Consumption-loan type models the Samuelson case

This is a further study of the overlapping generations model with fixed amount of fiat money. We show that when the economy is Samuelsonian then there exists some Pareto optimal stationary competitive equilibrium from some initial money holdings. Moreover, if the steady-state interest factor is less than unity, then a non-monetary Pareto optimal equilibrium exists from any initial money endowments.     

Informational diversity over time and the optimality of monetary equilibria

The temporal realizations of a random state variable in an overlapping generations model create an informational diversity between members of different generations and require a reexamination of the optimality that competitive equilibria might display in such an environment. Using an optimality criterion that reflects this informational diversity we prove the optimality of competitive equilibrium in a model with a fixed stock of fiat money, a single-spot market, and good endowments that follow a Markov process. The need for an optimality criterion that incorporates informational diversity is further motivated by studying the same model with the operation of complete contingent commodities markets.     

On the coexistence of money and higher-return assets and its social role

This paper adopts mechanism design to investigate the coexistence of fiat money and higher-return assets. We consider an economy with pairwise meetings where fiat money and risk-free capital compete as means of payment, as in [28]. The trading mechanism in pairwise meetings is chosen among all individually rational, renegotiation-proof mechanisms to maximize society?s welfare. We show that in any stationary monetary equilibrium capital commands a higher rate of return than fiat money.     

General equilibrium, markets, macroeconomics and money in a laboratory experimental environment

Summary. This paper reports on the use of laboratory experimental techniques to create relatively complete economic systems. The creation of these market systems reflects a first attempt to explore the nature of inherently interdependent environments and to assess the ability of simultaneous equations equilibrium models like the classical static general competitive equilibrium model, to predict aspects of system behaviors. In addition, the impact of the quantity of a fiat money was studied. The economies were successfully created. Classical models capture much of what was observed. Received: May 21, 1996; revised version: May 21, 1997     

On stationary overlapping generations models

Consider a stationary consumption–loan economy with fixed amount of fiat money. We show that although the economy is stationary if the number of goods and the number of ‘types’ of consumers are larger than one, there might be no Pareto optimal stationary competitive equilibrium.     

The upper turning point in the Austrian business cycle theory

This paper defends the relevance of Austrian Business Cycle theory (ABCT) within a fiat money regime, by providing an answer to whether a constant rate of credit expansion necessarily leads to a boom-bust cycle. We claim that this scenario has two potential outcomes, (1) a change in money demand brings the economy back towards equilibrium or (2) the economy will shift to a sub-optimal but still sustainable path. We identify capital heterogeneity effects and the Ricardo effect as distinctly Austrian explanations for an upper turning point, even in a fiat money regime.

     

A THEORY OF MONEY AND MARKETPLACES*

This article considers an infinitely repeated economy with divisible fiat money. The economy has many marketplaces that agents choose to visit. In each marketplace, agents are randomly matched to trade goods. There exist a variety of stationary equilibria. In some equilibrium, each good is traded at a single price, whereas in another, every good is traded at two different prices. There is a continuum of such equilibria, which differ from each other in price and welfare levels. However, it is shown that only the efficient single‐price equilibrium is evolutionarily stable.     

Sufficient conditions for the existence of sunspot equilibria

This paper reports on conditions on agents' preferences and endowments sufficient to guarantee the existence of sunspot equilibria in a simple overlapping generations model of pure exchange. Sunspot equilibria are those in which uncertainty extrinsic to the economy operates through expectations to yield a fulfilled expectations competitive equilibrium in which the extrinsic randomness has real effects on prices and allocations. The paper also provides necessary and sufficient conditions for these equilibria to have agents trading in a fixed stock of valued fiat money. The condition derived can be interpreted as requiring that intertemporal income effects appropriately dominate substitution effects.     

Money and storage in a differential information economy

Summary Is the use of fiat money essential in any efficient organization of exchange? We investigate this question in economies that are generalizations of the Townsend (1980) turnpike model that include limited commitment and differential information. We show that in the Townsend turnpike model fiat money is not essential unless there is limited commitment. Furthermore, fiat money has no role whenever there is storage with positive returns. In the presence of differential information fiat money is essential in overcoming incentive problems. This is the case even if there is storage with positive returns.We wish to thank Bart Taub, Anne Villamil and seminar participants at the University of Chicago, the Federal Reserve Bank of Minneapolis, Ohio State, the 1994 North American Summer Meeting of the Econometric Society, SEDC 1994, and Oberwolfach 1994.     

Fiat money and the value of binding portfolio constraints

We establish necessary and sufficient conditions for the individual optimality of a consumption-portfolio plan in an infinite horizon economy where agents are uniformly impatient and fiat money is the only asset available for intertemporal transfers of wealth. Next, we show that fiat money has a positive equilibrium price if and only if for some agent the zero short sale constraint is binding and has a positive shadow price (now or in the future). As there is always an agent that is long, it follows that marginal rates of intertemporal substitution never coincide across agents. That is, monetary equilibria are never full Pareto efficient. We also give a counter-example illustrating the occurrence of monetary bubbles under incomplete markets in the absence of uniform impatience.     

BEYOND SEARCH: FIAT MONEY IN ORGANIZED EXCHANGE*

A model of fiat money is constructed in which spatial separation and the logistics of communication are made explicit as in search theory, but exchange is organized by profit‐seeking business enterprises as in all market economies. Firms mitigate search costs by opening shops that are easily located. Equilibria may exist in which fiat money is used as a universal medium of exchange. When a monetary equilibrium exists, fiat money is essential. The model provides a foundation to cash‐in‐advance theory, without specifying in advance that one object will be used as the universal medium of exchange.     

Money and capital as competing media of exchange

We construct a model where capital competes with fiat money as a medium of exchange, and establish conditions on fundamentals under which fiat money can be both valued and socially beneficial. When the socially efficient stock of capital is too low to provide the liquidity agents need, they overaccumulate productive assets to use as media of exchange. When this is the case, there exists a monetary equilibrium that dominates the nonmonetary one in terms of welfare. Under the Friedman Rule, fiat money provides just enough liquidity so that agents choose to accumulate the same capital stock a social planner would.     

Concurrent trading in two experimental markets with demand interdependence

Summary. We report results from fifteen computerized double auctions with concurrent trading of two commodities. In contrast to prior experimental markets, buyers' demands are induced via CES earnings functions defined over the two traded goods, with a fiat money expenditure constraint. Sellers receive independent marginal cost arrays for each commodity. Parameters for buyers' earnings functions and sellers' costs are set to yield a stable, competitive equilibrium. In spite of the complexity introduced by the demand interdependence, the competitive model is a good predictor of market outcomes, although prices tend to be above (below) the competitive prediction in the low-price (high-price) market.     

Endogenous supply of fiat money

We consider whether reputation concerns can discipline the behavior of a long-lived self-interested agent who has a monopoly over the provision of fiat money. We obtain that when this agent can commit to a choice of money supply, there is a monetary equilibrium where it never overissues. We show, however, that monetary equilibria with no overissue do not exist when there is no commitment. This happens because the incentives this agent has to maintain a reputation for providing valuable currency disappear once its reputation is high enough. More generally, we prove that in the absence of commitment overissue happens infinitely often in any monetary equilibrium. We conclude by showing that imperfect memory can restore the positive result obtained with commitment.     

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.     

A simple model for study of the determination of the price level and the interaction of monetary and fiscal policy

Summary A representative-agent model with money holdings motivated by transactions costs, a fiscal authority that taxes and issues debt, no production, and a convenient functional form for agents' utility is presented. The model can be solved analytically, and illustrates the dependence of price determination on fiscal policy, the possibility of indeterminacy, even stochastic explosion, of the price level in the face of a monetary policy that holdsM fixed, and the possibility of a unique, stable price level in the face of a monetary policy that simply pegs the nominal interest rate at an arbitrary level.In a rational expectations, market-clearing equilibrium model with a costlessly-produced fiat money that is useful in transactions, the following things are true under broad assumptions.- A monetary policy that fixes the money stock may (depending on the transactions technology) be consistent with indeterminacy of the price level—indeed with stochastically fluctuating, explosive inflation.- A monetary policy that fixes the nominal interest rate, even if it holds the interest rate constant regardless of the observed rate of inflation or money growth rate, may deliver a uniquely determined price level.- The existence and uniqueness of the equilibrium price level cannot be determined from knowledge of monetary policy alone; fiscal policy plays an equally important role. Special case models with interest-bearing debt and no money are possible, just as are special cases with money and no interest-bearing debt. In each the price level may be uniquely determined.Determinacy of the price level under any policy depends on the public's beliefs about what the policy authority would do under conditions that are never observed in equilibrium.These points are not new. Eric Leeper [1991] has made most of them within a single coherent model. Woodford [1993], in a representative agent cash-in-advance model, has displayed the possibility of indeterminacy with a fixed quantity of money and the possibility of uniqueness with an interest-rate pegging policy. Aiyagari and Gertler [1985] use an overlapping generations model to make many of the points made in this paper, without discussing the possibility of stochastic sunspot equilibria. Sargent and Wallace [1981] and Obstfeld [1983] have also discussed related issues.This paper improves on Leeper by moving beyond his analysis of local linear approximations to the full model solution, as is essential if explosive sunspot equilibria are to be distinguished from explosive solutions to the Euler equations that can be ruled out as equilibria. It improves on the other cited work by pulling together into the context of one fairly transparent model discussion of phenomena previously discussed in isolation in very different models.We study a representative agent model in which there is no production or real savings, but transactions costs generate a demand for money. The government costlessly provides fiat money balances, imposes lump-sum taxes, and issues debt, but has no other role in the economy. We make restrictive assumptions about the form of the utility function and the form of a transactions cost term in the budget constraint.The model could be extended to include production, capital accumulation, non-neutral taxation, productive government expenditure, and a more general utility function without affecting the conclusions discussed in this paper. Indeed the model I informally matched to data in an earlier paper [1988] makes some such extensions. While such an extended model is more realistic, it is harder to solve. The version in my earlier paper [1988] was solved numerically and simulated. The bare-bones model of this paper allows an explicit analytic solution that may make its results easier to understand.This paper improved following comments from participants at seminars at Yale and the Atlanta Federal Reserve Bank. Eric Leeper and James Robinson were particularly helpful. Comments from Michael Woodford led to important corrections and clarifications.     

Inside and outside fiat money, gains to trade, and IS-LM

Summary. We build a one-period general equilibrium model with money. Equilibrium exists, and fiat money has positive value, as long as the ratio of outside money to inside money is less than the gains to trade available at autarky. We show that the nominal effects of government fiscal and monetary policy can be completely described by a diagram identical in form to the IS-LM curves introduced by Hicks to describe Keynes' general theory. IS-LM analysis is thus not incompatible with full market clearing, multiple commodities, and heterogeneous households. We show that as the government deficit approaches a finite threshold, hyperinflation sets in (prices converge to infinity and real trade collapses). At the other extreme, if the government surplus is too large, the economy enters a liquidity trap in which nominal GNP sinks and monetary policy is ineffectual. Received: January 2, 2002; revised version: April 8, 2002 Correspondence to: P. Dubey     

Does commodity money eliminate the indeterminacy of equilibrium?

Previous studies have shown that a random-matching model with divisible fiat money and without constraint on agents’ money inventories possesses a continuum of stationary single-price equilibria. Wallace (J. Econom. Theory 81 (1998) 223) conjectures that the indeterminacy can be eliminated by the use of commodity money. Instead, I find that in a similar random-matching model with dividend-yielding commodity money, a continuum of stationary single-price equilibria exists when the utility of dividend is not too high. This result casts doubt on the conventional belief that the indeterminacy of monetary equilibrium is be caused only by the nominal nature of money.     

A note on asymmetric and mixed strategy equilibria in the search-theoretic model of fiat money

Summary. The simple search-theoretic model of fiat money has three symmetric Nash equilibria: all agents accept money with probability 1; all agents accept money with probability 0; and all agents accept money with probability y in (0,1). Here I construct an asymmetric pure strategy equilibrium, payoff-equivalent to the symmetric mixed strategy equilibrium, where a fraction N in (0,1) of agents always accept money and 1-N never accept money. Counter to what has been conjectured previously, I find N > y. I also introduce evolutionary dynamics, and show that the economy converges to monetary exchange iff the initial proportion of agents accepting money exceeds N. Received: September 10, 1997; revised version: April 24, 1998     

Real Indeterminacy of Stationary Monetary Equilibria in Centralized Economies

We show that real indeterminacy of stationary equilibria, by which the set of stationary equilibria is a continuum and the real allocation varies among equilibria, may arise in some general equilibrium models with fiat money. The conditions under which such equilibria arise are: (i) each household optimally saves a constant amount of money; and (ii) at least two households face different budget constraints. We present various models, including a decentralized money search model and a centralized model with a monopoly firm, to explain how these conditions lead to real indeterminacy. Finally, we present a policy that uniquely implements any desirable outcome.