Stationarity without degeneracy in a model of commodity money

We develop a model of macroeconomic heterogeneity inspired by the Kiyotaki–Wright (J Polit Econ 97:924–954, 1989) formulation of commodity money, with the addition of linear utility and idiosyncratic shocks to savings. We consider two environments. In the benchmark case, the consumer in a meeting is chosen randomly. In the auctions case, the individual holding more money can be selected to be the consumer. We show that in both environments socially optimal trading decisions (that are individually acceptable) are stationary and solve a tractable static optimization problem. Savings decisions in the benchmark case are remarkably invariant to mean-preserving changes in the distribution of shocks. This result is overturned in the auctions case.     

Reporting bias in incomplete information model

Company financial reports are likely to be systematically biased. In this paper, we extend the Duffie and Lando (2001) model with a skewness correction which can account for both random and directional components of reporting noise.     

Macroeconomic implications of voucher privatization in a model with incomplete information

Voucher privatization implies a significant wealth transfer from state to private agents who, in turn, would increase consumption. This paper investigates the consequences of this wealth effect on the macroeconomic equilibrium in a high unemployment economy. The model builds on a two-stage sequential game between the government and private agents. We verify the existence of a pooling equilibrium in which private agents cannot guess whether a policy of fast privatization will be continued in the future or not. This configuration presents an endogenous probability of privatization slowdown; as a consequence, the wealth effect is moderated and the genuine fast privatizer government bears an “undue” credibility cost in terms of employment     

The Hahn-Solow macro model

The Hahn-Solow macromodel is characterized by fixed nominal wages, increasing returns on capital and pricesetting under an imperfect competitive environment. It proposes that a fall in unemployment is always accompanied by a rise in real wages. The two authors demonstrate that involuntary unemployment is compatible with equilibrium in the goods- and labormarket but they can hardly explain the macroeconomic records of the recent three decades in the US and in Europe.     

A model of electoral competition with incomplete information

A model of two-candidate electoral competition is developed in which voters are uncertain about the policy either candidate would implement if elected. Candidates simultaneously announce policy positions, from which voters attempt to infer the true positions the candidates would adopt. Announcing a position different from the true position is costly to the winning candidate, with these costs increasing as the difference between the true policy and the announced policy increases. A refinement of the sequential equilibrium concept is used to describe the behavior of candidates and voters.     

A model of insurance markets with incomplete information

The paper investigates how a competitive market would allocate insurance policies if firms were not able to determine the riskiness of individual consumers. It is demonstrated that if all firms have static expectations with regard to the policy offers of other firms, no stationary equilibrium may exist. A second equilibrium concept is then introduced which incorporates a different expectation rule. Each firm assumes that any policy will be immediately withdrawn which becomes unprofitable after that firm makes its own policy offer. This equilibrium is shown to exist and some of its welfare properties are investigated.     

The value of money in a dynamic equilibrium model

Summary. This paper studies the pricing of money in an infinite-horizon economy with heterogeneous agents, incomplete financial markets and arbitrary borrowing restrictions. Purchases of the consumption good are subject to a cash-in-advance constraint. Under general conditions I show that the price of money is equal to its fundamental value, where this value is defined over all state-price processes that are compatible with the existence of no-arbitrage opportunities. This equality implies that the cash-in-advance constraint is binding infinitely often for all agents in the economy. The analysis highlights certain differences in the determination of the price of money with respect to models with money in the utility function that bear on the optimal implementation of economic policies.Received: 23 October 2003, Revised: 26 August 2004 JEL Classification Numbers: D52, E44, G12.M.S. Santos: This paper is an outgrowth of an earlier collaboration with Michael Woodford. I have also benefitted from various discussions with Eduardo Gimenez, Alejandro Hernandez, and Miguel Iraola. Some very useful comments by an anonymous referee are greatly appreciated.     

A learning-based model of repeated games with incomplete information

This paper tests a learning-based model of strategic teaching in repeated games with incomplete information. The repeated game has a long-run player whose type is unknown to a group of short-run players. The proposed model assumes a fraction of ‘short-run’ players follow a one-parameter learning model (self-tuning EWA). In addition, some ‘long-run’ players are myopic while others are sophisticated and rationally anticipate how short-run players adjust their actions over time and “teach” the short-run players to maximize their long-run payoffs. All players optimize noisily. The proposed model nests an agent-based quantal-response equilibrium (AQRE) and the standard equilibrium models as special cases. Using data from 28 experimental sessions of trust and entry repeated games, including 8 previously unpublished sessions, the model fits substantially better than chance and much better than standard equilibrium models. Estimates show that most of the long-run players are sophisticated, and short-run players become more sophisticated with experience.     

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.     

The evolution of conventions under incomplete information

Summary. We formulate an evolutionary learning process with trembles for static games of incomplete information. For many games, if the amount of trembling is small, play will be in accordance with the games (strict) Bayesian equilibria most of the time. This supports the notion of Bayesian equilibrium. Often the process will select a specific equilibrium. We study an extension to incomplete information of the prototype conflict known as Chicken and find that the equilibrium selection by evolutionary learning may well be in favor of inefficient Bayesian equilibria where some types of players fail to coordinate.Received: 17 March 2003, Revised: 3 December 2003, JEL Classification Numbers: C72.     

Signaling via an agenda in multi-issue bargaining with incomplete information

Summary. While actual bargaining features many issues and decision making on the order in which issues are negotiated and resolved, the typical models of bargaining do not. Instead, they have either a single issue or many issues resolved in some fixed order, typically simultaneously. This paper shows that, when there is incomplete information, such an approach removes an important avenue for information transmission: the bargaining agenda itself. Compared to the standard model, pooling on offers by the informed is reduced and a signaling equilibrium arises when the agenda is determined endogenously. Signaling is carried out by use of an issue-by-issue bargaining agenda. Received: September 3, 1997; revised version: May 11, 1998     

Regulating a risk-averse firm under incomplete information

We examine the optimal regulatory policy for a risk-averse firm when the firm is imperfectly informed about its efficiency parameter for a project at the time of contracting. The firm’s risk aversion shifts the optimal regulatory policy from a fixed-price contract to a cost-plus contract. The optimal regulatory policy entails undereffort by an inefficient firm as in Laffont and Tirole (J Polit Econ 94(3):614–641, 1986) and the effort distortion increases as the firm becomes more risk-averse. Further, the regulator benefits from sequential contracting with the firm where the firm chooses contract terms gradually as it acquires information, albeit the benefit diminishes as the firm becomes more risk-averse.      

The information content of money in forecasting euro area inflation

This article contributes to the debate on the role of money in monetary policy by analysing the information content of money in forecasting euro-area inflation. We compare the predictive performance within and among various classes of structural and empirical models in a consistent framework using Bayesian and other estimation techniques. We find that money contains relevant information for inflation in some model classes. Money-based New Keynesian Dynamic Stochastic General Equilibrium (DSGE) models and Vector Autoregressions (VARs) incorporating money perform better than their cashless counterparts. But there are also indications that the contribution of money has its limits. The marginal contribution of money to forecasting accuracy is often small, money adds little to dynamic factor models, and it worsens forecasting accuracy of partial equilibrium models. Finally, nonmonetary models dominate monetary models in an all-out horserace.     

Optimal inflation in a model of inside money

There are several models of outside money in which some inflation accomplished through lump-sum transfers is optimal. It is shown here that inflation can be optimal in a model of inside money, essentially the model in Cavalcanti and Wallace (1999). The possibility of inflation comes about via the trades between people who can issue inside money, monitored people, and those who cannot, nonmonitored people. Inflation occurs at the optimum if the monitored people spend more in such meetings when they are buyers than they receive in such meetings when they are sellers.     

Payment networks in a search model of money

In a simple search model of money, we study a special kind of memory which gives rise to an arrangement resembling a payment network. Specifically, we assume that agents can pay a cost to have access to a central data base that keeps track of payments made and received. Incentives must be provided to agents to access the central data base and to produce when they have access to this arrangement. We study policies that can relax these incentive constraints. In particular, we show that a ‘no-surcharge’ rule has good incentive properties. Finally, we compare our model with the model of Cavalcanti and Wallace.     

Payoff continuity in incomplete information games: a comment

Kajii and Morris (J. Econ. Theory 82 (1998) 267) provide necessary and sufficient conditions for two priors to be strategically close. The restrictiveness of these conditions establishes that strategic behavior can be highly sensitive to the assumed prior. Their results thus recommend care in the use of priors in economic modelling. Unfortunately, their proof of a central proposition fails for zero probability types. This comment corrects their proof to account for these cases.     

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.     

Futures markets and commodity options: Hedging and optimality in incomplete markets

This paper examines the allocational roles of futures markets and commodity options in multi-good and multi-period economies. In a continuous-time model with time-additive utilities and homogeneous beliefs, trading in “unconditional” futures contracts, the market portfolio and a riskless asset gives any Pareto-optimal allocation. Individuals' optimal holdings of futures contracts in the continuous-time model are related to their consumption bundles and to their risk tolerances. It is shown that both hedging and “reverse hedging” behavior are possible. In the general model with discrete trading, options on portfolios of commodity options are shown to permit any unconstrained Pareto-optimal allocation.