Mechanism design for general screening problems with moral hazard

Summary We study the problem faced by an incomplete information monopolist seeking to design a line of contracts so as to simultaneously screen consumers by type and resolve the moral hazard problems associated with contract performance. We formulate the monopolist's problem as a mechanism design problem in which the set of consumer types is taken to be a Polish space, and the contract space an arbitrary compact metric space. Allowing for risk aversion on the part of the monopolist and consumers, and taking as the feasible set of mechanisms the collection of all measurable functions defined on the space of consumer types with values in the space of contracts, we present a new characterization of incentive compatibility in an infinite dimensional setting which allows us to reformulate the monopolist's design problem as an unconstrained optimization problem (i.e., as a problem without the incentive compatibility contraints). Using simple techniques, we then demonstrate the existence of an optimal screening mechanism for the monopolist. We thus extend the existing analysis of the incomplete information monopoly problem to an infinite dimensional setting with moral hazard, and we provide an existence result not available in the existing literature.I thank seminar participants at Indiana University, McGill University, and the University of Calgary for helpful comments. I also thank Kerry Back, Bob Becker, Praveen Kumar, Mark Johnson, Ramon Marimon, Murat Sertel, Bill Sealey, Gordon Sick, and Nicholas Yannelis for helpful comments. The comments and suggestions of an anonymous referee are especially appreciated. I am solely responsible for any errors.     

Mixed-strategy equilibria and strong purification for games with private and public information

This paper shows the existence of mixed-strategy equilibria for games with private and public information under general conditions. Under the additional assumptions of finiteness of action spaces and diffuseness and conditional independence of private information, a strong purification result is obtained for the mixed strategies in such games. As a corollary, the existence of pure-strategy equilibria follows. I am very grateful to Yeneng Sun, Nicholas C. Yannelis and M. Ali Khan for helpful discussions and suggestions. I also wish to thank an anonymous referee whose comments led to many improvements in the paper.     

Resolving distributional conflicts between generations

Summary. We describe a new approach to the problem of resolving distributional conflicts between an infinite and countable number of generations. We impose conditions on the social preferences that capture the following idea: If preference (or indifference) holds between truncated paths for infinitely many truncating times, then preference (or indifference) holds also between the untruncated infinite paths. In this framework we use such conditions to (1) characterize different versions of leximin and utilitarianism by means of equity conditions well-known from the finite setting, and (2) illustrate the problem of combining Strong Pareto and impartiality in an intergenerational setting.Received: 8 May 2002, Revised: 12 June 2003, JEL Classification Numbers: D63, Q01.Correspondence to: Geir B. AsheimWe thank Kaushik Basu, Marc Fleurbaey, David Miller, Tapan Mitra, Lars-Gunnar Svensson, and an anonymous referee for helpful comments. Asheim gratefully acknowledges the hospitality of the Stanford University research initiative on the Environment, the Economy and Sustainable Welfare, and financial support from the Hewlett Foundation through this research initiative.     

Second price auctions on general preference domains: two characterizations

Auction theory usually assumes the quasi-linearity of individual preferences. We drop this assumption and define an extension of second price mechanisms that applies to general preferences. It turns out that the extended second price mechanisms are the only rules satisfying efficiency, strategy-proofness, and a mild non-imposition property. Their definition is simple just as much as the definition of usual second price mechanisms: everyone reports his maximum willingness to pay and the bidder whose reported value is highest buys the auctioned object for the price equal to the second highest reported value. The characterization is valid if efficiency is replaced by envy-freeness. I gratefully acknowledge an associate editor and two anonymous referees for their very helpful comments. Hiroki Saitoh and Shigehiro Serizawa independently obtain a result that is closely related to my main result (see, Remark in Sect. 1). I thank them for sending me the paper and communication, and Yuji Fujinaka for informing me about their work. I also thank the financial support by KAKENHI (19310031).     

Non-stationary,stable Markov processes on a continuous state space

We extend our previous result on simple stable Markov (SSM) processes to the case where the state space is continuous. As anapplication we show the existence of a competitive general equilibrium of a cobweb model where price volatility is generated both by exogenous shocks and by stochastic, so called generating variables (that may be interpreted as sunspots) that govern the correlation of the rational beliefs of individual agents. I would like to thank Danish Social Science Foundation, The Carlsberg Foundation, Stanford Institute for Theoretical Economics (SITE) and Universita Cattolica for financial help. I would also like to thank Trinidad Casasus, Mordecai Kurz, an anonymous referee as well as participants at SITE, ESAM (2004) and ESEM (2004) for helpful discussions and comments. Peter Harremoes provided me with an illuminating counter example and Hiro Nakata provided many comments that helped improve the exposition of the paper. Part of this work is from a paper previously circulated under the title: “Sunspot rational belief structures: anonymity and endogenous uncertainty”.     

Bayesian estimation of duration models: An application of the multiperiod probit model

The multiperiod probit model is presented and Bayesian estimation using the Gibbs sampler with data augmentation is described. As an empirical illustration, the multiperiod probit model is then used to estimate a duration model using employment duration data for the Canadian province of New Brunswick. Bayesian estimation with unobserved heterogeneity is shown to be a simple extension of estimation of a duration model with no unobserved heterogeneity. More importantly, perhaps, some numerical problems encountered by other authors using Maximum Likelihood are avoided.I would like to thank M. Baker, G. Koop, A. Melino and D. Poirier for helpful comments and discussions. I would also like to thank M. Baker for providing his data.     

An efficiency characterization of plurality social choice on simple preference domains

Summary. We consider a model of social choice dealing with the problem of choosing a subset from a set of objects (e.g. candidate selection, membership, and qualification problems). Agents have trichotomous preferences for which objects are partitioned into three indifference classes, goods, bads, and nulls, or dichotomous preferences for which each object is either a good or a bad. We characterize plurality-like social choice rules on the basis of the three main axioms, known as Pareto efficiency, anonymity, and independence.Received: 29 August 2003, Revised: 3 June 2004, JEL Classification Numbers: D70, D71, D72.Biung-Ghi Ju: I am grateful to William Thomson and Jianbo Zhang for their helpful comments and discussions. I also thank Brandon Dupont, the participants in seminars at Iowa State University, University of Kansas, and the Midwest Theory Meeting at University of Notre Dame. I thank an anonymous referee for detailed comments and suggestions that were very helpful in simplifying the proof of Theorem 1 and in revising the paper.     

Existence,uniqueness, and stability of equilibrium in an OLG economy

Summary. This paper presents sufficient conditions for the existence of a unique and globally stable steady state equilibrium for OLG economies with production. The conditions impose separate requirements on the utility and production functions. Moreover, the conditions do not require assumptions concerning the third order derivatives of the production and utility functions.Received: 12 August 2002, Revised: 7 January 2003, JEL Classification Numbers: D50, D91, E13, O41.I would like to thank Nick Baigent, Laurie Conway, Karl Farmer, Christian Gehrke, and Hideo Konishi for helpful comments. I am grateful to an anonymous referee for his or her comments.     

An empirical note about additive outliers and nonstationarity in Latin-American inflation series

This note shows the empirical dangers of the presence of large additive outliers when testing for unit roots using standard unit root statistics. Using recent proposed procedures applied to four Latin-American inflation series, I show that the unit root hypothesis cannot be rejected.Jel classification: C2, C3, C5I want to thank Pierre Perron for useful comments on a preliminary version of this paper. Helpful comments from an anonymous referee, and Yiagadeesen Samy are appreciated. I thank the Editor Baldev Raj for useful comments about the final structure of this paper. Finally, I also thank André Lucas for helpful suggestions concerning the use of his nice computer program Robust Inference Plus Estimation (RIPE).First revision received: August 2001/Final revision received: December 2002     

The convergence of equilibrium strategies of approximating signaling games

Summary For a class of infinite signaling games, the perfect Bayesian equilibrium strategies of finite approximating games converge to equilibrium strategies of the infinite game. This proves the existence of perfect Bayesian equilibrium for that class of games. It is well known that in general, equilibria may not exist in infinite signaling games.I am very grateful to Karl Iorio with whom I derived most of the results in this paper. I am solely responsible for any remaining errors. I am also grateful to Robert Anderson, Debra Aron, Eddie Dekel, Raymond Deneckere, Michael Kirscheneiter, Steven Matthews, Roger Myerson, Daniel Vincent and Robert Weber for comments on previous drafts of this paper.     

On the impossibility of an envy-free Paretian liberal

This paper examines a close parallel between the theory of fairness and Harel and Nitzan's original definition of non-exchangeable rights system. Several independent definitions of fair rights assignment are proposed, and some new impossibility as well as possibility results are established.For helpful discussions I would like to thank Rajat Deb, Shlomo Weber and Hans Wiesmeth. I am also indebted to two anonymous referees of thisJournal for their valuable comments.     

Non-cooperative games with a continuum of players whose payoffs depend on summary statistics

Summary. We consider static non-cooperative games with a continuum of small players whose payoffs depend on their own actions and finitely many summary statistics of the aggregate strategy profile. We prove the existence of an equilibrium in pure strategies without any convexity restrictions on payoffs or the common action space. We show that this result applies to a broad class of monopolistic competition models. Received: April 13, 2001; revised version: December 18, 2001 RID="*" ID="*" The result in this paper generalizes a result in my PhD dissertation supervised by M. Ali Khan and Joe Harrington. I thank them for support and encouragement. I also thank Sung Kim, Bruce Nanney, Ashvin Rajan, Kali Rath, and an anonymous referee for comments. The usual disclaimer applies.     

A theorem on open coverings of a simplex and Scarf's core existence theorem through Brouwer's fixed point theorem

Summary This paper provides simple proofs of a theorem on open coverings of a simplex and Scarf's core existence theorem through Brouwer's fixed point theorem.I want to thank Daniel Abrams, Yakar Kannai, Herbert Scarf, Nicholas Yannelis, Jingang Zhao, and an anonymous referee for their helpful comments. I also gratefully acknowledge the financial support from the Alfred P. Sloan Foundation.     

Strong monotonicity in surplus sharing

Summary. We consider three new axioms for surplus sharing problems. The first is strong monotonicity which says that workers should be rewarded for increases in productivity and the second says that productive workers should receive some compensation. The third requires that the surplus sharing rule should be well defined (and continuous on) the set of threshold functions. We show that none of the standard "equitable" mechanisms satisfy any of these axioms and then present a constructive characterization of mechanisms which do. Using this we construct several new mechanisms. These are the Almost Flat mechanism, the Spread Aumann-Shapley mechanism, and the Spread Serial mechanism, which have many desirable properties.Received: 15 September 2002, Revised: 11 March 2003, JEL Classification Numbers: C71, H4.I would like to thank Hervé Moulin, Rich Mclean, Yves Sprumont and an anonymous referee for helpful comments.     

The structure of authority, federalism, commitment and economic growth

Summary. In a neoclassical growth model with many regions and a mobile factor, two federal arrangements are considered. In the first federal arrangement the central government chooses a uniform tax policy, whereas in the second each regional government chooses its own tax policy. The main result is that the first federal arrangement leads to high tax rates and economic stagnation, whereas the second leads to low tax rates and economic growth. This result stems from a time consistency problem. The lack of tax competition forces a time consistency problem on the central government under the first federal arrangement. In contrast, regional tax competition acts as a commitment device under the second federal arrangement. The fundamental feature in the environment that gives rise to different abilities of the state to commit is the different structure of authority within the state.Received: 10 February 2003, Revised: 2 December 2003, JEL Classification Numbers: H77, O41, E60, C73, E13.Ronald A. Edwards: This is a revision of Chapter 3 of my University of Minnesota Ph.D. I thank my advisor Edward C. Prescott for his encouragement and numerous helpful discussions. I also thank Tim Kehoe for many useful discussions as well as Beth Allen, Berthold Herrendorf, Arilton Teixeira and two anonymous referees for helpful comments. This research was assisted by an International Predissertation Fellowship from the Social Science Research Council and the American Council of Learned Societies with funds provided by the Ford Foundation.     

Existence of a continuous utility function with path monotonicity: the Wold approach

Summary This paper uses the approach of Wold to prove the existence of a continuous utility function on a subset ofR ⁿ with a path monotonicity assumption. This result is then extended to a Banach space.The research for this paper was begun while visiting the University of Cambridge and the London School of Economics in 1988. I should like to thank Dr. A. Beardon, Professor M. Desai, Professor L. Foldes and Dr. A. Horsley for their hospitality. Also, I am grateful to an anonymous referee for comments that led to an improvement in the exposition.     

Sequential capacity and price choices in a duopoly model with demand uncertainty

The paper is a revised version of chapter V of my thesis (Hviid, 1987). I would like to thank Huw Dixon, Clive Fraser, Birgit Grodal, Norman Ireland, Michael Teit Nielsen, Kevin Roberts, Peter Skott, and Bente Villadsen for helpful comments and discussion, and a referee for helpful suggestions. An earlier version was presented at the Universities of Aarhus, Copenhagen, Essex and Warwick. I am grateful to participants for many helpful suggestions and comments. The usual disclaimer applies. Financial support from The Danish Social Science Research Council is gratefully acknowledged.     

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     

The stability of generalised stackelberg equilibria in heterogeneous oligopoly

Conclusions In this paper we have derived sufficient conditions for the stability of the G. S. E. These conditions follow from the condition on the stability of the G. C. E., given by Okuguchi (1978).When the conditions for asymptotic stability are fulfilled, the existence of the G. S. E. may be demonstrated in the same way as the existence of the G. C. E. has been demonstrated by Okuguchi (1978), that is: the G. S. E. is the fixpoint of a contracting mapping. In the case of linear demand functions and quadratic cost functions we have found the rather strong result that the sufficient conditions for (asymptotic) stability of the G. C. E. imply the (asymptotic) stability of the G. S. E. as well.This conclusion may be surprising to followers of Stackelberg. Mostly the outcome of a Stackelberg oligopoly is considered as adisequilibrium.In this paper we have made clear that a firm maximizing expected profit and using a generalised Stackelberg strategy, like a firm using a generalised Cournot strategy, only correctly predicts inequilibrium the price of the other firms. (See also on this point Heertje and Furth (1979)).When the outcome of a G. S. E. gives one or more firms less profit than in a G. C. E. then they expect, any price change, under-taken by them, will lower their expected profit even more.I would like to thank Prof. Dr. A. Heertje and an anonymous referee for their useful comments on earlier drafts of this paper and D. Weatherall for his remarks on the english of the text.     

Patent Policy in an Endogenous Growth Model

We investigate how the patent policy affects economic growth and social welfare based on an endogenous growth model with R&D activities. We show that the patent length that maximizes the social welfare is finite. Moreover, by introducing compulsory licensing, we also show that the patent length that maximizes the social welfare is not infinite even if the royalty rate can be controlled. Received June 29, 2001; revised version received February 5, 2002 Published online: February 17, 2003 We wish to thank two anonymous referees for their constructive comments. We also thank Akira Yakita for his helpful comments.