results (for s Z 1) unambiguously indicate welfare losses from monetary conservatism due to its effect on debt accumulation. However, as already pointed out, the welfare losses displayed in Tables 1–3 provide only local information. Moreover, it is not clear whether the welfare losses under monetary conservatism are actually driven by an inflation target that was suboptimally fixed at p~ ¼ 0. To examine these issues, the following figures provide information about the desirability of monetary conservatism from a global perspective. Again starting with the case of s ¼ 1, the plots in the top row of Fig. 1 confirm that for z 4 0, and for environments both with and without fiscal impatience, the welfare losses relative to the unperturbed benchmark are increasing in g. Moreover, fixing some g 2 ð0,1Þ, the losses from monetary conservatism are increasing in z. As illustrated by the remaining plots of Fig. 1, the situation changes for s 41. For positive levels of debt, the MPE outcomes for g 2 ð0,1Þ continue to be unambiguously dominated by those implemented in the unperturbed benchmark game. Also the monotonicity of the welfare losses relative to that benchmark remains a robust phenomenon. But the clearcut desirability of institutions characterized by a lower degree of conservatism is overturned. Depending on the level of z, but irrespective of whether there is fiscal impatience or not, variations in g 2 ð0,1Þ may now give rise to welfare reversals. For example, for s ¼ 1:25, the welfare losses relative to the unperturbed benchmark are now decreasing in g. The basic pattern is that an increase in government debt tends to favor more conservative institutions over less conservative ones. This finding once again reflects the underlying trade-off between the direct (reduced nominal debt effect) and indirect (increased accumulation of debt) effects of monetary conservatism. Fig. 2 demonstrates that the adoption of an inflation target p~ different from zero has only a minor effect on these conclusions.15 Variations in the inflation target are found to induce close-to-proportional shifts in steady state inflation, but have only very small effects on government debt, with lower inflation targets resulting in marginally lower liabilities. As noticed earlier, Eq. (7) implies that there is no strict efficiency rationale for low inflation per se. In particular, the Friedman rule of zero nominal interest rates is equivalent to any other combination of monetary and fiscal policy instruments resulting in the same overall wedge ð1þ RÞð1þ tc Þ. As seen, for a given g 2 ð0,1Þ, an inflation target of p~ ¼ 0:03, which is consistent with the Friedman rule, even amplifies the welfare losses relative to the unperturbed 14 In the U.S., the average ratio over 1962–2006 of gross federal debt to GDP was at 49.1%, and the statistic for debt held by the public (i.e., excluding holdings of federal agencies) was at 35.8%. 15 Fig. 2 presents results for the case of g ¼ 0:9; the results for other values of g 2 ð0,1Þ are qualitatively very similar. They are available upon request, as are tables detailing the steady state implications of different inflation targets.
S. Niemann / Journal of Monetary Economics 58 (2011) 234–247
0
0 gamma = 0.9 gamma = 0.7 gamma = 0.5
-0.01
-0.005
welfare loss
welfare loss
-0.005
-0.015 -0.02 -0.025
-0.01 -0.015 -0.02
-0.03 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 z
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 z
0
-0.002 gamma = 0.9 gamma = 0.7 gamma = 0.5
-0.004 -0.006
gamma = 0.9 gamma = 0.7 gamma = 0.5
-0.008
-0.01
welfare loss
welfare loss
gamma = 0.9 gamma = 0.7 gamma = 0.5
-0.025
-0.03
-0.005
245
-0.015 -0.02
-0.01 -0.012 -0.014 -0.016 -0.018
-0.025
-0.02 -0.03 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55 z
-0.022 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55 z
0 -0.002
0 gamma = 0.9 gamma = 0.7 gamma = 0.5
-0.002
gamma = 0.9 gamma = 0.7 gamma = 0.5
-0.006 -0.008 -0.01 -0.012
-0.004 welfare loss
welfare loss
-0.004
-0.006 -0.008 -0.01
-0.014 -0.016 -0.018 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55 z
-0.012 -0.014 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55 z
Fig. 1. Welfare effects of monetary conservatism (g varying, p~ ¼ 0). The panels plot welfare losses relative to the unperturbed benchmark with purely benevolent policy makers (d ¼ b, g ¼ 0) for d ¼ 0:97 (left column) and d ¼ 0:965 (right column). Top row: s ¼ 1; middle row: s ¼ 1:1; bottom row: s ¼ 1:25.
benchmark. On the other hand, although a positive inflation target of p~ ¼ 0:03 helps to reduce the welfare losses from monetary conservatism by a small margin, the MPE outcomes continue to be dominated by those implemented in the unperturbed benchmark game. These findings obtain for all considered values of s Z1.16
16 For s o 1, the welfare ranking is reversed. As discussed, monetary conservatism gives rise to welfare gains relative to the unperturbed benchmark. Moreover, given g 2 ð0,1Þ, the relative welfare gains are increasing in the absolute value of z o 0 and decreasing in p~ .
246
S. Niemann / Journal of Monetary Economics 58 (2011) 234–247
0
0 pitilde = 0 pitilde = -0.03 pitilde = 0.03
-0.005
-0.005 -0.01 welfare loss
welfare loss
-0.01 -0.015 -0.02
-0.015 -0.02
-0.025
-0.025
-0.03
-0.03
-0.035
-0.035 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 z
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 z -0.005
0 -0.005
pitilde = 0 pitilde = -0.03 pitilde = 0.03
-0.01
-0.01 welfare loss
welfare loss
pitilde = 0 pitilde = -0.03 pitilde = 0.03
-0.015
pitilde = 0 pitilde = -0.03 pitilde = 0.03
-0.015
-0.02
-0.02 -0.025
-0.025
-0.03 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55 z 0
-0.03 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55 z 0 -0.002
pitilde = 0 pitilde = -0.03 pitilde = 0.03
-0.002
pitilde = 0 pitilde = -0.03 pitilde = 0.03
-0.006 -0.008 -0.01 -0.012
-0.004 welfare loss
welfare loss
-0.004
-0.006 -0.008 -0.01
-0.014 -0.016 -0.018 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55 z
-0.012 -0.014 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55 z
Fig. 2. Welfare effects of different inflation targets (g ¼ 0:9, p~ varying). The panels plot welfare losses relative to the unperturbed benchmark with purely benevolent policy makers (d ¼ b, g ¼ 0) for d ¼ 0:97 (left column) and d ¼ 0:965 (right column). Top row: s ¼ 1; middle row: s ¼ 1:1; bottom row: s ¼ 1:25.
5. Conclusion Absent commitment, dynamic monetary–fiscal interactions in an economy with nominal government debt arise from the interaction of a time-consistency problem and incentives to smooth distortions across time. This paper examines these interactions under the assumption that monetary and fiscal policies are directed by separate authorities who cannot commit over time and possibly pursue different objectives: The fiscal authority is myopic, while the monetary authority is inflation-averse (weight-conservative).
S. Niemann / Journal of Monetary Economics 58 (2011) 234–247
247
Monetary and fiscal institutions are key determinants of the economy’s steady state level of debt. For environments where a benchmark without monetary conservatism predicts non-negative steady state debt (s Z 1), increased conservatism implies that any given level of real liabilities can be sustained at a lower rate of inflation. However, since the economy’s improved debt tolerance is internalized, the MPE outcome features a steady state with higher indebtedness and possibly higher inflation. As a consequence, when compared to the non-conservative benchmark, monetary conservatism has adverse welfare implications. Conversely, if s o1, monetary conservatism induces higher government assets and generates welfare gains. These results obtain irrespective of the degree of fiscal impatience and are in contrast to established findings in much of the previous literature which neglects the endogeneity of fiscal policy in general and of government debt in particular. A critical model assumption has been to abstract from price stickiness and stochastic shocks; in addition, public spending has not been endogenized. As a consequence, monetary and fiscal distortions are completely equivalent, and there is no stabilization problem.17 It would therefore be interesting to reconsider this paper’s research question for a richer stochastic environment with sticky prices and endogenous government expenditure.
Acknowledgments I would like to thank the editor, Klaus Adam, and an anonymous referee for very valuable comments and suggestions. ¨ I would also like to thank Michael Evers, Monika Merz, Paul Pichler, Michael Reiter, Jurgen von Hagen and Leopold von Thadden for comments and discussions at various stages of this project. Appendix A. Supplementary data Supplementary data associated with this article can be found in the online version at doi:10.1016/j.jmoneco.2011.03.008. References Adam, K., Billi, R., 2008. Monetary conservatism and fiscal policy. Journal of Monetary Economics 55, 1376–1388. Adam, K., Billi, R., 2010. Distortionary fiscal policy and monetary policy goals. Mimeo, University of Mannheim. Barro, R., Gordon, D., 1983. A positive theory of monetary policy in a natural rate model. Journal of Political Economy 91, 589–610. Chari, V., Kehoe, P., 1990. Sustainable plans. Journal of Political Economy 98, 783–802. Council of Economic Advisers, 2008. Economic Report of the President. U.S. Government Printing Office, Washington. Dı´az-Gime´nez, J., Giovanetti, G., Marimon, R., Teles, P., 2008. Nominal debt as a burden on monetary policy. Review of Economic Dynamics 11, 493–514. Klein, P., Krusell, P., Rı´os-Rull, J.-V., 2008. Time-consistent public policy. Review of Economic Studies 75, 789–808. Klein, P., Quadrini, V., Rı´os-Rull, J.-V., 2005. Optimal time-consistent taxation with international mobility of capital. B.E. Journals—Advances in Macroeconomics 5 (1) Article 2. Kydland, F., Prescott, E., 1977. Rules rather than discretion: the inconsistency of optimal plans. Journal of Political Economy 85, 473–492. Leeper, E., 1991. Equilibria under ‘active’ and ‘passive’ monetary and fiscal policies. Journal of Monetary Economics 27, 129–147. Lucas, R., Stokey, N., 1983. Optimal fiscal and monetary policy in an economy without capital. Journal of Monetary Economics 12, 55–93. Malley, J., Philippopoulos, A., Woitek, U., 2007. Electoral uncertainty, fiscal policy and macroeconomic fluctuations. Journal of Economic Dynamics and Control 31, 1051–1080. Martin, F., 2009. A positive theory of government debt. Review of Economic Dynamics 12, 608–631. Nicolini, J.-P., 1998. More on the time consistency of monetary policy. Journal of Monetary Economics 41, 333–350. Niemann, S., Pichler, P., Sorger, G., 2008. Optimal fiscal and monetary policy without commitment. Discussion Paper No. 654, University of Essex. Ortigueira, S., Pereira, J., 2009. Markov-perfect optimal fiscal policy: the case of unbalanced budgets. Mimeo, European University Institute. Persson, T., Tabellini, G., 2000. Political Economics: Explaining Economic Policy. MIT Press, Cambridge. Rogoff, K., 1985. The optimal degree of commitment to an intermediate monetary target. Quarterly Journal of Economics 100, 1169–1190. Sargent, T., Wallace, N., 1981. Some unpleasant monetarist arithmetic. Federal Reserve Bank of Minneapolis Quarterly Review 5, 1–17. Svensson, L., 1985. Money and asset prices in a cash-in-advance economy. Journal of Political Economy 93, 919–944. Svensson, L., 1997. Optimal inflation targets, ‘conservative’ central banks, and linear inflation contracts. American Economic Review 87, 98–114. Walsh, C., 1995. Optimal contracts for central bankers. American Economic Review 85, 150–167.
17 Notice that the welfare losses from monetary conservatism if s Z 1 arise in a deterministic economy; in a stochastic setting, there emerge additional costs from suboptimal stabilization policies (Rogoff, 1985). In this sense, the welfare losses presented here should be interpreted as a lower bound.
Journal of Monetary Economics 58 (2011) 248–261
Contents lists available at ScienceDirect
Journal of Monetary Economics journal homepage: www.elsevier.com/locate/jme
Optimal disinflation in new Keynesian models Marcus Hagedorn University of Cologne, CMR – Center for Macroeconomic Research, Albertus-Magnus-Platz, 50923 K¨ oln, Germany
a r t i c l e in f o
abstract
Article history: Received 28 June 2009 Received in revised form 22 May 2011 Accepted 31 May 2011 Available online 23 July 2011
Central bankers’ conventional wisdom suggests that nominal interest rates should be raised to attain a lower inflation target. In contrast, I show that the standard New Keynesian monetary model with rational expectations and full credibility predicts that nominal interest rates should be decreased to attain this goal. Real interest rates, however, are virtually unchanged. These results also hold in recent vintages of New Keynesian models with sticky wages, price and wage indexation and habit formation in consumption. & 2011 Published by Elsevier B.V.
1. Introduction The standard strategy to assess the quantitative performance of monetary business cycle models is to investigate impulse responses to (monetary policy) shocks. Whereas New Keynesian models perform very well in these experiments (Woodford, 2003; Christiano et al., 2005), this paper demonstrates an inconsistency between one of the model’s main predictions and one aspect of observed monetary policy in a closed economy. Suppose the central bank wants to implement a lower inflation target. The most prominent example of such a regime change is presumably the 1970s, a period of high inflation, followed by the Volcker disinflation.1 Once a lower inflation regime is considered to be optimal, central bankers’ conventional wisdom suggests that nominal interest rates should be increased.2 But this is not what standard New Keynesian models predict. In these models the optimal policy response is to lower nominal interest rate right away and during the whole transition to the new steady-state.3 At least in the early eighties, the policy of increasing nominal interest rates was thus either suboptimal or not consistent with a New Keynesian model. The reason for this inconsistency is clear if prices are flexible. In the absence of pricing frictions, it is optimal to immediately adjust inflation to its new target level. The Fisher equation – the nominal interest rate equals the real interest rate plus the inflation rate – then implies that the nominal interest should be lowered immediately. This mechanism is related to what is typically referred to as the ‘expectations channel’. The central bank sets nominal interest rates, which are consistent with the private sector’s expectations of lower inflation rates in the future.
E-mail address:
[email protected] Primiceri (2006) and Sargent et al. (2006) support the view that this was indeed a target change. They both explain the high inflation and the subsequent disinflation as the optimal policy outcome of a rational policy maker who has to learn the ‘‘true’’ data generating mechanism. In both papers the government’s perception was that disinflation was too costly during the 1970s. The perceived inflation-unemployment trade-off became favorable, relative to the level of inflation, only in the late 1970s, which then led to a disinflation. Ireland (2007) and Milani (2006) estimate the Fed’s inflation target and find a sharp drop in its level in the late 1970s. 2 This conventional wisdom is very well conveyed in the excellent historical review of the Volcker disinflation by Lindsey et al. (2005). Erceg and Levin (2003) provide further references and state that the federal funds rate remained the main instrument of monetary policy, although the Federal Reserve’s stated operational target involved the stock of nonborrowed reserves from 1979:4 to 1982:3. 3 Alvarez et al. (2001) also suggest that standard monetary models contradict observed monetary policy. They, however, leave the question unanswered whether a model with nominal rigidities can overcome this conclusion. 1
0304-3932/$ - see front matter & 2011 Published by Elsevier B.V. doi:10.1016/j.jmoneco.2011.05.011
M. Hagedorn / Journal of Monetary Economics 58 (2011) 248–261
249
With sticky prices this expectations channel is also available but there is an additional ‘aggregate demand’ channel, which links lower aggregate demand to lower inflation rates. According to this channel, nominal interest rates are increased to raise real interest rates, which leads to lower aggregate demand and to lower inflation rates. Using this channel is however quite costly, since it requires an output contraction, which can be avoided when the expectations channel is used. Even with sticky prices it is then optimal to only use the expectations channel with the consequence that nominal interest rates are uniformly lowered to implement a lower inflation target. An immediate adjustment of inflation to its target level however is not necessarily optimal in the presence of pricing frictions. Instead, inflation and nominal interest rates are only gradually adjusted. The qualitative properties of optimal policy do not change if several features that are part of recent vintages of New Keynesian models, such as habit formation in consumption, sticky wages and wage and price indexation, are allowed for. Nominal interest rates are uniformly lowered to implement a lower inflation target. This result may appear counterintuitive since model-generated impulse response functions fit the data well. In particular, the inflation rate drops in response to a short-lived increase in nominal interest rates. The two experiments - implementing a lower inflation target on the one hand and monetary policy shocks on the other hand - thus lead to different conclusions. How can this apparent contradiction be reconciled?4 There are two reasons which explain the different conclusions. First, a short-lived increase in nominal interest rates does not create expectations of a lower inflation rate in the long run. As a result, the role of the expectations channel is diminished in the second experiment. Second, a positive shock to the nominal interest rate leads to a contraction in output and to lower inflation rates. Whereas it is optimal not to use this channel in the first experiment, an output contraction is an unavoidable consequence of a positive shock to nominal interest rates in the second experiment. Since the expectations channel is the key mechanism, I investigate whether the results of this paper depend on expectations being fully rational, the standard assumption in the New Keynesian literature. If current inflation expectations lead current inflation, the inconsistency between the model and monetary policy remains. If, however, current expectations lag current inflation, it can be optimal to increase nominal interest rates initially (eventually nominal interest rates are decreased) to implement a lower inflation rate. The reason is that this type of expectation formation strongly diminishes the role of the expectations channel and thus the aggregate demand channel has to be used to lower inflation. All results in this paper characterize optimal policy and do not hold if policy is not optimal. For example, Erceg and Levin (2003) find that nominal interest rates are increased in response to a persistent drop in the inflation target. However, this finding depends on their specification of the monetary policy rule, which does not describe the optimal policy.5 Another difference is that Erceg and Levin (2003) assume that the private sector has to learn the central bank’s inflation target, whereas this paper assumes perfect credibility.6 Section 5.2 discusses why their specification of the interest rate rule, and not their assumption of imperfect credibility, drives their findings. A key feature of their model is that expectations lead inflation so that the expectations channel remains powerful. Concerning the implications of a disinflation for output, most macroeconomists’ view is that a disinflation is associated with a recession. In the basic New Keynesian model, however, the opposite result holds: a disinflation causes an output boom (Ball, 1994; Ball et al., 2005). The reason is that a lower future inflation rate leads to preemptive price cuts in the current period, which stimulate demand and lead to an immediate output expansion. With sufficiently strong indexation of prices, as for example in Giannoni and Woodford (2004), the incentives for preemptive price cuts disappear since prices are automatically lowered when future inflation rates fall. Thus, a disinflation does not necessarily lead to an immediate expansion. The New Keynesian model, amended with full price indexation, is thus inconsistent with conventional wisdom about nominal interest rates but consistent with conventional wisdom about output. The next section considers a simple, analytically tractable sticky price model that aims at providing the intuition for the main results. Section 3 describes the model of Giannoni and Woodford (2004), which features habit formation in consumption, sticky wages and sticky prices, and indexation of prices and wages. The parameter estimates of Giannoni and Woodford (2004) and the results for the optimal paths of nominal and real interest rates and inflation are presented in Section 4. Section 5 considers two deviations from rational expectations: adaptive expectations and imperfect credibility. Section 6 concludes. All proofs are delegated to the Appendix.7
2. A simple model This section presents a basic New Keynesian model which includes, following Clarida et al. (1999), both cost-push shocks and shocks to the natural rate of interest. This model allows for theoretical results since it abstracts from several 4 Ireland (1995) and Yun (2005) both provide simulation results which also show a uniform decrease in the nominal interest rates during a disinflation. However, as this point is not the focus of their papers, they do not comment on the apparent contradiction. They also do not consider whether allowing for habit formation, price indexation, etc. could overturn their results. 5 Specifically, they use it ¼ 1:43ððpt þ pt1 þ pt2 þ pt3 Þ=4Þ0:64pn þ , where i is the nominal interest rate, p is the inflation rate and pn is the inflation target. A drop in pn then mechanically leads to a non-optimal increase in it. 6 Ball (1995a) also considers a disinflation in a simple New Keynesian model with imperfect credibility but the focus of this paper is on the welfare and output effects of a disinflation and not on nominal interest rates. 7 Available online at http://www.sciencedirect.com/science/journal/03043932.
250
M. Hagedorn / Journal of Monetary Economics 58 (2011) 248–261
features such as habit formation in consumption, sticky wages and wage and price indexation. All of these elements will be present in the general model below. The purpose of this simple model is to understand which properties of the model are crucial for the results. The economy is described by two equations.8 The first equation, the Phillips curve, summarizes the optimal price setting behavior of monopolistically competitive firms under a Calvo (1983)-style price adjustment mechanism:
pt ¼ kxt þ bEt pt þ 1 þ ut ,
ð1Þ
where pt is the inflation rate, xt is the output gap – the difference between log output with sticky prices and log output when prices are flexible – in period t and ut is, in the terminology of Clarida et al. (1999), a cost-push shock. The discount factor of the representative household is denoted as b 2 ð0,1Þ and k 4 0 is the ‘‘slope’’ of the Phillips curve, which depends on features such as the frequency of price changes and the sensitivity of prices to changes in marginal cost. The second equation, the IS equation, is derived from the standard consumption Euler equation of the representative household: xt ¼ Et xt þ 1 sEt ðit pt þ 1 rtn Þ,
ð2Þ rnt
9
is the real interest rate in period t if prices were flexible. where it is the nominal interest rate in period t and The policy experiment is as follows. At time t ¼0 the central bank is asked to implement an inflation target pL that is lower than the current inflation target pH . The goal is then to compute the sequence of nominal interest rates that implement the regime change. An optimal policy is a sequence pt and xt which minimizes the loss function 1 X
bt ½ðpt pn Þ2 þ lx ðxt xn Þ2 ,
ð3Þ
t¼0
subject to constraints (1) and (2). Here pn is the inflation target and equals pH without a regime change and equals pL o pH with a regime change. All results in this section hold for all values of pL o pH , but for the linearization to be appropriate, one should think of inflation targets sufficiently close to zero.10 The output target is denoted as xn and lx is the weight that is assigned to output stabilization. Two cases are considered for how the choice of xn is related to the inflation target pn . Either the output target xn is the same for both inflation targets or it is chosen to be consistent with the inflation target and the Phillips curve (1), that is xn ¼ ð1bÞpn =k. I now characterize it ðpH Þ and it ðpL Þ (for t ¼0,1, y), the paths for nominal interest rates under the two different regimes. The same notation is used for p and x to denote the dependence on the inflation target (pt ðpH Þ, pt ðpL Þ, xt ðpH Þ and xt ðpL Þ). It is important to note that both regimes start at the same high inflation target pH , so that the transition to the new low inflation target pL is (potentially) non-trivial. First two special cases are considered which are of pure theoretical interest but which are nevertheless useful to understand the modifications made in the standard environment. The two special cases are first flexible prices and second a zero weight assigned to output stabilization (lx ¼ 0). The characterization of optimal policy is simple under these assumptions. The inflation rate is always set equal to its target level since either the output gap is zero (if prices are flexible) or not a concern (if lx ¼ 0). The nominal interest rate then equals rtn þ pH without a target change and rtn þ pL with the new target. Thus the central bank immediately reduces the nominal interest rate by pH pL 4 0 to implement the lower inflation rate. Proposition 1 (Two special cases). If either prices are flexible or lx ¼ 0, the nominal interest rate is uniformly lower in the new regime: it ðpL Þit ðpH Þ ¼ pL pH o0. An immediate adjustment of inflation, nominal interest rates and output to their new target levels is also optimal in a model with sticky prices and lx 4 0 if there are no cost-push shocks (ut 0) and the output target is consistent with the inflation target (xn ¼ ð1bÞpn =k). If one of these two assumptions is relaxed – there are cost-push shocks or xn að1bÞpn =k – an inflation-output trade-off exists. The optimal adjustment of inflation to its new target level is then only gradual. But whether the adjustment of inflation is immediate or not, the implications for the path of nominal interest rates always have one property: if the new inflation target is lower (pL o pH ), then the nominal interest rate is uniformly lower it ðpL Þit ðpH Þ o 0 for all t. 8 A log-linearized version is considered for tractability, following Woodford (2003). Benigno and Woodford (2006) show that any optimal policy problem can be approximated through a problem with (L)inear constraints and a (Q)uadratic objective function. See Benigno and Woodford (2006) for a discussion of the advantages of the LQ approach. 9 All variables, except for inflation, are log deviations from their trend values. 10 To be fully consistent with interpreting the model as a linearization, one can resort to a ‘trick’ which is useful in a quantitative analysis (see for example Erceg and Levin, 2003). The new low inflation target pL ¼ 0 and the high inflation target pH ¼ 0:999t , where t denotes time. In both regimes, the unique steady-state equals 0 (since 0.999t converges to zero) and the linearization is thus appropriate. However, for the first couple of years after the regime change, the high inflation regime behaves as if pH ¼ 1.
M. Hagedorn / Journal of Monetary Economics 58 (2011) 248–261
251
The reason is that it is optimal to uniformly and immediately lower the inflation rate when the inflation target is decreased. The Fisher equation – the nominal interest rate i equals inflation p plus the real interest rate r – then implies that nominal interest rates track the inflation rate. As a consequence, nominal interest rates are lowered uniformly and right away. This optimal policy avoids the costly aggregate demand channel, which prescribes that real interest rates should be increased to contract output and thus lower inflation. Indeed, the real interest rate is (slightly) lower for a lower inflation target (rt ðpL Þrt ðpH Þ r 0 for all t). By the Fisher equation (i ¼ r þ p) a lower r leads to lower nominal interest rates by itself. However, it turns out in the quantitative exploration of the general model in the subsequent sections that the real interest rate only moves within narrow bands around its steady-state level. The quantitatively important reason for lower nominal interest rates is thus lower inflation rates and not lower real interest rates. The result, i.e. that nominal interest rates are lowered, holds for any size of pricing frictions, parameterized through k. But the optimal policy changes if the extent of price stickiness changes. For example, a smaller k (prices are more sticky) decreases jpt ðpL Þpt ðpH Þj, i.e. that it is optimal to slow down the speed of convergence to the new inflation target. The same arguments apply to an increase in lx , the weight of output in the loss function. A higher lx slows down adjustment, i.e. it lowers jpt ðpL Þpt ðpH Þj. This result is consistent with proposition 1, which considers the extreme case lx ¼ 0: If the weight on output is zero, immediate adjustment is optimal. Another interpretation of this result is that both a weak (a high lx ) and a tough (a low lx ) central banker decrease nominal interest rates and only the speed of the disinflation process differs.11 To get an analytical characterization of optimal policy, the zero bound on nominal interest rates is assumed to be not binding. All results for arbitrary sequences of shocks (identical in both regimes and known in period t¼0) can then be derived with a simple outcome. Additivity of shocks and the linear-quadratic nature of the problem imply that the differences pt ðpL Þpt ðpH Þ, xt ðpL Þxt ðpH Þ and it ðpL Þit ðpH Þ are unaffected by shocks. But the assumption that the zero bound on nominal interest rates is not binding is needed, since the optimal sequences pt ,xt and it are affected by shocks. Proposition 2. Assume that the zero bound on nominal interest rates is never binding. With cost-push shocks the nominal interest is uniformly lower in the new regime: it ðpL Þit ðpH Þ o0 for all t Z 0. If in addition xn ¼ ð1bÞpn and ut 0, both the inflation rate and the nominal interest rate are adjusted immediately to their new target levels, pt ¼ pL and it ðpL Þit ðpH Þ ¼ pL pH o 0 for all t Z0. 3. The general model Giannoni and Woodford (2004) extend the Rotemberg and Woodford (1997) sticky price model to allow for sticky wages, indexation of wages and prices to the lagged price index, and habit persistence in private consumption expenditures. Their linearized model is used except for one feature. Giannoni and Woodford (2004) assume that expenditure decisions are predetermined two quarters in advance and prices and wages are predetermined one quarter in advance. To simplify notation this complication is omitted and I assume that there are no decision lags.12 3.1. Optimal consumption decisions Optimal consumption decisions imply that the intertemporal consumption Euler equation holds. With habit persistence,13 the linearized version of the Euler equation is a generalization of the IS-equation (2) and has the form x~ t ¼ Et x~ t þ 1 j1 Et ðit pt þ 1 rtn Þ,
ð4Þ n rt
is the real where x~ t ¼ ðxt Zxt1 ÞbZEt ðxt þ 1 Zxt Þ, it is the nominal interest rate at t, pt is the inflation rate at t and interest rate that would prevail if prices and wages are flexible. In a steady-state rtn ¼ 1=b1.14 The coefficient 0 r Z r1 is the degree of habit persistence and j1 is the intertemporal elasticity of substitution, adjusted for habit persistence. Without habit persistence (Z ¼ 0) Eq. (4) reduces to the standard Euler/IS equation (2). With habit persistence (Z 4 0), an increase in the output gap xt decreases marginal utility in period t (which also depends on xt1 ) and decreases marginal utility in period t þ 1 (which also depends on xt þ 1 ). This is why x~ t and not only xt is the relevant variable for the Euler equation. 3.2. Optimal wage and price setting A discrete version of the optimizing model of staggered price setting following Calvo (1983), modified to allow for indexation of the price index during periods of no re-optimization, leads to the following log-linearized aggregate-supply 11
See for example Backus and Driffill (1985), Barro (1986) and Ball (1995b) for models where policy makers can be either weak or tough. The sensitivity analysis in Hagedorn (2008) shows that this assumption is inessential for the results. 13 Giannoni and Woodford (2004) assume that current utility depends on the household’s own past consumption level, and not on that of other households. This means the habit is internal rather than an external. 14 Note that the steady-state values are not subtracted from i and r. All other variables, except for inflation, are still log-deviations from their steady-state value. 12
252
M. Hagedorn / Journal of Monetary Economics 58 (2011) 248–261
relation:
pt gp pt1 ¼ xp op xt þ xp ðwt wnt Þ þ bEt ðpt þ 1 gp pt Þ,
ð5Þ
where 0 r gp r 1 is the degree of automatic indexation to the (lagged) aggregate price index. The parameters xp and xw measure the degree to which prices and wages are sticky respectively. Specifically, xp indicates the responsiveness of price inflation to the gap between marginal cost and current prices and xw indicates the responsiveness of wage inflation to the gap between households’ marginal rate of substitution (the wage on agents’ supply curve) and current wages. The coefficient op is the quantity-elasticity of marginal cost and ow is the quantity-elasticity of households’ marginal rate of n substitution.15 The real wage is denoted wt and wt is the ‘‘natural real wage’’, the equilibrium real wage when both wages and prices are flexible. Sticky wages thus induce real disturbances wt wnt , which have similar consequences to the costpush shocks in Section 2. To model sticky wages, Giannoni and Woodford (2004) follow Erceg et al. (2000) and assume staggered wage setting analogous to the staggered price setting in Calvo (1983). This gives the second equation of the supply side:
pwt gw pt1 ¼ xw ðow xt þ jx~ t Þ þ xw ðwnt wt Þ þ bEt ðpwtþ 1 gw pt Þ,
ð6Þ
w
where p is the nominal wage inflation that satisfies the identity wt ¼ wt1 þ pw t pt :
ð7Þ
Eq. (6) can equivalently be rewritten as
pwt gw pt1 ¼ kw ½ðxt dxt1 ÞbdEt ðxt þ 1 dxt Þ þ xw ðwnt wt Þ þ bEt ðpwtþ 1 gw pt Þ, 2
ð8Þ
where 0 r d r Z is the smaller root of Zjð1 þ bd Þ ¼ ½ow þ jð1 þ bZ Þd and kw ¼ xw Zj=d. 2
3.3. Welfare criterion and constraints To compute the optimal disinflation policy, a welfare criterion is specified and the constraints (4), (5), (7) and (8), which together characterize an equilibrium for a given policy, are simplified. n n To isolate the effects of a lower inflation target, I abstract from any real shocks.16 The variables wt and rt are set to their n n steady-state values, wt ¼ 0 and rt ¼ 1=b1. Next, Eq. (7) is solved for pw t ¼ wt wt1 þ pt and is substituted into the wage setting Eq. (8). Perfect-foresight equilibrium paths for inflation, output, wages and nominal interest rates are therefore characterized through two aggregate supply equations
pt gp pt1 ¼ xp op xt þ xp wt þ bðpt þ 1 gp pt Þ,
ð9Þ
wt wt1 þ pt gw pt1 ¼ kw ½ðxt dxt1 Þbdðxt þ 1 dxt Þxw wt þ bðwt þ 1 wt þ pt þ 1 gw pt Þ,
ð10Þ
and through the Euler/IS equation it pt þ 1 ð1=b1Þ ¼ jðx~ t þ 1 x~ t Þ,
ð11Þ
The objective of monetary policy is assumed to minimize deviations of price inflation, output, wage inflation and nominal interest rates from its target values. The discounted loss function then equals 1 X
bt ½ðpt gp pt1 ð1gp Þpn Þ2 þ lx ðxt Zxt1 ð1ZÞxn Þ2 þ
t¼0
1 X
bt ðpt þ wt wt1 gw ðpt1 þ wt1 wt2 Þð1gw Þpnw Þ2 ,
t¼0
ð12Þ where p , x and pw are the target values for price inflation, output and wage inflation, respectively, and where the identity pwt ¼ wt wt1 þ pt is used. n
n
n
4. Optimal disinflation The policy experiment is the same as in Section 2. At date t ¼0 the inflation target pn is lowered from pH to pL . 1 1 The monetary authority chooses sequences for the inflation rate fpt g1 t ¼ 0 , the output gap fxt gt ¼ 0 and wages fwt gt ¼ 0 to minimize the loss function (12) such that the constraints for optimal price setting (9), optimal wage setting (10) and optimal consumption decisions (11) are fulfilled. The main difference between the models in Sections 2 and 3 is that past values, for example, lagged inflation rates, affect current allocations in the general model but not in the simple model. This makes it necessary to specify initial 15 For more details on these coefficients, in particular how they are related to features such as the frequency of price and wage adjustment, see Giannoni and Woodford (2004) and Woodford (2003). 16 Section 2 shows that shocks do not affect it ðpL Þit ðpH Þ, the difference between nominal interest rates with and without a change in the inflation target.
M. Hagedorn / Journal of Monetary Economics 58 (2011) 248–261
253
conditions for these variables. It is assumed that the economy is in a steady-state with p ¼ pH before the policy change. The steady-state values of the three other endogenous variables – output, wages and nominal interest rates – have to fulfill the steady-state versions of Eqs. (9), (10) and (11). This choice seems reasonable since the paper wants to capture a regime change, where a low inflation rate is the new target after a period of high inflation. Note that only values of period t ¼ 1 variables are set equal to their steady-state values. Constraints from period t¼ 1 are not taken into account in the optimization problem, so that no multipliers for period t ¼ 1 constraints appear in the optimization problem. In particular multipliers are never set to their steady-state values, reflecting the fact that the central bank is not committed to past actions. The optimization however takes into account that the first period is different from subsequent periods, as is typically the case in a dynamic optimal policy problem with perfect commitment (Chari and Kehoe, 1999). The first-order conditions are computed in the Appendix and it is shown that they, together with the three constraints (9), (10) and (11), can equivalently be expressed as a difference equation of the form zt þ 1 ¼ Azt ,
ð13Þ
for a matrix A and a vector z, plus initial conditions which are identical to the first order conditions in the first period. The next step makes it necessary to compute the eigenvalues and eigenvectors of the matrix A, which is possible only once numerical values for all parameters are specified. The details are again laid out in the Appendix. The following section describes the choice of the parameters. 4.1. Parameter values The parameters are exactly those found in the quarterly model of Giannoni and Woodford (2004). They follow Rotemberg and Woodford (1997) and choose the parameters to minimize the distance between the theoretical model impulse response function and the estimated VAR impulse response functions. Table 1 shows their results for the wage and price persistence parameters (gp and gw ), the wage and price stickiness parameters (xp and xw ), the habit persistence parameter Z, the inverse of the intertemporal elasticity of substitution j and the elasticity parameter ow . Two parameters are calibrated directly in Giannoni and Woodford (2004). The discount factor b is set equal to 0.99 to match an steady-state real interest rate of 1%. They set op ¼ 1=3 to match the output elasticity with respect to hours. Two parameters, kw and d, are functions of other parameters as described in the last section. The values and the welfare weights are shown in Table 1 (additional parameter values). 4.2. Results Now that the model and its parameters are specified, the optimal policy response to a change in the inflation target for this model can be computed. To make the experiment ‘lowering the inflation target’ meaningful, the indexation parameter for inflation has to be strictly smaller than one, thus gp ¼ 0:99 o1. Otherwise only the change in inflation matters and the level of inflation is irrelevant for welfare. The details of the procedure are described in the Appendix. Fig. 1 shows the optimal sequence of nominal interest rates it to implement the inflation target pL ¼ 0. The dashed line at pH þ 1=b1 ¼ 0:01 þ 1=b1 ¼ 0:02 is the nominal interest rate in the steady-state before the target change (when the inflation target pH ¼ 0:01). The nominal interest rate after the target change takes values lower than pH þ1=b1 ¼ 0:02 in all periods t Z0. This says that nominal interest rates should be uniformly lowered to implement a lower inflation target. The slow speed of convergence to the new steady-state is a consequence of a high value of gp ¼ 0:99. For values close to but smaller than 1, changes in inflation are still the main (but not only) source of welfare losses and convergence is still slow. For smaller values of gp , the adjustment to the new steady-state is much faster. Nominal interest rates are however lowered for all values of gp , independently of the speed of convergence. To isolate the effect of the change in the inflation target, Fig. 2 shows the difference it ðpL Þit ðpH Þ between nominal interest rates with and without a target change. Again the nominal interest rates are uniformly lower if the inflation target Table 1 Parameter values. Estimated parameter values from Giannoni and Woodford (2004)
Z
gp
gw
xp
xw
j
ow
1
1
1
0.002
0.0042
0.7483
19.551
Additional parameter values b 16lx
lw
op
kw
d
0.99
0.004
1/3
0.0883
0.0356
0.0026
Parameter values used in the simulation in Section 4. A detailed description can be found in Section 4.1.
254
M. Hagedorn / Journal of Monetary Economics 58 (2011) 248–261
Optimal nominal interest rates
0.022 0.02 0.018 0.016 0.014 0.012 0.01 0
50
100
150 quarters
200
250
300
Fig. 1. Optimal nominal interest rates to implement a drop in the inflation target. The dashed line is the steady-state nominal interest rate without a target change. Parameter values are given in Table 1.
quarters
Difference in optimal nominal interest rates
0 -0.001
0
50
100
150
200
250
300
-0.002 -0.003 -0.004 -0.005 -0.006 -0.007 -0.008 -0.009 -0.01
Fig. 2. Difference it ðp Þit ðpH Þ in optimal nominal interest rates for inflation targets pL and pH , where pL o pH . Parameter values are given in Table 1. L
is smaller. Note that Fig. 2 is not just an rescaling of Fig. 1. The difference is that Fig. 2 also shows the optimal policy for the high inflation regime whereas Fig. 1 shows the nominal interest in the pre-regime-switch steady-state. These two paths differ since the problem is not time consistent, so that the old steady-state is not optimal in the first period even in the high inflation regime. This is the reason why Fig. 2 also shows the differences: to difference-out the effects due to timeinconsistency. The central bank can use two channels to lower the inflation rate, the aggregate demand channel and the expectations channel. Since the aggregate demand channel involves higher real interest rates and thus unnecessary output contractions, it is optimal to use the expectations channel only. The Fisher equation then implies that the nominal interest rate tracks the inflation rate. If the inflation target is decreased, it is optimal to uniformly lower the inflation rate (Fig. 3 shows the optimal inflation path) and therefore to uniformly lower nominal interest rates. Although the aggregate demand channel is not used, the Phillips curve implies that output cannot be fully stabilized. The fluctuations in output are however quite small, as Fig. 4 shows. Output never falls below 0.007% relative to its steady-state level. Consistent with conventional wisdom, output after a drop in the inflation target is lower than output without such a drop. At the same time, the real interest rate hardly moves. Fig. 5 shows that the real interest rate stays within a 0.002% point band around its steady-state value ð1=bÞ1, and has almost converged to it after a year. A comparison of the real interest
M. Hagedorn / Journal of Monetary Economics 58 (2011) 248–261
255
0.012
Optimal inflation rate πt
0.01 0.008 0.006 0.004 0.002 0 0
100
50
150 quarters
200
250
300
Fig. 3. The solid line is the optimal inflation rate path after a drop in the inflation target. The dashed line is the inflation rate pH before the target change. Parameter values are given in Table 1.
4 3 2
Optimal output
1
quarters
0 -1
0
50
100
150
200
250
300
-2 -3 -4 -5 -6 -7
Fig. 4. The solid line is the optimal output (multiplied with 105) after a drop in the inflation target. The dashed line is the optimal output path without a target change.
rate with and without a drop in the inflation target strengthens this observation. The difference of the real interest rate between these two regimes is about 0.00002%, i.e. virtually zero. In other words, variations in real interest rates are kept to a minimum and the aggregate demand channel is inactive. The quantitative results in this section show that the theoretical conclusions drawn from the restricted model in Section 2 do not change once features such as habit persistence, indexation and sticky wages are added. Nominal interest rates are uniformly lowered to implement a lower inflation target and real interest rates are virtually unchanged. This result is confirmed in a sensitivity analysis available in Hagedorn (2008), which shows that for a wide range of parameterizations, neither different objective functions for the central bank, nor different welfare weights, nor different parameter values, nor different assumptions about the predeterminateness of consumption, prices and wages lead to a different conclusion.
5. Adaptive expectations and imperfect credibility In all versions of the New Keynesian model considered so far, inflation expectations equal realized inflation. Two popular modifications of the standard model relax this assumption: adaptive expectations and imperfect credibility. I now discuss whether these modifications can change the conclusions drawn so far.
256
M. Hagedorn / Journal of Monetary Economics 58 (2011) 248–261
Optimal path of the real interest rate
1.012
1.012
1.011
1.011
1.010
1.010
1.009 0
1
2
3
4
5 6 quarters
7
8
9
10
Fig. 5. The solid line is the optimal path of the real interest rate (multiplied with 100) after a drop in the inflation target.
5.1. Adaptive expectations The model is the same as in Section 2 except for one difference. Expected inflation Et pt þ 1 is linked to current inflation and past expectations here: Et pt þ 1 ¼ lEt1 pt þð1lÞfð1gÞpt þ gpt þ 1 g,
ð14Þ
for some l, g 2 ½0,1, whereas expectations are fully rational in the previous section, Et pt þ 1 ¼ pt þ 1 (nested in (14) for l ¼ 0 and g ¼ 1). If l 4 0 current expectations are linked to past expectations and if g 40 expectations have a rational component. This section demonstrates that the shape of optimal policy depends on whether current expectations lag or lead current inflation. To this end two special cases are considered: no link to past expectations (l ¼ 0) so that expectations lead inflation and no rational component (g ¼ 0) so that expectations lag inflation. Two equations then describe an equilibrium:
pt ¼ kxt þ bEt pt þ 1 ,
ð15Þ
xt ¼ xt þ 1 sðit Et pt þ 1 r n Þ:
ð16Þ
Note that all shocks are set equal to zero (the same arguments as in the previous section would establish that results would be unchanged if shocks were added). Again, the policy experiment is to implement an inflation target pL that is lower than the current inflation target p n . An optimal policy is then a sequence pt and xt which minimizes the loss function 1 X
bt ½ðpt pn Þ2 þ lx ðxt xn Þ2 ,
ð17Þ
t¼0
subject to the two constraints (15) and (16). The next proposition states that allowing for adaptive expectations and l ¼ 0 does not change the main conclusions of this section. Nominal interest rates are lowered to implement a lower inflation target. Proposition 3. Assume that the zero bound on nominal interest rates is never binding and l ¼ 0 (no link to past expectations). Then nominal interest rates are uniformly lower in the new regime: it ðpL Þit ðpH Þ o 0 for all t Z 0. The reason for this result is that current inflation expectations lead current inflation, as is also the case in a rational expectations equilibrium. This explains why the results with this type of adaptive expectations are qualitatively not much different from the previous results with rational expectations. This conclusion can change if expectations lag inflation (if l 4 0 and g ¼ 0) as is illustrated in Fig. 6. In this case nominal interest rates are indeed first increased to implement a lower inflation target. The reason is that expectations lagging inflation and Eq. (15) imply that output xt ¼
pt bEt pt þ 1 o0: k
ð18Þ
M. Hagedorn / Journal of Monetary Economics 58 (2011) 248–261
257
0.045
Nominal interest Rates
0.04 0.035 0.03 0.025 0.02 0.015 0.01 0
5
10
15
20
25 30 quarters
35
40
45
50
Fig. 6. Nominal interest rates in a disinflation with adaptive expectations. Expectations lag inflation since l ¼ 0:5 and g ¼ 0. Other parameters values are k ¼ 0:024, lx ¼ 0:048, b ¼ 0:99 and s ¼ 0:161 .
Thus a disinflation will necessarily lead to a recession and thus to an increase in real interest rates. Depending on parameters, the increase in real interest rates can be large enough so that nominal interest rates initially also increase despite a drop in inflation rates. The explanation is that adaptive lagging expectations render the expectations channel substantially less effective than with rational expectations. Reducing inflation thus requires using the aggregate demand channel resulting in higher real interest rates and lower output. 5.2. Imperfect credibility The previous section established that the formation of expectations can matter for the path of optimal nominal interest rates. Unfortunately the formation of expectations is completely exogenous and thus all conclusions fully depend on the assumptions made about adaptive expectations. An alternative approach with endogenous expectations – learning the inflation target – is discussed in this section. The results derived for adaptive expectations are however useful to understand the results with endogenous expectations as they serve as reduced-form benchmark. The specific model considered in this section is developed in Erceg and Levin (2003) (EL). They consider a New Keynesian model with capital accumulation and staggered wage and price contracts of fixed duration (4 quarters). Monetary policy is not perfectly credible since households cannot observe the central bank’s inflation target but need to disentangle persistent and transitory shifts in the inflation target through observing monetary policy. Monetary policy is described through the following interest rate reaction function: gy gp ð4Þ n it ¼ gi it1 þð1gi Þ r þ pð4Þ þ ð p p Þ þ ðlnðy =y Þg Þ ð19Þ t t4 y , t t 1gi t 1gi n where pð4Þ t ¼ ðpt þ pt1 þ pt2 þ pt3 Þ=4, i is the nominal interest rate, y is the output, p is the inflation rate, p is the inflation target, r is the steady-state real interest rate, and g y is the steady-state output growth rate.17 Erceg and Levin (2003) find that their New Keynesian model with imperfect credibility accounts well for the dynamics of output, inflation and nominal interest rates during the Volcker disinflation (modeled as a very persistent drop in the inflation target). In particular, inflation is persistent, there are substantial welfare costs, and nominal interest rates are increased at the beginning of a disinflation. Fig. 7 replicates their results, which also shows the results with perfect credibility.18 Fig. 7 suggests that the imperfect credibility can change the conclusion of this paper, namely that nominal interest rates should be immediately decreased to implement a lower inflation target. However, this would be a misinterpretation of Erceg and Levin (2003). They show that their model can account for the dynamics of key variables whereas my paper considers the optimal policy during a disinflation. Three experiments are conducted to demonstrate this claim. The main argument is that a drop in pn mechanically leads to an increase in it, if pð4Þ does not fall fast enough (because of learning). However, this mechanical increase is not optimal. Instead, an optimal policy would, as suggested by the analysis in this paper, presumably involve a drop in the intercept of the monetary policy, which is consistent with the new inflation target.
17
They use the following parameters: gi ¼ 0:21, gp ¼ 0:64 and gy ¼ 0:25. I am grateful to Chris Erceg and Andy Levin for providing me with their Matlab code, which is used to reproduce their results and also to generate all the other results in this section. 18
258
M. Hagedorn / Journal of Monetary Economics 58 (2011) 248–261
Fig. 7. Replicates Fig. 6 in Erceg and Levin (2003): Disinflation under alternative informational assumptions about the inflation target.
First, it is shown that a higher value for gp ¼ 1:2 leads to an increase in nominal interest rates with full information about the central bank’s inflation target (Fig. 8 panel C). As is demonstrated in this paper, this is clearly not optimal. The explanation is that a higher value for gp leads to a larger mechanical increase in nominal interest rates, which is not offset by the small drop in pð4Þ t . Next, a different interest rate rule is considered, which sets the nominal interest rate equal to the inflation target. To ensure determinacy (otherwise the linear rational expectations model cannot be solved) the term 1:01ðpt30 pnt30 Þ is
M. Hagedorn / Journal of Monetary Economics 58 (2011) 248–261
259
Fig. 8. EL - Imperfect observability is the Erceg/Levin interest rate rule (19) under imperfect observability (same as in Fig. 7); simple – full information is the simple interest rate rule (Eq. 20) under full information; simple – imperfect observability is the simple interest rate rule (Eq. 20) under imperfect observability; EL (strong) – full information is the Erceg/Levin interest rate rule (19) under full information with gp ¼ 1:2.
added, which does not affect the results. The monetary policy rule then equals it ¼ pnt þ1:01ðpt30 pnt30 Þ:
ð20Þ
Fig. 8 shows the result of this thought experiment with full information and imperfect credibility. The nominal interest rate immediately jumps to its new target level, inflation slowly converges to its new target level and output drops. Thus, even with imperfect credibility, the results shown in Fig. 8 are consistent with the main conclusion of this paper: Nominal interest rates are uniformly lowered. Finally, Fig. 8 shows that the monetary policy, described in Eq. (20), leads to smaller welfare losses. Inflation adjusts faster to its new target level and output is always closer to its target level.
260
M. Hagedorn / Journal of Monetary Economics 58 (2011) 248–261
5.3. Optimal policy This section makes no attempt to derive the optimal policy.19 Instead it establishes two results. First, if monetary policy is not optimal, the nominal interest rate can increase before it eventually converges to its target level. However, this result is driven by the specification of the interest rate rule and not by an assumption on the observability of the inflation target. Second, the results for adaptive expectations can be used to understand why increasing nominal interest rates is unlikely to be the optimal policy in a model with imperfect credibility, at least in the framework of EL. As shown in EL, current period one-period ahead inflation expectations lead the current inflation rate, both in the data during the Volcker disinflation (Fig. 2 panel C in EL) and in their model (Fig. 7 in EL). Section 5.1 demonstrates that this type of expectation formation implies that nominal interest rates are uniformly lowered to implement a lower inflation target. Whether expectations have this property in all models of imperfect credibility is certainly beyond the scope of this paper. Two thoughts however suggest that imperfect credibility is unlikely to change the conclusions of this paper, at least in an empirically relevant model. First, if by assumption expectations lag current inflation the policy maker has no choice but to use the aggregate demand channel to reduce inflation. But whether inflation leads or lags current inflation is endogenous in a model with imperfect credibility and thus is at least partially controlled by the policy maker. A reasonable guess is that, if possible, the central bank tries to avoid a situation where expectations lag current inflation as this would lead to a drop in output. Second, an empirically relevant model should replicate EL’s finding that expectations lead inflation in the data during the Volcker disinflation. Overturning the conclusion that nominal interest is uniformly lowered in a model with imperfect credibility thus requires at least one further modification of the standard model, a modification not discussed in Sections 3 and 4.
6. Conclusion The results in this paper imply that there is an inconsistency between central bankers’ conventional wisdom and one implication of New Keynesian models. Conventional wisdom suggests that nominal interest rates should be increased to implement a lower inflation target. In contrast, the optimal policy in a New Keynesian model is to uniformly lower nominal interest rates. This result holds both in a basic New Keynesian model with sticky prices and in extensions of this model, such as Giannoni and Woodford (2004), which allow for sticky wages, price and wage indexation and habit formation in consumption. The reason is that the aggregate demand channel, which raises real interest rates to contract aggregate demand which then leads to lower inflation rates, is too costly relative to the expectations channel. The expectations channel sets nominal interest rates consistent with the private sector’s expectations of lower inflation rates in the future. Real interest rates are basically constant and thus a costly output contraction is avoided. Recent work by Christiano et al. (2005) adds two more features to the model of Giannoni and Woodford (2004): Capital formation (with adjustment costs and variable utilization rates) and firms must borrow working capital to finance their wage bill. Adding capital puts an additional constraint on the real interest rate – it has to equal the marginal productivity of capital – and thus makes the aggregate demand channel less effective. The expectations channel is not affected since real interest rates are basically kept constant anyway when nominal interest rates track the inflation rate. These arguments are consistent with the experiments in Christiano et al. (2005). For example, they find larger increases in inflation in response to a decrease in nominal interest rates when they drop the assumption of variable capital utilization (see row 1 of Fig. 6 in Christiano et al., 2005). The assumption that firms finance their wage bill through borrowing capital would further strengthen my results. An increase in nominal interest rates increases firms’ marginal costs and thus leads to price increases. Adding this feature to the model would make increasing nominal interest rates an even worse choice to implement a lower inflation target. Again Christiano et al. (2005) conduct experiments that support these arguments. When they drop the assumption that firms have to borrow their wage bill, a decrease in nominal interest rates leads to larger increases in inflation rates (see row 5 of Fig. 6 in Christiano et al., 2005). Assuming adaptive instead of fully rational expectations does not change these conclusions if expectations lead realized inflation. If, however, current expectations lag current inflation, the role of the expectations channel is strongly diminished and the aggregate demand channel has to be used to implement a lower inflation target. Depending on parameters it can then be optimal to increase nominal interest rates initially. These experiments assign an important role to the specific (exogenous) assumptions about the formation of expectations. They also explain the findings derived in the environment of Erceg and Levin (2003), a model where the low inflation target is not perfectly credible.20 The reason is that expectations lead inflation in Erceg and Levin (2003) and therefore the results for adaptive expectations suggest that a uniform lowering 19 This would be a daunting task as this is a dynamic optimal policy problem with an informed policy maker. Any policy choice reveals private information to households something the policy maker takes into account. Solving this dynamic signaling program is beyond the scope of this paper. 20 Ball (1995a) is another example with an imperfectly credible inflation target.
M. Hagedorn / Journal of Monetary Economics 58 (2011) 248–261
261
of nominal interest rates is optimal.21 Thus, although imperfect credibility seems to be a candidate to overcome the conclusion of this paper, the mechanism behind such a reasoning is not obvious. In particular, it is unclear how a policy that leads to private sector expectations lagging inflation and thus to substantial output losses can be optimal.22
Acknowledgements ¨ I would like to thank Klaus Adam (the associate editor), Robert King (the editor), an anonymous referee, Dirk Kruger, and the seminar participants at the European Central Bank for their helpful comments and suggestions that have been incorporated throughout the paper. Appendix A. Supplementary data Supplementary data associated with this article can be found in the online version at doi:10.1016/j.jmoneco.2011.05.011.
References Alvarez, F., Lucas, R.J., Weber, W.E., 2001. Interest rates and inflation. American Economic Review 91, 219–225. Backus, D., Driffill, J., 1985. Inflation and reputation. American Economic Review 75, 530–538. Ball, L.M., 1994. Credible disinflation with staggered price setting. American Economic Review 84, 282–289. Ball, L.M., 1995a. Disinflations with imperfect credibility. Journal of Monetary Economics 35, 5–23. Ball, L.M., 1995b. Time-consistent policy and persistent changes in inflation. Journal of Monetary Economics 36, 329–350. Ball, L.M., Mankiw, N.G., Reis, R., 2005. Monetary policy for inattentive economies. Journal of Monetary Economics 52, 703–725. Barro, R.J., 1986. Reputation in a model of monetary policy with incomplete information. Journal of Monetary Economics 17, 3–20. Benigno, P., Woodford, M., 2006. Linear-quadratic approximation of optimal policy problems. NBER Working Paper W12672. Calvo, G.A., 1983. Staggered prices in a utility-maximizing framework. Journal of Monetary Economics 12, 383–398. Chari, V.V., Kehoe, P., 1999. Optimal fiscal and monetary policy. In: Taylor, J., Woodford, M. (Eds.), Handbook of Macroeconomics, vol. 1. North-Holland, Amsterdam. Christiano, L.J., Eichenbaum, M., Evans, C.L., 2005. Nominal rigidities and the dynamic effects of a shock to monetary policy. Journal of Political Economy 113, 1–45. Clarida, R., Gali, J., Gertler, M., 1999. The science of monetary policy: a new Keynesian perspective. Journal of Economic Literature 37, 1661–1707. Erceg, C.J., Henderson, D.W., Levin, A.T., 2000. Optimal monetary policy with staggered wage and price contracts. Journal of Monetary Economics 46, 281–313. Erceg, C.J., Levin, A.T., 2003. Imperfect credibility and inflation persistence. Journal of Monetary Economics 50, 915–944. Gaspar, V., Smets, F., Vestin, D., 2006. Adaptive learning, persistence, and optimal monetary policy. Journal of the European Economics Association 4, 376–385. Giannoni, M.P., Woodford, M., 2004. Optimal inflation targeting rules. In: Bernanke, B.S., Woodford, M. (Eds.), The Inflation-Targeting Debate. University of Chicago Press, Chicago, pp. 93–162. Goodfriend, M., King, R.G., 2005. The incredible Volcker disinflation. Journal of Monetary Economics 52, 981–1015. Hagedorn, M., 2008. Nominal and real interest rates during an optimal disinflation in New Keynesian models. ECB Working Paper No. 878, European Central Bank. Ireland, P.N., 1995. Optimal disinflationary paths. Journal of Economic Dynamics and Control 19, 1429–1448. Ireland, P.N., 2007. Changes in the Federal Reserve’s inflation target: causes and consequences. Journal of Money, Credit and Banking 39, 1851–1882. Lindsey, D.E., Orphanides, A., Rasche, R., 2005. The Reform of October 1979: How It Happened and Why. Finance and Economics Discussion Paper No. 2005-02. Federal Reserve Board of Washington. Milani, F., 2006. The Evolution of the Fed’s Inflation Target in an Estimated Model under RE and Learning. Mimeo, University of California, Irvine. Milani, F., 2007. Expectations, learning and macroeconomic persistence. Journal of Monetary Economics 54, 2065–2082. Orphanides, A., Williams, J.C., 2004. Imperfect knowledge, inflation expectations and monetary policy. In: Bernanke, B., Woodford, M. (Eds.), The InflationTargeting Debate. University of Chicago Press. Orphanides, A., Williams, J.C., 2005a. The decline of activist stabilization policy: natural rate misperceptions, learning, and expectations. Journal of Economics Dynamics and Control 29, 1927–1950. Orphanides, A., Williams, J.C., 2005b. Inflation scares and forecast-based monetary policy. Review of Economic Dynamics 8, 498–527. Orphanides, A., Williams, J.C., 2006. Monetary policy with imperfect knowledge. Journal of the European Economics Association 4, 366–375. Primiceri, G.E., 2006. Why inflation rose and fell: policymakers’ beliefs and US postwar stabilization policy. Quarterly Journal of Economics 121, 867–901. Rotemberg, J.J., Woodford, M., 1997. An optimization-based econometric framework for the evaluation of monetary policy. NBER Macroeconomics Annual, vol. 12; 1997, pp. 297–346. Sargent, T.J., Williams, N., Zha, T., 2006. Shocks and government beliefs: the rise and fall of American inflation. American Economic Review 96, 1193–1224 . Woodford, M., 2003. Interest and Prices: Foundations of a Theory of Monetary Policy. Princeton University Press, Princeton. Yun, T., 2005. Optimal monetary policy with relative price distortions. American Economic Review 95, 89–109.
21 Goodfriend and King (2005) also consider the Volcker disinflation in an environment where agents are uncertain whether the disinflation plan is credible. Private sector beliefs are however exogenous and not derived from Fed policy. The exogenous specification of beliefs implies that expectations lag inflation and thus Goodfriend and King (2005) find a strong increase in real and nominal interest rates during a disinflation (not surprisingly given the results for adaptive expectations in this paper). 22 At least in the environment of Erceg and Levin (2003), such a mechanism seems not to be present. There is a large literature that assumes that agents have imperfect knowledge of the economy. The key result in this literature is that the persistence of inflation (expectations) is raised and that the trade-off between inflation and output stabilization is distorted. This result, for example, helps to account for inflation scares (Orphanides and Williams, 2005b), leads to different conclusions about optimal monetary policy (Orphanides and Williams, 2004, 2005a, 2006; Gaspar et al., 2006), and improves the fit of DSGE models (Milani, 2007).
Journal of Monetary Economics 58 (2011) 262–272
Contents lists available at ScienceDirect
Journal of Monetary Economics journal homepage: www.elsevier.com/locate/jme
Did gold-standard adherence reduce sovereign capital costs? Ron Alquist a,n, Benjamin Chabot b a b
Bank of Canada, 234 Wellington Street, Ottawa, Canada ON K1A 0G9 Federal Reserve Bank of Chicago and NBER, USA
a r t i c l e in f o
abstract
Article history: Received 16 December 2009 Received in revised form 10 March 2011 Accepted 22 March 2011 Available online 30 March 2011
A commonly cited benefit of the classical gold standard is that it reduced borrowing costs by signaling a country’s commitment to financial probity. Using a new dataset, this paper tests whether gold-standard adherence was negatively correlated with the cost of capital. Conditional on UK risk factors, there is no evidence that the bonds issued by countries off gold earned systematically higher excess returns than the bonds issued by countries on gold. This conclusion is robust to allowing betas to differ across exchange-rate regimes; to including other determinants of the country risk premium; and to controlling for the British Empire effect. & 2011 Elsevier B.V. All rights reserved.
1. Introduction The gold standard before 1914 is generally considered to be a prime example of an exchange-rate regime’s ability to confer credibility on a country’s macroeconomic policy. The ‘‘good-housekeeping seal of approval’’ interpretation of the gold standard is that gold convertibility ensured that the government acted consistently over time, so adherence to gold served as a signal of financial probity. According to this view, countries that always maintained convertibility or suspended it only during widely agreed-upon circumstances, such as war, should have been rewarded with lower borrowing costs. Despite this sharp prediction, economists have reached conflicting conclusions about the effect of gold-standard adherence on sovereign borrowing costs. In a seminal study, Bordo and Rockoff (1996) compare the coupon yields (coupon–price ratios) of sovereign bonds issued by nine countries and find substantial cross-country variation in preWorld War I yields. They attribute the yield differences to differing commitments to gold. These findings are consistent with the country studies of Martin-Acena (1993) and Sussman and Yafeh (2000), and were confirmed in a larger crosssection of countries by Obstfeld and Taylor (2003). The reduction in borrowing costs associated with adhering to gold is estimated to be about 30–40 basis points per year (Bordo and Rockoff, 1996; Obstfeld and Taylor, 2003). On the other hand, Ferguson and Schularick (2006) find no evidence that the capital market rewarded gold-standard adherence and conclude that membership in the British Empire was key to reducing borrowing costs (British Empire effect). Clemens and Williamson (2004) examine capital flows rather than bond yields and present evidence that goldstandard adherence was only marginally important compared with fundamental determinants of capital productivity. Flandreau and Zumer (2004) conclude that adhering to the gold standard had a negligible influence on coupon yields conditional on other covariates intended to capture the effect of fiscal and monetary policy on sovereign borrowing costs. They argue that international lenders focused on variables that forecast a country’s ability to repay its external debt and that these forecasts assigned little weight to the exchange-rate regime. Mitchener and Weidenmier (2009) compare
n
Corresponding author. Tel.: þ 1 613 782 8672. E-mail address:
[email protected] (R. Alquist).
0304-3932/$ - see front matter & 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.jmoneco.2011.03.006
R. Alquist, B. Chabot / Journal of Monetary Economics 58 (2011) 262–272
263
within-country coupon yields of bonds with and without gold clauses and conclude that the international capital market placed little weight on gold-standard adherence. The crux of the disagreement can be traced to differences in the available data. In contrast to today, sovereign borrowers during the gold-standard era issued debt with different maturities and at infrequent intervals. As a result, a typical nineteenth-century sovereign borrower had only a handful of maturities trading at any given time, making it impossible to compare a cross-section of bonds with matched maturities. To complicate matters further, most countries issued bonds with embedded options that make it impossible to compute yield-to-maturity and, thus, prevent direct comparisons of yields across countries. Data limitations have forced past researchers to infer borrowing costs by comparing the coupon yield of bonds at different points of the yield curve. Typically, a single representative bond is chosen for each country based on availability, liquidity or the amount outstanding. The coupon yield is observed for as long as possible, after which another representative bond is chosen. Because bonds with the same (unobserved) discount rate can have very different coupon yields attributable to differences in time to maturity or coupon amounts, there is no guarantee that the observed differences in the coupon yield of bonds with different maturities actually are due to differences in the exchange-rate regime rather than the term structure of the borrower’s external debt. In light of these challenges, it is not surprising that authors using different representative bonds have arrived at conflicting conclusions. Since it is unlikely that a consensus can be reached with the existing data, this paper proposes a test of the goodhousekeeping hypothesis based on a new and much larger sample of realized holding-period returns. With over 55,000 bond returns, this new dataset represents an almost fortyfold increase in the size of the cross-section of available bond prices.1 It consists of every regularly quoted sovereign bond from the official quotation list of the London Stock Exchange between 1870 and 1907. Measuring the cost of capital by computing monthly holding-period returns avoids the difficulty of inferring discount rates from the coupon yield of bonds with different times to maturity. Holding-period returns is a new way to measure the cost of capital in tests of the good-housekeeping hypothesis, but it is very common in assetpricing tests that try to account for cross-sectional differences in expected bond returns using ex-ante observable characteristics. The evidence indicates that adherence to the gold standard did not reduce the cost of capital. Across a variety of specifications and samples, there is no systematic link between a country’s adherence to gold and the risk-adjusted return of its sovereign debt. Conditional on British risk factors, the returns of bonds issued by countries on and off gold are statistically indistinguishable from one another. Nor are there systematic differences in the sensitivity of bond returns to pervasive risk factors across exchange-rate regimes. These findings cast doubt upon the good-housekeeping hypothesis and support the conclusion reached by Flandreau and Zumer (2004) that gold-standard adherence did not have an economically important effect on the cost of capital. Section 2 discusses the logic of the gold standard as a repeated game. Section 3 examines the close parallels between tests of the good-housekeeping hypothesis and asset-pricing tests designed to detect differences in mean returns across securities. Section 4 describes the empirical specification, methods and data used to test the good-housekeeping hypothesis. Section 5 reports the results and Section 6 presents a set of robustness tests. 2. The gold standard as a repeated game Bordo and Kydland (1995) model the gold standard as a credible commitment mechanism that evolved to overcome the time-inconsistency problem associated with international borrowing. Borrowers and lenders in the international capital market play a repeated game in which the government chooses a mix of borrowing, taxation, and inflation to minimize the deadweight loss for a given level of revenue. The government’s ability to print money and thereby reduce the real burden of its nominally denominated external debt creates an incentive problem when it only cares about the welfare of its residents (Bohn, 1991). Foreign lenders recognize the distorted incentives of the borrowing country and are unwilling to lend funds without a credible commitment that the government will repay the real value of its debt. In the repeated game, a government can overcome the time-inconsistency problem by adopting an easy-to-monitor policy that prevents it from devaluing its currency. The good-housekeeping hypothesis is that adherence to gold served as such a mechanism. The gold-standard equilibrium strategy consists of the government’s commitment to currency stability by standing ready to convert local currency into gold on demand. In response, the international bond market rewards the government that ties its currency to gold with a lower cost of capital. The empirical implication of the good-housekeeping hypothesis is that the international capital market assigned a lower price to, and demanded commensurately higher expected returns from, bonds issued by countries that did not adhere to the gold standard. The ‘‘good-housekeeping’’ repeated game equilibrium relies on the capital market forgoing current expected profits to punish governments that have left gold. For example, if two different countries issue bonds with identical expected cash flows, the equilibrium punishment strategy requires investors to assign different prices if the countries have differing 1 The appendices with supplemental materials describing this new dataset are available on Science Direct. To the best of our knowledge, the two largest previous samples of nineteenth-century sovereign bond prices are the datasets available from Global Financial Data (GFD) used by Obstfeld and Taylor (2003) and the one constructed by Ferguson and Schularick (2006). GFD contains 892 annual observations while Ferguson and Schularick’s dataset contains 1461 annual observations.
264
R. Alquist, B. Chabot / Journal of Monetary Economics 58 (2011) 262–272
Table 1 Selected tests of the good-housekeeping hypothesis. Authors
Baseline regression specification
Controls in Xit0
Bordo–Rockoff
SPREADit ¼ ai þ bi SPREADWt þ dGSit þ Xit0 g þ eit eit ¼ ri eit1 þ uit
Lagged money growth Lagged deficit-GNP ratio
Obstfeld–Taylor
SPREADit ¼ ai þ bi SPREADWt þ d1 DEF GSit þ d2 NODEF GSit þ Xit0 g þ eit eit ¼ ri eit1 þ uit
Lagged inflation Lagged debt-output level Export–GDP ratio Real income per capita Terms of trade British Empire dummy War dummies
Flandreau–Zumer
SPREADit ¼ ai þ dGSit þ Xit0 g þ eit eit ¼ ri eit1 þ uit
Interest service–revenue ratio Reserves–bank notes ratio Exports per capita Deficit-revenue ration Exchange-rate volatility Default Memory of default Enfranchised population Political crisis dummies
Notes: SPREADit ¼ Yieldit YieldUK,t. In Bordo and Rockoff (1996), SPREADWt ¼ YieldAVG,t YieldUK,t, where YieldAVG,t is the average of all coupon yields in their sample. In Obstfeld and Taylor (2003), SPREADWt ¼ YieldWt YieldUK,t , where YieldWt is the GDP-weighted average of all coupon yields in their sample.
commitments to gold. Assigning different prices to the same expected cash flow creates a statistical arbitrage opportunity. Therefore, the repeated game equilibrium requires a collective action mechanism to prevent arbitrage-seeking investors from pushing the prices of otherwise identical off- and on-gold bonds together. Large institutional investors who were both sufficiently patient to play the punishment strategy and large enough to influence equilibrium prices, such as the Council of Foreign Bondholders and investment banks that underwrote bond issues, were good candidates to punish countries that abandoned the gold standard. The available archival evidence suggests that the Council was effective at both organizing lenders when borrowers defaulted and renegotiating with large borrowers like Argentina, Brazil, and Turkey (Mauro and Yafeh, 2003). The test of the hypothesis that off-gold bonds earned higher risk-adjusted returns than on-gold bonds is an empirical test of whether these organizations were sufficiently powerful to punish countries that left gold. 3. Testing the good-housekeeping hypothesis The theory proposed by Bordo and Kydland yields a clear prediction: Countries were rewarded with a low discount rate if they maintained gold convertibility. But bond discount rates vary for reasons other than a country’s gold-standard adherence, and any test of the hypothesis needs to control for other determinants of a country’s risk premium. Traditional tests of the good-housekeeping hypothesis compare the coupon yields of bonds off and on gold, controlling for other risk factors by estimating regressions that are very similar to asset-pricing tests designed to detect cross-sectional differences in returns, conditional on other pervasive risk factors. Indeed, Bordo and Rockoff write that their empirical specification of the good-housekeeping hypothesis is ‘‘inspired by the capital asset pricing model’’ (Bordo and Rockoff, 1996). The empirical specifications of selected tests of the good-housekeeping hypothesis are reproduced in Table 1. All of these tests examine the effect of gold-standard adherence on risk-adjusted returns by formally testing for a shift in the intercept (d o0) of a model that controls for other determinants of the sovereign risk premium. The regression tests are formulated to detect a common difference in the mean risk-adjusted coupon yield between on- and off-gold countries. The specifications listed in Table 1 are very similar to factor model-based asset pricing tests of whether cross-sectional variation in ex-ante observable characteristics generates differences in mean excess returns.2 Both control for risk using factor models and test whether an observable characteristic affects risk-adjusted returns by examining cross-sectional differences in portfolio intercepts. Traditional tests of the good-housekeeping hypothesis and factor model based tests are thus fully consistent with each another. Holding-period returns are a natural way to measuring borrowing costs when the number of bonds is too small to identify the yield curve or to compare coupon yields at matched maturities. Like coupon yields, holding-period returns are correlated with the unobservable discount rate and can be used to infer differences in expected returns (Campbell, 1995). Unlike coupon yields, holding-period returns include both the expected coupon yield and the expected capital gain. Many sovereign bonds during the late nineteenth century traded well above or below par, and rational investors surely expected capital losses or gains when purchasing these bonds. Returns incorporate these expected changes. 2
For example, Cornell and Green (1991), Fama and French (1993), and Elton et al. (1995).
R. Alquist, B. Chabot / Journal of Monetary Economics 58 (2011) 262–272
265
4. Empirical methods Using the holding-period returns of value-weighted country portfolios accounts for both maturity mismatch and embedded options. For each country, the holding-period return of the value-weighted portfolio of bonds outstanding is computed. If country i has J bonds outstanding at time t, the return of country i’s portfolio is Rit ¼
J X
wijt Rijt
ð1Þ
j¼1
where wijt is the market-value weight of bond j in country i at time t; Rijt ¼(Pijt þCijt)/Pijt 1 is the gross holding-period return of bond j in country i; Pijt is the price of the bond at time t; and Cijt is the coupon payment, if any, between time t–1 and time t. The return and amount outstanding of all bonds is directly observable, as is whether a bond has been called and redeemed at par. The use of holding-period returns rather than coupon yields to measure borrowing costs accounts for the maturity mismatch caused by both differences in maturity and embedded options contained in many of the sovereign bonds issued during this period. For example, redemption options gave the borrower the right to repay the bond at par between prespecified dates. In addition, sinking fund clauses committed the borrower to redeem annually a fixed portion of the debt outstanding and often granted the issuer the option of buying back the debt in the open market or redeeming it at par. In both cases the timing of the return of principal depended upon the future path of market prices. If two countries had bonds that matured at different dates, differences in observed coupon yields could be due to observing different points on identical yield curves (term structures) rather than actual differences in yield curves. If the bond also contained an embedded option, the measurement error becomes more acute. The existence of embedded options biases the coupon-yield measures common in the good-housekeeping literature. These options create what Flandreau and Zumer (2004) call ‘‘conversion risk’’. Flandreau and Zumer (2004) control for conversion risk by carefully selecting bonds with conversion options that are likely to be far out-of-the-money. This strategy minimizes the measurement error problem, but, with the London data used in this paper, it comes at the cost of having to exclude many countries that only have bonds with embedded options in or close to in-the-money. Prepayment risk is rare in modern-day sovereign bond markets but quite common in the markets for mortgage-backed securities, real-estate investment trusts and corporate bonds. Studies that examine the returns of these securities face exactly the same problem as the one this paper faces: Does an observable trait explain differences in expected returns? The use of holding-period returns and factor models of the type that inspired Bordo and Rockoff’s specification are commonly used to measure differences in risk-adjusted returns across bond portfolios with different maturities and embedded options.3 Thus, the use of holding-period returns to measure sovereign borrowing costs facilitates the comparison of bonds with different, possibly stochastic, maturities and takes account of expected capital gains and losses. 4.1. Leveraged portfolios The hypothesis that expected returns differ across exchange-rate regimes can be tested by forming a leveraged portfolio that mimics the return associated with purchasing all bonds issued by countries off gold and selling short all bonds issued by countries on gold.4 At the beginning of each holding period, all bonds are assigned either to an on-gold or off-gold portfolio. If a country adopts the gold standard, that country’s bonds is removed from the off-gold portfolio and added to the on-gold portfolio at the beginning of the next holding period and vice versa. If the good-housekeeping hypothesis is valid, the leveraged portfolio should earn a positive risk-adjusted return. Contemporary and modern sources provided the dates that each country joined or left gold.5 In cases where it is difficult to determine de jure versus de facto adherence to the gold standard, the country is coded as adhering to gold from the de jure convertibility date. In many cases, gold-standard adherence can be determined quite precisely because the month, and sometimes even the day, on which a country adopted or abandoned convertibility was widely reported. In the cases where only the year that a country adopted the gold standard could be found, adherence is dated from January 1 of that year. It is important to stress that because of how gold-standard adherence is dated, the benchmark regressions are biased toward finding evidence in favor of the good-housekeeping hypothesis. The London capital market may have anticipated switches in gold-standard adherence and repriced bonds in response to the change in expectations. If the goodhousekeeping hypothesis is valid, the bonds issued by countries off gold that switch to being on gold experience a capital gain as the market reprices them at a lower discount rate. If the market anticipates the switch from off to on, the returns of 3 Bond factor models in the spirit of Fama and French (1993) and Elton et al. (1995) typically include market, term structure and default factors similar to the stock market (market), consol (term structure) and corporate bond (default) factors. These models are often used to test for differences in the risk-adjusted return (alpha) of bond portfolios that have different maturities and embedded options. 4 To be clear, the test is formulated in this way not because nineteenth-century investors actually formed a leveraged portfolio based on goldstandard adherence but because doing so is a way to test for differences in mean returns across the two exchange-rate regimes. 5 A detailed list of the sources can be found in the appendices. The appendices with supplemental materials are available on Science Direct.
266
R. Alquist, B. Chabot / Journal of Monetary Economics 58 (2011) 262–272
the off gold portfolio are high even before the date of official convertibility. Similarly, the bonds issued by countries on gold that switch off experience a capital loss as the market reprices them at a higher discount rate. Again, if the market anticipates such a switch, the returns of the on-gold portfolio are lower even before the country official abandons convertibility. Thus, the returns of the off-gold portfolio are biased upward due to the dating procedure while the returns of the on-gold portfolio are biased downward. The two effects bias the returns of the leveraged portfolio upward. By sorting bonds into off- and on-gold portfolios and using this dating procedure, the good-housekeeping hypothesis is extended every advantage in the empirical test.6 4.2. Empirical specification A leveraged portfolio that is long in the bonds issued by countries off gold and short in the bonds issued by countries on gold is formed every period. If the two portfolios were equally risky, and the market punished bonds issued by countries off gold, this strategy would have generated positive excess returns. The key words are ‘‘equally risky’’. Investors during the late nineteenth century almost surely demanded compensation for risks beyond those embodied in gold-standard adherence. If exposure to other risk factors differed across portfolios, differences in holding-period returns may have been due to exposure to the other risks and not exclusively due to the differences in gold-standard adherence. The factor pricing model controls for pervasive risk and compares the return of a test portfolio to that of a similarly risky portfolio of British financial assets. The estimated regression is: Rit Rft ¼ ai þ b1 ðRCON,t Rft Þ þ b2 ðRMKT,t Rft Þ þ b3 ðRCORP,t Rft Þ þ et
ð2Þ
where Rit is the time t return of portfolio i; RCON,t is the time t return on the UK government consol; RMKT,t is the return on the value-weighted portfolio of all British equities at time t; and RCORP,t is the value-weighted portfolio of UK corporate bonds. The London banker’s bill rate is the proxy for the risk-free rate Rft. ai is called Jensen’s alpha after Jensen (1967), who proposed using it to measure a portfolio’s return controlling for risk. Alpha measures the difference between portfolio i’s return and the return of the portfolio of British securities with percentage weights. b1 invested in the UK government consol, b2 invested in the value-weighted UK stock market portfolio, b3 invested in the value-weighted British bond market portfolio, and 1 b1 b2 b3 invested in the London banker’s bill. The excess return of the leveraged portfolio is estimated with the regression equation: Roff ,t Ron,t ¼ a þ b~ 1 ðRCON,t Rft Þ þ b~ 2 ðRMKT,t Rft Þ þ b~ 3 ðRCORP,t Rft Þ þ et
ð3Þ
where b~ k ¼ b~ off ,k b~ on,k by construction. The betas of the leveraged portfolio in Eq. (3) are equal to the difference in the sensitivities of the off- and on-gold portfolios to fluctuations in the UK risk factors. A test of the good-housekeeping hypothesis amounts to the test that a is greater than zero. An advantage of this test is that it addresses the problem that countries did not leave gold randomly. If a country wanted to remain on gold but was forced off due to a negative business-cycle shock, it is important to distinguish between excess returns due to exposure to business-cycle risk and the repeated game punishment. If business-cycle shocks had been correlated across countries, UK investors could have legitimately demanded higher expected returns as compensation for bearing greater business-cycle risk. In this case, the good-housekeeping hypothesis could be false, but the returns of the bonds issued by countries on gold would be lower because they were less exposed to British business-cycle risk. By comparing foreign returns with this control group of similarly risky UK securities, it is possible to disentangle the two effects and test whether investors demanded a premium due to gold-standard adherence or business-cycle risk. 4.3. Data These methods necessarily require monthly return data from a large cross-section of sovereign bonds. The dataset consists of a sample of sovereign and colonial bonds that were traded on the London Stock Exchange between 1870 and 1907. It contains the bid and ask prices and coupon payments for every foreign government bond regularly quoted on the exchange. The data represent a broad cross-section of bonds issued by countries both on and off gold (Fig. 1). The prices are sampled every 28 days from the official Friday quotation list published in the Money Market Review and the Economist.7 The price and coupon data are used to compute a time series of 28-day holding-period returns corrected for sovereign defaults.8 6 In an early draft, we controlled for anticipation effects by forming perfect-foresight portfolios. The bonds were assigned bonds to the off- and ongold portfolios up to two years before the actual change in status occurred. The conclusion that gold-standard adherence did not affect sovereign borrowing costs is robust to this alternative coding scheme. These results are available upon request. 7 The holding period is 28 days because the sources published the London Stock Exchange official bid and ask prices every Friday. The prices were sampled every four weeks. 8 More information on the underlying data is contained in the appendices available on Science Direct.
Argentina Australia Austria-Hungary Belgium Brazil British Guiana Bulgaria Canada Ceylon Chile China Colombia Costa Rica Denmark Ecuador Egypt France Germany Greece Guatemala Hawaii Honduras Hong Kong Italy Jamaica Japan Liberia Mauritius Mexico Netherlands New Zealand Nicaragua Norway Orange Free State Paraguay Peru Portugal Russia Saint Lucia Santo Domingo South Africa Spain Straits Settlements Sweden Trinidad Turkey United States Uruguay Venezuela
1907
1906
1904
1905
1903
1902
1901
1900
1899
1898
267
1897
1896
1895
1893
1894
1892
1891
1889
1890
1887
1888
1885
1886
1883
1884
1881
1882
1880
1879
1877
1878
1876
1875
1873
1874
1872
1871
1870
R. Alquist, B. Chabot / Journal of Monetary Economics 58 (2011) 262–272
1 1
Fig. 1. Gold Standard Adherence by Country, 1870–1907. Notes: Countries are coded by year, even if we know the month the country adopted the gold standard. For example, Austria–Hungary adopted gold on August 2, 1892, but we code it as adhering from January 1, 1892 for this table. In cases where a country adhered to the gold standard for less than a year, we code it as adhering to gold for the entire year in the table. For example, Greece adhered to gold from January 1885–September 1885. We code it as adhering to gold for all of 1885.
4.4. Sample of countries In addition to the challenges associated with consistently measuring the sovereign cost of capital during the late nineteenth century, a possible explanation for the lack of consensus among previous tests of the good-housekeeping hypothesis is that each study uses a different sample. Since the sample of countries represented in the dataset spans those considered in previous studies, it is possible to examine the effect of varying the sample of countries. The tests are conducted on the full sample of countries, as well as on subsamples corresponding to those used in Bordo and Rockoff (1996), Bordo and Schwartz (1999), Obstfeld and Taylor (2003), and Flandreau and Zumer (2004).9
4.5. Country weights It is also important to guard against the possibility that the conclusions are driven by outliers. Some countries have much larger bond issues than others, and any conclusions should be robust to the weighting scheme. To address this problem, both value-weighted and equally weighted portfolios are used. The value-weighted portfolio weights each bond 9
The countries in these subsamples are listed in the appendices available on Science Direct.
268
R. Alquist, B. Chabot / Journal of Monetary Economics 58 (2011) 262–272
by its market value. For example, if the market value of all Argentine bonds is ten times that of Danish bonds, the returns of Argentine bonds receive ten times the weight of returns of Danish bonds in the value-weighted portfolio. Thus, weighting returns by the market value of the debt outstanding weights large bond issues more heavily. The equally weighted portfolio is used to assess if large borrowers drive the conclusions; it consists of individual country portfolios that are themselves value-weighted. If there are N countries in the sample, the return of each country portfolio receives a weight of 1/N. This weighting scheme does not bias the portfolio’s returns toward those of the large borrowers. 5. Empirical results Table 2 reports the individual regression results for the off- and on-gold value-weighted and equally weighted portfolios. It also reports the regression results for the leveraged portfolio in Eq. (3) that is long the off-gold portfolio and short the on-gold portfolio. The table shows that the British factor model does well in accounting for the variation in offand on-gold portfolio returns. The adjusted R-squared statistics are respectable for monthly data—between 12% and 20%. When one forms the leveraged portfolio by taking the difference between the off- and on-gold portfolios, the R-squared statistics are low, which suggests that the returns from the leveraged portfolio are approximately white noise. This finding is what one expects under the null hypothesis that the gold standard was not a determinant of sovereign borrowing costs. Sorting bonds into off- and on-gold portfolios did not generate systematically higher returns after controlling for the UK market factors. The difference between the unconditional mean return of off-gold and on-gold bonds was about 1.4–1.5% per year, depending on the weighting scheme. This evidence seems to suggest the presence of a gold premium: Off-gold bonds paid higher returns to induce investors to hold them because they were perceived to be riskier. But projecting the returns on the market factors shows that the difference in risk-adjusted returns, measured by the alphas, are economically small, statistically insignificant, and have signs opposite to those predicted by the good-housekeeping hypothesis. The betas obtained from the leveraged portfolio indicate that the off-gold bond portfolio is more sensitive to fluctuations in the UK government consol index and the British corporate bond index than the on-gold portfolio. This evidence suggests that the higher unconditional mean return of the off-gold portfolio compared with that of the on-gold portfolio is attributable to the off-gold portfolio’s greater exposure to the risk associated with fluctuations in these UK risk factors. Thus, going long on bonds issued by countries off gold and shorting bonds issued by countries on gold would have generated positive returns, but the excess returns represented compensation for bearing more risk associated with fluctuations in the UK market factors rather than failing to adhere to the gold standard. To examine the sensitivity of this conclusion to changing the sample, Table 3 reports the regression results for leveraged off-gold minus on-gold portfolios using different subsamples of countries. Depending on the sample, sovereign off-gold bonds generated an average return between 1.6% and 2.5% higher per year than the average return generated by bonds on gold. Again, the excess return is primarily attributable to differences in exposure to business-cycle risk rather than market punishment for not adhering to gold. Once market risk is controlled for by comparing the leveraged portfolios with similarly risky British securities, the excess returns vanish. The alphas of the leveraged portfolios decrease in size and, in all cases, are not statistically different from zero. In two out of the five country samples, the negative alphas contradict the empirical implication of the good-housekeeping hypothesis. In both the full sample and the Obstfeld–Taylor sample, off-gold bonds earned smaller risk-adjusted returns than on-gold bonds. The betas in Panel A are positive with only two exceptions. In general, the off-gold portfolios are more sensitive to movements in the returns of UK government consol, stock, and corporate bond indices than the on-gold portfolios, Table 2 Excess return regressions: off- and on-gold portfolios. Value-weighted
Equally weighted
Off gold
On gold
Off on
Off gold
On gold
Off on
a
4.24 0.11 ( 0.08)
2.71 0.49 (0.72)
1.53 0.59 ( 0.44)
4.33 0.90 ( 0.51)
2.90 0.91* (1.92)
1.43 1.80 ( 1.09)
bCON
0.359*** (3.97)
0.132*** (2.78)
0.227** (2.40)
0.321*** (2.60)
0.153*** (4.63)
0.168 (1.45)
bMKT
0.407*** (5.00)
0.305*** (7.18)
0.101 (1.19)
0.730*** (6.57)
0.245*** (8.26)
0.485*** (4.66)
bCORP
0.365 (3.73)***
0.100(1.96)*
0.265 (2.58)***
0.212 (1.58)
0.101*** (2.83)
0.111 (0.88)
0.208
0.126
0.062
0.179
0.180
0.087
Mean excess return
R
2
Notes: The regressions are Eqs. (2) and (3). bCON, bMKT, and bCORP are the coefficients associated with the UK government consol, the British equity market index, and UK corporate bond index, respectively. The mean excess return and estimated alpha are expressed in annualized percentage points. Heteroskedasticity and autocorrelation robust t-statistics are in parentheses. n Indicates significance at the 10% level. nn Indicates significance at the 5% level. nnn Indicates significance at the 1% level.
R. Alquist, B. Chabot / Journal of Monetary Economics 58 (2011) 262–272
269
Table 3 Excess return regressions: off-gold portfolio—on-gold portfolio.
Panel A: Value-weighted Mean excess return
a bCON bMKT bCORP 2
R Success rate (%) Panel B: Equally weighted Mean excess return
a bCON bMKT bCORP 2
R Success rate (%)
Full
Bordo–Rockoff
Bordo–Schwartz
Obstfeld–Taylor
Flandreau–Zumer
1.53 0.59 ( 0.44) 0.227** (2.40) 0.101 (1.19) 0.265*** (2.58) 0.062
2.33 0.48 (0.34) 0.141 (1.45) 0.000 ( 0.01) 0.387*** (3.69) 0.045
1.58 0.08 (0.07) 0.052 (0.60) 0.167** (2.17) 0.145 (1.56) 0.027
2.26 0.37 ( 0.23) 0.217** (1.99) 0.134 (1.37) 0.365*** (3.09) 0.069
2.52 0.70 (0.49) 0.314*** (3.18) 0.013 (0.15) 0.272** (2.54) 0.047
24.1
68.9
48.4
39.1
78.7
1.43 1.80 ( 1.09) 0.168 (1.45) 0.485*** (4.66) 0.111 (0.88) 0.087
2.39 0.91 (0.75) 0.082 (0.97) 0.076 (1.01) 0.232** (2.54) 0.030
2.29 0.95 (0.82) 0.011 (0.14) 0.167** (2.29) 0.130 (1.48) 0.028
2.22 0.39 ( 0.28) 0.094 (0.97) 0.304*** (3.50) 0.231** (2.21) 0.078
2.36 0.39 (0.32) 0.187** (2.19) 0.154** (2.01) 0.188** (2.04) 0.053
8.0
78.1
84.2
36.2
64.3
Notes: The regressions are Eqs. (2) and (3). bCON, bMKT, and bCORP are the coefficients associated with the UK government consol, the British equity market index, and UK corporate bond index, respectively. The mean excess return and estimated alpha are expressed in annualized percentage points. Heteroskedasticity and autocorrelation robust t-statistics are in parentheses. *Indicates significance at the 10% level. nn Indicates significance at the 5% level. nnn Indicates significance at the 1% level.
suggesting that the higher unconditional returns associated with holding the off-gold bonds were compensation for bearing risk. UK investors demanded a premium to bear this additional risk, and the higher returns did not reflect a punishment for abandoning gold. That the alphas are close to zero implies that a portfolio of British shares and bonds with the same exposure to the UK indices would generate statistically identical returns. Because the UK securities were not being punished for violating the rules of the gold standard, the average excess return is compensation for bearing business-cycle risk. The alphas reported in Table 3 indicate that portfolios selected based on gold-standard adherence do not outperform portfolios of UK securities with the same exposure to business-cycle risk. However, a test that alpha equals zero is a joint test of the good-housekeeping hypothesis and the risk and return model implied by the excess return regression. To be certain that the small alphas are not due to model misspecification, the alphas of the leveraged portfolios can be compared with the alphas based on selecting bonds randomly.10 For each subsample in Table 3, the excess return portfolios are computed by randomly assigning the same sample of securities to one of two portfolios. Bonds are assigned in the same proportion as the proportion of gold-standard adherence. After computing 1000 random portfolios, the proportion of times the portfolio selected using the gold standard criterion earns a larger excess return than a portfolio selected at random is reported.11 Table 3 reports the proportion of times the leveraged gold-sorted portfolios beat portfolios formed at random, or the ‘‘success rate’’. The results are consistent with the conclusion that gold-standard adherence did not matter for the excess returns of sovereign bonds. In the full sample, sorting sovereign bonds into value-weighted portfolios based on gold would have earned greater excess returns than sorting bonds randomly only 24.1% of the time. Although the success rate exceeds 50% for the Bordo–Rockoff and Flandreau–Zumer samples, it is less than 50% for the Obstfeld–Taylor sample. The Obstfeld– Taylor sample contains more countries than the Bordo–Rockoff and Flandreau–Zumer samples, but fewer than are contained in the full sample, indicating that some of the disagreement about the effect of gold on borrowing costs may be attributable to the set of countries being studied. Overall, portfolios selected by gold-standard adherence do no better than portfolios selected at random.
10 Expected a will equal zero if the British portfolios do a good job of capturing consumption risk. But if the model is misspecified, the expected alpha of a random portfolio will be different from zero. The model may be misspecified in such a way that a random portfolio happens to have a negative alpha. In that case, the portfolio selected using gold-standard adherence could have an alpha statistically indistinguishable from zero and yet still significantly outperform randomly selected portfolios. This finding would cast doubt on the null hypothesis that gold-standard adherence does not matter for sovereign borrowing costs. 11 For example, in the value-weighted Bordo–Rockoff sample of sovereign bonds, 56% of the observed returns are returns of bonds on the goldstandard. The excess return portfolio from the same sample of countries is computed by randomly buying 44% of the bonds each period and shorting the other 56%. The random portfolio’s alpha is computed and then compared with the alpha of the gold-sorted portfolio. This step is repeated 1000 times, resulting in 1000 sample alphas. By comparing the number of times that the leveraged gold portfolio outperformed a randomly selected portfolio, it is possible to see whether sorting bonds by gold-standard adherence results in higher returns than would be expected from randomly assigning bonds to portfolios.
270
R. Alquist, B. Chabot / Journal of Monetary Economics 58 (2011) 262–272
Taken together, these pieces of evidence all point in the same direction. Differences in bond returns represented compensation for exposure to British risk factors and did not reflect a gold premium. 6. Sensitivity analysis This section shows that the paper’s main finding is robust to changes in model specification. First, altering the factor model by permitting the betas to differ across exchange-rate regimes has no effect on our results. Second, the inclusion of additional determinants of the country’s risk premium also does not alter the conclusions about the good-housekeeping hypothesis. Third, the results are robust to the exclusion of British colonial bonds from the sample. 6.1. Gold-standard adherence and betas Differences between the returns of bonds issued by countries on gold and those issued by countries off gold appear to be explained by differences in their betas. The finding that the betas differ with gold-standard adherence is not new. For example, Bordo and Rockoff (1996) and Obstfeld and Taylor (2003) both observe that the countries’ market betas appear to vary with gold-standard adherence. Neither set of authors formally tests for differences in the betas by allowing them to vary with gold-standard adherence, but both point out that countries on gold tend to have smaller betas than those off gold over their respective samples.12 Thus, it is possible that gold-standard adherence and the betas are correlated with one another. In that case, adhering to gold could reduce the cost of capital by reducing the beta of a country’s bonds. The international capital market may have viewed bonds issued by countries on gold as less sensitive to business-cycle risk than those issued by countries off gold, so that a country could lower its cost of capital by adhering to gold. To examine this possibility, the following equation is estimated for the subset of the individual bonds that change their gold status: Rit Rft ¼ ai þ
3 X j¼1
bj ðRjt Rft Þ þ
3 X
dj ðRjt Rft ÞGSit þ eit
ð4Þ
j¼1
where j¼1,y,3 corresponds to the UK government consol (CON), the British equity portfolio (MKT), and the UK corporate bond portfolio (CORP), respectively; and GSit is an interaction dummy variable equal to 1 if the issuing country is on gold at time t. The regression produces three interaction coefficients equal to the difference between the beta on gold and the beta off gold. To ensure that differences in the three betas are identified, the issuing country’s bonds need to be traded while it is both on and off gold. The dataset contains 86 such bonds. Thus, it is possible to estimate 86 separate time-series regressions that result in 258 ( ¼3 86) interaction coefficients. Fig. 2 shows the histogram of the t-statistics from the interaction coefficients. The distribution of interaction coefficients is symmetric and centered on zero. Fifteen of the 258 (5.8%) are statistically different from zero at the 5% significance level and 22 (8.5%) at the 10% significance level. Using the Simes (1986) modified Bonferroni test, the joint null hypothesis that all interaction coefficient are jointly equal to zero cannot be rejected. While the difference in returns between the off- and on-gold portfolios can be explained by differences in the betas, the differences in betas do not appear to be attributable to gold-standard adherence. The result is what one would expect if gold-standard adherence had no effect on the cost of capital. 6.2. Fiscal, monetary, and trade controls Gold-standard adherence may act as a proxy for following prudent fiscal and monetary policies, as proposed by Flandreau and Zumer (2004). It is therefore important to test whether gold reduces sovereign borrowing costs conditional on covariates that capture the risks associated with weak fiscal and monetary policies. In addition, other studies of the good-housekeeping hypothesis have included macroeconomic controls like the lagged inflation rate and the deficit–GDP ratio to detect deviations from the commitment to gold (Bordo and Rockoff, 1996; Obstfeld and Taylor, 2003). Including covariates to capture these risks in the factor model facilitates comparison with these other studies. We control for fiscal, monetary, and trade shocks by forming factor-mimicking portfolios using data on the deficit–GDP ratio, annual inflation, and the export–GDP ratio that are available for 22 countries.13 Columns 1–3 in Table 4 show that 12 In addition, Ferguson and Schularick (2006) find that differences in mean coupon yields between British Empire and non-Empire bonds disappear when they control for market risk and that the betas of Empire bonds are smaller than those of non-Empire bonds. 13 Fama and French (1995) and Daniel and Titman (1997) use an identical procedure to evaluate the effect of size and value characteristics on equity returns. The factor-mimicking portfolios are formed in the following way. First, at the beginning of each year the countries are sorted into three mutually exclusive categories – high, medium, and low – based on the value of each characteristic. The high category contains the top one-third of countries while the low category contains the bottom one-third of countries. Second, the bonds issued by countries in the high and low categories are used to form valueweighted portfolios. Third, a factor-mimicking portfolio is constructed by forming a leveraged high minus low (HML) portfolios for each of the three macroeconomic variables. For example, the deficit HML portfolio is the portfolio formed by buying sovereign bonds in the top one-third of the deficitGDP category and selling short the sovereign bonds in the bottom one-third of the deficit-GDP category.
R. Alquist, B. Chabot / Journal of Monetary Economics 58 (2011) 262–272
271
70 60 50 40 30 20 10 0 < -2
-2
-1.5
-1
-0.5
0
0.5
1
1.5
2
>2
Fig. 2. Interaction coefficient t-statistics. Notes: The histogram reports the robust t-statistics associated with the 258 interaction terms that result from estimating Eq. (4) for each of the 86 bonds that were traded when the issuing country was both on and off the gold standard.
Table 4 Excess return regressions: macroeconomic risk factors and independent countries. Full sample
Mean excess return
a bCON bMKT bCORP bDEF–GDP bINF bEXP GDP R
2
Ind. countries
Off gold
On gold
Off on
Off gold
On gold
Off on
4.27 0.03 (0.02) 0.345*** (3.86) 0.366*** (4.48) 0.381*** (3.97) 0.061 ( 1.03) 0.124*** ( 2.88) 0.172***( 3.75) 0.237
2.59 0.24 (0.36) 0.157*** (3.40) 0.185*** (4.39) 0.143*** (2.89) 0.089*** (2.94) 0.053** ( 2.38) 0.189*** ( 8.01) 0.252
1.68 0.21 ( 0.16) 0.188** (2.00) 0.181** (2.10) 0.238** ( 2.35) 0.150** ( 2.41) 0.071 ( 1.57) 0.017 (0.36) 0.091
4.24 0.11 ( 0.08) 0.359*** (3.97) 0.407*** (5.01) 0.365*** (3.73)
3.21 0.81 (1.01) 0.117** (2.07) 0.353*** (6.98) 0.097 (1.59)
1.02 0.92 ( 0.65) 0.242** (2.46) 0.054 (0.611) 0.268** (2.52)
0.208
0.112
0.052
Notes: The regressions are Eqs. (2) and (3). The portfolios are value-weighted. bCON, bMKT, and bCORP are the coefficients associated with the UK government consol, the British equity market index, and UK corporate bond index, respectively. bDEF–GDP, bINF, and bEXP–GDP refer to the coefficients associated with the deficit, inflation, and export factor-mimicking portfolios, respectively. The mean excess return and estimated alpha are expressed in annualized percentage points. The ‘‘Ind. Countries’’ sample includes all independent countries in the sample and excludes the British colonies. Heteroskedasticity and autocorrelation robust t-statistics are in parentheses. *Indicates significance at the 10% level. nn Indicates significance at the 5% level. nnn Indicates significance at the 1% level.
including the factor-mimicking portfolios has no effect on the conclusions. The off-gold minus on-gold portfolio alpha remains indistinguishable from zero. 6.3. Controlling for the British empire effect Accominotti et al. (forthcoming) demonstrate that dummy-variable regression tests of the effect of membership in the British Empire on borrowing costs are misspecified. They show that pooling bonds issued by British colonies with bonds issued by independent countries can lead to biased parameter estimates and misleading inferences in yield-spread regressions. To ensure that the conclusions about the effect of gold standard adherence on sovereign borrowing costs are robust, the British colonies are excluded from the portfolio sorts and the test is re-run on the subset of bonds that were issued by independent countries. Columns 4–6 in Table 4 report the alphas and betas obtained from forming off- and on-gold portfolios for the set of independent countries in the sample (i.e., bonds not issued by British colonies). The unconditional difference between ongold and off-gold bond returns shrinks when colonial bonds are excluded, and the risk-adjusted return of the off-gold minus on-gold portfolio decreases. Importantly, the main result that gold-standard adherence is uncorrelated with riskadjusted return is unaffected when the colonial bonds are omitted.
272
R. Alquist, B. Chabot / Journal of Monetary Economics 58 (2011) 262–272
7. Conclusion Using a comprehensive new dataset, we find no evidence to support the good-housekeeping hypothesis. Although the bonds issued by countries off gold did earn higher unconditional returns than the bonds of countries on gold, this difference vanishes conditional on exposure to common risk factors. This evidence leads us to reject the goodhousekeeping hypothesis and is consistent with Flandreau and Zumer’s (2004) finding that the effect of gold-standard adherence on borrowing costs vanishes with the inclusion of other explanatory variables that capture default risk. This conclusion is robust. There is no evidence of a gold-standard effect in any of the subsamples of countries included in previous studies. The results are not sensitive to adding fiscal, monetary, and trade controls to account for macroeconomic shocks that can affect the commitment to gold. Finally, omitting the British colonies from the benchmark specification does not alter the paper’s conclusions. These results cast doubt on the perceived benefits of the classical gold standard in particular and fixed exchange-rate regimes more generally. A widely cited benefit of the gold standard – arguably the most credible fixed exchange-rate regime in modern history – is that it reduced borrowing costs. Whatever other benefits a credible fixed exchange-rate regime confers, the international capital market did not reward gold-standard adherence with a lower cost of capital.
Acknowledgments We thank the anonymous referee, Jeremy Atack, Christiane Baumeister, Charles Calomiris, Wei Dong, Robert Lafrance, Associate Editor Edward Nelson, Kim Oosterlinck, Gregor Smith, Linda Tesar, and Marc Weidenmier, as well as seminar participants at the NBER, the Center for Financial Studies, and the Canadian Economic Association annual meetings for comments and suggestions. David Finer, Maggie Jim, and Rob Precht provided first-rate research assistance. The views expressed in the paper represent the authors own and should not be attributed to the Bank of Canada, the Federal Reserve Bank of Chicago, or the Federal Reserve System. Appendix A. Supplementary material Supplementary material associated with this article can be found in the online version at doi:10.1016/j.jmoneco.2011.03. 006. References Accominotti, O., Flandreau, M., Rezzik, R. The spread of empire: clio and the measurement of colonial borrowing costs. Economic History Review, forthcoming. doi:10.1111/j.1468-0289.2010.00536.x. Bohn, H., 1991. Time consistency of monetary policy in the open economy. Journal of International Economics 30, 249–266. Bordo, M.D., Kydland, F., 1995. The gold standard as a rule. Explorations in Economic History 32, 423–464. Bordo, M.D., Rockoff, H., 1996. The gold standard as a good-housekeeping seal of approval. Journal of Economic History 56, 389–428. Bordo, M.D., Schwartz, A.J., 1999. The operation of the specie standard: evidence for core and peripheral countries: 1880–1990. In: Bordo, M.D. (Ed.), The Gold Standard and Related Regimes: Collected Essays. Cambridge University Press, New York, pp. 238–317. Campbell, J., 1995. Some lessons from the yield curve. Journal of Economic Perspectives 9, 129–152. Clemens, M.A., Williamson, J.G., 2004. Wealth bias in the first global capital market boom, 1870–1913. Economic Journal 114, 304–337. Cornell, B., Green, K., 1991. The investment performance of low-gradebond funds. Journal of Finance 46, 29–48. Daniel, K., Titman, S., 1997. Evidence on the characteristics of cross-sectional variation in common stock returns. Journal of Finance 52, 1–33. Elton, E.J., Gruber, M.J., Blake, C.R., 1995. Fundamental economic variables, expected returns, and bond fund performance. Journal of Finance 50, 1229–1256. Fama, E.F., French, K.R., 1993. Common risk factors in the returns on stocks and bonds. Journal of Financial Economics 33, 3–56. Fama, E.F., French, K.R., 1995. Size and book-to-market factors in earnings and returns. Journal of Financial Economics 50, 131–155. Ferguson, N., Schularick, M., 2006. The empire effect: the determinants of country risk in the first age of globalization, 1880–1913. Journal of Economic History 66, 283–312. Flandreau, M., Zumer, F., 2004. In: The Making of Global Finance. Organization for Economic Cooperation and Development, Paris 1880–1913. Jensen, M.C., 1967. The performance of mutual funds in the period 1945–1964. Journal of Finance 23, 389–416. Martin-Acena, P., 1993. Spain during the classical gold standard years, 1880–1914. In: Bordo, M.D., Capie, F. (Eds.), Monetary Regimes in Transition. Cambridge University Press, New York, pp. 135–172. Mauro, P., Yafeh, Y., 2003. The Corporation of Foreign Bondholders. IMF Working Paper No. 03/107. Mitchener, K., Weidenmier, M.D., 2009. Are Hard Pegs Ever Credible in Emerging Markets? Evidence from the Classical Gold Standard, NBER Working Paper No. 15401. Obstfeld, M., Taylor, A.M., 2003. Sovereign risk, credibility, and the gold standard: 1870–1913 versus 1925–31. Economic Journal 113, 241–275. Simes, S.J., 1986. An improved bonferroni procedure for multiple tests of significance. Biometrika 73, 751–754. Sussman, N., Yafeh, Y., 2000. Institutions, reforms, and country risk: lessons from japanese government debt in the Meiji period. Journal of Economic History 60, 442–467.
Journal of Monetary Economics 58 (2011) 273–289
Contents lists available at ScienceDirect
Journal of Monetary Economics journal homepage: www.elsevier.com/locate/jme
News shocks and business cycles Robert B. Barsky a,b, Eric R. Sims b,c, a
University of Michigan, United States NBER, United States c University of Notre Dame, United States b
a r t i c l e i n f o
abstract
Article history: Received 22 July 2010 Received in revised form 2 March 2011 Accepted 3 March 2011 Available online 15 March 2011
This paper proposes and implements a novel structural VAR approach to the identification of news shocks about future technology. The news shock is identified as the shock orthogonal to the innovation in current utilization-adjusted TFP that best explains variation in future TFP. A favorable news shock leads to an increase in consumption and decreases in output, hours, and investment on impact – more suggestive of standard DSGE models than of recent extensions designed to generate news-driven business cycles. Though news shocks account for a significant fraction of output fluctuations at medium frequencies, they contribute little to our understanding of recessions. & 2011 Elsevier B.V. All rights reserved.
1. Introduction Most modern theories of the business cycle assume that fluctuations are driven by changes in current fundamentals, such as aggregate productivity. The last several years have witnessed a resuscitation of an older theory in which business cycles can arise without any change in fundamentals at all. The news-driven business cycle hypothesis – originally advanced by Pigou (1927) and reincarnated in its modern form chiefly in Beaudry and Portier (2004) – posits that business cycles might arise on the basis of expectations of future fundamentals. If favorable news about future productivity can set off a boom today, then a realization of productivity which is worse than expected can induce a bust without any actual reduction in productivity itself ever occurring. As such, this theory of business cycles addresses several of the concerns with conventional theories—booms and busts can happen absent large changes in fundamentals and no technological regress is required to generate recessions. It has proven challenging to make news shocks about future fundamentals work in the context of relatively standard business cycle models, a point first recognized by Barro and King (1984) and later emphasized in Cochrane (1994). In a neoclassical setting, the wealth effect of good news about future productivity causes households to desire more consumption of both goods and leisure. A reduction in labor supply leads to a reduction in output. Falling output and rising consumption necessitate a fall in investment. Not only does good news about the future tend to cause a ‘‘bust’’ today, the implied negative comovement among macroeconomic aggregates is difficult to reconcile with the strong positive unconditional comovement of these series in the data. In sharp contrast to the predictions of standard neoclassical models, recent empirical evidence suggests that news shocks about future productivity do induce positive comovement among the major macroeconomic aggregates. In particular,
Corresponding author at: University of Notre Dame, Department of Economics, 434 Flanner Hall, Notre Dame, IN 46556, USA. Tel.: þ 1 574 631 6309. E-mail address:
[email protected] (E.R. Sims).
0304-3932/$ - see front matter & 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.jmoneco.2011.03.001
274
R.B. Barsky, E.R. Sims / Journal of Monetary Economics 58 (2011) 273–289
Beaudry and Portier (2006), Beaudry et al. (2008), and Beaudry and Lucke (2010) propose two alternative VAR-based schemes for identifying news shocks. Under either orthogonalization scheme, their identified shocks are associated with a large, broad-based economic expansion occurring in anticipation of future TFP improvement. In addition, they find that news shocks are a quantitatively important source of fluctuations in output at business cycle frequencies. This paper reassesses the empirical evidence in favor of the news driven business cycle. In particular, it proposes and implements a novel approach for the identification of news shocks about future productivity. In a VAR featuring a utilization-adjusted measure of aggregate TFP and several forward-looking variables, a conventional surprise technology shock is identified as the reduced form innovation in TFP. Our news shock is then identified as the shock orthogonal to the TFP innovation that best explains future variation in measured TFP. This identification strategy is an application of principal components. It identifies our news shock as the linear combination of reduced form innovations orthogonal to the TFP innovation which maximizes the sum of contributions to TFP’s forecast error variance over a finite horizon. Relative to the estimation and specification of a fully-developed DSGE model, this approach imposes a minimum of theoretical restrictions and allows the data to speak for itself. If the empirical measure of TFP accurately measures ‘‘true’’ technology, then under circumstances satisfied in most theoretical models of news-driven cycles, this empirical approach will correctly identify the structural news shock. In a more general sense, this approach will be informative about the importance of structural shocks which affect future measured TFP. Section 2 details the empirical strategy and speaks to its suitability. This empirical strategy is taken to US data in Section 3. A key result is that a positive realization of our news shock (i.e. one which portends future increases in observed TFP) is associated with an impact increase in consumption and declines in output, investment, and hours of work. After the impact effects, these aggregate variables largely track, rather than anticipate, movements in TFP. In addition, our news shocks are associated with disinflation and with increases in stock prices, consumer confidence, real wages, and real interest rates. Our news shock captures much of the low frequency movements in TFP and other aggregate variables. In contrast, the surprise technology shock leads to largely transitory impulse responses of TFP, output, consumption, investment, and hours. While important for output fluctuations at medium to low frequencies, a historical decomposition reveals that our news shocks alone fail to account for output declines in four out of six US recessions between 1961 and 2007. Section 3.4 discusses the differences between these results and those in the existing literature. A key difference is that our identified news shock explains a significant fraction of variation in TFP at business cycle frequencies, whereas the shocks identified by Beaudry and Portier (2006) and Beaudry and Lucke (2010) do not. Section 4 places these results in the broader literature and points out some implications for macroeconomic modeling. While a large literature has developed seeking to build models capable of generating positive impact comovement in response to news, our estimated impulse responses are consistent with the predictions of a wide class of existing DSGE models, including the most basic neoclassical ones. Even without generating positive impact comovement, it is shown that the inclusion of news shocks can nevertheless improve the fit of these models along a number of dimensions. Because our news shock does explain an important share of output’s variance at medium frequencies, we argue that the literature should move away from ‘‘fixing’’ impact comovements and toward deeper structural explanations for the observed predictability of future TFP. 2. Empirical strategy Assume that aggregate technology is well-characterized as following a stochastic process driven by two shocks. The first is the traditional surprise technology shock of the real business cycle literature, which impacts the level of technology in the same period in which agents see it. The second is the news shock which is differentiated from the first in that agents observe the news shock in advance. Letting A denote technology, this stochastic structure can be expressed in terms of the moving average representation: " # lnAt ¼ ½B11 ðLÞ B12 ðLÞ
e1,t e2,t
ð1Þ
e1,t is the conventional surprise technology shock while e2,t is the news shock. The only restriction on the moving representation is that B12(0) ¼0, so that news shocks have no contemporaneous effect on technology. The following is an example process satisfying this assumption: lnAt ¼ lnAt1 þ e1,t þ e2,tj
ð2Þ
Given the timing assumption, e2 has no immediate impact on the level of technology but portends a change in technology j periods into the future. In a univariate context, it would not be possible to separately identify e1 and e2 given an observed time series of lnAt . The identification of news shocks must come from surprise movements in variables other than technology. As such, estimation of a vector autoregression (VAR) seems sensible. In a system featuring an empirical measure of observed aggregate TFP and several forward-looking variables, we identify the surprise technology shock as the reduced form
R.B. Barsky, E.R. Sims / Journal of Monetary Economics 58 (2011) 273–289
275
innovation in TFP. The news shock is then identified as the shock that best explains future movements in TFP not accounted for by its own innovation. This identification strategy is closely related to Francis et al.’s (2007) maximum forecast error variance approach, which builds on Faust (1998) and Uhlig (2003, 2004). 2.1. Identifying news shocks Let yt be a k 1 vector of observables of length T. One can form the reduced form moving average representation in the levels of the observables either by estimating a stationary vector error correction model (VECM) or an unrestricted VAR in levels: yt ¼ BðLÞut
ð3Þ
Assume there exists a linear mapping between innovations and structural shocks: ut ¼ A0 et
ð4Þ
This implies the following structural moving average representation: yt ¼ CðLÞet
ð5Þ 1 t ¼ A0 ut .
0
The impact matrix must satisfy A0 A0 ¼ R, where R is the variance–covariance matrix where CðLÞ ¼ BðLÞA0 and e of innovations, but it is not unique. For some arbitrary orthogonalization, A~ 0 (e.g. a Choleski decomposition), the entire space of permissible impact matrices can be written as A~ 0 D, where D is a k k orthonormal matrix (DD0 ¼ I). The h step ahead forecast error is yt þ h Et1 yt þ h ¼
h X
Bt A~ 0 Det þ ht
ð6Þ
t¼0
The share of the forecast error variance of variable i attributable to structural shock j at horizon h is then: 0 Ph P 0 0 ~0 0 ~ e 0 ð ht ¼ 0 Bt A~ 0 Dej ej 0 D0 A~ 0 Bt Þei t ¼ 0 Bi, t A 0 cg A 0 Bi, t Oi,j ðhÞ ¼ i ¼ P P 0 h ei 0 ð ht ¼ 0 Bt RB0t Þei t ¼ 0 Bi, t RBi, t
ð7Þ
The ei denotes selection vectors with one in the ith place and zeros elsewhere. The selection vectors inside the parentheses in the numerator pick out the jth column of D, which will be denoted by c. A~ 0 c is a k 1 vector corresponding to the jth column of a possible orthogonalization and has the interpretation as an impulse vector. The selection vectors outside the parentheses in both numerator and denominator pick out the ith row of the matrix of moving average coefficients, which is denoted by Bi, t . Let observed TFP occupy the first position in the system, and let the unanticipated shock be indexed by 1 and the news shock by 2. Eqs. (1) and (2), which provide the motivation for our identification strategy, imply that these two shocks account for all variation in TFP at all horizons:
O1,1 ðhÞ þ O1,2 ðhÞ ¼ 1 8h
ð8Þ
In a multivariate VAR setting, it is unreasonable to expect this restriction to hold at all horizons. Instead, we propose picking parts of the impact matrix to come as close as possible to making this expression hold over a finite subset of horizons. With the surprise shock identified as the innovation in observed TFP, O1,1 ðhÞ will be invariant at all h to alternative identifications of the other k 1 structural shocks. As such, choosing elements of A0 to come as close as possible to making the above expression hold is equivalent to choosing the impact matrix to maximize contributions to O1,2 ðhÞ over h. Since the contribution to the forecast error variance depends only on a single column of the impact matrix, this suggests choosing the second column of the impact matrix to solve the following optimization problem: 0 Ph 0 H 0~ ~ X ¼ 0 Bi, t A 0 cg A 0 Bi, t c ¼ argmax O1,2 ðhÞ ¼ t P ð9Þ 0 h h¼0 t ¼ 0 Bi, t RBi, t s.t. A~ 0 ð1,jÞ ¼ 0
8j 41
cð1,1Þ ¼ 0
ð10Þ
c0 c ¼ 1
ð11Þ
So as to ensure that the resulting identification belongs to the space of possible orthogonalizations of the reduced form, the problem is expressed in terms of choosing c conditional on an arbitrary orthogonalization, A~ 0 . H is some finite truncation horizon. The first two constraints impose that the news shock has no contemporaneous effect on the level of TFP. The third restriction (that c have unit length) ensures that c is a column vector belonging to an orthonormal matrix. Uhlig (2003) shows that this maximization problem can be rewritten as a quadratic form in which the non-zero portion of c is the eigenvector associated with the maximum eigenvalue of a weighted sum of the lower (k 1) (k 1) submatrices
276
R.B. Barsky, E.R. Sims / Journal of Monetary Economics 58 (2011) 273–289
of ðB1, t A~ 0 Þ0 ðB1, t A~ 0 Þ over t. In other words, this procedure essentially identifies the news shock as the first principal component of observed TFP orthogonalized with respect to its own innovation. 2.1.1. Comparison with other approaches The common assumption in the news shock literature is that a limited number of shocks lead to movements in aggregate technology. Our identification strategy is based solely on this assumption, and does not rely upon (potentially invalid) auxiliary assumptions about other shocks or on the persistence of variables. Our approach is a partial identification strategy only identifying the two technology shocks. As such, it can be conducted on a system with any number of variables without having to impose additional assumptions. Our identification strategy encompasses the existing identifying assumptions in the empirical literature on news shocks. Beaudry and Portier (2006) and Beaudry et al. (2008) propose identifying news shocks with the innovation in stock prices orthogonalized with respect to TFP innovations. Were the conditions required for this identification to be valid satisfied, our approach would identify (asymptotically) exactly the same shock. Beaudry and Lucke (2010) propose using a combination of short and long run restrictions to identify news shocks. This identification is similar to ours as the truncation horizon gets arbitrarily large (i.e. as H-1). Long run identification is problematic in this context for several reasons. First, identification at frequency zero is based on sums of VAR coefficients, which are biased in finite samples. Summing up biased coefficients exacerbates the bias, and the resulting identification and estimation are often unreliable (Faust and Leeper, 1997). Francis et al. (2007) show that medium run identification similar to that proposed here performs better in finite samples than does long run identification. Secondly, because identification is not based on the zero frequency, one need not take an explicit stance on the order of integration of variables or on the cointegrating relationships among them. As noted by Fisher (2010), vector error correction models paint very different pictures concerning the importance of news shocks depending on the number of assumed common trends. Estimation of a VAR in levels will produce consistent estimates of the VAR impulse responses and is robust to cointegration of unknown form.1 Third, in practice the long run restricted VARs leave a large share of the TFP variance unexplained at business cycle frequencies, a point which is revisited in Section 3.4. 2.2. Suitability Recent work has questioned the ability of structural VARs to adequately recover shocks from economic models. Following the recommendation of Chari et al. (2008), data are simulated from a dynamic stochastic general equilibrium (DSGE) model to examine the performance of our empirical approach. A four variable system identical to the main empirical specification in Section 3 is estimated on model generated data, and it is shown that our empirical approach performs very well. 2.2.1. The model Consider a neoclassical model with real frictions (habit formation in consumption and investment adjustment costs), augmented with both news and surprise technology shocks of the form specified in (2) above. The model can be written as a planner’s problem: ! 1 þ 1=Z 1 X Nt t max ð12Þ b E0 lnðCt bC t1 Þct 1 þ 1=Z t¼0 s.t. It Kt þ 1 ¼ ð1dÞKt þ 1f It It1
ð13Þ
Yt ¼ At Kty Nt1y
ð14Þ
Yt ¼ Ct þ It þ Gt
ð15Þ
Gt ¼ gt Yt
ð16Þ
lnAt ¼ gA þ lnAt1 þ e1,t þ e2,tj
ð17Þ
lngt ¼ ð1rÞlng þ rlngt1 þ e3,t
ð18Þ
lnct ¼ nlnct1 þ e4,t
ð19Þ
1 Indeed, when there is uncertainty concerning the nature of common trends in the data, estimating the VAR in levels is the ‘‘conservative’’ approach as advocated by, for example, Hamilton (1994).
R.B. Barsky, E.R. Sims / Journal of Monetary Economics 58 (2011) 273–289
277
Variable definitions are standard. It is assumed that the government consumes a stochastic share, gt, of private output.
fðÞ is a convex function describing costs associated with adjusting investment, with f00 ðÞ ¼ g Z 0. The following values are chosen for the remaining parameters: b ¼ 0:99, b¼0.8, c ¼ 1, Z ¼ 1, d ¼ 0:025, y ¼ 0:33, g ¼ 0:3, g ¼ 0:2, gA ¼0.0025, n ¼ 0:8, and r ¼ 0:95. These parameters imply steady state features in line with US data. There are three periods of anticipation for news shocks (i.e. j ¼3). The standard deviation of the unanticipated technology shock is 0.66 percent and the standard deviation of the news shock is 0.33 percent. The standard deviations of the remaining two shocks are set at 0.15 percent.
2.2.2. Monte Carlo results Two thousand different data sets with 191 observations each are generated, which correspond to the sample size in our benchmark estimation. VARs featuring log technology (lnAt ), log consumption, log output and log hours are estimated on each generated data set, which coincides with the benchmark empirical VAR in Section 3. The systems are estimated in levels and include three lags of each variable. The news shock is identified by maximizing the variance share of technology over a ten year horizon. These are the same specifications used in the benchmark empirical VAR. Fig. 1 depicts both theoretical and estimated impulse responses averaged over the simulations to a news shock that technology will be permanently higher. The theoretical responses are solid black and the average estimated responses over the simulations are depicted by the dashed line. The shaded gray areas are the 7one standard deviation confidence bands from the simulations. Although investment does not appear directly in the system, its response is imputed as the output response less the share-weighted consumption response. A number of features from the simulations stand out. The estimated empirical impulse responses are roughly unbiased on impact and for most horizons thereafter. A favorable news shock leads to rising consumption but falling output, hours, and investment on impact in the model. After impact, the aggregate variables track movements in technology. The empirical identification captures these features quite well. The estimated responses to a news shock are only slightly downward biased at long horizons, and the estimated dynamics are very close to the true dynamics at all horizons. The median correlation between the identified and true news shock is 0.81.
Consumption
0.4
Percent
Percent
Technology
0.2
0.4 0.2
0 0
5
10 Horizon
15
0
20
0
5
15
20
15
20
Hours
0.8
0.2
0.6
0.1
Percent
Percent
Output
10 Horizon
0.4 0.2 0 -0.2
0 -0.1 -0.2
0
5
0
5
10 15 Horizon Investment
20
0
5
10 Horizon
Percent
1.5 1 0.5 0 -0.5 10 Horizon
15
20
Fig. 1. Model and Monte Carlo estimated impulse responses to news shocks. The solid line shows the theoretical impulse response to a news shock from the model presented in Section 2.2. The dashed line is the average estimated impulse responses from a Monte Carlo simulation with 2000 repetitions and 191 observations per repetition. The estimated VAR includes TFP, consumption, output, and hours, all in levels. The investment response is imputed as the output response less the share-weighted consumption response. The shaded gray areas are the one 7 one standard deviation confidence bands from the 2000 Monte Carlo repetitions. The horizontal axes refer to forecast horizons and the units of the vertical axes are percentage deviations (times 100).
278
R.B. Barsky, E.R. Sims / Journal of Monetary Economics 58 (2011) 273–289
A number of additional experiments were run to test how sensitive the simulation results are to mis-specification and/or mis-measurement. While our preferred empirical measure of TFP attempts to control for unobserved factor utilization, one might nevertheless remain concerned about this issue. The model above is thus modified to include endogenous capital utilization and labor effort, but the estimated VARs use a measure of TFP failing to control for those factors. The simulation results remain remarkably good. Our intuition for this is twofold: first, a news shock has relatively small effects on unobserved input variation on impact, and, second, utilization and effort are constant over long time horizons, so forecasting TFP a number of periods out without accounting for unobserved input variation ends up being relatively innocuous. 2.2.3. Discussion A more general objection to our empirical approach would be that a number of structural shocks, which are not really ‘‘news’’ in the sense defined by the literature, might affect a measure of TFP in the future without impacting it immediately. Among these shocks might be research and development shocks, investment specific shocks, and reallocative shocks. Our identification (and any other existing VAR identifications) would obviously confound any true news shock with these shocks. If this is the case our empirical approach would provide an upper bound on the business cycle importance of true news shocks. While open to this possibility, we nevertheless view our approach as a well-defined exercise in the statistical sense and believe it conveys important information about the predictability of future TFP for which structural models should be able to account. This section of the paper concludes by addressing the implications of news shocks for VAR invertibility. FernandezVillaverde et al. (2007) discuss the conditions under which DSGE models produce moving average representations in the observables which can be inverted into a VAR representation in which the VAR innovations correspond to economic shocks. Invertibility problems potentially arise when there are unobserved state variables which do not enter the estimated VAR (Watson, 1986). Leeper et al. (2008) stress that anticipated shocks to future state variables are potentially problematic for VAR invertibility. As emphasized by Watson (1986) and Sims and Zha (2006), non-invertibility is not an either/or proposition, and the inclusion of forward-looking variables into the VAR helps to mitigate invertibility issues in practice. Our battery of simulation results suggest that invertibility is not a major concern here. Blanchard et al. (2009) study the implications for VARs of agents facing signal extraction problems. They consider a framework in which agents receive news about productivity that is contaminated with noise. The essential point of their paper is that it is not possible to separately identify true news shocks and noise shocks by structural VAR methods alone. Nevertheless, even when the news is contaminated with noise, a structural VAR method such as ours should correctly identify the response of the economy to the noisy signal, which is the news shock from the perspective of the agents in the model. The variance of the noise becomes an underlying structural parameter that affects the impact multipliers and lag coefficients of the VAR—the more noisy the signal, the less agents respond to it. Given the variance of the noise, the VAR will yield appropriate impulse response functions to a perceived news shock. Separating the effects of noise shocks from true news shocks requires more structure. Blanchard et al. (2009) employ moment and likelihood methods to estimate a structural model with news and noise. Barsky and Sims (2010) study a VAR that includes consumer confidence as a noisy signal of future TFP in conjunction with a DSGE model, estimating the parameters by indirect inference. 3. Empirical evidence This section presents the main results of the paper. It begins with a brief discussion of the data. 3.1. Data The most critical data series needed to proceed is an empirical measure of aggregate technology. The Solow residual is not particularly appealing, primarily due to the fact that standard growth accounting techniques make no attempt to control for unobserved input variation (labor hoarding and capital utilization). Since identification of the news shock requires orthogonalization with respect to observed technology, it is important that the empirical measure of technology adequately control for unobserved input variation. To address these issues, this paper uses a quarterly version of the Basu et al. (2006) total factor productivity (TFP) series, which arguably represents the state of the art in growth accounting. Their essential insight is to exploit the first order condition which says that firms should vary intensity of inputs along all margins simultaneously. As such, they propose measuring unobserved input variation as a function of observed variation in hours per worker. They also make use of industry level data to allow for non-constant returns to scale in the production function. As the industry level data are only available at an annual frequency, it is not possible to construct a quarterly technology series with both the unobserved input and returns to scale corrections. This paper uses a quarterly measure using only the utilization correction. Formally, this TFP series presumes a constant returns to scale production function of the form: Y ¼AF(ZK,EQH), where Z is capital utilization, E is labor effort, H is total labor hours, and Q is a labor quality adjustment. The traditional uncorrected Solow residual is then DlnA ¼ DlnYyDlnKð1yÞDlnQH, where y is capital’s share. The utilization correction subtracts from this DlnU ¼ yDlnZ þð1yÞDlnE, where observed labor variation is used as a proxy for unobserved variation in both labor and capital. The standard Solow residual is both more volatile and procyclical than the resulting corrected TFP measure. In particular, the standard deviation of the HP detrended Solow residual is roughly 33 percent larger than for
R.B. Barsky, E.R. Sims / Journal of Monetary Economics 58 (2011) 273–289
279
the adjusted series. The correlation between HP detrended output and the Solow residual is roughly 0.8, while the output correlation with corrected TFP is about half that at 0.4. The output measure is the log of real output in the non-farm business sector at a quarterly frequency. The consumption series is the log of real non-durables and services. The hours series is total hours worked in the non-farm business sector. These series are converted to per capita terms by dividing by the civilian non-institutionalized population aged 16 and over. The consumption data are from the BEA; the output, hours, and population data are from the BLS. The measure of stock prices is the log of the real S&P 500 Index, taken from Robert Shiller’s website. The measure of inflation is the percentage change in the CPI for all urban consumers. Use of alternative price indexes produces similar results. Both the stock price and inflation series are converted to a quarterly frequency by taking the last monthly observation from each quarter. The consumer confidence data are from the Michigan Survey of Consumers, and summarize responses to a forward-looking question concerning aggregate expectations over a five year horizon. For more on the confidence data, see Barsky and Sims (2010).2 Our benchmark data series spans the period 1960–2007. 3.2. Results This subsection presents the main results of the paper. It begins with a four variable system identical to the Monte Carlo simulations in Section 2.1. It then proceeds to estimate a larger, seven variable system. 3.2.1. A four variable system Four variables are included in the benchmark system: the corrected TFP series, non-durables and services consumption, real output, and hours worked per capita. These are the same series used in the model-based simulations of Section 2.1. The system is estimated in the levels of all variables. While several of these series appear to be I(1), estimating the system in levels will produce consistent estimates of impulse responses and is robust to cointegration of unknown form. Our results are very similar when either imposing cointegrating relationships on the data or when estimating a vector error correction model (VECM). The system features three lags in accord with the selection of the Schwartz Information Criterion. The truncation horizon in the identification problem is set at H¼40. In words, our news shock is identified as the shock orthogonal to TFP innovations which best accounts for unexplained movements in TFP over a ten year horizon. Fig. 2 shows the estimated impulse responses to the identified news shock. The shaded gray areas are 7one standard error confidence bands from the bias-corrected bootstrap procedure of Kilian (1998). TFP rises rather rapidly, reaching a peak response of slightly more than 0.2 percentage points some five years subsequent to the shock. Consistent with simple permanent income intuition, consumption jumps up about 0.2 percentage points on impact, rising further over time. Output and hours both decline on impact. Only after measured TFP beings to increase do these series begin to rise. Investment also jumps down on impact before recovering after a few quarters.3 As will be argued in Section 4, these responses are at least broadly consistent with the implications of conventional neoclassical models. In particular, there is no large output ‘‘boom’’ in anticipation of increases in TFP. Fig. 3 shows the estimated responses to the surprise technology shock, identified as the reduced form innovation in TFP. Quite strikingly, TFP’s response to its own innovation appears largely transitory.4 Output, consumption, hours, and investment all rise on impact before reverting. Given the transitory nature of the TFP response, the consumption response is quite naturally small. In contrast, the output and investment increases on impact are large before reverting to their preshock values. 3.2.2. A seven variable system Next consider a larger system. In addition to the four variables in the benchmark system, we also include a measure of stock prices, consumer confidence, and inflation. There are several reasons for including these additional variables. Stock prices and consumer confidence are naturally forward-looking, and previous research has shown them to be prognostic of future movements in economic activity in general and TFP in particular (e.g. Beaudry and Portier, 2006; Barsky and Sims, 2010). Inflation is forward-looking in the standard monetary models of the business cycle that are now popular among central banks (e.g. Smets and Wouters, 2007). As such, including these additional variables in the system will help in the identification of our news shock, as well as serving to ameliorate any potential invertibility issues (see Watson, 1986 or Section 2.2). Fig. 4 shows the estimated responses of TFP, consumption, output, hours, and investment to our identified news shock. These responses are similar to those shown from the smaller system in Fig. 2. Output, hours, and investment all decline on 2 The specific survey question is: ‘‘Looking ahead, which would you say is more likely—that in the country as a whole we’ll have continuous good times during the next five years, or that we’ll have periods of widespread unemployment or depression, or what?’’ The series is constructed as the percentage of respondents giving a favorable answer less the percentage giving an unfavorable answer plus 100. 3 As in Section 2.2, the investment response is imputed as output less the share-weighted consumption response, where it is assumed that consumption is 70 percent of output, which is in line with the data. 4 Care must be taken when discussing permanent vs. transitory responses from a system estimated in levels. Re-estimating the system as a VECM leads to a very similar response of TFP to its own innovation, which gives us comfort in characterizing the response to a surprise technology shock as ‘‘largely transitory’’.
280
R.B. Barsky, E.R. Sims / Journal of Monetary Economics 58 (2011) 273–289
x 10-3
TFP 6
2
Percent
Percent
3
1 0 -1
4 2
x 10-3
10 15 20 25 30 35 40 Horizon
5
Output 5
5
Percent
Percent
Consumption
0 5
10
x 10-3
0 -5
x 10-3
10 15 20 25 30 35 40 Horizon Hours
0
-5 5
10 15 20 25 30 35 40 Horizon
5
10 15 20 25 30 35 40 Horizon
Investment
0.015 Percent
0.01 0.005 0 -0.005 -0.01 5
10 15 20 25 30 35 40 Horizon
Fig. 2. Empirical impulse responses to news shock: four variable VAR. The solid lines are the estimated impulse responses to our news shock from a four variable VAR featuring TFP, consumption, output, and hours. The investment impulse response is imputed as output minus the share-weighted consumption response. The shaded gray areas are the 7 one standard deviation confidence band from 2000 bias-corrected bootstrap replications of the reduced form VAR. The horizontal axes refer to forecast horizons and the units of the vertical axes are percentage deviations.
impact followed by relatively quick reversals; consumption rises. The dynamic paths of these variables largely track – as opposed to anticipate – the estimated time path of TFP. With the inclusion of the additional variables in the system there is somewhat more predictability in the time path of TFP, so that its response is larger here than in Fig. 2. Fig. 5 shows the responses of these variables to the surprise technology shock. These are very similar to what is estimated in the smaller system. In particular, TFP’s response continues to appear largely transitory. Fig. 6 shows the responses of stock prices, inflation, and consumer confidence to a news shock. Consistent with the results in Beaudry and Portier (2006), stock prices rise significantly on impact. There is some evidence of reversion at longer horizons, though it is not possible to reject that the impulse response is consistent with stock prices following a random walk. Inflation is estimated to fall significantly in response to good news. This response is broadly consistent with the New Keynesian framework in which current inflation equals an expected present discounted value of future marginal costs. Consumer confidence rises on impact, which is consistent with the empirical findings in Barsky and Sims (2010). Table 1 depicts the share of the forecast error variance of the variables in the seven variable VAR attributable to our news shock at various horizons. The numbers in parentheses are the standard errors from the bootstrap replications used to construct the confidence bands for the impulse responses. Our news shock accounts for more than one quarter of the variance of TFP at a horizon of four years and more than 40 percent at a horizon of ten years. The second to last row of the table shows the total contribution to TFP’s forecast error variance of our news shock and the surprise technology shock. These two shocks combine to explain roughly 95 percent of the variation in TFP at frequencies up to ten years. Our news shock accounts for a relatively small share of the forecast error variances of consumption at short horizons, and a somewhat larger share of the forecast error variance of output. The shock contributes more significantly to the variance decomposition of hours at high frequencies and much less so at lower frequencies. At longer horizons our news shock contributes more significantly to the variance decomposition of the aggregate variables excluding hours, explaining between 10 and 40 percent of the variance of output at business cycle frequencies. Relative to much of the identified VAR literature, these contributions to the forecast error variance of output are large. This suggests that news shocks are
R.B. Barsky, E.R. Sims / Journal of Monetary Economics 58 (2011) 273–289
8
x 10-3
TFP 3
4 2 0
x 10-3
10 15 20 25 30 35 40 Horizon
5
Output 3
x 10-3
10 15 20 25 30 35 40 Horizon Hours
2 Percent
4 Percent
0
-2 5
2 0 -2
1 0 -1
-4
-2 5
20
1
-1
-2
6
Consumption
2 Percent
Percent
6
x 10-3
281
x 10-3
10 15 20 25 30 35 40 Horizon
5
10 15 20 25 30 35 40 Horizon
Investment
Percent
15 10 5 0 -5 5
10 15 20 25 30 35 40 Horizon
Fig. 3. Empirical impulse responses to surprise technology shock: four variable VAR. The solid lines are the estimated impulse responses to the surprise technology shock, which is simply the reduced form innovation in the VAR. The shaded gray areas are the 7one standard deviation confidence band from 2000 bias-corrected bootstrap replications of the reduced form VAR. The horizontal axes refer to forecast horizons and the units of the vertical axes are in percentage deviations.
a potentially important component behind economic fluctuations, though not necessarily in the way that the extant literature has suggested. The final row of the table shows the total fraction of the forecast variance of output explained by our news and surprise technology shocks combined. At business cycle frequencies, these two shocks combine to leave more than 50 percent of the variance of output unexplained. This means that non-technology shocks (i.e. ‘‘demand’’ shocks) are an important driving force behind fluctuations, a result which is backed up in both the identified VAR literature and in estimated DSGE models. In order to get a better sense for how important our news shocks have been in explaining particular episodes, Fig. 7 plots a historical decomposition of real output. The subplots focus in on a one year centered window around the NBER defined recession dates, treating the 1980 and 1981–1982 recessions as one event. The dashed lines show the simulated value of output from the seven variable the VARs as if our news shocks were the only stochastic disturbances. The solid line shows the time path of actual output. In four out of six recessions (not counting the most recent one, for which there is insufficient data), the simulated time path of output in response to news shocks is increasing during recessions, not decreasing. The two exceptions are the 1973–1975 recession and the 1980 recession. In neither of these events, however, do our news shocks explain a large share of the output decline. On the basis of these simulations, it is difficult to conclude that news shocks have been a major driving force behind post-war US recessions. As will be discussed more in Section 4, most theoretical models have strong testable predictions concerning the behavior of equilibrium prices in response to news shocks. In particular, both real wages and real interest rates should rise following a good news shock. The rise in the wage comes from a reduction in labor supply and the rise in the interest rate comes from a reduction in savings supply, both resulting from the positive wealth effect associated with good news. To see whether this prediction is borne out in the data, measures of both series are included in our empirical VAR. The real wage is measured as the log of real hourly compensation in the non-farm business sector, and the real interest rate as the Baa corporate bond yield less expected inflation, where the expected inflation number from the Michigan Survey of
282
R.B. Barsky, E.R. Sims / Journal of Monetary Economics 58 (2011) 273–289
x 10-3
TFP 10 Percent
Percent
6 4 2 0
0
x 10-3
5
Output
10 15 20 25 30 35 40 Horizon Hours
0.01
10
Percent
Percent
5
10 15 20 25 30 35 40 Horizon
5 0 -5
0.005 0 -0.005 -0.01
5
Percent
Consumption
-5 5
15
x 10-3
10 15 20 25 30 35 40 Horizon
5
10 15 20 25 30 35 40 Horizon
Investment
0.03 0.02 0.01 0 -0.01 -0.02 5
10 15 20 25 30 35 40 Horizon
Fig. 4. Empirical impulse responses to news shock: seven variable VAR. The solid line is the estimated impulse response to a news shock from a seven variable VAR featuring TFP, consumption, output, hours, stock prices, consumer confidence, and inflation. The shaded gray areas are the 7 one standard deviation confidence band from 2000 bias-corrected bootstrap replications of the reduced form VAR. The horizontal axes refer to forecast horizons and the units of the vertical axes are percentage deviations.
Consumers. These measures are included in our seven variable VAR, replacing the consumer confidence and inflation measures. Consistent with model predictions, both rise on impact (figures omitted). The real wage is estimated to be significantly higher for a number of periods and its long horizon response is of similar magnitude to the response of output. While statistically insignificant, the interest rate response is economically large and positive for a number of periods after impact. 3.3. Sensitivity The result that our news shock induces negative impact comovement among aggregate variables is robust to alternative lag structures in the reduced form system as well as to various different assumptions and/or specifications concerning the long run relationships among the series.5 In the interest of space, these results are only described qualitatively here. At all tested lag lengths, output, investment, and hours decline on impact in response to a favorable news shock, while consumption rises. With more lags in the reduced form system the impulse responses are less smooth and there is more evidence of reversion in all series at longer horizons, but the basic qualitative nature of the responses is unchanged. The results are also similar with fewer lags. Similar results obtain when estimating VECM models with either assumed or estimated common trends. We prefer the levels specification because invalid assumptions concerning common trends can yield misleading results (Fisher, 2010). Nevertheless, our results about the effects of news shocks are qualitatively similar when estimating VECMs. The main differences in the VECM specifications concern the quantitative contribution of news shocks to the variance decomposition of the variables at medium and low frequencies. The impact effects of news on aggregate variables are always very similar, and the reverting behavior of TFP to the surprise technology shock continues to manifest itself. 5 Our results are also qualitatively robust with alternative measures of observed TFP. Application of our identification to a system with the Solow residual in place of the utilization-adjusted TFP measure again finds negative impact comovement, with output, hours, and investment all declining in anticipation of good news. The main difference is that the response of the Solow residual itself to the news shock appears far more transitory than the response of the TFP measure in Figs. 2 and 4.
R.B. Barsky, E.R. Sims / Journal of Monetary Economics 58 (2011) 273–289
Stock Prices
0.08
Inflation
0.4 0.2
Percentage Points
0.06
Percent
283
0.04 0.02 0 -0.02
0 -0.2 -0.4 -0.6 -0.8 -1
-0.04
-1.2 5
10 15 20 25 30 35 40 Horizon
5
10 15 20 25 30 35 40 Horizon
Consumer Confidence
4 3
Points
2 1 0 -1 -2 5
10 15 20 25 30 35 40 Horizon
Fig. 5. Empirical impulse responses to news shock: seven variable VAR (‘‘information variables’’). These are impulse responses of the ‘‘information variables’’ from the seven variable VAR described in Section 3. The shaded gray areas are the 7one standard deviation confidence band from 2000 biascorrected bootstrap replications of the reduced form VAR.
One might be concerned that our identification confuses genuine news about neutral technology with investment specific technology shocks.6 If vintages of capital are not adequately measured, then fluctuations in the relative price of investment will show up as movements in TFP, particularly over long periods of time. This would mean that what is identified as news may actually reflect investment specific technical change. To address this issue, several different metrics of the relative price of investment were included as additional variables in the VAR. As in Fisher (2006), the relative price of investment is constructed using different measures of the investment price deflator from the NIPA accounts divided by different measures of consumption price deflators. In none of these specifications is our identified news shock strongly correlated with the relative price of investment, and the basic patterns of our identified impulse responses do not change. A specification was also run in which our news shock was restricted to affect neither TFP nor the relative price of investment on impact. This yields very similar results to our benchmark. In the interest of space, these figures are omitted from the paper.
3.4. Relation with earlier work The most well-known empirical works in the news shock literature are papers by Beaudry and Portier (2006), Beaudry et al. (2008), and Beaudry and Lucke (2010). These authors estimate two to five variable systems featuring measures of TFP, stock prices, and other macroeconomic aggregates. They propose two alternative orthogonalization schemes aimed at isolating news shocks—the first is to associate the news shock with the stock price innovation orthogonalized with respect to TFP, and the second combines short and long run restrictions to identify the news shock. These authors argue that both orthogonalization schemes yield very similar results. They find that news shocks lead to positive conditional comovement among macroeconomic aggregates on impact, that aggregate variables strongly anticipate movements in technology, and that news shocks account for the bulk of the variance of aggregate variables at business cycle frequencies. 6 Fisher (2006), for example, finds that investment specific technology shocks account for important business cycle frequency movements in hours. This result is completely compatible with ours, as we find that neither news nor surprise technology shocks account for much of the movements of hours at horizons between 6 and 32 quarters. As noted in our discussion of the variance decomposition in Section 3.2, news shocks and technology shocks also leave a large share of output fluctuations unexplained at business cycle frequencies. This is also consistent with an important role for investment specific shocks. We are grateful to an anonymous referee for suggesting this robustness check.
284
R.B. Barsky, E.R. Sims / Journal of Monetary Economics 58 (2011) 273–289
8
x 10-3
TFP
5
x 10-3
Consumption
Percent
Percent
6 4 2
0 -5
0 -2
-10 5
10 15 20 25 30 35 40 Horizon
5
Output
0.01
4
Hours
2 Percent
Percent
0.005
x 10-3
10 15 20 25 30 35 40 Horizon
0 -0.005 -0.01
0 -2 -4
-0.015
-6 5
10 15 20 25 30 35 40 Horizon
5
10 15 20 25 30 35 40 Horizon
Investment
0.03 Percent
0.02 0.01 0 -0.01 -0.02 5
10 15 20 25 30 35 40 Horizon
Fig. 6. Empirical impulse responses to surprise technology shock: seven variable VAR. The solid lines are the impulse responses of the variables to the contemporaneous innovation in TFP from the seven variable system. The shaded gray areas are the 7 one standard deviation confidence band from 2000 bias-corrected bootstrap replications of the reduced form VAR. The horizontal axes refer to forecast horizons and the units of the vertical axes are percentage points.
Table 1 Forecast error variance decomposition. h ¼1
h ¼4
h ¼8
h ¼16
h ¼24
h ¼40
TFP
0.000 (0.00)
0.062 (0.06)
0.126 (0.11)
0.269 (0.14)
0.366 (0.15)
0.454 (0.16)
Consumption
0.050 (0.09)
0.234 (0.18)
0.377 (0.24)
0.493 (0.27)
0.524 (0.27)
0.507 (0.26)
Output
0.111 (0.07)
0.091 (0.10)
0.242 (0.18)
0.382 (0.23)
0.429 (0.24)
0.431 (0.24)
Hours
0.622 (0.23)
0.200 (0.16)
0.105 (0.13)
0.092 (0.15)
0.094 (0.16)
0.089 (0.15)
Stock price
0.140 (0.17)
0.200 (0.20)
0.185 (0.20)
0.189 (0.21)
0.193 (0.22)
0.181 (0.21)
Confidence
0.245 (0.21)
0.343 (0.22)
0.353 (0.22)
0.333 (0.22)
0.310 (0.20)
0.286 (0.18)
Inflation
0.138 (0.18)
0.220 (0.18)
0.226 (0.15)
0.205 (0.15)
0.191 (0.14)
0.180 (0.14)
1.000 0.731
0.948 0.282
0.943 0.364
0.951 0.451
0.948 0.491
0.910 0.520
Total TFP Total output
The letter h refers to the forecast horizon. The numbers denote the fraction of the forecast error variance of each variable at various forecast horizons to our identified news shock. Standard errors, from a bootstrap simulation, are in parentheses. ‘‘Total TFP’’ shows the total variance of TFP explained by our news shock and the TFP innovation combined. ‘‘Total output’’ shows the total variance of output explained by the news shock and the TFP innovation combined.
R.B. Barsky, E.R. Sims / Journal of Monetary Economics 58 (2011) 273–289
285
-10.78
-10.86 1969-1970 Recession
-10.87
1973-1975 Recession -10.80
-10.88 -10.82
-10.89
-10.84
-10.90 -10.91
-10.86
-10.92 -10.88
-10.93
-10.90
-10.94 1969Q1 1969Q3 1970Q1 1970Q3 1971Q1 1971Q3 Actual GDP
1973Q1 1973Q3 1974Q1 1974Q3 1975Q1 1975Q3 1976Q1 Simulated GDP -10.46
-10.64
1990-1991 Recession
-10.66
1980 and 1981-1982 Recessions
-10.48
-10.68 -10.70
-10.50
-10.72 -10.52
-10.74 -10.76
-10.54 -10.78 -10.80 1979
1980
1981
1982
1983
-10.56 1989Q3
1990Q1
1990Q3
1991Q1
1991Q3
1992Q1
-10.26 -10.28 -10.30 -10.32 2001 Recession
-10.34 -10.36 -10.38 2000Q1
2000Q3
2001Q1
2001Q3
2002Q1
2002Q3
Fig. 7. Historical simulation of output. In these figures the solid line is the actual level of log real output. The dashed line is the simulated log level if news shocks were the only stochastic disturbance. The shaded areas correspond to recession dates as defined by the NBER. The units of the vertical axes are the log of output per capita. The horizontal axes refer to dates.
The conditions under which either of these orthogonalization schemes are valid are encompassed by our identification strategy. In particular, were the conditions required for the pure recursive identification satisfied, our identification would (asymptotically) identify the same shock and impulse responses. Likewise, their long run identifying assumption in the second orthogonalization scheme rests on the same implicit assumption underlying our identification—that a limited number of shocks account for variation in measured technology. It is, however, more restrictive in the sense that it imposes that both kind of technology shocks permanently impact the level of TFP. Ours, in contrast, only imposes that the two technology shocks together explain the bulk of movements in TFP, without taking a stand on whether both permanently impact TFP.
286
R.B. Barsky, E.R. Sims / Journal of Monetary Economics 58 (2011) 273–289
In practice, there is a large quantitative and qualitative difference between our results and theirs in the estimated effects of news shocks on TFP itself. The shock identified by these authors typically does not have any noticeable effect on TFP for several years. Indeed, Beaudry and Portier (2006) note that ‘‘growth beyond its [TFP’s] initial level takes somewhere between 12 and 16 quarters’’ (p. 1303) following a news shock, while in Beaudry et al. (2008), they state ‘‘it [news shock] has almost no impact on TFP during the first five years’’ (p. 3). In contrast, our news shock begins to affect TFP soon after impact, and explains TFP movements well at both short and long horizons. That these authors’ identified shock has such a delayed effect on TFP makes its interpretation as a news shock problematic. Application of their identification strategies reveals that roughly one-third of the TFP forecast error variance is left unexplained at business cycle frequencies. In other words, some other structural shock orthogonal to TFP’s innovation potentially accounts for twice as much variation in TFP at these frequencies than does what these authors deem the news shock. In comparison, our identification leaves less than 5 percent of TFP’s variance unaccounted for at business cycle frequencies, as shown in the second to last row of Table 1. Our identification strategy and results are more consistent with the nascent theoretical literature on news shocks, which generally assumes delays between arrival of news and adoption of less than two years. An alternative approach to the VAR-based methodology of studying the implications of news shocks for aggregate variables would be the estimation of a fully specified DSGE model. This is the approach taken by Schmitt-Grohe and Uribe (2008), who argue that news shocks about future technology are quantitatively important for understanding fluctuations. While there are some differences (particularly in the impact behavior of output and investment to news), our conclusions about the importance of news shocks at medium frequencies are similar. In practice, estimation of a fully specified model in this context is problematic, as there is no consensus on what the appropriate theoretical structure is in which news shocks have a chance to be the primary driver of output fluctuations. 4. Discussion This section discusses our results, places them in the context of the existing literature, points out some unresolved issues, and suggests avenues for future research. A large literature has developed that seeks to develop theoretical models which generate positive impact comovement in response to good news. This has not proven to be a particularly easy task. Among papers in this growing literature are Beaudry and Portier (2004), Den Haan and Kaltenbrunner (2006), and Jaimovich and Rebelo (2009). Our empirical results suggest that this excessive focus on the impact effects of news shocks has been somewhat misplaced. A similar point is made by Leeper and Walker (2011). To make this point concrete, we show here that a simple, textbook neoclassical growth model augmented with news shocks is capable of generating impulse responses which are very similar to those that are estimated in the data. The model is a special case of the one presented in Section 2.2 in which there are no investment adjustment costs. So as to better fit the data, the process for technology is modified so that news diffuses slowly into TFP: lnAt ¼ gt1 þ lnAt1
ð20Þ
gt ¼ rgt1 þ ut
ð21Þ
Eq. (21) is simply a ‘‘smooth’’ version of the news process shown in (2) above. Given the timing assumption, ut can be interpreted as a news shock since it has no contemporaneous effect on the level of technology. The parameters of the model are chosen to fit the estimated impulse responses of TFP, consumption, output and hours to the news shock from the seven variable VAR. The impulse responses from this parameterized model are shown as the dashed line in Fig. 8, along with the empirical impulse responses (solid line) and confidence regions (shaded gray) from Fig. 4. The model’s impulse responses lie very closely to those estimated in the data at all horizons and are completely contained by the shaded confidence regions. In short, this simple model appears to provide a very good fit to the data, at least along this dimension. The various ‘‘fixes’’ that have been proposed to deal with negative impact comovement of quantities in response to news shocks appear unnecessary. The dimension along which the model does not fare well is in the behavior of the value of the firm. In the data, stock prices rise in response to our identified news shock, whereas in the model they fall. In the version of the model without any adjustment costs, the value of the firm is just equal to the capital stock, which falls for a few periods in response to good news. Even with substantial adjustment costs the value of the firm will still initially fall due to the rise in the real interest rate. Christiano et al. (2008) document this phenomenon in detail. Walentin (2009) proposes that limited enforcement of financial contracts can potentially help to generate stock price appreciations in anticipation of higher future productivity. Jinnai (2010) successfully builds a model in which the value of the firm rises in response to news even though investment falls. Our empirical results along these dimensions should help inform researchers building detailed DSGE models. Given that positive comovement among aggregate variables is a ubiquitous feature of the data, news shocks as estimated here cannot be the sole driving force behind fluctuations. The first interior row of Table 2 shows selected correlations among HP filtered aggregate variables for the period 1960–2007 (using smoothing parameter 1600). These correlations are all positive and strong, but many are far from one. The second interior row of the table shows the
R.B. Barsky, E.R. Sims / Journal of Monetary Economics 58 (2011) 273–289
Percent
2
15
5
10 15 Horizon
5 0 10 15 Horizon
Percent
0.08 0.06
Hours
10 15 Horizon
20
Value of the Firm
0.02 0
-0.02
-0.02
20
5
0.04
-0.01 10 15 Horizon
20
-0.005 -0.01
0
10 15 Horizon
0
20
0.01
5
5
0.005
Investment
0.03 0.02
0
0.01
10
5
Consumption
x 10-3
5
-5
20
Output
x 10-3
-5
Percent
10
4
0
Percent
Technology
x 10-3
Percent
Percent
6
287
5
10 15 Horizon
20
Fig. 8. Empirical impulse responses vs. RBC model impulse responses. The solid lines are the estimation empirical responses, identical to those shown in Fig. 4. The shaded gray areas are the 7 one standard error bootstrap confidence bands. The dashed lines are the theoretical responses from the best-fitting parameterization of the simple RBC model. The horizontal axes refer to forecast horizons and the units of the vertical axes are percentage deviations.
Table 2 Unconditional business cycle moments.
US data Only news Only surprise Both shocks
corr(y,c)
corr(y,i)
corr(y,n)
corr(y,y/n)
corr(c,i)
corr(c,n)
0.82 0.35 0.97 0.50
0.78 0.94 0.99 0.97
0.86 0.91 0.99 0.95
0.49 0.08 0.99 0.82
0.61 0.63 0.96 0.29
0.69 0.70 0.95 0.20
This table shows selected business cycle moments (HP filtered with smoothing parameter 1600) for (i) US data, 1960–2007; (ii) the model of Section 4 with only news shocks; (iii) the model of Section 4 with only surprise technology shocks; and (iv) the model of Section 4 with both surprise and technology shocks.
correlations that would obtain if the news shocks were the only stochastic disturbance in the simple model as presented above (parameterized as described). While the correlations between output and investment and output and hours are reasonably close to those in the data, the correlations involving consumption and other aggregates are negative. This is clearly at odds with the data. The next row of the table shows the resulting moments if a surprise technology shock was the only stochastic disturbance in the model. The shock is assumed to follow a stationary AR(1) process with autoregressive coefficient 0.98 and standard deviation of 0.75 percent. This calibration produces an impulse response of technology that matches the observed response of TFP to its own innovation in our VARs. Here the resulting correlations are all nearly one, which is too high relative to the data. The final row shows the correlations that result if both the permanent news shock and the transitory surprise technology shock are included in the model. Relative to the one shock model, the two shock version fits better on many dimensions—the correlations are all positive but not too close to one. The above exercise is meant to be illustrative but makes two related points. First, conventional business cycle models are capable of qualitatively matching the dynamic, conditional responses of many aggregate variables to news about
288
R.B. Barsky, E.R. Sims / Journal of Monetary Economics 58 (2011) 273–289
future technology. Second, even if news shocks do not induce positive comovement on impact, they can nevertheless be an important part of the data generating process and can help to explain some features of the data. In particular, the presence of news shocks can work to lower the correlations among aggregate variables that obtain in a simple one shock RBC model, in much the same way that, for example, government spending or distortionary tax shocks do (Christiano and Eichenbaum, 1992; McGrattan, 1994). New research points out several additional channels by which news shocks help to better fit the data. Kurmann and Otrok (2010), using a similar methodology to that pursued here, argue that news shocks help to explain the slope of the term structure of interest rates. Mertens (2010) shows how news shocks can help to account for the comovement between output and interest rates that have puzzled economists since King and Watson (1996). Our results suggest that research should move more toward medium frequencies and in finding structural explanations for news, and away from trying to resolve impact comovement problems. News shocks (or more generally slow technological diffusion) can be an important propagation mechanism, even if the shocks do not induce high frequency comovement (Andolfatto and MacDonald, 1998; Leeper and Walker, 2011). Most of the theoretical work in the news area assumes that good news is ‘‘manna from heaven’’—that is, agents receive word in advance that aggregate technology will exogenously change at some point in the future. This assumption seems unrealistic; searching for a deeper structural explanation for what has been empirically identified and labeled as ‘‘news’’ is a promising avenue for future work. SchmittGrohe and Uribe (2011), for example, argue that a common trend shock to both neutral and investment specific technology is an important driving force behind fluctuations. The impulse responses of aggregate variables to their common trend shock are very similar to the responses to our news shock. 5. Conclusion The news-driven business cycle hypothesis offers the tantalizing possibility that business cycles could emerge absent any (ex post) change in fundamentals. If good news about the future can set off a boom today, then a realization worse than anticipated can set off a bust. For this story to work, however, good news about the future must induce broad-based comovement, which is not the prediction of standard macro models. Existing empirical evidence suggesting that news shocks do lead to broad-based comovement have spawned a new literature searching for theoretical frameworks capable of delivering business cycle-like behavior when driven by news shocks about future technology. This paper has taken a closer look at the empirical evidence in favor of this theory of fluctuations. It implemented a novel empirical approach for identifying news shocks that are directly based on the implications of theoretical models of news-driven business cycles. In contrast to the existing literature, a good realization of our news shock is associated with an increase in consumption and impact declines in output, hours, and investment. After impact, aggregate variables largely track, as opposed to anticipate, predicted movements in measured TFP. The estimated impulse responses are broadly consistent with the implications of standard macro models. While important at medium to low frequencies, a historical decomposition reveals that news shocks have not been a major source of post-war US recessions. News shocks nevertheless do help to explain several features of the data. While we find no evidence to support the ‘‘boom-bust’’ story advanced by the literature, incorporating news shocks into existing models and seeking deeper structural explanations for what manifests itself as ‘‘news’’ seem like promising avenues for future research.
Acknowledgments We thank John Fernald of the San Franciso Fed for providing us with his TFP data. We are grateful to an anonymous referee, Rudi Bachmann, Nick Bloom, Daniel Cooper, Wouter Den Haan, Lutz Kilian, Bob King, Miles Kimball, Bernd Lucke, Matthew Shapiro, and numerous seminar participants for helpful comments and advice. Any remaining errors are our own. References Andolfatto, D., MacDonald, G., 1998. Technology diffusion and aggregate dynamics. Review of Economic Dynamics 1 (2), 338–370. Barro, R., King, R., 1984. Time separable preferences and intertemporal substitution models of business cycles. Quarterly Journal of Economics 99 (4), 817–839. Barsky, R., Sims, E., 2010. Information, animal spirits, and the meaning of innovations in consumer confidence. NBER Working Paper 15049. Basu, S., Fernald, J., Kimball, M., 2006. Are technology improvements contractionary? American Economic Review 96 (5), 1418–1448. Beaudry, P., Lucke, B., 2010. Letting different views about business cycles compete. In: NBER Macroeconomics Annual 2009, vol. 24, pp. 413–455. Beaudry, P., Portier, F., 2004. An exploration into Pigou’s theory of cycles. Journal of Monetary Economics 51 (6), 1183–1216. Beaudry, P., Portier, F., 2006. News, stock prices, and economic fluctuations. American Economic Review 96 (4), 1293–1307. Beaudry, P., Dupaigne, M., Portier, F., 2008. The international propagation of news shocks. Unpublished manuscript, University of British Columbia. Blanchard, O., L’Hullier, J., Lorenzoni, G., 2009. News, noise, and fluctuations: an empirical exploration. NBER Working Paper 15015. Chari, V., Kehoe, P., McGrattan, E., 2008. Are structural VARs with long run restrictions useful in developing business cycle theory? Journal of Monetary Economics 55 (8), 1337–1352. Christiano, L., Eichenbaum, M., 1992. Current real business cycle theories and aggregate labor market fluctuations. American Economic Review 82 (3), 430–450. Christiano, L., Ilut, C., Motto, R., Rostagno, M., 2008. Monetary policy and stock market boom bust cycles. Unpublished manuscript, Northwestern University. Cochrane, J., 1994. Shocks. In: Carnegie-Rochester Conference Series on Public Policy, vol. 41, no. 1, pp. 295–364.
R.B. Barsky, E.R. Sims / Journal of Monetary Economics 58 (2011) 273–289
289
Den Haan, W., Kaltenbrunner, G., 2006. Anticipated growth and business cycles in matching models. Unpublished manuscript, Euro Area Business Cycle Network. Faust, J., 1998. The robustness of identified VAR conclusions about money. In: Carnegie-Rochester Conference Series on Public Policy, vol. 49, no. 1, pp. 207–244. Faust, J., Leeper, E., 1997. When do long run identifying restrictions give reliable results? Journal of Business and Economic Statistics 15 (3), 345–353. Fernandez-Villaverde, J., Rubio-Ramirez, J., Sargent, T., Watson, M., 2007. ABCs (and Ds) of understanding VARs. American Economic Review 97 (3), 1021–1026. Fisher, J., 2006. The dynamic effects of neutral and investment specific technology shocks. Journal of Political Economy 114 (3), 413–451. Fisher, J., 2010. Comment on: letting different views about business cycles compete. In: NBER Macroeconomics Annual 2009, vol. 24, pp. 457–474. Francis, N., Owyang, M., Roush, J., 2007. A flexible finite horizon identification of technology shocks. Unpublished manuscript, Federal Reserve Bank of St. Louis. Hamilton, J., 1994. Time Series Analysis. Princeton University Press, Princeton. Jaimovich, N., Rebelo, S., 2009. Can news about the future drive the business cycle? American Economic Review 99 (4), 1097–1118. Jinnai, R., 2010. News shocks, product innovations, and business cycles. Unpublished manuscript, Texas A&M University. Kilian, L., 1998. Small sample confidence intervals for impulse response functions. Review of Economics and Statistics 80 (2), 218–230. King, R., Watson, M., 1996. Money, prices, interest rates and the business cycle. Review of Economics and Statistics 78 (1), 35–53. Kurmann, A., Otrok, C., 2010. News shocks and the slope of the term structure of interest rates. Unpublished manuscript, University of Virginia. Leeper, E., Walker, T., 2011. Information flows and news driven business cycles. Review of Economic Dynamics 14 (1), 55–71. Leeper, E., Walker, T., Yang, S.C., 2008. Fiscal foresight: analytics and econometrics. NBER Working Paper 14028. McGrattan, E., 1994. The macroeconomic effects of distortionary taxation. Journal of Monetary Economics 33 (3), 573–601. Mertens, E., 2010. Structural shocks and the comovements between output and interest rates. Journal of Economic Dynamics and Control 34 (6), 1171–1186. Pigou, A., 1927. Industrial Fluctuations. MacMillan, London. Schmitt-Grohe, S., Uribe, M., 2008. What’s news in the business cycle? NBER Working Paper 14215. Schmitt-Grohe, S., Uribe, M., 2011. Business cycles with a common trend in neutral and investment specific productivity. Review of Economic Dynamics 14 (1), 122–135. Sims, C., Zha, T., 2006. Does monetary policy generate recessions? Macroeconomic Dynamics 10 (2), 231–272. Smets, F., Wouters, R., 2007. Shocks and frictions in US business cycles: a Bayesian DSGE approach. American Economic Review 97 (3), 586–606. Uhlig, H., 2003. What drives GNP? Unpublished manuscript, Euro Area Business Cycle Network. Uhlig, H., 2004. Do technology shocks lead to a fall in total hours worked? Journal of the European Economic Association 2 (2–3), 361–371. Walentin, K., 2009. Expectation driven business cycles with limited enforcement. Sveriges Riksbank Working Paper No. 229. Watson, M., 1986. Vector autoregressions and cointegration. In: Engle, R., McFadden, D. (Eds.), Handbook of Econometrics. Elsevier, Amsterdam, pp. 2843–2915.
Journal of Monetary Economics 58 (2011) 290–304
Contents lists available at ScienceDirect
Journal of Monetary Economics journal homepage: www.elsevier.com/locate/jme
Aggregate real exchange rate persistence through the lens of sectoral data Laura Mayoral a,b,, Marı´a Dolores Gadea c a b c
Institute for Economic Analysis (CSIC), Campus UAB, 08193 Bellatera, Barcelona, Spain Barcelona GSE, Spain Department of Applied Economics, University of Zaragoza, Spain
a r t i c l e in f o
abstract
Article history: Received 20 January 2010 Received in revised form 19 June 2011 Accepted 22 June 2011 Available online 30 June 2011
A novel approach to analyzing real exchange rate (RER) persistence and its sources is presented. Using highly disaggregated data for a group of EU-15 countries, it is shown that the distribution of sectoral persistence is highly heterogeneous and skewed to the right, so that a limited number of sectors are responsible for the high levels of persistence observed at the aggregate level. Quantile regression has been employed to investigate whether traditional theories, such as the lack of arbitrage due to nontradability or imperfect competition combined with price stickiness, are able to account for the slow reversion to parity of RERs. & 2011 Elsevier B.V. All rights reserved.
1. Introduction Most of the empirical literature on purchasing power parity (PPP) and real exchange rate (RER) persistence focuses on the analysis of aggregate data, where RERs are constructed with aggregate price indices. The general consensus is that aggregate RERs may converge to parity in the long run, although the rate at which this happens is very slow, with half-lives (HL) in the range of 3–5 years (Rogoff, 1996). Thus, while the high volatility of real exchange rates could potentially be explained by monetary or financial shocks, the rate of reversion to parity seems to be too slow to be compatible with plausible nominal rigidities, giving rise to the so-called PPP puzzle. Several avenues have been pursued to shed more light on this issue. Recent literature has focused on the analysis of disaggregate real exchange rates, cf. Carvalho and Nechio (forthcoming), Crucini et al. (2010a,b), Crucini and Shintani (2008), Kehoe and Midrigan (2007), Imbs et al. (2005a) and Crucini et al. (2005), etc. One common finding is that there is a considerable degree of heterogeneity across sectors. Nevertheless, the relation between aggregate and sectoral RER persistence is more controversial. Some authors have found large divergences between sectoral and aggregate reversion rates. Using Eurostat data, Imbs et al. (2005a) report standard HL estimates in the range of 3–5 years when aggregate data are used, but considerably smaller, around 1 year, when sectoral data are employed. On the other hand, several authors have found very similar estimates using both types of data, suggesting that the aggregation bias is not a robust feature in the data (Gadea and Mayoral, 2009; Crucini and Shintani, 2008; Chen and Engel, 2005). The results recently presented in Mayoral (2009) help to clarify the contrasting empirical findings outlined above. She has studied the relations between measures of persistence computed at different aggregation levels and has shown that there is a close connection between them. She proves that the impulse response (IR) function computed with aggregate
Corresponding author at: Institute for Economic Analysis (CSIC), Campus UAB, 08193 Bellatera, Barcelona, Spain. Tel.: þ 34 935 806 612.
E-mail address:
[email protected] (L. Mayoral). 0304-3932/$ - see front matter & 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.jmoneco.2011.06.003
L. Mayoral, M. Dolores Gadea / Journal of Monetary Economics 58 (2011) 290–304
291
data equals the average of the sectoral impulse responses and that a similar relation also holds for other scalar measures associated with the IR. These results are the starting point of this paper. They imply that since aggregate persistence—as measured by the IR or the associated scalar tools—is completely determined by the behavior of the sectors, the aggregate HL or the cumulative impulse response (CIR) can also be estimated using sectoral data. By using disaggregate information, it is possible to break down aggregate persistence into the persistence of its different subcomponents, thereby obtaining a lot of valuable information about the sources of aggregate persistence. Another interesting implication of her results is that they unveil the nature of the relation between sectoral and aggregate persistence: the aggregate response to a shock is the average of the individual responses and since averages are very nonrobust measures, a situation where most sectors present relatively quick reversion to parity, but where a few of them are highly persistent, is compatible with a highly persistent aggregate RER. The goal of this paper is to investigate the causes of the slow reversion to parity of aggregate real exchange rates through the analysis of sectoral ones. Using highly disaggregate price data on a group of EU-15 real exchange rates (defined against the U.K. pound), a twofold strategy is implemented. First, aggregate RER persistence is broken down into the persistence of its different components. This allows us to identify interesting features of the sources that drive aggregate persistence and to show that it is determined, to a large extent, by the behavior of a limited number of sectors in the upper quantiles of the distribution of persistence. Second, the factors that have traditionally been put forward to account for the slow reversion to parity of RERs, in particular, the lack of arbitrage in nontradable goods and the existence of nominal rigidities combined with pricing-to-market are more thoroughly investigated. Special emphasis is placed on explaining the behavior of the upper (conditional) quantiles of the distribution of sectoral persistence because, as mentioned before, they determine, to a large degree, the persistence observed at the aggregate level. To do so, recent quantile panel regression techniques are employed. Our main results can be summarized as follows. Firstly, a high degree of heterogeneity as well as high and positive skewness in the speed of reversion of EU sectoral RERs are documented. Sectors belonging to the durable category are those that show the lowest speed of reversion to parity: on average, they account for around 40% of the long-run cumulative effect of shocks to aggregate RERs. By contrast, services present the fastest speed of reversion. Secondly, our quantile panel regression analysis shows that variables related to the market structure of the intermediate inputs and to the price stickiness of the final goods have a significant effect on sectoral persistence. Furthermore, the impact of these variables tends to be larger, the higher the quantile considered. Interestingly, once the market structure of the intermediate inputs has been taken into account, that of the final goods does not appear to be important in explaining sectoral persistence. Finally, variables related to the tradability of goods are not significant either, implying that traditional theories that attribute the slow speed of reversion of RERs to the existence of nontraded goods in the consumption basket do not explain EU current trade patterns very well. These conclusions are in agreement with modern trade theories (cf. Carvalho and Nechio, forthcoming; Chari et al., 2002). The rest of the paper is structured as follows. Section 2 presents a brief overview of the literature that has dealt with RER persistence at different levels of aggregation. Section 3 introduces the variables that are used in the paper as well as the different databases employed in their construction. Section 4 provides estimates of aggregate RER persistence computed with both aggregate and sectoral data, tests whether these estimates are equal and explores the distribution of sectoral persistence. Section 5 analyzes whether the traditional theories (lack of arbitrage due to nontradability and/or imperfect competition and price stickiness) are able to explain the distribution of sectoral persistence. Section 6 concludes. An Appendix presents additional explanations not included in the main text.1
2. Related literature There is a considerable evidence of a large degree of sectoral heterogeneity in the speed of reversion of RERs (Crucini and Shintani, 2008; Imbs et al., 2005a). Starting with the contribution of Imbs et al. (2005a) (IMRR henceforth), several papers have looked at the causal relation between heterogeneity in sectoral exchanges rates and the slow speed of reversion observed at the aggregate level. IMRR show that persistence estimates based on sectoral RERs are, on average, considerably smaller than those obtained for the aggregate rate itself. They argue that estimates of aggregate persistence rely upon the implicit assumption that relative prices converge to parity at the same speed, and that it is precisely the failure to allow for heterogeneity in adjustment dynamics at the sectoral level which induces a positive bias in persistence estimates when aggregate data are employed. To illustrate their main arguments, consider a very simple model for the sectoral exchange rate in sector i, qi,t , which allows for heterogeneous speed of price adjustment
1
qi,t ¼ gi þ ai qi,t1 þ vi,t ,
ð1Þ
vi,t ¼ ri ut þ ei,t ,
ð2Þ
This appendix can be found in the online version of the paper.
292
L. Mayoral, M. Dolores Gadea / Journal of Monetary Economics 58 (2011) 290–304
where qi,t ¼ pi,t pni,t st ,
ð3Þ
pi,t and pi,t are the logs of the price of sector i in the domestic and foreign countries, respectively, and st is the nominal exchange rate, measured as domestic per foreign currency units. The processes ut and ei,t represent an aggregate and an idiosyncratic shock, respectively, and are assumed to be mutually independent, zero-mean i.i.d. processes. The parameter ai varies across sectors and captures the heterogeneity in price adjustment dynamics, while ri measures the impact of the common shock ut on sector i. These coefficients are assumed to be draws from the distribution of the random variables a and r. Without loss of generality, the expected value of r is normalized to 1.2 Under the previous assumptions, it is easy to obtain the dynamics of the aggregate RER, Qt, as the expected value of (1) over the distribution of sectors (Lewbel, 1994). P j j Recall that the moving average representation of qi,t is given by qi,t ¼ 1 j ¼ 0 ai L ðri ut þ ei,t Þ. It follows that n
Qt ¼ Es ðqt Þ ¼ Es ðr þ arLþ a2 rL2 . . .Þut þ Es ð1þ aL þ a2 L2 . . .ÞEs ðe:,t Þ ¼
1 X
Es ðaj rÞutj ,
ð4Þ ð5Þ
j¼0
where Es ðÞ denotes expectation across the distribution of sectors. For a simple model such as that of (1), IMRR base their sectoral estimates of persistence on the IR of the process q t ¼ a q t1 þ at , where a ¼ Es ðaÞ, which is given by IRq ðhÞ ¼ a h :
ð6Þ
The IR of the aggregate RER to a unitary shock in ut can be easily obtained from (4) as follows: IRQ ðhÞ ¼ Es ðah rÞ:
ð7Þ
2.1. Aggregation bias IMRR’s main claim is that estimates of the HL obtained from (7) are considerably larger than those obtained from (6). Using Eurostat data, they report estimates of the aggregate HL in the range of 3–5 years, while those based on sectoral data are considerably smaller, around 1 year. They argue that the PPP puzzle is due to a positive bias in aggregate estimates arising because individual heterogeneity is not explicitly taken into account by standard estimates. Chen and Engel (2005) provide a number of criticisms of the methods of IMRR. From a theoretical point of view, they argue that the analytical results provided by IMRR to justify the aggregation bias are different from the claims made in their empirical work. While in the latter they focus on the behavior of the HL across aggregation levels, analytically they demonstrate that the first autocorrelation of Qt is larger than the average of the first autocorrelations of qi,t . From an empirical perspective, they argue that the Eurostat data is plagued with measurement error that could make the series appear much less persistent than they actually are. Using similar data to IMRR, but with corrections for data entry errors and for small-sample bias, Chen and Engel show that the aggregation bias, as measured by the difference between the HLs in the aggregate model and that obtained from an IR similar to that in (6) is, in fact, small.3 These results have been corroborated by Crucini and Shintani (2008). Using a different dataset, an extensive annual micro-panel of individual retail goods and services in local currency prices in major cities from 1990 to 2005, and a different estimation strategy, they find that the aggregation bias is not a robust feature in the data. While they are able to find some evidence for the U.S., they fail to do so for the other locations in their dataset. Gadea and Mayoral (2009, GM henceforth) have put forward a further objection to IMRR’s methods. They argue that the different persistence behavior of aggregate and sectoral exchange rates reported by IMRR is not due to an upward bias in aggregate data estimates, but rather to a negative bias affecting IMRR’s sectoral persistence measures. Building on the results in Mayoral (2009), GM propose to measure average sectoral persistence by averaging the individual IRs, instead of by averaging the AR coefficients and then computing the IR of the resulting process as in (6). For the simple models considered here, the IR of sector i to a unitary change in the aggregate shock ut is given by IRuqi ðhÞ ¼ ahi ri .4 Averaging across sectors, it is obtained that IRuq ðhÞ ¼ Es ðah rÞ:
ð8Þ
Defining the aggregation bias (AB) as the difference between the aggregate and the average of the sectoral IRs to a unitary shock in ut, it is easy to see that AB ¼ IRQ ðhÞIRuq ðhÞ ¼ 0
for all h:
ð9Þ
P 2 j 2 It is also assumed that the support of a is strictly smaller than 1, that 1 j ¼ 0 Eða Þ o 1 and that ei,t is independent from a. The assumptions in this section are only imposed to simplify the explanation and the main arguments are valid in a more general setting (see Mayoral, 2009 for details). 3 However, Imbs et al. (2005b) replied to this paper and showed that their results survive each of the criticisms raised by Chen and Engel. 4 See Mayoral (2009) for details.
L. Mayoral, M. Dolores Gadea / Journal of Monetary Economics 58 (2011) 290–304
293
It follows that since the IR is a highly nonlinear function, averaging the AR coefficients and then computing the IR, as IMRR do, or averaging the individual responses, may yield very different results. In fact, Jensen’s inequality ensures that, for most empirically relevant cases, the former measure is smaller than the latter. The intuition of this result is clear: since the IR function is convex, highly persistent sectors increase the mean considerably. However, in the computations of IMRR, these sectors are eliminated in the first stage when the model AR coefficients are averaged. This translates, not surprisingly, into lower estimates of persistence. Using similar data and a similar estimation strategy to those employed in IMRR’s paper, GM have shown that the aggregation bias is not statistically different from zero. 2.2. Total heterogeneity effect More recently, Carvalho and Nechio (forthcoming, henceforth CN) have introduced a theoretical model with sticky prices that departs from the existing literature by allowing for heterogeneity in the frequency of price changes across sectors. To gauge the impact of allowing for heterogeneity, they compare the persistence implied by two models sharing the same average frequency of price changes, one that allows for heterogeneity and another that does not. They denote as total heterogeneity effect (THE) the difference in persistence implied by these two models. This quantity is further broken down into two components: a counterfactuality effect (CE) and an aggregation effect (AE). Using the IRðhÞ as the persistence measure, these effects can be defined as THE ¼ IRQ ðhÞIRq ðhÞ ¼ CE þAE, where
and
CE ¼ IRvq ðhÞIRq ðhÞ,
ð10Þ
AE ¼ IRQ ðhÞIRvq ðhÞ,
ð11Þ
IRvq ðhÞ
is the sectoral average of the response of qi,t to a unitary change in the reduced-form shock vi,t , given by
IRvq ðhÞ ¼ Es ð h Þ:
a
ð12Þ
CN use this decomposition to account for the different results found in the literature. They argue that while both AE and CE are strictly greater than zero, the latter accounts for the largest part of THE. Thus, since different authors have reported estimates of different quantities (IMRR provide estimates of THE and GM and Crucini and Shintani, 2008 of AE), different results are bound to arise. Notice that AB and the AE, defined in (9) and in (11), respectively, are very similar. The difference between them stems from the shocks that are assumed to change when computing the IRs. CN consider a unitary change in the aggregate shock, ut, and a unitary change in the reduced-form shock, vi,t , to compute the aggregate and the individual IRs, respectively. On the other hand, in the computation of AB, the aggregate and the individual IRs are both based on unitary changes in the aggregate shock ut. Notice further that, under independence of a and r, IRuq ðhÞ ¼ Es ðah rÞ ¼ Eðah Þ ¼ IRvq ðhÞ, which implies that AE ¼ AB ¼ 0, that is, there is no aggregation effect even if the individual IRs are computed with respect to their reduced-form shock vi,t . If a and r are not independent, the direction of the correlation between ah1 and r will determine whether AE is positive or negative. In CN’s model, this correlation is actually positive (meaning that higher a’s obtain greater weights, on average) and this is why they obtain that AE 4 0. If the correlation were negative, however, the opposite would be obtained. CN’s observation that AE is small in Eurostat data can be interpreted as saying that the correlation between ah and r is close to zero. In the following sections, the relation established in (9) will be exploited to investigate the sources of aggregate persistence by analyzing sectoral RERs. Considering aggregate and sectoral IRs related to the same macro-shock has two advantages: firstly, it enables a better understanding of the role of aggregation in the transmission of shocks, since the same shock is hitting both the sectors and the aggregate process; and, secondly, it allows us to pin down a close relation between sectoral and aggregate behavior. Since IRQ and IRuq are the same function, aggregate persistence can be estimated using either sectoral or aggregate data. The use of sectoral data yields considerably more efficient estimates as will be shown in Section 4 and, more importantly, it allows us to break down aggregate persistence into the persistence of its subcomponents. 3. The data This section provides definitions of the variables employed in this paper and describes the sources employed in their elaboration. To construct sectoral RERs, the Eurostat Harmonized Index of Consumer Prices (HICP) for 11 European countries ranging from 1996:1 to 2007:12 have been employed. These countries and their corresponding abbreviations are Austria (AU), Belgium (BE), Denmark (DK), Finland (FI), France (FR), Germany (GE), Italy (IT), the Netherlands (NL), Spain (SP), Sweden (SW) and the United Kingdom (UK).5 Eurostat provides data corresponding to different levels of aggregation. We 5 All the EU-15 countries were initially considered. However, four of them (Portugal, Luxembourg, Greece and Ireland) present important data shortages in the other datasets employed in this paper. For this reason, they were dropped from the analysis.
294
L. Mayoral, M. Dolores Gadea / Journal of Monetary Economics 58 (2011) 290–304
focus on the most disaggregate level, which contains prices from 94 sectors. Nominal exchange rates are obtained from the Main Economic Indicators of the OECD and sectoral RERs are defined against the U.K. pound according to (3). Aggregate RERs have been constructed by aggregating sectoral RERs using Eurostat price weights.6 Section 5 uses a number of variables to account for the persistence of European sectoral exchange rates. These variables belong to three categories: those that are a proxy for market structure and price stickiness, those that measure the degree of openness of the sectors, and some controls. Four datasets have been employed to construct them: the Comtrade (United Nations Commodity Trade Statistic Database), the OECD Structural Analysis Statistics (STAN, Edition 2008), the Input–Output Tables (IOT) from the OECD and data on the frequency of price changes (see Dhyne et al., 2006 and the references therein).7 While definitions of these variables are provided below, their connections with RER persistence are spelled out in Section 5. 3.1. Market structure and price stickiness Two proxies for market structure have been elaborated, the price-cost margin and the intra-industry trade index. 3.1.1. Price-cost margin (PCM) The PCM index proxies the degree of profitability of an industry. It is defined as PCM c,i ¼
VAc,i Wc,i , VAc,i þCM c,i
ð13Þ
where VAc,i is the total value added of sector i (the value of total production minus the cost of materials) in country c,Wc,i is the labor compensation and CMc,i denotes the cost of materials. In addition, the PCM of the inputs employed in the production of good i has been computed as follows: Input-PCMc,i ¼
G X
og PCMc,g ,
ð14Þ
g¼1
where PCMc,g is the price-cost margin of input p defined as in (13) and og and G denote the share of good g and the total number of inputs involved in the production of sector i, respectively. The weights og are the relative contribution of the corresponding input g to the production of good i, as stated by the Input–Output Tables of country c. 3.1.2. Intra-industry trade (IIT) The IIT refers to the exchange of products belonging to the same industry and characterizes the nature of competition via the substitutability between domestic and foreign products. Two different indices have been computed, one that evaluates the degree of IIT for sector i in country c and another that measures the amount of IIT associated with the intermediate items needed to produce good i. The IIT index for sector i in country c is defined as in Grubel and Lloyd (1975) PRi j ¼ 1 jXc,j Mc,j j IIT c,i ¼ 1 PR , ð15Þ i ðX þMc,j Þ j ¼ 1 c,j where Ri is the number of goods (at six digits of disaggregation) in sector i according to the Comtrade database and Xc,j (Mc,j Þ represents total exports (imports) of good j in country c. The intermediate-goods IIT index (denoted as Input-IIT) is computed as the weighted average of IIT indices for each of the inputs employed in the elaboration of good i, that is Input-IIT c,i ¼
G X
og IIT c,g :
ð16Þ
g¼1
3.1.3. Price stickiness To proxy for price stickiness, data on the frequency of price changes at the sectoral level are usually employed. Unfortunately, for most of the countries in our dataset, data with ample and homogenous product coverage does not seem to be available.8 In spite of this limitation, a rough proxy of price stickiness has been elaborated as follows. Firstly, Kehoe and Midrigan (KM, 2007)’s data have been employed. They provide estimates of the per period probability of no-price adjustment corresponding to 57 sectors for AU, 56 for FR, 46 for BE and 31 for SP. Secondly, for the countries not considered in KM, the data summarized by Dhyne et al. (2006) have been considered. They select a representative 50-product sample with good coverage for 10 European countries. These products have been assigned to the different 6 The weights employed to aggregate sectoral RERs are the average over the period 1996–2007 of those used to aggregate sectoral prices in the different countries. Price data on some sectors are missing for some countries. See Eurostat for more details. 7 See the Appendix for more details on these datasets. 8 For some countries, such as AU and BE, the number of product categories for which frequencies of price changes are recorded is high (639 and 583, which amounts to 90 and 68% of total CPI, respectively) but for the others, it is only around 50 products (10% of total CPI).
L. Mayoral, M. Dolores Gadea / Journal of Monetary Economics 58 (2011) 290–304
295
Eurostat sectors following a similar criteria to KM.9 This allows us to obtain frequencies of no-price adjustment corresponding to approximately 30 sectors for the countries not included in KM study, with the exception of SW and DK. Since the amount of missing data is very large, two versions of the infrequency of price adjustment have been elaborated. The first one (STICK) fills in the missing values as follows: if data on the probability of no-price adjustment of sector j in country c is missing but there is information for other countries, the average of the available infrequencies for sector j is assigned. The second version (STICK2) does not fill in missing values. The procedure above is far from ideal since information on many sectors is missing and, with the exception of AU, BE and FR, the quality of the estimates of the remaining sectors is questionable.10 To overcome these limitations, a different route has also been explored. Dhyne et al. (2006) found that the frequency of price changes is positive and significantly related to the volatility of inflation of the corresponding good (although not by its average level of inflation). This suggests that the volatility of inflation could potentially be used as a proxy for price stickiness.11 We have regressed KM’s sectoral frequencies on the mean and the standard deviation of sectoral inflation. A similar regression has been performed using the data elaborated with Dhyne et al. (2006)’s sample. In both cases, the coefficient associated with the volatility of sectoral inflation was large, positive and highly significant.12 So, the volatility of sectoral inflation has also been used to proxy for price stickiness. According to this interpretation, sectors with larger inflation volatility would tend to present less persistent RERs. The volatility of inflation, VOLc,i , is defined as the standard deviation of the inflation rate of sector i in country c, which is defined as INFLc,i,t ¼ 1200ðpc,i,t pc,i,t1 Þ. 3.2. Tradability of goods Tradability of sector i is proxied by its degree of openness, defined as OPc,i ¼
Xc,i þ Mc,i , GDPc,i
ð17Þ
where GDPc,i is the total GDP of sector i in country c for 2003. As for the group of variables related to market structure, the P degree of openness of the intermediate inputs has also been calculated. It is defined as Input-OPci ¼ Gg ¼ 1 og OPcg , where c OPg denotes the degree of openness of the intermediate good g, computed as in (17). 3.3. Control variables The level of inflation in sector i has been employed as an additional control. To this effect, the variable INFLc,i , defined as the average of INFLc,i,t over the period 1996–2007, has been considered. 4. Aggregate persistence and aggregation bias This section describes the econometric models and methods employed to estimate IRs and other persistence measures. In addition, it formally tests the existence of an ‘aggregation bias’ in European RERs. Finally, it provides a description of the distribution of sectoral persistence.
4.1. Econometric models and methods It is assumed that sectoral RERs follow a linear specification, similar to that in (1) and (2). More specifically, the RER of sector i in country c at time t, qi,t , is given by qi,t ¼ ai,0 þ
K X
ai,k qi,tk þvi,t , vi,t ¼ ri ut þ eit for t ¼ 1, . . . ,T, i ¼ 1, . . . ,N:
ð18Þ
k¼1
As shown by Lewbel, the aggregate of (18) follows an AR ð1Þ process. Thus Qt ¼
1 X
Aj Qtj þut :
ð19Þ
j¼0
9
See KM for details. Since the number of products is very small, all sectors for which some information is available have been maintained. Notice that sectoral estimates are likely to be very imprecise since, most of the time, only data on a single product was available per sector. 11 The advantage of this variable is that it is available for all sectors and countries. As noted by Wooldridge (2001), introducing a proxy variable, even if it is an imperfect proxy, can actually reduce asymptotic variances and mitigate bias. 12 Both panel and country by country regressions were carried out and the results were identical. Mean sectoral inflation was never significant in these regressions. 10
296
L. Mayoral, M. Dolores Gadea / Journal of Monetary Economics 58 (2011) 290–304
Sectoral IRs, defined as the responses of qi,t to unitary changes in ut and vt, have been considered. The impulse response of sector i to a unitary change in ut or vt is given, respectively, by IRuqi ð0Þ ¼ ri and IRvqi ð0Þ ¼ 1 and h X
IRgqi ðhÞ ¼
ai,k IRgqi ðhkÞ for g ¼ fu,vg and h Z 1:
ð20Þ
k¼1
Average sectoral persistence is computed as the mean of the individual IRs, that is, IRgq ðhÞ ¼ where oi are Eurostat sectoral weights. The IR of Qt to a unitary change in ut is given by IRQ ð0Þ ¼ 1 and h X
IRQ ðhÞ ¼
Aj IRQ ðhjÞ
for hZ 1:
PN
i¼1
oi IRgqi ðhÞ, for g ¼ fu,vg,
ð21Þ
j¼1
Since IRðhÞ is a vector of numbers, it is customary to use scalar measures. Two of these scalar tools are employed: the half life (HL) and the cumulative impulse response (CIR). The HL is defined as the value of the IRðhÞ that satisfies IRQ ðt,h ¼ HLÞ ¼ 0:5, or, alternatively, IRuq ðh ¼ HLÞ ¼ 0:5 if sectoral data are employed.13 The cumulative impulse response P P (CIR) at horizon h is defined as CIRðhÞ ¼ hl¼ 0 IRQ ðt,lÞ, or, equivalently, CIRðhÞ ¼ hl¼ 0 IRuq ðlÞ. 4.2. Estimation To obtain estimates of the IRs and the scalar measures of persistence, the following methods have been employed.14 In the presence of sectoral heterogeneity, Qt might display complicated dynamics, as Eq. (19) shows. Following Kuersteiner (2005), AR(K) models have been fitted to aggregate RERs, where K has been chosen according to the general-to-specific (GTS) approach (Ng and Perron, 1995).15 Since RERs are, in general, highly persistent, bias-corrected estimates have been computed (see the Appendix). Then, estimates of IRQ have been obtained based on expression (21). To estimate IRvq ðhÞ, bias-corrected AR(k) processes have been fitted to all sectors, the resulting estimates have been plugged to (20) and a weighted average of the individual IRs has been calculated. Estimation of IRuq ðhÞ is similar, the only difference being that, in this case, estimates of all the model parameters, ai s and ri , are required. See the Appendix for a description of how estimates of ri are obtained. Confidence intervals for the IRs have been calculated using bootstrap methods. Details are provided in the Appendix. 4.3. Testing Formal tests have been carried out to check whether the aggregation bias and the aggregation effect, defined in (9) and (11), respectively, are qual to zero. The following null hypotheses have been formulated and tested: Test A: H0A :
G X
ðIRvq ðhÞIRuq ðhÞÞ2 ¼ 0,
ð22Þ
ðIRQ ðhÞIRuq ðhÞÞ2 ¼ 0,
ð23Þ
ðIRQ ðhÞIRvq ðhÞÞ2 ¼ 0:
ð24Þ
h¼0
Test B: H0B :
G X h¼0
Test C: H0C :
G X
h¼0
H0A entails that the two sectoral IRs described above are identical up to lag G. H0B and H0C correspond to the hypotheses that AB¼0 and AE¼ 0, respectively. The horizon G has been set to 36, 60 and 84 (3, 5 and 7 years, respectively). Bootstrap techniques have been employed to carry out the tests. A description of the methods employed is reported in the Appendix. 4.4. Empirical results Fig. 1 presents the plots of our estimates for IRQ and IRuq ðhÞ as well as their confidence bands at the 5% significance level for each of the countries in our dataset. Estimates of IRvq ðhÞ are not reported to enhance visibility, since they are basically identical to those of IRuq ðhÞ. These plots show that, although European Union markets are very integrated, EU RERs are highly persistent. Estimates of the IRs based on aggregate and sectoral data are, in general, very similar, as predicted by the 13
As in Kilian and Zha (2002), the HL is defined as the largest value of HL such that IRQ ðt,HL1Þ Z 0:5 and IRQ ðt,HL þ 1Þ o 0:5. As a preliminary analysis, panel unit root tests have been applied to EU RERs (Levin et al., 2002; Im et al., 2003). The results, not reported for reasons of space, show that the unit root hypothesis could be rejected in most cases, in line with the previous literature. In accordance with these results, the estimation of the parameters has been restricted, so that the sum of the autoregressive coefficients is smaller than 1. 15 Kuersteiner (2005) has shown that, if the GTS approach is employed to select K, consistent and asymptotically normal estimates of the coefficients of an AR ð1Þ process can be obtained. In the present paper, a maximum of 36 AR terms has been employed throughout. 14
L. Mayoral, M. Dolores Gadea / Journal of Monetary Economics 58 (2011) 290–304
AU
BE
DK
297
FI
FR
2.5
2.5
2
2
2
2
2
1.5
1.5
1.5
1.5
1.5
1
1
1
1
1
IR
IR
IR
2.5
IR
2.5
IR
2.5
0.5
0.5
0.5
0.5
0
0
0
0
0
−0.5
−0.5
−0.5
−0.5
−0.5
−1
−1
−1 0
20
40
60
0
20
h
40
60
−1 0
20
h
GE
40
60
−1 0
20
40
h
IT
2.5
0.5
0
SP
2.5
2
2
2
2
1.5
1.5
1.5
IR
0.5
0.5
0.5
0.5
0
0
0
0
0
−0.5
−0.5
−0.5
−0.5
−0.5
−1
−1
−1
−1
20
40
60
0
20
h
40
60
0
20
h
40
60
1
IR
IR
IR
IR
1
0.5
0
40
2.5
1.5
1
60
SW
2.5
2
1
40 h
1.5 1
20
h
NL
2.5
60
60
−1 0
20
h
40
60
0
20
h
h
Fig. 1. Aggregate IRs estimated with aggregate and sectoral data. Note: This graph shows the IR to an aggregate shock estimated using both aggregate (IR-Q) and sectoral (IR-qu) RERs for the group of European countries considered in this study.
Table 1 RER persistence with aggregate and sectoral data. h
Cumulative impulse response (h) 12
AU BE DK FI FR GE IT NL SP SW
HL 36
u
v
60 u
Q
q
q
Q
q
9.55 9.05 10.41 8.64 10.00 9.53 10.35 9.91 10.92 8.87
8.60 8.59 9.10 8.03 9.03 8.29 8.61 8.93 9.25 8.15
8.55 8.59 8.96 7.92 8.98 9.31 8.59 8.78 9.22 8.38
22.59 23.04 27.42 18.50 23.96 21.28 31.19 26.56 35.94 17.88
18.99 20.22 21.24 16.56 22.04 18.04 20.96 21.02 25.97 17.48
v
q
Q
qu
qv
Q
qu
qv
19.08 20.21 20.76 16.29 22.03 18.18 21.21 20.83 26.07 18.33
27.91 31.82 37.80 18.48 28.11 24.33 48.88 37.52 67.57 15.65
26.76 29.14 30.61 19.75 30.23 24.66 28.38 28.88 42.55 22.39
27.08 29.14 29.86 19.51 30.31 24.89 29.20 28.91 43.09 23.35
37.52 40.18 44.08 36.04 37.21 31.32 60.51 44.19 118.53 22.38
36.57 37.26 37.33 12.02 37.61 18.33 36.99 37.32 85.47 20.06
36.75 37.32 36.99 12.06 37.66 18.39 37.23 37.42 91.11 20.30
Note: Q, qu and qv denote CIR or HL measures obtained from IRQ ,IRuq and IRvq , respectively.
theoretical results in Section 2. Interestingly, estimates based on sectoral data are considerably more efficient than those based on aggregate persistence, as shown by the fact that the confidence bands associated with IRQ are considerably wider than the sectoral ones. Table 1 displays some summary statistics corresponding to the estimated IRs, namely, the HL and three values of the CIRc ðhÞ (for h corresponding to 1, 3 and 5 years). Q, qu and qv correspond to measures obtained from IRQ, IRuq ðhÞ and IRvq ðhÞ, respectively. The values of the HLs are in line with those found in previous studies displaying values between 3 and 5 years. In addition, the different measures of aggregate persistence computed with aggregate and disaggregate data are very close, corroborating the graphs in Fig. 1. In view of Table 1, it is not surprising that the null hypotheses H0A , H0B and H0C cannot be rejected for any of the countries in our dataset (the corresponding figures are reported in the Appendix). This has two important practical implications: firstly, the fact that H0A cannot be rejected implies that considering sectoral IRs that refer to changes in the aggregate or the
298
L. Mayoral, M. Dolores Gadea / Journal of Monetary Economics 58 (2011) 290–304
1.2
1.2
1
food energy non−durables durables services
1
0.8 0.8 0.6
IR
IR
0.6 0.4
0.4 0.2 0.2 0 bin1 bin2 bin3 bin4 bin5
−0.2
0
−0.4
−0.2 0
10
20
30 h
40
50
60
0
10
20
30
40
50
60
h
Fig. 2. IRs of different groups of sectors. Note: This graph depicts the IRs to an aggregate shock associated to the RERs of some groups of sectors. On the left-hand side, goods are classified in the bins described in Section 4.3, while on the right-hand side sectors are categorized as food, energy, nondurables, durables or services.
reduced-form shock is irrelevant in our sample. Since IRvq ðhÞ is easier to compute, the rest of the paper will use this function to derive the scalar measures of sectoral persistence. To simplify the notation, the superindex ‘v’ will be dropped hereinafter. Secondly, the fact that neither H0B nor H0C could be rejected implies that estimates of aggregate persistence can also be obtained by averaging sectoral estimates. 4.5. The distribution of sectoral persistence Many studies have documented the existence of a high degree of heterogeneity in the persistence of sectoral RERs (see Imbs et al., 2005a; Crucini and Shintani, 2008, for recent references) and the dataset considered in this paper is not an exception. Density functions corresponding to CIR(h) for different values of h, namely, h¼{36, 60, 84} months, have been estimated for all the countries in our dataset.16 In addition to a considerable degree of heterogeneity, the densities display substantial skewness to the right, which is higher, the longer the horizon of the CIR considered. Average skewness is 0.7810, 1.1779 and 1.8150 for h¼{36, 60, 84}, respectively. Since persistence is a long-term property, the pattern of the densities of the different CIR indicates that persistence is highly heterogeneous and asymmetric and that these characteristics are accentuated with the horizon considered. These two features have an immediate implication on the aggregate IR; since it is an average of the individual responses and averages are very nonrobust measures, it will be most likely driven by a few highly persistent sectors. 4.5.1. Persistence by groups of sectors To look more closely at the distribution of sectoral persistence, the sectors, ranked by their persistence level, have been grouped into five categories. To make the different groups as homogeneous as possible, the size of the bins has been determined such that the variance around the bin’s average persistence is kept fixed. This gives us a number of sectors per bin of 2, 21, 34, 19 and 2 for bins 1–5, respectively. See the Appendix for a list of the sectors included in each bin.17 The left-hand graph in Fig. 2 plots the IRs associated with each of these bins. As this figure shows, the persistence implied by the sectors in bins 1–5 is very different. The IRs of bins 1–3 present a relatively quick reversion to parity as opposed to those of bins 4 and, more especially, 5, which do not display clear signs of mean reversion. To compare this classification with traditional ones, two long-established categories have also been considered. The first classifies goods as food (F), durables (D), nondurables (ND), services (S) and energy (E). The second one, as traded (T) and nontraded (NT).18 The right-hand graph in Fig. 2 depicts the IRs corresponding to the first of these categories. It shows that they are considerably closer together than those in the left-hand side of this figure, suggesting the existence of 16
See the Appendix for details on the estimation and graphs of the densities. Estimates have been obtained using the panel described above. Sectors have been ranked according to their IR evaluated at h ¼HL since this measure allowed us to construct bins with very similar within-group variability. Alternative measures of persistence have been employed and the results were qualitatively identical. A genetic algorithm was employed to assign sectors to bins. 18 Services are considering as NT (with the exception of air travel and financial services) while all other sectors are considered as traded. 17
L. Mayoral, M. Dolores Gadea / Journal of Monetary Economics 58 (2011) 290–304
299
important within-group heterogeneity. D and ND are as the most persistent groups of sectors while the IRs corresponding to F, E and S decay more quickly. Exploring the internal composition of the persistence bins lead to similar conclusions: although bin structure changes as the degree of persistence increases, there is considerable heterogeneity within each bin. Services tend to be concentrated in the least persistent bins. The 26 sectors in the service category are mainly located in the first three bins (2, 13 and 10 sectors in bins 1–3, respectively) and only one (financial services) is located in bin 5. By contrast, durables are usually found in the most persistent ones. The number of durable sectors in bins 1–5 is 0, 1, 11, 10 and 1, respectively. On the other hand, sectors in the ND, E and F categories tend to be spread over the intermediate bins (2–4). While F and E are quite homogeneously spread over bins 2–4, ND are slightly more concentrated towards bins 3 and 4. In view of the previous results, it is not surprising to see that nontradables are, in general, less persistent than tradables. Of the 29 sectors in the NT category, only 1 is located in bin 4 and none in bin 5. The opposite behavior is found for traded goods, which clearly dominate in the most persistent bins.19 The heterogeneous composition of the bins shows that there is no clear-cut relationship between traditional categories and persistence. This result underscores the fact that these classifications may not be the optimal way to organize our analysis of RER persistence. The traded versus nontraded distinction seems to be particularly problematic for this purpose. Although it is clear that this result may derive, in part, from the fact that CPI-based RERs for traded goods contain a substantial amount of nontraded inputs, which blurs the differences between traded and nontraded goods in our data, it also suggests that other forces than the lack of arbitrage may be driving the persistence of RERs.
4.5.2. Sectoral contribution to persistence To explore the above-mentioned trends further, the contribution of each sector and group of sectors to aggregate persistence has been quantified. Using Eq. (9), it is possible to evaluate the percentage contribution of group j to the aggregate IR at horizon h, denoted as PC c,j ðhÞ, as PNj PC c,j ðhÞ ¼
i¼1
oji IRqi ðt,hÞ
IRQ ðt,hÞ
,
where oji is the weight associated with sector i in group j, and Nj is the number of sectors in group j, with
ð25Þ PJ
j¼1
Nj ¼ N.
Thus, the percentage contribution of group j to the aggregate cumulative response, PC-CIRc,j ðhÞ, is defined as P PC-CIRc,j ðhÞ ¼ hr ¼ 1 PC c,j ðrÞ. Similarly, the relative contribution of group j to the aggregate HL of country c, denoted as PN PC-HLc,j , has been computed as PC-HLc,j ¼ i ¼j 1 oji IRqi ðt,h ¼ HLÞ=IRQ ðt,h ¼ HLÞ. Table 2 presents the estimated values of the PC-HL and the PC-CIR(h) corresponding to the two traditional classifications considered above. The first column presents the average across countries of the weights that Eurostat assigns to each of these categories in order to build the price index. For example, the average Eurostat weight (across countries) of all the products labeled as food is 23%. This column is included so that it is possible to evaluate whether the percentage contribution to total persistence is larger or smaller than the percentage weight in the aggregate RER. Columns 2–4 displays the average percentage contribution of the group of sectors to the aggregate CIR(h), PC-CIRc,j ðhÞÞ, for three different values of h¼{12, 36, 60}. The last column presents the contribution to the HL, PC-HLc,j , for each of the groups. In the short run (one year), the impact of shocks in all groups is very similar, as shown by the fact that the contribution to CIR(12) of each group is almost equal to its corresponding initial weight. However, as longer horizons are analyzed, the picture changes substantially. Durable goods become the group with the highest contribution to long-run persistence. They account for 38% of the total cumulative effect of shocks in the long-term (CIR(60)).20 Moreover, their contribution to the cumulative response relative to the initial weight of the group increases substantially as longer horizons are considered. For instance, their contribution to CIR(60) (38%) exceeds its corresponding initial weight (27%) by 41%. Within this group, the electronic products and the clothing and personal effects subcategories are the most persistent components. Their long-run contribution to the CIR exceeds their initial weights by 60% and 50%, respectively. On the other hand, the contribution of the services and energy sectors to aggregate persistence decreases when distant horizons are considered. Their contribution to CIR(60) is only 60% that of their initial weight for energy, and 76% in the case of services. The traded/ nontraded goods categories also display a clear pattern: the percentage contribution of the traded goods category to total persistence is bigger than its initial weight and increases with the horizon considered. For instance, the contribution to medium and long-run persistence, as measured by CIR(36) and CIR(60) exceeds its initial weight by 6% and 14%, respectively. So, the nontraded category seems to be less persistent than the traded one, as shown by the fact that its contribution to CIR(60) is only 76% its initial weight. Nevertheless, the discrepancies between the traded and nontraded groups appear to be considerably smaller than those obtained with the first classification described above, suggesting that these two categories might not be that different, as has been pointed out by other authors (Crucini and Shintani, 2008; Chari et al., 2002; Engel, 1999). 19
Graphs on the composition of the bins are reported in the Appendix. Estimates of the CIR at distant horizons need to be taken with caution since it is generally difficult to estimate IRFs at long lags and it is even more so in our case since HICP indices only start in 1996. 20
300
L. Mayoral, M. Dolores Gadea / Journal of Monetary Economics 58 (2011) 290–304
Table 2 Aggregate persistence by groups of sectors
ðnÞ
.
h
Weights
CIR(h)
HL
12
36
60
1. ENERGY 2. NONDURABLES 3. FOOD Food Alcohol and tobacco 4. DURABLES Clothing and personal effects Durables for the dwelling Motor vehicles Electronic products Recreational and cultural 5. SERVICES Services relating to the dwelling Transport Financial services Recreational and cultural services Other services TOTAL
10 6 23 18 5 27 10 6 7 2 4 34 10 5 1 15 2 100
9 6 26 20 6 25 10 5 7 2 1 34 9 4 2 16 2 100
8 7 24 19 5 31 13 6 8 2 2 29 9 4 2 12 2 100
6 8 23 18 5 38 16 8 9 3 2 26 7 3 3 11 2 100
6 8 23 17 6 41 19 8 9 3 2 23 7 3 3 8 2 100
TRADED NONTRADED TOTAL
62 38 100
61 39 100
66 34 100
71 29 100
74 26 100
Note: This table presents the contribution (in %) of each group of sectors to aggregate persistence, as measured by the cumulative impulse response (CIR) and the half life (HL).
5. Accounting for RER persistence The goal of this section is to investigate whether there is a plausible theoretical explanation for the cross-sectional persistence patterns identified in the previous section. Our analysis primarily focuses on analyzing the behavior of the upper quantiles of the distribution since, as shown in the previous section, they shape, to a large extent, the persistence observed at the aggregate level. Standard regression methods only provide a single summary measure of the conditional distribution of the dependent variable (the conditional mean), given the predictors. However, the corresponding estimates are not necessarily indicative of the response of the dependent variable to the regressors in other parts of the conditional distribution. Since we are particularly interested in explaining the behavior of the most persistent sectors, the use of quantile regression techniques will provide us with a more complete picture of the covariate effects at the right tail of the distribution of RER persistence. Explanations of the slow convergence to PPP have traditionally been related to one (or several) of the following theories: barriers to trade, such as tariffs or transportation costs, that can be high enough to prevent some goods and services from being traded and, therefore, arbitraged (Swan, 1960; Salter, 1959); imperfect competition practices, such as pricing-to-market (PTM), combined with price stickiness that are able to create a wedge between the prices of the same good sold in different markets, violating the Law of One Price (LOP) (Crucini et al., 2010b; Carvalho and Nechio, forthcoming; Chari et al., 2002); and different consumption preferences across countries that mean that inflation measurements are computed on different consumption baskets, so there is no reason for exchange rate changes to offset official measures of inflation differences (Engel, 1993). By focusing on harmonized sectoral price data, it is reasonable to discard different consumption preferences as a source of deviations from PPP since disaggregate prices for a homogeneous basket of goods are considered. Thus, in this section, only the first two potential explanations are explored. In what follows, the set of independent and dependent variables used to test the theories above, the econometric techniques employed in our empirical exercise and the results obtained are discussed. 5.1. Independent and dependent variables This section presents the theoretical connections between the variables introduced in Section 3 and the persistence of RERs. 5.1.1. Market structure and price stickiness Intra-industry trade (IIT): Faruqee (1995) has shown that sectors with a larger degree of intra-industry trade exhibit a greater degree of PTM which, in turn, leads to more persistent RERs. The intuition is clear: in the presence of intra-industry
L. Mayoral, M. Dolores Gadea / Journal of Monetary Economics 58 (2011) 290–304
301
trade, domestic and foreign firms supply product varieties that are differentiated but still mutually substitutable. Thus, exporting firms will have some pricing power for their differentiated products and, due to the existence of substitutability between domestic and foreign product varieties, will tend to stabilize their prices in local currency terms, which will increase price rigidities. Since domestic and foreign products are more substitutable in intra-industry than in interindustry trade, ceteris paribus, a greater degree of intra-industry trade leads to more persistent exchange rates. The existence of PTM at the intermediate goods level can also have an impact on the persistence of the relative price of the final goods. As firms use other firms’ output as inputs, their prices tend to move more closely together. Thus, the stickiness of the intermediate goods can endogenously increase the stickiness of final goods prices and spill over from one firm to another (Kehoe and Midrigan, 2007). The index Input-IIT c,i tries to capture this effect. A positive relation between this variable and RER persistence is expected. Price-cost margin (PCM): Imperfect competition will typically involve market segmentation and price discrimination across the destination markets (Goldberg and Knetter, 1997). A classical measure of imperfect competition is the price-cost margin variable. The higher the value of the PCM, the lower the competition in that sector. Thus, a large value of this variable will be associated with a high pricing power that could lead to PTM and to more persistent RERs (Faruqee, 1995). The degree of competition at the intermediate goods level is measured by Input-PCM c,i and, for similar reasons as above, a larger value of this variable will be associated with stickier final goods prices and, thus, with more persistent RERs. Price stickiness: A classic explanation for the persistence of RERs is that they are the result of money shocks interacting with sticky prices (Dornbusch, 1976). Kehoe and Midrigan (2007) and Carvalho and Nechio (forthcoming) present models where the persistence of sectoral real exchange rates depends explicitly on the frequency of price adjustments in the sector. In these models, the lower the frequency of price adjustment, the higher the persistence of RERs. 5.1.2. Tradability of goods Openness: Conventional wisdom suggests that the more traded goods are, the more important the forces of arbitrage are and, therefore, the degree of openness should have a negative impact on RER persistence. Bergin and Feenstra (2001) and Faruqee (1995) emphasize that, under PTM and nominal rigidities, an increase in openness fosters price adjustment when changes in the exchange rate take place, offsetting the impact of exchange rate movements and, thus, reducing RER persistence.21 As before, the degree of openness of the intermediate inputs has also been calculated (Input-OPci Þ. For similar reasons, a negative relation between this index and the persistence of deviations from PPP is expected. 5.1.3. Control variables Inflation: It has been argued that a higher inflation rate can lead to a more rapid price adjustment (Ball and Mankiw, 1994) and, thus, to a lower degree of nominal rigidities. Some studies have shown that PPP tends to hold well for high inflation countries (McNown and Wallace, 1989) and that a higher level of inflation is associated with a lower level of real exchange rate persistence (Cheung and Lai, 2000). Thus, a negative relation between inflation and persistence is expected. Following previous studies, other control variables, such as government spending and the volatility of the exchange rate (see Cheung et al., 2001) were also considered. However, these variables were not significant and did not seem to have any important impact on the coefficients of the remaining variables so, for the sake of brevity, they were not included in the benchmark specifications. 5.1.4. Dependent variables Our main dependent variable is the sectoral CIR. To capture the explanatory power of the independent variables at different moments of the lifetime of the shocks, several values of h have been considered, namely, h¼{12,36,60}, in order to measure the short (h¼12), medium h¼36 and long-run (h ¼{60}) effect of shocks. For completeness, sectoral HLs have also been analyzed. 5.2. Econometric methods In order to examine the empirical relations between RER persistence and the various theories outlined above, both a standard and a quantile panel regression analysis have been carried out. The following model for the conditional quantile t associated with the response of the corresponding persistence measure in sector i of country c has been considered (Koenker, 2004): Qyc,i ðtjxc,i Þ ¼ ai þx0c,i bðtÞ,
i ¼ 1, . . . ,N, c ¼ 1, . . . ,C,
ð26Þ
where (yc,i ,xc,i Þ denote the values of the dependent and independent variables, respectively. See the Appendix for further details on the estimation strategy.22 With respect to the standard panel regression analysis, the following model has been 21 Other approaches to measure the degree of openness of the final and the intermediate goods, such as transportation costs, proxied by the distance between national capitals, have also been tried. Alternatively, trade barriers have also been measured as in Anderson and van Wincoop (2003) and Novy (2008). None of these variables turned out to be significant or had any significant impact on the coefficients of the other variables, so they were dropped from the analysis. 22 Estimates have been obtained by using an R code provided by the author.
302
L. Mayoral, M. Dolores Gadea / Journal of Monetary Economics 58 (2011) 290–304
Table 3 Quantile regression results.
t
Cumulative impulse response (h) 12 M2A
Input-IIT 0.5 0.7 0.9 Panel
HL 36
M2B
M2A
60 M2B
M2A
M2B
M2A
M2B
1.40a 1.33a 1.53a 1.66a
1.80a 1.62a 1.94a 2.19a
8.83a 9.90a 9.06a 9.90a
7.79a 11.86a 14.67a 10.71a
15.41a 24.35a 27.13a 18.96a
14.16a 21.84a 29.16a 25.39a
22.41a 31.88a 55.60a 35.53a
21.66a 32.50a 46.17b 32.04a
Input-PCM 0.5 0.7 0.9 Panel
4.34 5.13a 10.02a 4.53a
3.22 4.30 7.52a 3.69v
19.83b 23.08a 34.12a 21.82a
8.94 14.38 17.32 12.14
28.59 60.86a 61.24a 49.02a
8.01 35.88 32.43b 76.90a
52.08a 107.13a 308.75a 105.67a
51.02b 76.19a 345.54a 72.65a
VOL-STICK 0.5 0.7 0.9 Panel
0.38a 0.34a 0.26a 0.44a
1.07 0.85 1.32 1.27
1.12a 1.14a 0.98a 1.27a
0.46 1.78 0.13 2.13
1.24v 1.70a 2.08a 1.94a
1.02a 1.39a 0.48 2.72a
6.46 6.17 10.55 20.04
0.07 0.09 0.03 0.05
0.01 0.02 0.05 0.04
0.94a 0.94a 0.80a 0.99a
INFL 0.5 0.7 0.9 Panel
0.88a 0.84a 0.67a 0.77a
2.25a 1.96a 1.52a 2.35a
3.37 1.89 4.94 0.02 2.31a 2.08a 1.71a 1.64a
3.95a 3.32a 2.89a 3.33a
3.82a 3.30a 1.64a 2.16a
Note: This table presents the results of the quantile and standard panel estimation. M2A and M2B uses VOL and STICK as proxies for price stickiness. a Denote significance at the 5% level. b Denote significance at the 10% level.
considered: yc,i ¼ yi þx0c,i b þuc,i ,
ð27Þ
where the parameters have been estimated using the fixed-effects estimator, as the Hausmann test rejected the hypothesis of consistency of the random-effects estimator. 5.3. Results Four models have been estimated: M1 (A and B) includes all the regressors mentioned in Section 5.1 while M2 (A and B) only contains the variables that turned out to be significant in the regressions performed in M1. Models 1A and 2A use VOL as a proxy for price stickiness while Models 1B and 2B use STICK.23 Conditional quantile regressions for all the deciles have been computed although, for the sake of brevity, full regression results are only presented for the quantiles tk ¼ f0:5,0:7,0:9g. Similar models have also been estimated using standard panel techniques. Table 3 presents the estimated coefficients and, to save space, only figures corresponding to models M2A and M2B are reported.24 The conclusions obtained in the larger models were identical and can be summarized as follows. The most important group of variables to account for RER persistence appear to be those related to the market structure of the inputs. In particular, the IIT variable associated with the intermediate goods (Input-IIT) has the expected positive sign and is always significant at the 5% significance level in all the models considered. Input-PCM also shows a positive relation with sectoral RER persistence that is generally significant, especially in the medium and long run and when higher quantiles are considered. It is remarkable that the coefficients associated with these variables tend to increase considerably the farther the horizon of the CIR and the higher the quantile considered. Interestingly, after controlling for the market structure of the intermediate inputs, the market structure of the final goods turns out not to be important in explaining RER persistence.25 Both IIT and PCM have the expected positive signs but they are not significant. This result underscores the importance of price complementarities in explaining RER persistence. PTM at the intermediate goods level makes prices across firms move in a similar way, so that price stickiness spills over 23 The variable STICK2 was also employed (see its definition in Section 3). The results were, in general, weaker. This is not surprising since, for most countries, only around 30 sectors were employed in the regressions. 24 Estimates for Models 1A and 1B are reported in the Appendix. 25 The correlation between the two sets of measures is high: 0.30 for IIT and input-IIT and 0.45 for PCM and its corresponding input. If the input variables are not included in the regression, those of the final goods are generally significant.
L. Mayoral, M. Dolores Gadea / Journal of Monetary Economics 58 (2011) 290–304
303
from one firm to another (Kehoe and Midrigan, 2007). Our results suggest that the impact of this spillover is key in determining persistence at the aggregate level and, once it has been accounted for, the market structure of the final goods is no longer relevant. The degree of price stickiness, as measured by STICK, does not have a significant impact on RER persistence. However, this result should be taken with caution given the limitations of this variable described above. Nevertheless, and in line with the theoretical predictions, a higher degree of inflation volatility is associated with a lower degree of persistence, as captured by the negative sign of the variable VOL, which is highly significant in all models. Interestingly, the coefficients of the quantile regression parameters are considerably larger in absolute value as farther horizons and higher quantiles are considered. Finally, the estimated coefficients for the remaining variables are fairly similar independently of the proxy of price stickiness employed. With respect to the variables that capture the degree of tradability, openness appears, in general, with the expected negative sign for the quantiles to the right of the median although its sign is positive to the left of this value. The variable that captures the degree of tradability of the inputs, Input-OP, usually presents a positive sign, especially in the upper quantiles, suggesting a positive relation between the degree of openness of the inputs and RER persistence. Nevertheless, neither OP nor Input-OP are significant in any of the models considered. The lack of significance of these variables confirms recent findings that suggest that traded and nontraded goods have similar characteristics (Engel, 1999; Chari et al., 2002) and, therefore, this distinction is not key in accounting for persistence. Another aspect that may have a role in explaining the lack of significance of these variables is that CPI data, even at the very disaggregate level considered in this paper, does not allow us to completely disentangle traded and nontraded goods because the price of traded goods involves nontraded components as well, such as marketing and distribution services. In addition, the European Union is an area where trade barriers are very low since tariffs have been eliminated and trade costs are relatively small and, therefore, one could expect that the traded/nontraded categories are less important than in other geographical areas. The effect of inflation is puzzling. This variable has a positive and very significant effect on RER persistence, indicating that a higher level of inflation is related to higher persistence levels, the opposite of what the theory predicts. Further research is needed to identify the forces that drive this positive relationship. The results of the standard panel regression are very much in line with the discussion above. However, notice that the coefficients of the panel and the quantile regression analysis are, in many instances, very different, especially when higher quantiles are considered. For some of the key variables (Input-IIT, INFL and VOL) these coefficients are also statistically different. This result underscores the importance of considering quantile regression analysis if one is interested in exploring the behavior of the upper tail of the distribution of persistence. Summarizing, our results are in agreement with theoretical models such as Chari et al. (2002) and Carvalho and Nechio (forthcoming). PTM at the intermediate goods level and price stickiness seem to be the key determinants of RER persistence. The classical dichotomy that classifies goods into traded and nontraded appears not to account for European RER persistence.
6. Conclusions Using recent econometric results that show how the IR of the aggregate RER can be decomposed into those corresponding to its sectoral components, it has been argued that not all the sectors have the same importance in determining the persistence observed in the aggregate RER. Traditional theories of RER persistence (nontradability and nominal rigidities combined with pricing-to-market) have been investigated by means of quantile panel regression techniques. Our results suggest that persistence in the upper quantiles of sectoral persistence is explained by factors related to the stickiness of final goods prices and the market structure of their inputs. Since the behavior in the upper quantiles determine, to a large extent, the persistence observed at the aggregate level, it is concluded that pricing-tomarket and price stickiness are two key factors in explaining the slow reversion to PPP of European RERs. Further research is needed to clarify whether these conclusions can be extended to other economic areas.
Acknowledgement We are very grateful to the editor and an anonymous referee for their very useful comments. We are also indebted to Luis J. Alvarez, Herve´ Le Bihan, Emmanuel Dhyne, Esther Gordo, Virgiliu Midrigan and Fabio Rumler for sharing their data with us. Laura Mayoral is a member of the Barcelona GSE Research Network funded by the Government of Catalonia. Financial support from the Spanish Government CICYT projects SEJ2006-00369 and ECO2008-03040 is gratefully acknowledged. The usual disclaimer applies.
Appendix A. Supplementary data Supplementary data associated with this article can be found in the online version at doi:10.1016/j.jmoneco.2011.06.003.
304
L. Mayoral, M. Dolores Gadea / Journal of Monetary Economics 58 (2011) 290–304
References Anderson, J., van Wincoop, E., 2003. Gravity with gravitas: a solution to the border puzzle. American Economic Review 93, 170–192. Ball, L., Mankiw, N.G., 1994. Asymmetric price adjustment and economic fluctuations. Economic Journal 104, 247–261. Bergin, P.R., Feenstra, R.C., 2001. Pricing-to-market, staggered contracts, and real exchange rate persistence. Journal of International Economics 54, 333–359. Carvalho, C., Nechio, F. Aggregation and the PPP puzzle in a sticky-price model. American Economic Review, forthcoming. Chari, V.V., Kehoe, P.J., McGrattan, E.R., 2002. Can sticky price models generate volatile and persistent real exchange rates? Review of Economic Studies 69, 533–563. Chen, S.-S., Engel, Ch., 2005. Does ‘aggregation bias’ explain the PPP puzzle. Pacific Economic Review 10, 49–72. Cheung, Y.-W., Lai, K.S., 2000. On cross-country differences in the persistence of real exchange rates. Journal of International Economics 50, 375–397. Cheung, Y.-W., Chinn, M., Fujii, E., 2001. Market structure and the persistence of sectoral real exchange rates. International Journal of Finance and Economics 6, 95–114. Crucini, M.J., Telmer, Ch.I., Zachariadis, M., 2005. Understanding European real exchange rates. American Economic Review 95, 724–738. Crucini, M.J., Shintani, M., 2008. Persistence in law of one price deviations: evidence from micro-data. Journal of Monetary Economics 55, 629–644. Crucini, M.J., Tsuruga, T., Shintani, M., 2010a. Accounting for persistence and volatility of good-level real exchange rates: the role of sticky information. Journal of International Economics 81, 48–60. Crucini, M.J., Tsuruga, T., Shintani, M., 2010b. The law of one price without the border. The Economic Journal 120, 462–480. ¨ Dhyne, E., A´lvarez, L.J., Le Bihan, H., Veronese, G., Dias, D., Hoffmann, J., Jonker, N., Lunnemann, P., Rumler, F., Vilmunen, J., 2006. Price setting in the euro area. Some stylized facts from individual consumer price data. Journal of Economic Perspectives 20, 171–192. Dornbusch, R., 1976. Expectations and exchange rate dynamics. Journal of Political Economy 84, 1161–1176. Engel, Ch., 1993. Real exchange rates and relative prices: an empirical investigation. Journal of Monetary Economics 32, 35–50. Engel, Ch., 1999. Accounting for U.S. real exchange rate changes. Journal of Political Economy 107, 507–538. Faruqee, H., 1995. Pricing to market and the real exchange rate. IMF Working Papers 95/12. Gadea, M.D., Mayoral, L., 2009. Aggregation is not the solution: the PPP puzzle strikes back. Journal of Applied Econometrics 24, 875–894. Goldberg, P.K., Knetter, M., 1997. Goods prices and exchange rates: what have we learned. Journal of Economic Literature 35, 1243–1272. Grubel, H.G., Lloyd, P., 1975. Intra-Industry Trade: The Theory and Measurement of International Trade in Differentiated Products. MacMillan, London. Im, K.S., Pesaran, M.H., Shin, Y., 2003. Testing for unit roots in heterogeneous panels. Journal of Econometrics 115, 53–74. Imbs, J., Muntaz, A., Ravn, M.O., Rey, H., 2005a. PPP strikes back: aggregation and the real exchange rate. Quarterly Journal of Economics 120, 1–43. Imbs, J., Muntaz, A., Ravn, M.O., Rey, H., 2005b. Aggregation bias does explain the PPP puzzle. Mimeo. Kehoe, P.J., Midrigan, V., 2007. Sticky prices and sectoral real exchange rates. Federal Reserve Bank of Minneapolis, Research Department Working Paper 656. Kilian, L., Zha, T., 2002. Quantifying the uncertainty about the half-life of deviations from PPP. Journal of Applied Econometrics 17, 107–125. Koenker, R., 2004. Quantile regression for longitudinal data. Journal of Multivariate Analysis 91, 74–89. Kuersteiner, G.M., 2005. Automatic inference for infinite order vector autoregression. Econometric Theory 21, 85–115. Levin, A., Lin, C.F., Chu, C., 2002. Unit root tests in panel data: asymptotic and finite-sample properties. Journal of Econometrics 108, 1–24. Lewbel, A., 1994. Aggregation and simple dynamics. American Economic Review 84, 905–918. Mayoral, L., 2009. Heterogeneous dynamics, aggregation and the persistence of economics shocks. UFAE and IAE Working Papers 08. McNown, R., Wallace, M.S., 1989. National price levels, purchasing power parity, and cointegration: a tests of four high inflation economies. Journal of International Money and Finance 8, 533–545. Ng, S., Perron, P., 1995. Unit root tests in ARMA models with data dependent methods for selection of the truncation lag. Journal of the American Statistical Association 90. Novy, D., 2008. Gravity Redux: Measuring International Trade Costs with Panel Data. University of Warwick. Rogoff, K., 1996. The purchasing power parity puzzle. Journal of Economic Literature 34, 647–668. Salter, W., 1959. Internal and external balance: the role of price and expenditure effects. Economic Record 35, 226–238. Swan, T., 1960. Economic control in a dependent economy. Economic Record 36, 51–66. Wooldridge, J., 2001. Econometric Analysis of Cross Section and Panel Data. The MIT Press.
