Exchange economies with asymmetric information: competitive equilibrium and core

Summary. A replica theorem is shown to hold for exchange economies with asymmetric information. In a replicated exchange economy with asymmetric information the set of all core elements with equal treatment is nonempty, but it is in general only a subset of the core. Nevertheless, the replica theorem and the presence of at least one core element with equal treatment suffice to show existence of a competitive quasi-equilibrium. Conditions on the initial endowments and the communication system are given to ensure that every competitive quasi-equilibrium is a competitive equilibrium.Received: 24 February 2003, Revised: 3 July 2003JEL Classification Numbers: C70, D50, D82.I thank an anonymous referee whose comments led to an improvement of the paper.     

Lotteries, Sunspots, and Incentive Constraints

We study a prototypical class of exchange economies with private information and indivisibilities. We establish an equivalence between lottery equilibria and sunspot equilibria and show that the welfare and existence theorems hold. To establish these results, we introduce the concept of the stand-in consumer economy, which is a standard, convex, finite consumer, finite good, pure exchange economy. With decreasing absolute risk aversion and no indivisibilities, we prove that no lotteries are actually used in equilibrium. We provide a simple numerical example with increasing absolute risk aversion in which lotteries are necessarily used in equilibrium. We also show how the equilibrium allocation in this example can be implemented in a sunspot equilibrium. Journal of Economic Literature Classification Numbers: D11, D50, D82.     

Private Value Allocations in Large Economies with Differential Information

We consider a Radner-type (e.g., Radner, 1968, Econometrica36, 31–58) pure exchange economy with differential information and a continuum of agents. We show that under appropriate assumptions the set of Aumann–Shapley private value allocations in such an economy coincides with the set of Radner competitive equilibrium allocations. Journal of Economic Literature Classification Numbers: C71, D51, D82.     

Arbitrage and equilibrium with portfolio constraints

We consider a multiperiod financial exchange economy with nominal assets and restricted participation, where each agent’s portfolio choice is restricted to a closed, convex set containing zero, as in Siconolfi (Non-linear Dynamics in Economics and Social Sciences, 1989). Using an approach that dates back to Cass (CARESS Working Paper, 1984; J Math Econ 42:384–405, 2006) in the unconstrained case, we seek to isolate arbitrage-free asset prices that are also quasi-equilibrium or equilibrium asset prices. In the presence of such portfolio restrictions, we need to confine our attention to aggregate arbitrage-free asset prices, i.e., for which there is no arbitrage in the space of marketed portfolios. Our main result states that such asset prices are quasi-equilibrium prices under standard assumptions and then deduces that they are equilibrium prices under a suitable condition on the accessibility of payoffs by agents, i.e., every payoff that is attainable in the aggregate can be marketed through some agent’s portfolio set. This latter result extends previous work by Martins-da-Rocha and Triki (Working Paper, University of Paris 1, 2005).     

Incomplete Markets, Allocative Efficiency, and the Information Revealed by Prices

We compare rational expectations equilibria with different degrees of information revelation through prices. These equilibria arise in a two-period exchange economy with finitely many states and signals, multiple commodities and incomplete financial markets for nominal assets. We show that there are always equilibria where information is redundant in the sense of being of no value to the uninformed traders. We give conditions under which for a generic set of economies, parametrized by endowments and utilities, there exist open sets of equilibria for which allocative and informational efficiency are independent, with implications for monetary policy. Journal of Economic Literature Classification Numbers: D52, D60, D82, E52.     

Open core and quasi-equilibria with lower semi-continuous preferences

Summary. This note introduces a new concept of core –open core, using which it shows a quasi-equilibrium existence result in an economy where consumers' preference relations are assumed to be lower semi-continuous, but not necessarily to have open lower sections nor to be open valued, such as the lexicographic ordering. As an application, a competitive equilibrium existence result without non-satiation assumption is proved. Received: October 28, 1996; revised version: November 4, 1997     

Oligopoly equilibria in exchange economies: a limit theorem

In a pure exchange economy, agents have the possibility of behaving strategically by putting only a part of their initial endowments on the market. An oligopoly equilibrium is defined to be a Nash equilibrium of the game in which agents choose simultaneously quantities to be put on the market. It is proved that under standard hypotheses, the oligopoly equilibrium leads to the competitive equilibrium when the economy is replicated an infinite number of times. Received: May 26, 1999; revised version: April 3, 2000     

CREDIBILITY AND RENEGOTIATION OF OUTCOME FUNCTIONS IN IMPLEMENTATION*

Recent research has been motivated by the fact that the outcome function in implementation may not be “credible”. On the one hand, the players may try to renegotiate the final outcome, if there is another outcome which they prefer. On the other hand, the “social planner” may have an incentive not to implement the finaloutcome, if there is another outcome which he prefers. I show that in the exchange economy, the first problem is not serious. a planner with unlimited commitment power can design a “collusion-proof” mechanism, which is stable against all sorts of group devciation, including the ex post trade of goods among the agents. I will, However, argue tha hte second problem (the planner's commitment problem) can be very serious.     

The Macroeconomics of Financial Crises: How Risk Premiums and Liquidity Traps Affect Policy Options

The paper offers an overview of what structural models of the IS-LM and Mundell-Fleming variety can tell about the macroeconomics of economic crises. In addition to demonstrating how the emergence of risk premiums in money and capital markets can generate liquidity traps at positive interest rates and may drive economies into recessions, it shows the following: (1) Fiscal policy works even in a small, open economy under flexible exchange rates when the country is stuck in a liquidity trap; (2) Near the fringe of liquidity traps, there may be perfect traps, in which neither monetary nor fiscal policy works when used in isolation but policy coordination is called for; and (3) Massive financial crises in the domestic money market may even destabilize the economy.     

Feasible Bayesian Implementation with State Dependent Feasible Sets

This paper considers feasible Bayesian implementation for an environment with state dependent feasible sets. We assume no externality in individual feasibility constraint sets and no exaggeration on the part of agents, but allow for flexible information structures. Bayesian Incentive Compatibility, Closure, and Bayesian Monotonicity are found to be necessary and sufficient for feasible Bayesian implementation. This result is applied to an exchange economy where agents have fixed preferences but uncertain initial endowments and complete information. A condition called the Endowment Condition, which is weaker than Individual Rationality, is identified as necessary and sufficient for feasible Nash implementation.Journal of Economic LiteratureClassification Numbers: D70; D71; D74; D82.     

External debt sustainability and policy rules in a small globalized economy

The paper develops a Post Keynesian macroeconomic model which discusses the conditions that lead to an external debt crisis in a small developing economy fully integrated to global goods and financial markets. The focus is on how policy rules affect the stability of the economy. Two kinds of policy rules are discussed, namely inflation target and real exchange rate target, implemented through an interest rate operation procedure (IROP). It is argued that in both cases the evolution of the real exchange rate should be closely monitored to avoid external instability. It is also suggested that a real exchange rate target may be more effective to stabilize the economy if there is a strong tendency towards the equality of the foreign and domestic real interest rates.     

Auctions of Heterogeneous Objects

Simultaneous sealed bid auctions of heterogeneous objects are analyzed. Each bidder's reservation value for an object depends upon the other objects he obtains. Bidders' reservation values are common knowledge. In simultaneous first-price auctions, the set of Walrasian equilibrium allocations contains the set of pure strategy Nash equilibrium allocations which in turn contains the set of strict Walrasian equilibrium allocations. Hence, pure strategy Nash equilibria (when they exist) are efficient. Mixed strategy Nash equilibria may be inefficient. In simultaneous second-price auctions, any efficient allocation can be implemented as a pure strategy Nash equilibrium outcome if a Walrasian equilibrium exists.Journal of Economic LiteratureClassification Numbers: D44, D51.     

An Elementary Approach to Approximate Equilibria with Infinitely Many Commodities

We prove the existence of approximate equilibria in a finite exchange economy with a countably infinite number of commodities and nonconvex preferences, when every trader has an excess demand set that is finitely spannable, i.e., that could be covered by a union of its convex subsets in finitely many steps. We show that the bound on the norm of the per capita aggregate excess demand is reciprocally related to the square root of the population. Extensions are also made to the case where countably many commodities are indivisible. The proofs are elementary. Journal of Economic Literature Classification Numbers: D50, C62, D52.     

The strong sequential core in a dynamic exchange economy

Summary. Dynamic exchange economies with uncertainty are considered where the information is released over infinite time. The strong sequential core of such an economy consists of those consumption streams that can be improved upon by no coalition at no moment of time. Non-emptiness of the strong sequential core is established given a high enough discount factor. Moreover, sufficient conditions are given under which the strong sequential core contains only time and history independent consumption streams.Received: 22 August 2002, Revised: 22 May 2003, JEL Classification Numbers: C71, C73, D51, D52.Correspondence to: P. Jean-Jacques HeringsJean-Jacques Herings would like to thank the Netherlands Organization for Scientific Research for financial support.     

Quantitative growth effects of subsidies in a search theoretic R&D model

Should government subsidize R&D and does it matter how these subsidies are allocated? We examine these questions in a dynamic model where R&D is described as sequential sampling from a distribution of new ideas. Successful discoveries affect future available resources and incentives for further R&D. Consequently, there may be under-investment in R&D. We study the effect of government interventions aimed at fostering growth through R&D. Calibrating the model with aggregate data from the Israeli business sector allows us to quantitatively compare two forms of support resembling those actually used to encourage R&D in the Israeli business sector: (i) an unrestricted subsidy that may be used at the recipients' discretion to finance R&D or other investments, (ii) a subsidy earmarked by the government for R&D activities only. While there is no theoretical way to determine which of the two subsidies will have a greater impact on search for new ideas and growth, we find that in the calibrated economy both subsidies have a significant but similar impact on the economy's output and TFP growth rates. Accordingly, in the case of the Israeli business sector, the incentives to conduct R&D were sufficiently strong, and no R&D-specific encouragement was needed. However, a sensitivity analysis reveals that for economies characterized by other parameter values this result may not be true. Correspondence to: B. Bental     

Integral stabilization policy and flexible exchange rates

Summary Under a floating exchange rate system, exchange rates influence economic activity through their effect on the trade balance. Nevertheless, exchange rate movementsper se do not prevent integral fiscal and monetary policies from achieving a target for domestic economic activity²⁴. At the same time, since the exchange rate continuously moves to preserve asset market equilibrium, the (potential) balance of payments may not be equilibrated when the authorities have attained their internal target. In that event, the continued movement in exchange rates may produce cycles in economic activity which in turn lead to exchange rate oscillations. Finally, the reader is warned that the introduction of inside and outside lags into the system may produce additional oscillatory behavior or even explosiveness, as Phillips demonstrated for the closed economy. However, these new possibilities would arise independently of the floating exchange rate system and could not be attributed to it.     

A structural model of price and exchange rate dynamics in a small open economy

Conclusions A major result following from the analysis of ourstructural model of inflation under flexible exchange rates is that there is no such thing asstructural inflation in the long run. Long-run inflation rather becomes a purely monetary phenomenon if exchange rates are flexible and if on an international level functioning capital markets are postulated. While, in the light of the assumptions made in Part III, this finding is not nearly as paradoxical as it may appear at first sight, it can hardly be overemphasized considering the ongoing theoretical discussion and the empirical research on the Scandinavian approach to inflation and recalling that the Scandinavian model is basically intended to picture equilibrium dynamics.The results concerning equilibrium price and exchange rate dynamics also apply to the equilibriumlevels of prices and the exchange rate, i. e., the equilibrium price level depends exclusively on monetary factors while the equilibrium exchange rate is determined by a purchasing power parity element and the structural productivity gap component.Turning to the results of our analysis of disequilibrium dynamics, the overall picture does not change very much. Here the qualitative pattern of adjustment of both prices and the exchange rate is again completely independent of structural variables, but is exclusively determined by four adjustment coefficients. However, the particular quantitative values assumed by prices and the exchange rate during the adjustment process do indeed reflect the impact of the productivity gap.No conclusions can be derived from our model on the amount of time it takes to return to the neighbourhood of equilibrium once the economy has been subjected to some kind of external shock. A casual examination of post-1973 developments and especially the Swiss experience suggest, however, that in the case of a disturbance as, e. g., in the form of a monetary contraction (relative to the rest of the world), the economy may take so long to return to the neighbourhood of long-run equilibrium that the negative real consequences of the overvaluation of the domestic currency during the adjustment process provide a momentous rationale for short-run stabilization interventions in the foreign exchange market.We should like to thank Peter Bernholz and an anonymous referee for helpful comments on a previous version of this paper.     

Stone–Geary preferences in overlapping generations economies under pure exchange: A note

We incorporate Stone–Geary preferences into an overlapping generations economy under pure exchange, and explore stability, indeterminacy, and cycles with positive levels of saving and nonnegative public debt. A stable nontrivial steady state exists for parameter values, for which there does not exist equilibrium in the model with purely logarithmic utility function. We also show the possibility of a period-doubling bifurcation (a two-cycle).     

Price dynamics in an exchange economy

The pure exchange model is the foundation of the neoclassical theory of value, yet equilibrium predictions and price adjustment dynamics for this model remained untested prior to the experiment reported in this paper. With the exchange economy replicated several times, prices and allocations in most experiment sessions adjust toward the competitive equilibrium in continuous double auction trading, though adjustment is much slower than in previous commodity flow (or perishable good) double auction market experiments. Price adjustment is evaluated by comparing its extent within each market replication (or trading period) to its extent across trading periods. More price adjustment occurs within trading periods than across trading periods, so price adjustment data are evaluated with the disequilibrium Hahn process model (Hahn and Negishi in Econometrica 30:463–469, 1962) of within-period trades. This paper introduces a stochastic version the Hahn process model and demonstrates that a linear approximation to this stochastic model yields an autoregressive process with a near unit root when the adjustment rate is low. In effect, the autoregressive price adjustment model studied extensively by time series econometricians over the past 30 years can be viewed as a reduced form of a stochastic disequilibrium exchange economy price adjustment model. Estimation of the model demonstrates that price adjustment in the exchange economy experiment is considerably slower than in economies without income effects, which suggests that the price discovery process may be a significant factor in the slow adjustment documented by applied econometricians.     

Stochastic and structural fiscal policy in a monetary stationary economy

In the framework of a monetary asset pricing model which is simple enough to generate closed form formulae for equilibrium price functions the interactions between output, fiscal policy, and asset markets is investigated. With money yielding liquidity services in the exchange process real stock prices are negatively correlated with anticipated (stochastic) fiscal policy changes, while the impact of unanticipated (structural) fiscal policy on the stock market depends qualitatively on the ‘business cycle’ of the economy. It is shown that the monetary character of the economy, more precisely the role of money in the exchange process, is critical for the relationship between fiscal policy and real share prices. Moreover, while contingent fiscal policy measures may be successful in stabilizing the real interest rate on money they are incapable of achieving a stable term structure of the real rate on stocks. In contrast, uncontingently higher public expenditures generally promote the volatility of the real rates on financial assets.