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Economic Theory
Macroeconomics
Mathematical Economics
Computational Economics

Macroeconomics
General Equilibrium Theory
Mathematical Economics
Computational Economics

May 2003 (Oral) Mathematical Economics (with distinction), Macroeconomics
May 2002 (Written) Macroeconomics (with distinction), Microeconomics

Monetary Equilibrium with Heterogeneous Agents and Incomplete Financial Markets: Theory and Computation

Professor John Geanakoplos
Professor Tony Smith
Professor Truman Bewley

Ph.D., Economics, Yale University, 2006 (Expected)
M.Phil., Economics, Yale University, 2004
M.A., Economics, Yale University, 2002
M.A., Economics, Peking University, 2001
B.A., Economics, Renmin University of China, 1998

Carl A. Anderson Fellowship, Cowles Foundation, 2005–2006
Cowles Foundation Prize, 2003, 2004
Yale University Graduate Fellowship, 2001–2005
China Economic Research Fellowship, 1999, 2000
Renmin University of China Fellowship, 1994–1997

Winner of Raymond Powell Teaching Prize, Yale University, 2004
Teaching Assistant, Graduate Macroeconomics, Yale University, Spring 2004
Teaching Assistant, Introductory Microeconomics, Yale University, Fall 2003
Teaching Assistant, Graduate Econometrics, Peking University, Spring 2000, Fall 2000
Teaching Assistant, Intermediate Macroeconomics, Peking University, Fall 1999
Teaching Assistant, Intermediate Microeconomics, Peking University, Spring 1999

Visitor, Max Planck Institute for Research on Collective Goods (Bonn, Germany), Nov.–Dec. 2004

Midwest Economic Theory Meetings, University of Kansas, October 2005
Asian Workshop on General Equilibrium Theory, University of Tokyo, June 2005
European Workshop on General Equilibrium Theory, University of Zurich, May 2005
CARESS-Cowles Conference on General Equilibrium Theory, Yale University, April 2005
Max Planck Institute for Research on Collective Goods, Bonn, December 2004

Rasmusen, Eric, 1994, Games and Information: An Introduction to Game Theory, Chapter 7–10, Cambridge: Blackwell Publisher; Chinese Edition by Beijing Sanlian and Peking University Press, 2003

Professor John Geanakoplos
Department of Economics
Yale University
PO Box 208281
New Haven, CT 06520-8281
Phone: (203) 432-3397
Fax: (203) 432-6167
Email: john.geanakoplos@yale.edu

Professor Tony Smith
Department of Economics
Yale University
PO Box 208268
New Haven, CT 06520-8268
Phone: (203) 432-3583
Fax: (203) 432-2128
Email: tony.smith@yale.edu

Heterogeneous agents and incomplete financial markets have long been thought to be important for asset pricing, welfare and distributional issues. As a result, recent decades have witnessed significant advances in research along this direction, from the perspectives of both general equilibrium theory and quantitative macroeconomics. In my dissertation, I continue this strand of study into monetary economies. The dissertation stays in the framework of Walrasian equilibrium and focuses on two types of benchmark monetary models, the Baumol–Tobin model and the cash-in-advance model.

I. Stationary Monetary Equilibrium in a Baumol–Tobin Exchange Economy: Theory and Computation (job market paper)

I compute a stationary monetary equilibrium in a Baumol–Tobin exchange economy with two assets (money and short-term bonds) and long-lived, heterogeneous consumers who face uninsurable idiosyncratic endowment risk. In the model, each consumer must pay a fixed cost to exchange bonds for goods or money, but it is costless to exchange money for goods. If the bond pays a positive nominal interest rate, consumers will still hold money in equilibrium to avoid paying the transaction cost. Unlike in an economy with a cash-in-advance constraint, the velocity of money in this economy is not fixed at one, but instead depends on the economic fundamentals.

In contrast to the representative agent cash-in-advance model (e.g., Lucas and Stokey, 1987; Woodford, 1994), the heterogeneity in the model requires me to solve for the equilibrium distribution of asset holdings across consumers. Jovanovic (1982), Romer (1986), and Alvarez, Atkeson and Kehoe (2002) characterize the equilibrium analytically in related heterogeneous agent economies, but with complete markets and other simplifying assumptions. The incorporation of incomplete financial markets necessitates the use of computational methods to characterize the equilibrium.

I extend the numerical methods developed in a large recent literature on computing stationary equilibria with one endogenous state variable (e.g. Imrohoroglu, 1992; Huggett, 1993; Aiyagari, 1994) to handle two endogenous state variables (money and bonds) and the corresponding market-clearing conditions. I also prove that the value function is continuous even in the presence of fixed costs. This result permits me to use standard value-function approximation methods to solve the consumer’s decision problem.

I analyze the quantitative properties of the equilibrium by using calibrated parameters. Because this model has bonds and money, it is well suited for studying the effects of transaction costs and inflation on real variables in a fully-optimizing equilibrium framework.

First, when the exogenous transaction cost is reduced, the nominal and real interest rates fall, and the velocity of money increases. This prediction about the velocity of money is consistent with the data: financial innovation in the U.S. has reduced transaction costs in the past decades, and at the same time the velocity of money has increased. Because lenders lose and borrowers gain, the model predicts that the change in average utility can be ambiguous.

Second, increasing the exogenous growth rate of money increases the steady-state inflation rate, and decreases the real interest rate, in accordance with the Mundell–Tobin effect. To the best of my knowledge, this model is the first fully-optimizing equilibrium model with long-lived consumers which features a quantitatively significant Mundell-Tobin effect. Moreover, increasing inflation also decreases the real amount of money held, increases the average frequency of bond-money transactions, and decreases average utility. As in Lucas (2000), the welfare cost of inflation appears to be a concave function of the inflation rate, which implies a larger marginal gain from reducing lower inflation. Like other studies, I get a small welfare cost of inflation, with a magnitude less than half of a percent of income at a ten-percent annual inflation rate.

I also identify the highest real interest rate consistent with equilibrium. Because the real interest rate declines as inflation increases (the Mundell–Tobin effect), the highest real interest rate is attained under Friedman’s rule. Friedman advocated a steady decrease in the growth rate of money so as to implement an equilibrium with a zero nominal interest rate. Implementing such an equilibrium in my model is not straightforward: with positive transaction costs consumers do not lend (because money is more liquid than bonds and yet pays the same rate of return), so that borrowing must be ruled out to ensure that the bond market clears. Despite this difficulty, I show that it is possible to implement Friedman’s rule in this model. But the deflation rate is not equal to the discount rate, as Friedman suggests, but rather equal to the equilibrium interest rate in an incomplete-markets economy with a single asset — a risk-free bond — and a natural borrowing constraint. Moreover, an equilibrium that implements Friedman’s rule does not necessarily Pareto dominate a zero-inflation equilibrium.

II. Existence of Monetary Equilibria in a Baumol–Tobin Economy: The Two Period Case (joint with Ingolf Schwarz)

We study the existence and nominal determinacy properties of monetary equilibria in a two-period Baumol–Tobin model with a central bank and a fiscal authority. The central bank may peg the interest rate or control the money supply. If the fiscal authority sets a Ricardian fiscal plan through redistributing its seigniorage and tax income, under standard conditions there exists a monetary equilibrium for any strictly positive price level and equivalent martingale measure. Under a non-Ricardian fiscal policy with exogenously fixed nominal transfers, the existence result can be established as long as the government maintains a positive commodity tax.

III. Monetary Equilibria in a Cash-in-Advance Economy with Incomplete Financial Markets (joint with Ingolf Schwarz)

We study the existence and nominal determinacy properties of monetary equilibria in a two-period general equilibrium model with incomplete financial markets (GEI), fiat money, fiscal and monetary policies and a cash-in-advance constraint. The central bank either pegs the interest rate or money supply while the fiscal authority sets a Ricardian or a non-Ricardian fiscal plan. We prove the existence of monetary equilibria in all four scenarios. In Ricardian economies, the conditions required for existence are not more restrictive than in standard GEI. In non-Ricardian economies, the sufficient conditions for existence require either a gains-to-trade hypothesis or a positive commodity tax. In the Ricardian economy, neither the price level nor the equivalent martingale measure is determinate.