On partial contracting

This paper investigates contracting situations where giving away some control rights enhances both the donor's and the receiver's incentives to cooperate in the future. We define a partial contracting framework with nonverifiable actions for which either control is contractible (contractible control actions) or the right to transfer control ex post to another party is contractible (transferable control actions). Under incomplete information, when control over particular actions is transferable but not contractible, it can be optimal to give one party the right to transfer control over a particular action to the other party, in order for that party to build a reputation regarding her willingness to cooperate in the future.     

The option of joint purchase in vertically differentiated markets

Summary. Within the framework proposed by Mussa and Rosen (1978) for modelling quality differentiation, consumers are assumed to make mutually exclusive purchases. A unique pure strategy equilibrium exists in this case. In this note, we allow consumers to buy simultaneously different variants of the differentiated good. We call this the “joint purchase option”. The paper proposes a detailed analysis of price competition when this option is opened: first, we show that either uniqueness, or multiplicity, or absence of price equilibrium arise, depending on the utility derived from joint purchase relative to exclusive purchase. Second, we characterize these equilibria, whenever they exist. Received: July 25, 2001; revised version: October 21, 2002 RID="*" ID="*" The second author gratefully acknowledges the financial support from Interuniversity Attraction Pole Program- Belgian State- Federal Office for Scientific, Technical and Cultural Affairs under contract PAI 5/26. Correspondence to: X.Y. Wauthy     

A strategy-proofness characterization of majority rule

Summary. A feasible alternative x is a strong Condorcet winner if for every other feasible alternative y there is some majority coalition that prefers x to y. Let (resp., denote the set of all profiles of linear (resp., merely asymmetric) individual preference relations for which a strong Condorcet winner exists. Majority rule is the only non-dictatorial and strategy-proof social choice rule with domain , and majority rule is the only strategy-proof rule with domain . Received: August 29, 2000; revised version: November 13, 2002 RID="*" ID="*"We are grateful to Wulf Gaertner and our two referees for insightful comments on a previous draft. Correspondence to: D. E. Campbell     

On extensive form implementation of contracts in differential information economies

Summary. In the context of differential information economies, with and without free disposal, we consider the concepts of Radner equilibrium, rational expectations equilibrium, private core, weak fine core and weak fine value. We look into the possible implementation of these concepts as perfect Bayesian or sequential equilibria of noncooperative dynamic formulations. We construct relevant game trees which indicate the sequence of decisions and the information sets, and explain the rules for calculating ex ante expected payoffs. The possibility of implementing an allocation is related to whether or not it is incentive compatible. Implementation through an exogenous third party or an endogenous intermediary is also considered. Received: November 19, 2001; revised version: April 17, 2002 RID="*" ID="*" This paper comes out of a visit by Nicholas Yannelis to City University, London, in December 2000. We are grateful to Dr A. Hadjiprocopis for his invaluable help with the implementation of Latex in a Unix environment. We also thank Leon Koutsougeras and a referee for several, helpful comments. Correspondence to: N.C. Yannelis     

Pareto efficient insurance contracts when the insurer's cost function is discontinuous

Summary. We consider the problem of efficient insurance contracts when the cost structure includes a fixed cost per claim. We prove existence of efficient insurance contracts and that the indemnity function in such contracts is non-decreasing in the damage. We further show that either there is no insurance, or the indemnity is positive for all losses, or efficient insurance contracts have a unique jump. We study variants of the model and provide a generalization to the case of non expected utilities. Our results are then applied to Townsend's model of deterministic auditing. Received: November 8, 2000; revised version: March 12, 2002 RID="*" ID="*" We are grateful to F. Salanié for pointing out an error in the previous version of the paper and for suggesting Proposition 6 to us. Correspondence to: R.-A. Dana     

Optimal design of pension funds: a mission impossible?

Summary. Nowadays many employers offer their employees the possibility of an insurance against too large losses in income when retiring or becoming disabled. This paper models the optimization problem of the employer when setting up such a so-called pension fund. Not surprisingly, it turns out that the optimal solution depends on the premium the employees are willing to pay at most for such an insurance. Since this is private information for an employee and hence not known to the employer, he needs to collect information regarding these maximum premiums. It is shown that if employees' characteristics only differ in the maximum premium they are willing to pay, the employer is unable to perfectly inform himself on these maximum premiums, i.e. he cannot create the right incentives for his employees to reveal their maximum premiums truthfully. Received: March 20, 2000; revised version: March 11, 2002 RID="*" ID="*" The authors acknowledge the helpful comments and suggestions of an anonymous referee. The research of J. Suijs is made possible by a fellowship of the Royal Netherlands Academy of Arts and Sciences (KNAW). Correspondence to: J. Suijs     

Medical insurance with rank-dependent utility

Summary. A well-known result in the medical insurance literature is that zero co-insurance is never second-best for insurance contracts subject to moral hazard. We replace the usual expected utility assumption with a version of the rank-dependent utility (RDU) model that has greater experimental support. When consumers exhibit such preferences, we show that zero co-insurance may in fact be optimal, especially for low-risk consumers. Indeed, it is even possible that the first-best and second-best contracts are identical. In this case, there is no “market failure”, despite the informational asymmetry. We argue that these RDU results are in better accord with the empirical evidence from US health insurance markets. Received: February 26, 2001; revised version: October 4, 2002 RID="*" ID="*"The authors would particularly like to thank Simon Grant, John Quiggin, Peter Wakker and an anonymous referee for valuable comments and suggestions on earlier drafts. The paper has also benefitted from the input of seminar audiences at The Australian National University, University of Auckland, University of Melbourne and University of Sydney. Ryan also gratefully acknowledges the financial support of the ARC, through Grant number A000000055. Correspondence to:R. Vaithianathan     

Information at equilibrium

Summary. In a game with rational expectations, individuals simultaneously refine their information with the information revealed by the strategies of other individuals. At a Nash equilibrium of a game with rational expectations, the information of individuals is essentially symmetric: the same profile of strategies is also an equilibrium of a game with symmetric information; and strategies are common knowledge. If each player has a veto act, which yields a minimum payoff that no other profile of strategies attains, then the veto profile is the only Nash equilibrium, and it is is an equilibrium with rational expectations and essentially symmetric information; which accounts for the impossibility of speculation. Received: June 20, 2001; revised version: January 9, 2002 RID="*" ID="*" We wish to thank Pierpaolo Battigalli, Fran?oise Forges, Franco Donzelli, Leonidas Koutsougeras, Aldo Rustichini, Rajiv Vohra and Nicholas Yannelis for their comments. Correspondence to: H. Polemarchakis     

On the geography of conventions

Summary. We study an evolutionary model in which heterogenous boundedly rational agents interact locally in order to play a coordination game. Agents differ in their mobility with mobile agents being able to relocate within a country. We find that mobile agents enjoy a higher payoff and always benefit from increased mobility, while immobile agents benefit from increased mobility at low levels of mobility only. This wedge in payoffs weakly increases as mobility increases. Some extensions are discussed. Received: January 10, 2001; revised version: December 4, 2002 RID="*" ID="*" We thank, without implicating in any way, George Mailath for helpful discussions. Some of the ideas in this paper were developed during the V Conference of the Society for the Advancement of Economic Theory in Ischia, Italy. The NSF provided financial support. Correspondence to: T. Temzelides     

Individual welfare,social deprivation and income taxation

Summary. In a homogeneous framework where individuals can only be distinguished on the basis of their incomes, we examine the incidence of taxation on the amount of deprivation felt in the society. We conceive deprivation in terms of utility or well-being rather than just in terms of income and we measure it by comparing the deprivation profiles arising in the different situations. We identify the restrictions to be imposed on the utility function which guarantee that a more progressive system of taxes always results in less social deprivation. We show that, in general, it is not possible to get an equivalence and realize a social improvement in terms of social deprivation by substituting a more progressive system of taxes for a less progressive one. Received: September 20, 1999; revised version: March 6, 2002 RID="*" ID="*" This paper forms part of the research programme of the TMR network Living Standards, Inequality and Taxation [Contract No. ERBFMRXCT 980248] of the European Communities whose financial support is gratefully acknowledged. Chakravarty wishes to express his sincere gratitude to the French Ministry of Education for financing his stay at DELTA during which this paper was written. The authors would like to thank Stephen Bazen, Nicolas Gravel and an anonymous referee, whose comments have helped to improve the paper, but they retain sole responsibility for remaining deficiencies. Correspondence to: P. Moyes     

Evolutionary foundations of aggregate-taking behavior

Summary. I show that aggregate-taking behavior is often evolutionarily stable for finite population in symmetric games in which payoff depends only on own strategy and an aggregate. I provide economic examples exhibiting this phenomenon. Received: August 27, 2001; revised version: January 29, 2002 RID="*" ID="*" The paper has profited from the comments of Maria Montero, Burkhard Hehenkamp, Wolfgang Leininger, and Dave Furth. Financial support from the DFG via Postgraduate Programme at the University of Dortmund and via SFB 504 at the University of Mannheim is acknowledged. RID="*" ID="*" Present address: University of Mannheim, SFB 504, L 13, 15, 68131 Mannheim, Germany (e-mail: possajen@sfb504.uni-mannheim.de)     

Domestic and international strategic interactions in environment policy formation

Summary. In this paper, we establish the most possilbe general formulation of the technology governing carbon-gas emission, giving rise to global external diseconomies, and ty to explore into the strategic interactions,both domestic and international, when an individual country decides on the environmental policies. Through the comparison among emission taxes, quotas, and standard in the perfectly competitive private economies, we find that the first two policies are equivalent but they are different in effects by virtue of what we may call the tax-exemption effect of emission standards. Such a difference in the policy effect further affects the other country's welfare through the global externalities, amplified through whether the government can precommit to either the emission tax or the emission standard. Received: January 16, 2001; revised version: April 16, 2002 RID="*" ID="*" The authors thank the valuable comments by an anonymous referee. Ministry of Education and Science for its financial support is also greatly acknowledged. Correspondence to:K. Kiyono     

A common trends model of UK core inflation

In this paper the long-run trend in RPI inflation (core inflation) for the UK over the 1961–1997 period is estimated within the framework of a multivariate common trends model which extends the bivariate VAR approach of Quah and Vahey (1995). In this context core inflation is directly linked to money and wage growth and interpreted as the long-run forecast of inflation from a small-scale, cointegrated macroeconomic system. First version received: September 1999/Final version received: October 2001 RID="*" ID="*"  We thank two anonymous referees for many helpful comments and suggestions. Work on this paper was partially conducted when C. Morana was at Heriot-Watt University.     

Candidate stability and nonbinary social choice

Summary. The requirement that a voting procedure be immune to the strategic withdrawal of a candidate for election can be formalized in different ways. Dutta, Jackson, and Le Breton (Econometrica, 2001) have recently shown that two formalizations of this candidate stability property are incompatible with some other desirable properties of voting procedures. This article shows that Grether and Plott's nonbinary generalization of Arrow's Theorem can be used to provide simple proofs of two of their impossibility theorems. Received: August 15, 2001; revised version: March 11, 2002 RID="*" ID="*" Parts of this article were previously circulated in somewhat different form in a working paper with the same title by the second author. We are grateful to Michel Le Breton and an anonymous referee for their comments. Correspondence to:J.A. Weymark     

Incentives in market games with asymmetric information: the core

Summary. This paper examines the ex ante core of a pure exchange economy with asymmetric information in which state-dependent allocations are required to satisfy incentive compatibility. This restriction on players' strategies in the cooperative game can be interpreted as incomplete contracts or partial commitment. An example is provided in which the incentive compatible core with nontransferable utility is empty; the game fails to be balanced because convex combinations of incentive compatible net trades can violate incentive compatibility. However, randomization of such strategies leads to ex post allocations which satisfy incentive compatibility and are feasible on average. Hence, convexity is preserved in such a model and the resulting cooperative games are balanced. In this framework, an incentive compatible core concept is defined for NTU games derived from economies with asymmetric information. The main result is nonemptiness of the incentive compatible core. Received: December 26, 2001; revised version: June 11, 2002 RID="*" ID"*" This work was financed, in part, by contract No 26 of the programme “P?le d'attraction interuniversitaire” of the Belgian government, and, in part, by research grant SBR93-09854 from the U.S. National Science Foundation. Much of my thinking about this topic was developed during a wonderful visit to CORE for the 1991–1992 academic year (on sabbatical from the University of Pennsylvania). This paper was originally circulated in December 1991 as CARESS Working Paper #91-38, Center for Analytic Research in Economics and the Social Sciences, Department of Economics, University of Pennsylvania and in February 1992 as CORE Discussion Paper 9221, Center for Operations Research and Econometrics, Université Catholique de Louvain, Louvain-la-Neuve, Belgium. RID="*" ID="*" At the very start of my research, Jean-Fran?ois Mertens was almost a co-author. Fran?ois Forges provided detailed comments at a later stage, during my visit to THEMA, Université Cergy-Pontoise, in Spring 1997. They are entitled to the customary disclaimer.     

Estimating the stationary distribution of a Markov chain

Summary. Let be a Markov chain with a unique stationary distribution . Let h be a bounded measurable function. Write and . This paper explores conditions for the consistency and asymptotic normality of the estimate of of assuming the existence of a solution to the Poisson equation . Our framework covers the case of nonirreducible Markov chains arising in many growth models in economics. Received: October 8, 2001; revised version: April 8, 2002 RID="*" ID="*" Thanks are due to Professors Rabi Bhattacharya, Nicholas Kiefer and Timothy Vogelsang on an earlier draft for helpful conversations, and a referee for insightful comments. Correspondence to: M.Majumdar     

Evolutionary economics and the counterfactual threat: on the nature and role of counterfactual history as an empirical tool in economics

Counterfactual conditional statements are ubiquitous in any scientific endeavour. This paper contains an analysis of the nature of counterfactual conditionals and the conditions under which they are considered assertable by scientists. The paper then applies this analysis to the use of counterfactuals in evolutionary economics, arguing that because evolutionary economics is inherently concerned with historical processes it cannot avoid the use of counterfactual history as one of its tools of empirical analysis. We discuss the strengths and pitfalls of counterfactual history. We argue that because evolutionary economics starts from the foundation that randomness may be inherent in any economic system, the very aspects of evolutionary economics that make counterfactual history a desirable empirical tool also make that tool difficult to employ. RID="*" ID="*" We thank the participants of the International Seminar on Evolutionary Economics as a Research Programme in Stockholm, May 1997, for many helpful comments. We also thank Lorri Baier for many helpful substantive and textual comments. Correspondence to: R. Cowan     

Estimating a mixture of stochastic frontier regression models via the em algorithm: A multiproduct cost function application

Researchers have become increasingly interested in estimating mixtures of stochastic frontiers. Mester (1993), Caudill (1993), and Polachek and Yoon (1987), for example, estimate stochastic frontier models for different regimes, assuming sample separation information is given. Building on earlier work by Lee and Porter (1984), Douglas, Conway, and Ferrier (1995) estimate a stochastic frontier switching regression model in the presence of noisy sample separation information. The purpose of this paper is to extend earlier work by estimating a mixture of stochastic frontiers assuming no sample separation information. This case is more likely to occur in practice than even noisy sample separation information. In order to estimate a mixture of stochastic frontiers with no sample separation information, an EM algorithm to obtain maximum likelihood estimates is developed. The algorithm is used to estimate a mixture of stochastic (cost) frontiers using data on U.S. savings and loans for the years 1986, 1987, and 1988. Statistical evidence is found supporting the existence of a mixture of stochastic frontiers. First version received: 3/13/01/Final version received: 6/17/02 RID="*" ID="*"  I am grateful to Ram Acharya, Janice Caudill, and especially James R. Barth for several helpful comments on an earlier version of the paper. During the revision process I benefitted greatly from the suggestions of the Associate Editor and three anonymous referees.     

The economic effects of restrictions on government budget deficits: imperfect private credit markets

Summary. The present paper is an extension of Ghiglino and Shell [7] to the case of imperfect consumer credit markets. We show that with constraints on individual credit and only anonymous (i.e., non-personalized) lump-sum taxes, strong (or “global”) irrelevance of government budget deficits is not possible, and weak (or “local”) irrelevance can hold only in very special situations. This is in sharp contrast to the result for perfect credit markets. With credit constraints and anonymous consumption taxes, weak irrelevance holds if the number of tax instruments is sufficiently large and at least one consumer's credit constraint is not binding. This is an extension of the result for perfect credit markets. Received: August 28, 2001; revised version: March 25, 2002 RID="*" ID="*" We thank Todd Keister, Bruce Smith, and two referees for helpful comments. Correspondence to: C. Ghiglino     

Dictatorial domains

Summary. In this paper, we introduce the notion of a linked domain and prove that a non-manipulable social choice function defined on such a domain must be dictatorial. This result not only generalizes the Gibbard-Satterthwaite Theorem but also demonstrates that the equivalence between dictatorship and non-manipulability is far more robust than suggested by that theorem. We provide an application of this result in a particular model of voting. We also provide a necessary condition for a domain to be dictatorial and use it to characterize dictatorial domains in the cases where the number of alternatives is three. Received: July 12, 2000; revised version: March 21, 2002 RID="*" ID="*" The authors would like to thank two anonymous referees for their detailed comments. Correspondence to: A. Sen