Prudent expectations equilibrium in economies with uncertain delivery

In an economy with private information, we introduce the notion of objects of choice as lists of bundles out of which the market selects one for delivery. This leads to an extension of the model of Arrow–Debreu that is used to study trade ex ante with private state verification. Under the assumption that agents are prudent, equilibrium is characterized by the fact that agents consume bundles with the same utility in states that they do not distinguish. This is a weaker condition than the restriction of equal consumption imposed by Radner (Econometrica 36(1), 31–58, 1968), therefore, some no trade situations are avoided and the efficiency of trade increases.     

Capacity constrained firms in (labor) markets with adverse selection

Summary. We discuss a competitive (labor) market where firms face capacity constraints and individuals differ according to their productivity. Firms offer two-dimensional contracts like wage and task level. Then workers choose firms and contracts. Workers might be rationed if the number of applicants exceeds the capacity of the firm. We show that under reasonable assumptions on the distribution of capacity an equilibrium in pure strategies (by the firms) exists. This result stands in contrast to the case of unlimited capacity. The utility level is uniquely determined in equilibrium. No rationing occurs in equilibrium, but it does off the equilibrium path. Received: December 29, 1999; revised version: November 30, 2000     

Dynamic adverse selection and the supply size

In this paper we examine the problem of dynamic adverse selection in a stylized market where the quality of goods is a seller׳s private information while the realized distribution of qualities is public information. We obtain that full trade occurs in every dynamic competitive equilibrium. Moreover, we show that if prices can be conditioned on the supply size then a dynamic competitive equilibrium always exists, while it fails to exist if prices cannot be conditioned on the supply size and the frequency of exchanges is high enough. We conclude that the possibility to condition prices on the supply size allows us to reach efficiency in the limit for exchanges becoming more and more frequent, while otherwise the welfare loss due to delays of exchanges remains bounded away from zero.     

Moral hazard and general equilibrium in large economies

Summary. The paper analyzes a two period general equilibrium model with individual risk, aggregate uncertainty and moral hazard. There is a large number of households, each facing two individual states of nature in the second period. These states differ solely in the household's vector of initial endowments, which is strictly larger in the first state (good state) than in the second state (bad state). In the first period each household chooses a non-observable action. Higher levels of action give higher probability of the good state of nature to occur, but lower levels of utility. Households' utilities are assumed to be separable in action and the aggregate uncertainty is independent of the individual risk. Insurance is supplied by a collection of firms who behave strategically and maximize expected profits taking into account that each household's optimal choice of action is a function of the offered contract. The paper provides sufficient conditions for the existence of equilibrium and shows that the appropriate versions of both welfare theorems hold. Received: December 7, 1998; revised version: October 25, 1999     

Collusion and group lending with adverse selection

In an environment with correlated returns, this paper characterizes optimal lending contracts when the bank faces adverse selection and borrowers have limited liability. Group lending contracts are shown to be dominated by revelation mechanisms which do not use the ex post observability of the partners' performances. However, when collusion between borrowers under complete information is allowed, group lending contracts are optimal in the class of simple revelation mechanisms (which elicit only the borrower's own private information) and remain useful with extended revelation mechanisms.     

Insurance contracts with imprecise probabilities and adverse selection

Summary. This article deals with optimal insurance contracts in the framework of imprecise probabilities and adverse selection. Agents differ not only in the objective risk they face but also in the perception of risk. In monopoly, a range of configurations that VNM preferences preclude appears: a pooling contract may be optimal, incomplete coverage may be offered to high risks, low risks may be better covered.Received: 1 November 2001, Revised: 15 April 2003, JEL Classification Numbers: D81, D82, G22.Useful suggestions by Emmanuelle Auriol, Bernard Bensaïd, Michéle Cohen, Isaac Meilijson and the anonymous referee are acknowledged. Correspondence to: M. Jeleva     

Equilibrium in a decentralized market with adverse selection

Summary. This paper deals with trade volume and distribution of surplus in markets subject to adverse selection. In a model where two qualities of a good exist, I show that if trade is decentralized (i.e. conducted via random pairwise meetings of agents), then all units of the good are traded, and all agents have positive ex-ante expected payoffs. This feature is present regardless of the quality distribution, and persists in the limit as discounting is made negligible. This offers a sharp contrast to models of centralized trade with adverse selection (Akerlof, Wilson). Received: April 2, 2001; revised version: March 29, 2002 RID="*" ID="*" This research was funded by a grant from UQAM. I wish to thank Roberto Serrano and seminar participants at UQAM, Queen's University at Kingston, the 2001 CEME General Equilibrium Conference (Brown University), and the 2001 North American Summer Meeting of the Econometric Society (University of Maryland) for comments.     

General equilibrium and resource economics

Summary. For a number of reasons a large class of general equilibrium models from the field of resource economics does not allow for an equilibrium analysis along the lines of the theory of infinite dimensional commodity spaces. The reasons concern the choice of the commodity space and the applicability of properness assumptions with respect to preferences and the technology. This paper illustrates the difficulties and shows for a prototype model how the problems can successfully be tackled by the use of a limit argument on equilibria in the truncated economies. Received: May 2, 1996; revised version: May 13, 1998     

General equilibrium with endogenous securities and moral hazard

Summary. This paper studies a class of general equilibrium economies in which the individuals endowments depend on privately observed effort choices and the financial markets are endogenous. The environment is modeled as a two-stage game. Individuals first make strategic financial-innovation decisions. They then act in a Radner-type economy with the previously designed securities. Consumption goods, portfolios, and effort levels are chosen competitively (i.e., taking prices as given). An equilibrium concept is adapted for these moral hazard economies and its existence is proven. It is shown through an example how incentive motives might lead to the endogenous emergence of financial incompleteness.Received: 18 March 2002, Revised: 16 February 2004, JEL Classification Numbers: D52, D82, G10, G22.This paper is based on an essay from my Ph.D. dissertation at the University of Chicago. I am thankful for comments from Fernando Alvarez, Rodrigo Cerda, Pierre-André Chiappori, Rubens P. Cysne, Carlos E. da Costa, Milton Harris, Lars Stole, Juan P. Torres-Martínez, Paulo K. Monteiro, Philip Reny, Iván Werning, an anonymous referee, and seminar participants at the 6th SAET Conference and the 22th SBE Meeting. Financial support from CNPq is gratefully acknowledged.     

General equilibrium in economies with uncertain delivery

We consider a general equilibrium model of trade ex ante with differential information in which agents choose plans of state-contingent lists of bundles. Being unable to verify that the state of nature is s and not t, an agent has to accept the delivery of any bundle in the list for delivery in state s or in the list for delivery in state t. Under the assumption that each state of nature can be verified by at least one agent, we establish existence of equilibrium and we show that the equilibrium allocation satisfies a notion of coalitional incentive compatibility.     

No-arbitrage Equilibria with Differential Information: An Existence Proof

On the example of a pure exchange financial economy with two periods incomplete nominal-asset markets and differential information of the adverse selection’s type, Cornet-De Boisdeffre (J Math Econ 38:393-410, 2002) introduced refined concepts of no-arbitrage prices and equilibria, which extended to the asymmetric information setting the classical concepts of the symmetric information literature. We now assess existence issues and extend a standard property of symmetric information models. Namely, we prove that a no-arbitrage equilibrium always exists, as long as financial markets preclude arbitrage, under the same standard conditions, whether agents have symmetric or asymmetric information.     

Signaling in markets with two-sided adverse selection

Summary. The paper analyzes an economy with two-sided adverse selection, focusing on equilibria that satisfy a refinement based on the notion of strategic stability. In the familiar case of one-sided adverse selection, agents reveal all of their private information as long as the contract space is rich enough. However, with two-sided adverse selection, the sufficient conditions for separation are much stronger. Received: September 3, 1999; revised version: December 3, 1999     

On the continuity of equilibrium and core correspondences in economies with differential information

Summary. We study upper semi-continuity of the private and coarse core and the Walrasian expectations equilibrium correspondences for economies with differential information, with Boylan (1971) topology on agents information fields.Received: 16 January 2004, Revised: 28 October 2004, JEL Classification Numbers: D50, D82, C70. Correspondence to: Ezra EinyWe wish to thank Carlos Herves, Nicholas Yannelis, and an anonymous referee for their helpful comments.     

An evolutionary analysis of insurance markets with adverse selection

The equilibrium nonexistence problem in Rothschild and Stiglitz's insurance market is reexamined in a dynamic setting. Insurance firms are boundedly rational and offer menus of insurance contracts which are periodically revised: profitable competitors' contracts are imitated and loss-making contracts are withdrawn. Occasionally, a firm experiments by withdrawing or innovating a random set of contracts. We show that Rothschild and Stiglitz's candidate competitive equilibrium contracts constitute the unique long-run market outcome if innovation experiments are restricted to contracts which are sufficiently “similar” to those currently on the market.     

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.     

Liquidity supply and adverse selection in a pure limit order book market

This paper analyzes adverse selection costs and liquidity supply in a pure open limit order book market. We relax assumptions of the Glosten/Såndas modeling framework regarding marginal zero profit order book equilibrium and the parametric market order size distribution. We show that using average zero profit conditions considerably increases the empirical performance while a nonparametric specification for market order size combined with marginal zero profit conditions does not. A cross sectional analysis corroborates the finding that adverse selection costs are more severe for smaller capitalized stocks. We also find additional support for one of the central hypothesis put forth by the theory of limit order book markets, which states that liquidity supply and adverse selection costs are inversely related. Furthermore, adverse selection cost estimates based on our structural model and those obtained using popular model-free methods are strongly correlated. This indicates the robustness of the theory-based approach.     

Competitive and core allocations in large economies with differential information

Summary. We study the core and competitive allocations in exchange economies with a continuum of traders and differential information. We show that if the economy is “irreducible”, then a competitive equilibrium, in the sense of Radner (1968, 1982), exists. Moreover, the set of competitive equilibrium allocations coincides with the “private core” (Yannelis, 1991). We also show that the “weak fine core” of an economy coincides with the set of competitive allocations of an associated symmetric information economy in which the traders information is the joint information of all the traders in the original economy. Received March 22, 2000; revised version: May 1, 2000     

On the nonexistence of recursive equilibrium in stochastic OLG economies

We study a class of stochastic Overlapping generations (OLG) economies that have one-memory equilibria, that is equilibria that are determined by the current and past realizations of the states of uncertainty. This class is negligible, but important. In particular, it contains all the known examples of nonexistence of recursive equilibrium. We show that, within this restricted domain, the existence of recursive equilibrium is actually typical, and such examples are therefore nonrobust. We thank Felix Kubler, Herakles Polemarchakis and Steve Spear for many useful discussions. This paper was started while the first author was visiting Columbia Business School.     

Assortative matching, adverse selection, and group lending

This note reconsiders a theoretical result asserted to explain the success of group lending programs in LDCs. It has been claimed that if groups are allowed to form themselves, risky and safe borrowers will sort themselves into relatively homogenous groups. This “positive assortative matching” can be exploited by lenders to solve an adverse selection problem that would otherwise undermine the effectiveness of such lending programs. I show that the positive assortative matching result does not necessarily hold if earlier models are extended to incorporate dynamic incentives.