More on money as a medium of exchange

Summary We extend the analysis of Kiyotaki and Wright, who study economies where the commodities that serve as media of exchange (or, commodity money) are determined endogenously. Kiyotaki and Wright consider only steady-state, pure-strategy equilibria; here we allow dynamic and mixed-strategy equilibria. We demonstrate that symmetric, steady-state equilibria in mixed-strategies always exist, while sometimes no such equilibria exist in pure-strategies. We prove that the number of symmetric steady-state equilibria is generically finite. We also show, however, that for some parameter values there exists a continuum of dynamic equilibria. Further, some equilibria display cycles.We thank the National Science Foundation and the University of Pennsylvania Research Foundation for financial support, as well as seminar participants at Stanford University, the London School of Economics, the Econometric Society World Congress in Barcelona, and the Conference on Monetary Theory and Financial Institutions at the Federal Reserve Bank of Minneapolis for their comments or suggestions. Alberto Trejos provided research assistance. The views expressed here are those of the authors and not necessarily those of the Federal Reserve Bank of Minneapolis or the Federal Reserve System.     

Implementing Arrow-Debreu equilibria by trading infinitely-lived securities

Summary. We show that Arrow-Debreu equilibria with countably additive prices in infinite-time economy under uncertainty can be implemented by trading infinitely-lived securities in complete sequential markets under two different portfolio feasibility constraints: wealth constraint, and essentially bounded portfolios. Sequential equilibria with no price bubbles implement Arrow-Debreu equilibria, while those with price bubbles implement Arrow-Debreu equilibria with transfers. Transfers are equal to price bubbles on initial portfolio holdings. Price bubbles arise in sequential equilibrium under the wealth constraint if some securities are in zero supply or negative prices are permitted, but cannot arise with essentially bounded portfolios.Received: 19 November 2003, Revised: 24 February 2004, JEL Classification Numbers: D50, G12, E44.Correspondence to: Jan WernerWe acknowledge helpful discussions with Roko Aliprantis, Subir Chattopaydhyay, Steve LeRoy, Manuel Santos, and seminar participants at Brown University, University of Pennsylvania, NBER Workshop in General Equilibrium Theory, SITE 2000, the 2000 World Congress of the Econometric Society, and Federal Reserve Bank of Kansas City. The views expressed herein are those of the authors and do not necessarily reflect the views of Federal Reserve Bank of Kansas City or the Federal Reserve System.     

Why is there money? Endogenous derivation of `money' as the most liquid asset: a class of examples

Summary. The monetary character of trade, use of a common medium of exchange, is shown to be an outcome of an economic general equilibrium. Monetary structure can be derived from price theory in a modified Arrow-Debreu model. Two constructs are added: transaction costs and market segmentation in trading posts (with a separate budget constraint at each transaction). Commodity money arises endogenously as the most liquid (lowest transaction cost) asset. Government-issued fiat money has a positive equilibrium value from its acceptability for tax payments. Scale economies in transaction cost account for uniqueness of the (fiat or commodity) money in equilibrium. Received: February 15, 2002; revised version: August 12, 2002 RID="*" ID="*" This paper has benefited from seminars and colleagues' helpful remarks at the University of California - Santa Barbara, University of California - San Diego, NSF-NBER Conference on General Equilibrium Theory at Purdue University, Society for the Advancement of Behavioral Economics at San Diego State University, Econometric Society at the University of Wisconsin - Madison, SITE at Stanford University-2001, Federal Reserve Bank of Kansas City, Federal Reserve Bank of Minneapolis, Midwest Economic Theory Conference at the University of Illinois - Urbana Champaign, University of Iowa, Southern California Economic Theory Conference at UC - Santa Barbara, Midwest Macroeconomics Conference at University of Iowa, University of California - Berkeley, European Workshop on General Equilibrium Theory at University of Paris I, Society for Economic Dynamics at San Jose Costa Rica, World Congress of the Econometric Society at University of Washington, Cowles Foundation at Yale University. It is a pleasure to acknowledge comments of Henning Bohn, Harold Cole, James Hamilton, Mukul Majumdar, Harry Markowitz, Chris Phelan, Meenakshi Rajeev, Wendy Shaffer, Bruce Smith, and Max Stinchcombe.     

A monetary mechanism for sharing capital: Diamond and Dybvig meet Kiyotaki and Wright

Summary. A model is presented in which banks update public records, accept deposits of fiat money and intermediate capital. I show that inside money is more liquid than outside money, increasing the turnover rates of idle capital. The model offers a simple explanation for the dual role of financial institutions: Banks are monitored and can issue nominal assets upon request, which helps them to transfer capital in sufficiently high rates and to also become intermediaries. The model shares some features with those of Diamond and Dybvig [5], and Kiyotaki and Wright [7].Received: 18 February 2003, Revised: 16 February 2004, JEL Classification Numbers: E51, G21, G24.Ricardo de O. Cavalcanti: I thank two anonymous referees, Susumu Imai, B. Ravikumar and Neil Wallace, as well as participants at the Economic Theory symposium Recents Developments in Money and Finance, and seminar participants at the Richmond Fed, Queens University, and Sabanci University for comments on an early draft. The hospitality and financial support of the Cleveland Fed Central Bank Institute and CNPq are greatfully appreciated. The authors opinions are not necessarily those of the Federal Reserve Bank of Cleveland or the Federal Reserve System.     

Distributional aspects of the divisibility of money: an example

Summary. I highlight the importance of the distributional aspects of moneys divisibility by comparing a search-theoretic model with random transfers of indivisible money balances, to one with deterministic transfers of partially divisible balances. Randomization allows price flexibility, as if money were fully divisible. Partial divisibility does not, but allows money redistributions. An example of the relevance of such extensive margin aspects of divisibility is provided.JEL Classification Numbers: D30, D83, E40.I thank Dean Corbae and seminars participants at the Federal Reserve Bank of Richmond, University of Texas at Austin, Purdue University, the Midwest Macroeconomics Meetings, the Central Bank Institute of the Federal Reserve Bank of Cleveland, and the meetings of the Society for the Advancement of Economic Theory, where this work has been presented during the years 2002 and 2003.     

Liquidity of secondary capital markets: Allocative efficiency and the maturity composition of the capital stock

Summary We investigate the function of liquid financial markets for the allocation of productive capital. We consider an economy where agents endogenously choose among capital production technologies with differing gestation periods. Long-gestation capital investments must be rolled-over in secondary capital markets. The use of such investment technologies therefore requires the support of liquid financial markets. We investigate how changes in the liquidity of these markets (i.e., in the costs of transacting) affect (a) the choice of capital production technology, (b) per capita income and the per capita capital stock, (c) the level of financial market activity, (d) the real return on savings and (e) welfare in a steady state equilibrium. Improvements in financial market liquidity raise rates of return on savings, and favor the increased use of long gestation capital investments. However, such improvements may or may not lead to higher levels of real activity or steady state welfare. We describe conditions under which various outcomes occur.We have benefited from the comments of seminar participants at the Board of Governors of the Federal Reserve System, the Federal Reserve Bank of Minneapolis, the International Monetary Fund, Berkeley, Boston College, Boston University, Brown, Chicago, Illinois, Miami, UC San Diego, Simon Fraser, University of British Columbia, University of Washington, Yale, the Canadian Macro Study Group Meetings, the Murrary S. Johnson Conference (University of Texas/Federal Reserve Bank of Dallas), and the Far West Rotating Economic Theory Conference. We would also like to thank John Bryant, Andreas Hornstein, Dan Peled, Bill Schworm, Karl Shell, Bart Taub and an anonymous referee for their comments on an earlier draft of the paper.     

Dynamic equilibria with unemployment due to undernourishment

Summary We provide characterization and stability results for the stationary equilibria of a competitive infinite-horizon model that incorporates the nutritional requirements of physical labor. We find that for many aggregate land stocks, there is a large continuum of stationary equilibrium unemployment rates. Since unemployment can be seen to stem from inequality in the initial distribution of land ownership, we suggest that certain land reforms can reduce unemployment.Many of our results were developed while Streufert visited the Indian Statistical Institute. Ray is grateful for financial support from the Warshow Endowment of Cornell University, and Streufert thanks the Institute for Research on Poverty and the Graduate School, both at the University of Wisconsin-Madison. We are also thankful for the useful comments of an editor, a referee, and seminar participants at Wisconsin, Yale, the Federal Reserve Bank of Minneapolis, and the Midwest Mathematical Economics Conference.     

A model of the federal funds market

Summary This paper develops a stochastic general equilibrium model of the federal funds market that incorporates non-Fisherian effects on interest rates stemming from both supply and demand shocks to reserves. Such a model may reconcile the widespread belief in a liquidity effect of money supply shocks with the difficulty many researchers have had in finding empirical support for such an effect. The model also cautions against interpreting the observed negative correlation between the federal funds rate and innovations to nonborrowed reserves as empirical confirmation of the ability of the Federal Reserve to lower short-term real interest rates.This paper should not be interpreted as reflecting the views of the Board of Governors of the Federal Reserve System or its staff. We gratefully acknowledge lengthy discussions and correspondence with V. V. Chari, Marty Eichenbaum, and especially Larry Christiano, that helped to clarify many issues. We were told many institutional details by Jim Clouse and Josh Feinman, and we received many helpful comments from David Altig, Michael Dotsey, and participants at the conference on Recent Research on the Liquidity Effect of Monetary Policy, 1993, Federal Research Bank of Cleveland, the conference on Recent Macroeconomic Research: Lessons for Policymaking, 1993, Federal Reserve Bank of Atlanta and the conference on Operating Procedures and the Conduct of Monetary Policy, 1992, Federal Reserve Bank of St. Louis.     

Decentralized credit and monetary exchange without public record keeping

Summary. We relax a standard assumption on the matching technology in a search model of money. In particular, agents may remain in a long-term partnership as long as it is in their self-interest. With this simple modification, it is possible to support self-enforcing, intertemporal trade which resembles credit without a public record keeping device. We examine conditions for co-existence of currency and credit and the welfare gains/losses associated with the introduction of money.Received: 20 April 2003, Revised: 10 July 2003JEL Classification Numbers: E0.An earlier version of this paper was entitled Money and Search with Enduring Relationships. We wish to thank Narayana Kocherlakota, Rachel Kranton, Jeff Lacker, Andrei Shevchenko, Shouyong Shi, Ted Temzelides, Chris Waller, and especially David Andofolatto, Gabriele Camera, Drew Saunders, and Randy Wright for helpful comments on that earlier draft, as well as seminar participants at the University of Pennsylvania, Purdue University, American Economic Association Meetings, Summer Econometric Society Meetings, and NBER Summer Workshop. Corbae wishes to thank the Research Department at the Federal Reserve Bank of St. Louis for research support.Correspondence to: D. Corbae     

Liquidity and Liquidation

The manager of a firm that is selling an illiquid asset has discretion as to the sale price: if he chooses a high (low) selling price, early sale is unlikely (likely). If the manager has the option to default on the debt that is collateralized by the illiquid asset, the optimal selling price depends on whether the manager acts in the interests of owners or creditors. We model the former case. In equilibrium the owner will always offer the illiquid asset for sale at a strictly higher price than he paid, and will default if he fails to sell. As a result, upon successful sales the illiquid asset changes hands at successively higher prices. We also consider a generalization of the model which permits sellers to finance sales using either debt or preferred stock, or both. This allows derivation of an optimal capital structure. We are indebted to seminar participants at the University of California, Los Angeles; University of California, Santa Barbara; Utah State University; University of Miami; Federal Reserve Bank of Atlanta; Federal Reserve Bank of San Francisco and Federal Reserve Bank of Kansas City. We have received helpful comments from Tom Cooley.     

On characterizing equilibria of economies with externalities and taxes as solutions to optimization problems

Summary We characterize equilibria of general equilibrium models with externalities and taxes as solutions to optimization problems. This characterization is similar to Negishi's characterization of equilibria of economies without externalities or taxes as solutions to social planning problems. It is often useful for computing equilibria or deriving their properties. Frequently, however, finding the optimization problem that a particular equilibrium solves is difficult. This is especially true in economies with multiple equilibria. In a dynamic economy with externalities or taxes there may be a robust continuum of equilibria even if there is a representative consumer. This indeterminacy of equilibria is closely related to that in overlapping generations economies.An earlier version of this paper, entitled Externalities and Taxes in General Equilibrium, was presented at the North American meetings of the Econometric Society, June 1988, at the University of Minnesota. We are grateful to David Backus, Kenneth Judd, Patrick Kehoe, and Rodolfo Manuelli for helpful conversations. National Science Foundation grants SES 86-18325 and SES 87-08616 provided financial support.The views expressed herein are those of the authors and not necessarily those of the Federal Reserve Bank of Minneapolis or the Federal Reserve System.     

Inflation,growth and exchange rate regimes in small open economies

Summary. This paper compares the merits of alternative exchange rate regimes in small open economies where financial intermediaries perform a real allocative function, there are multiple reserve requirements, and credit market frictions may or may not cause credit rationing. Under floating exchange rates, raising domestic inflation can increase production if credit is rationed. However, there exist inflation thresholds: increasing inflation beyond the threshold level will reduce domestic output. Endogenously arising volatility may be observed independently of the exchange rate regime. Private information - with high rates of domestic inflation - increases the scope for indeterminacy and economic fluctuations.Received: 26 March 2002, Revised: 29 October 2002JEL Classification Numbers: E32, E44, F33.P.L. Hernandez-Verme: I would like to thank Leonardo Auernheimer, Valerie Bencivenga, Dean Corbae, Scott Freeman, Todd Keister, Beatrix Paal, and Maxwell Stinchcombe for very helpful comments and suggestions. Very special thanks are due to Bruce D. Smith. The paper also benefited from the discussions in the seminars in CIDE, the Federal Reserve Bank of Atlanta, the Federal Reserve Bank of Kansas City, Indiana University, ITAM, Purdue University, the Second Annual Missouri Economics Conference, Texas A&M, the University of Missouri and the University of Texas at Austin.     

Fiat money in the Kiyotaki-Wright model

Summary We study versions of the Kiyotaki-Wright (1989) model with fiat money and show that: (1) The use of a low storage cost fiat money may be necessary for specialization and trade, (2) there can be valued fiat money steady states which are indeterminate, (3) there are no nontrivial steady-states in which all trades consist of fiat money for goods, (4) fiat money may be valued even if it is not the least costly-to-store object, and lastly, (5) two fiat monies with different storage costs may both be valued.We thank Randall Wright for comments and helpful discussions.The views expressed herein are those of the authors and not necessarily those of the Federal Reserve Bank of Minneapolis or the Federal Reserve System.     

Existence of a competitive equilibrium in a one sector growth model with heterogeneous agents and irreversible investment

Summary. We prove existence of a competitive equilibrium in a version of a Ramsey (one sector) model in which agents are heterogeneous and gross investment is constrained to be non negative. We do so by converting the infinite-dimensional fixed point problem stated in terms of prices and commodities into a finite-dimensional Negishi problem involving individual weights in a social value function. This method allows us to obtain detailed results concerning the properties of competitive equilibria. Because of the simplicity of the techniques utilized our approach is amenable to be adapted by practitioners in analogous problems often studied in macroeconomics. Received: September 13, 2001; revised version: December 9, 2002 RID="*" ID="*" We are grateful to Tapan Mitra for pointing out errors as well as making very valuable suggestions. Thanks are due to Raouf Boucekkine and Jorge Duran for additional helpful discussions. We also thank an anonymous referee for his/her helpful comments. The second author acknowledges the financial support of the Belgian Ministry of Scientific Research (Grant ARC 99/04-235 “Growth and incentive design”) and of the Belgian Federal Goverment (Grant PAI P5/10, “Equilibrium theory and optimization for public policy and industry regulation”). Correspondence to: C. Le Van     

A model to analyse financial fragility

Summary. This paper sets out a tractable model which illuminates problems relating to individual bank behaviour, to possible contagious inter-relationships between banks, and to the appropriate design of prudential requirements and incentives to limit ‘excessive’ risk-taking. Our model is rich enough to include heterogeneous agents, endogenous default, and multiple commodity, and credit and deposit markets. Yet, it is simple enough to be effectively computable and can therefore be used as a practical framework to analyse financial fragility. Financial fragility in our model emerges naturally as an equilibrium phenomenon. Among other results, a non-trivial quantity theory of money is derived, liquidity and default premia co-determine interest rates, and both regulatory and monetary policies have non-neutral effects. The model also indicates how monetary policy may affect financial fragility, thus highlighting the trade-off between financial stability and economic efficiency.Received: 6 November 2003, Revised: 6 October 2004 JEL Classification Numbers: D52, E4, E5, G11, G21.C.A.E. Goodhart, P. Sunirand, D.P. Tsomocos: We are grateful to T.F. Bewley, S. Bhattacharya, F. Hahn, C. Mayer, H.S. Shin and seminar participants at the Bank of Austria, Bank of England, Bank of Norway, Bank for International Settlements, Brown University, the 7th Annual Macroeconomic Conference, Crete, EcoMod-IIOA International Conference, Brussels, the 2nd Oxford Finance Summer Symposium and Nuffield, Oxford, the Hong Kong Institute for Monetary Research, Purdue University, the University of Birmingham, the VI SAET Conference, Rhodes, Yale University, and especially an anonymous referee and H.M. Polemarchakis for helpful comments. The views expressed are those of the authors and do not necessarily reflect those of the Bank of England. Correspondence to: D.P. Tsomocos     

Limited participation,private money,and credit in a spatial model of money

Summary. The purpose of this paper is to explore the implications of private money issue for the effects of monetary policy, for optimal policy, and for the role of fiat money. A locational model is constructed which gives an explicit account of the role for money and credit, and for limited financial market participation. When private money issue is prohibited, there is a liquidity effect as the result of a money injection from the central bank, but this effect goes away when private money is permitted. Private money issue changes dramatically the nature of optimal monetary policy. With private money, fiat currency is no longer used in transactions involving goods, but currency and central bank reserves play an important part in the clearing and settlement of private money returned for redemption.Received: 5 May 2003, Revised: 1 December 2003JEL Classification Numbers: E4, E5.The author thanks seminar participants at the Federal Reserve Bank of Richmond and Duke University, conference participants at the Texas Monetary Conference at U.T. Austin, February 2002, and the Conference on Recent Developments in Money and Finance at Purdue University, May 2003, as well as Gabriele Camera, Ed Nosal, Will Roberds, and two anonymous referees for their helpful comments and suggestions.     

Indivisibilities,lotteries, and sunspot equilibria

Summary We analyze economies with indivisible commodities. There are two reasons for doing so. First, we extend and provide some new insights into sunspot equilibrium theory. Finite competitive economies with perfect markets and convex consumption sets do not allow sunspot equilibria; these same economies with nonconvex consumption sets do, and they have several properties that can never arise in convex environments. Second, we provide a reinterpretation of the employment lotteries used in contract theory and in macroeconomic models with indivisible labor. We show how socially optimal employment lotteries can be decentralized as competitive equilibria without lotteries once sunspots are introduced.We thank Kenneth Arrow, Aditya Goenka, Ed Green, Jeremy Greenwood, Walter Heller, Steve Matthews, Herve Moulin, Roger Meyerson, Jim Peck, Patrick Kehoe, Ramon Marimon, Ed Prescott, Richard Rogerson, Nancy Stokey and Raghu Sundaram for their comments. We also thank participants in seminars at Northwestern, Yale, USC, Cornell, Barcelona, Madrid, Santander, and the Canadian Economics Association annual meetings in Victoria. We are grateful to the National Science Foundation (through grants SES-8606944 and SES-8821225), the Center for Analytic Economics, the Thorne Fund, and the University of Pennsylvania Research Foundation for research support. The views expressed here are those of the authors, and not necessarily those of the Federal Reserve System or the Federal Reserve Bank of Minneapolis.     

Competitive equilibrium when preferences change over time

Summary. We show the existence of a competitive equilibrium in an economy with many consumers whose preferences may change over time. The demand correspondence of an individual consumer is determined by the set of subgame-perfect equilibrium outcomes in his intrapersonal game. For additively separable preferences with concave period utility functions that are unbounded above, this demand correspondence will satisfy the usual boundary conditions. Whenever consumers can recall their own mixed actions, this correspondence is convex-valued. This ensures the existence of a symmetric competitive equilibrium.Received: 29 July 2004, Revised: 17 November 2004, JEL Classification Numbers: D51, D91, C73. Correspondence to: Thomas MariottiWe thank Michele Piccione for useful comments and suggestions. The views expressed herein are those of the authors and not necessarily those of the Federal Reserve Bank of Minneapolis or the Federal Reserve System.     

Education and income of the states of the United States: 1840–2000

This article introduces original annual average years of schooling measures for each state from 1840 to 2000. Our methodology results in state estimates similar to those reported in the United States Census from 2000 back to 1940 and national, turn of the century estimates strikingly close to those presented by Schultz (Schultz, T. (1961). In N. B. Henry (Ed.), Social forces influencing American education. Chicago: University of Chicago Press.) and Fishlow (Fishlow, A. (1966). In H. Rosovsky (Ed.), Industrialization in two systems. John Wiley & Sons). To further determine the validity of our state schooling estimates, we first combine original data on real state per worker output with existing data to provide a more comprehensive series of real state output per worker from 1840 to 2000. We then estimate aggregate Mincerian earnings regressions and discover that the return to a year of schooling for the average individual in a state ranges from 11% to 15%. This range is robust to various time periods, various estimation methods, various assumptions about the endogeneity of schooling and is in line with the body of evidence from the labor literature. All views expressed here are the authors’ and not necessarily those of the Federal Reserve Bank of Atlanta or the Federal Reserve System.     

Optimal contracts in a dynamic costly state verification model

Summary. This paper describes optimal contracts in a dynamic costly state verification model with stochastic monitoring. An agent operates a risky project on behalf of a principal who can observe the projects revenues at a cost. We show that an optimal contract exists such that, at any history, either the principal claims the projects entire revenues or promises to claim nothing in the future. In particular, the agents expected income rises with time. Moreover, except in at most one period, the principal claims all revenues when audit occurs. We provide conditions under which all optimal contracts satisfy these properties.Received: 4 February 2004, Revised: 4 June 2004, JEL Classification Numbers: D8, C7. Correspondence to: Cyril MonnetWe wish to thank Patrick Bolton, Vitor Gaspar, Mark Guzman, Martin Hellwig, Narayana Kocherlakota, Thorsten Koeppl, Albert Marcet, Benny Moldovanu, Ernst-Ludwig von Thadden and seminar participants at the University of Mannheim, the University of Minnesota, the Society for Economics Dynamics Meetings in New York and the Society for the Advancement in Economic Theory in Rhodos for helpful comments and discussions. The views expressed herein are those of the authors and may not reflect the views of the European Central Bank, the Eurosystem, the Federal Reserve Bank of Dallas or the Federal Reserve System.