Type interaction models and the rule of six

In this paper, I describe and analyze a class of type interaction models. In these models, an infinite population of agents with discrete types interact in groups of fixed size and possibly change their types as a function of those interactions. I then derive conditions for these models to produce multiple equilibria. These conditions demonstrate a trade off between the number of types and the size of the interacting groups. For deterministic interaction rules, I derive the rule of six: the number of agent types plus the group size must be at least six in order to support multiple equilibria given a spanning assumption.Troy Tassier provided help with early versions of this model. Ken Arrow, Bob Axelrod, Larry Blume, Steven Durlauf, David Harris, John Holland, Lu Hong, Mercedes Pascual, Rick Riolo, and Carl Simon provided input on earlier drafts of this research. Financial support from the National Science Foundation, the James S. McDonnell Foundation and the John D. and Catherine T. MacArthur Foundation is gratefully acknowledged.     

Ranking investment projects

Summary. This paper describes conditions under which one investment project dominates a second project in terms of net present value, irrespective of the choice of the discount rate. The resulting partial ordering of projects has certain similarities to stochastic dominance. However, the structure of the net present value function leads to characterizations that are quite specific to this context. Our theorems use Bernstein's (1915) innovative results on the representation and approximation of polynomials, as well as other general results from the theory of equations, to characterize the partial ordering. We also show how the ranking is altered when the range of discount rates is limited or the rate varies period by period. Received: January 5, 2002; revised version: October 29, 2002 RID="*" ID="*" We thank Robert Driskill, Andrea Maneschi, Roy Radner, and participants of seminars at NYU, Notre Dame, Purdue, and Washington University for helpful comments. The present version of the paper has benefited from comments by a referee and the editor. Foster is grateful for support from the John D. and Catherine T. MacArthur Foundation through its network on Inequality and Poverty in Broader Perspective. Correspondence to: T. Mitra     

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.     

Revealed stochastic preference: a synthesis

Summary. The problem of revealed stochastic preference is whether probability distributions of observed choices in a population for various choice situations are consistent with a hypothesis of maximization of preference preorders by members of the population. This is a population analog of the classical revealed preference problem in economic consumer theory. This paper synthesizes the solutions to this problem that have been obtained by Marcel K. Richter and the author, and by J. C. Falmagne, in the case of finite sets of alternatives, and utilizes unpublished research of Richter and the author to give results for the non-finite choice sets encountered in economic consumer theory.Received: 13 March 2003, Revised: 11 February 2004, JEL Classification Numbers: D1, C6.The preparation of this paper was supported by the E. Morris Cox endowment at the University of California, Berkeley. I am indebted to Robert Anderson, Salvador Barbara, Werner Hildenbrand, Rosa L. Matzkin, and Aviv Nevo for useful suggestions and comments. I am especially indebted to Marcel K. Richter, who was the source of many of the ideas and arguments contained in this paper.     

Nonlinear models with panel data

Panel data play an important role in empirical economics. With panel data one can answer questions about microeconomic dynamic behavior that could not be answered with cross sectional data. Panel data techniques are also useful for analyzing cross sectional data with grouping. This paper discusses some issues related to specification and estimation of nonlinear models using panel data.JEL Classification: C230The research behind this paper was supported by the National Science Foundation, the Gregory C. Chow Econometric Research Program at Princeton University, and Danish National Research Foundation (through CAM at the University of Copenhagen). The author thanks Ekaterini Kyriazidou, Hong Li, Marina Sallustro, and the editors for helpful suggestions.     

Candidate stability and probabilistic voting procedures

Summary. We extend the analysis of Dutta, Jackson and Le Breton (Econometrica, 2001) on strategic candidacy to probabilistic environments. For each agenda and each profile of voters preferences over running candidates, a probabilistic voting procedure selects a lottery on the set of running candidates. Assuming that candidates cannot vote, we show that random dictatorships are the only unanimous probabilistic voting procedures that never provide unilateral incentives for the candidates to withdraw their candidacy at any set of potential candidates. More flexible probabilistic voting procedures can be devised if we restrict our attention to the stability of specific sets of potential candidates.Received: 4 February 2003, Revised: 14 September 2004, JEL Classification Numbers: D71, D72.This is a revised version of a chapter of my Ph.D. Dissertation submitted to the Universitat Autónoma de Barcelona. I am indebted to my supervisor Salvador Barberá for his advice and constant support. I am grateful to Dolors Berga and an anonymous referee for their detailed comments and suggestions. I thank José Alcalde, Walter Bossert, Bhaskar Dutta, Lars Ehlers, Jordi Massó, Diego Moreno, Clara Ponsatí, Yves Sprumont, and William Thomson for many helpful comments and discussions. I thank the hospitality of the C.R.D.E. at the Université de Montréal and the Department of Economics of the University of Warwick where parts of this research were conducted. Financial support through Research Grant 1998FI00022 from Comissionat per Universitats i Recerca, Generalitat de Catalunya, Research Project PB98-870 from the Ministerio de Ciencia y Tecnología, and Fundación Barrié de la Maza is gratefully acknowledged.     

Stable partitions in a model with group-dependent feasible sets

Summary. In this paper we consider a model of group formation where group of individuals may have different feasible sets. We focus on two polar cases, increasing returns, when the set of feasible alternatives increases if a new member joins the group, and decreasing returns, when a new member has an opposite effect and reduces the number of alternatives available for the enlarged group. We examine two notions, stability and strong stability of group structures, that correspond to Nash and Strong Nash equilibrium of the associated non-cooperative game, and identify the classes of stable and strongly stable environments.Received: 29 June 2003, Revised: 17 February 2004, JEL Classification Numbers: C71, C72, D62, D71.The previos version of this paper has been written while the second author was visiting the Technical University of Dresden. He wishes to thank the Alexander von Humboldt Foundation for its generous support and the Technical University of Dresden for its hospitality. The authors are grateful to an anonymous referee for useful comments.     

Federal Stability in Unequal Societies

The stability of federal systems is a thorny issue. Several scholars have attempted to come to grips with this problem and have proposed mechanisms or institutions which may contribute to the stabilization of federal systems. In many instances, however, the underlying mechanisms and micro-foundations are poorly specified. In this paper I build upon existing models dealing with decentralization and secession to incorporate unequal income distributions and externalities of public goods. Based on this some insights may be derived on the appropriate mechanisms to foster federal stability. JEL Classification: H77, H41, C72 This paper partly draws on research funded by the Swiss National Science Foundation (Grant No. 5004-0487882/1). An earlier version entitled ‘‘Federalism and the Size of Nations’’ was presented at the conference ‘‘Micro-Foundations of Federal Institutional Stability’’ at Duke University (Durham, April 30–May 1, 2004). Comments by participants at this conference and greatly appreciated. First version: March 2004, this version: November 1, 2004     

Two-sided altruism, Lindahl equilibrium, and Pareto optimality in overlapping generations models

Summary. This paper extends the Samuelsonian overlapping generations general equilibrium framework to encompass a variety of altruistic preferences by recasting it into a Lindahl equilibrium framework. The First and the Second Welfare theorems hold for Lindahl equilibrium with respect to the Malinvaud optimality criterion but not with respect to the Pareto optimality criterion. A complete characterization of Pareto optimal allocations is provided using the Lindahl equilibrium prices.Received: 2 October 2003, Revised: 13 September 2004, JEL Classification Numbers: D51, D62, D64, C62.An earlier draft of the paper was prepared for presentation at the Sixth World Congress of the Econometric Society, 1990, Barcelona, Spain. Much of this work was done when I was at Yale University and University of California-San Diego. I am grateful to an anonymous referee of this journal and to Don Brown, Vince Crawford and Joel Sobel for many insightful comments and encouragements on an earlier draft of the paper.     

Computing equilibria in finance economies with incomplete markets and transaction costs

Summary. Transaction costs on financial markets may have important consequences for volumes of trade, asset pricing, and welfare. This paper introduces an algorithm for the computation of equilibria in the general equilibrium model with incomplete asset markets and transaction costs. We show that economies with transaction costs can be analyzed with differentiable homotopy techniques and thus in the same framework as frictionless economies despite the existence of non-differentiabilities of agents asset demand functions and the existence of locally non-unique equilibria. We introduce an equilibrium selection concept into the computation of economic equilibria that picks out a specific equilibrium in the presence of a continuum of equilibria.Received: 2 December 2002, Revised: 15 November 2004, JEL Classification Numbers: C61, C62, C63, C68, D52, D58, G11, G12. Correspondence to: P. Jean-Jacques HeringsThis research started when Jean-Jacques Herings enjoyed the generous hospitality of the Cowles Foundation for Research in Economics at Yale University. His research has been made possible by a fellowship of the Royal Netherlands Academy of Arts and Sciences and a grant of the Netherlands Organisation for Scientific Research. We thank audiences at Stanford University, UC San Diego, and Venice for discussions on the subject. We are very grateful to an anonymous referee for very helpful comments on an earlier draft.     

Is assortative matching efficient?

Summary. This paper develops some general conditions under which complementarities between individual agents imply that assortative matching is efficient. Our analysis has four main findings. First, when agents are organized into equal-sized groups, just as in Becker (1973), the presence of within-group complementarities is sufficient for stratification to be efficient. Second, if group sizes vary, assortative matching may not be efficient even though complementarities are present, unless particular functional form assumptions are imposed. Third, the connection between assortative matching, complementarities and efficiency reemerges if one considers sequences of replications of the economy in which individual coalitions are uniformly bounded in size. Fourth, the presence of feedbacks from the composition of group memberships has important effects on efficient allocations and breaks any simple link between assortative matching and efficiency. Together, these results suggest that the characterization of the cross-section evolution of an efficiently sorted economy is likely to be highly complex. Received: September 25, 2001; revised version: February 26, 2002 RID="*" ID="*" We thank William Brock for many helpful conversations and Scott Page for detailed comments on an earlier draft of this paper. The National Science Foundation, John D. and Catherine T. MacArthur Foundation and Center for Urban Land Economic Research have generously provided financial support. Correspondence to: S. N. Durlauf     

Identification of consumers’ preferences when their choices are unobservable

Summary. We provide conditions under which the heterogenous, deterministic preferences of consumers in a pure exchange economy can be identified from the equilibrium manifold of the economy. We extend those conditions to consider exchange economies, with two commodities, where consumers preferences are random. For the latter, we provide conditions under which consumers heterogenous random preferences can be identified from the joint distribution of equilibrium prices and endowments. The results can be applied to infer consumers preferences when their demands are unobservable.Received: 8 May 2003, Revised: 14 September 2004, JEL Classification Numbers: D12, D51.I am very grateful to an anonymous referee, Donald Brown, and Daniel McFadden for their detailed comments and insightful suggestions. Section 2 of this paper is joint work with Donald J. Brown; it is included here for publication with his permission. Those results were presented at the 1990 Workshop on Mathematical Economics at the University of Bonn, the 1992 SITE Workshop on Empirical Implications of General Equilibrium Models at Stanford University, and, more recently, at the June 2000 Conference in Honor of Rolf Mantel, in Buenos Aires, Argentina. The comments of the participants at those conferences and workshops are much appreciated. The research presented in this paper was supported by NSF Grants SES-8900291, SBR-9410182, and SES-0241858. This paper is dedicated to Marcel K. Richter, who has inspired much of my research.     

The structure of the Nash equilibrium sets of standard 2-player games

Summary. In this paper I study a class of two-player games, in which both players action sets are [0,1] and their payoff functions are continuous in joint actions and quasi-concave in own actions. I show that a no-improper-crossing condition is both necessary and sufficient for a finite subset A of to be the set of Nash equilibria of such a game.Received: 21 November 2002, Revised: 9 September 2004, JEL Classification Numbers: C65, C72.I am grateful to an editor of the journal and an anonymous referee for their very helpful comments. I also would like to thank the seminar participants at City University of Hong Kong, Georgia State University, Northwestern University, and Rice University.     

On the definition of differentiated products in the real world

Summary. This paper proposes an abstract model of commodity differentiation that incorporates manufacturing imprecision and dimensioning and tolerancing standards. The potential consistency of such a model based on engineering consideration is analyzed. For a large pure exchange economy, competitive equilibria exist and are Pareto optimal. Production issues such as the derived demand for intermediate products, continuity of cost functions, and product selection and technology issues such as mass customization, agile manufacturing, and manufacturability are discussed.Received: 21 June 2003, Revised: 1 March 2004, JEL Classification Numbers: D51, L15, D21.This work was supported by the National Science Foundation through research grants DMI-9816144 and DMI-0070257. This paper was presented at the Institute of Economics, University of Copenhagen in Fall 2000. As always, Birgit Grodal was an energetic and enthusiastic academic host during my month-long visit. I wish to thank Marcus Berliant for a long, pleasant, and helpful conversation. An anonymous referee read the paper carefully and provided helpful comments.     

Nash implementing non-monotonic social choice rules by awards

Summary. By a slight generalization of the definition of implementation (called implementation by awards), Maskin monotonicity is no more needed for Nash implementation. In fact, a weaker condition, to which we refer as almost monotonicity is both necessary and sufficient for social choice correspondences to be Nash implementable by awards. Hence our framework paves the way to the Nash implementation of social choice rules which otherwise fail to be Nash implementable. In particular, the Pareto social choice rule, the majority rule and the strong core are almost monotonic (hence Nash implementable by awards) while they are not Maskin monotonic (hence fail to be Nash implementable in the standard framework).Received: 12 April 2004, Revised: 18 March 2005, JEL Classification Numbers: D 79.I thank François Maniquet, Efe Ok and Ipek Ozkal-Sanver for their valuable contributions. The paper is part of a project on Electoral System Design supported by Bilgi University Research Fund.     

The Sun Also Rises: Productivity Convergence Between Japan and the USA

The growth process for a technological leader is different from that of a follower. While followers can grow through imitation and capital deepening, a leader must undertake original research. This suggests that as the gap between the leader and the follower narrows, the follower must undertake more genuinely innovative R&D and possibly face a slower overall growth rate. The results of a dynamic panel equilibrium-correction model of productivity growth suggest that the productivity gap with the USA had a strong effect on the growth of Japanese manufacturing, and that changes in R&D intensity also made a significant contribution. Moreover, the effect of the productivity gap was significantly higher in industries that had higher R&D intensities, higher levels of human capital, and were more open to exports. This paper is based upon Chapter 5 of my D.Phil. thesis at the University of Oxford. It was partly written while I was a Visiting Scholar at the Foundation for Advanced Information & Research, Tokyo, and was supported by a Sanwa Bank Foundation Research Fellowship and ESRC grants R000234954 and R000237500.     

The micro-foundations of intertemporal price discrimination

Summary. This paper investigates the optimality of intertemporal price discrimination for a durable-good monopoly in a model where infinitely-lived households face an intertemporal budget constraint, and consume both durable goods and non-durable goods. We prove that the optimal price of the durable good is not constant, and may decrease or increase over time. Some households may choose to purchase the durable good at a later date, and pay lower or higher prices, since the gain in discounted utility of consuming more of the non-durable good more than compensates for the loss in utility from delaying the consumption of the durable good.Received: 12 March 2004, Revised: 7 January 2005, JEL Classification Numbers: D40, D42, D91.I would like to thank C.D. Aliprantis, the Editor, and an anonymous referee for their generous advice, and constructive comments and suggestions. I have also enjoyed discussions with John Quah on the subject. Research support from the Wharton-SMU Research Centre, Singapore Management University, is gratefully acknowledged.     

Dynamic costly state verification

Summary. I study a model of dynamic risk sharing with costly state verification (CSV). In the model, a risk neutral agent enters an infinitely repeated relationship with a risk averse agent. In each period, the risk averse agent receives a random income which is observed only by himself, unless the risk neutral agent engages in costly monitoring. I provide a set of characterizations for the optimal contract, and I show that CSV has interesting effects on the long run distribution of the agents expected utilities.Received: 19 February 2003, Revised: 11 February 2004, JEL Classification Numbers: D8.This research was initially joint work with Bruce Smith. I thank Bruce for the inspiration. I thank Fernando Alvarez, Narayana Kocherlakota, Steve Spear, and an anonymous referee for helpful comments. I also thank seminar participants at Carnegie Mellon University, Federal Reserve Banks of Minneapolis, Federal Reserve bank of Richmond, Duke University, SUNY Buffalo, University of Rochester, University of Pittsburgh, University of Western Ontario, the 1998 Econometric Society winter meeting, the 1999 SED meeting, and the 1999 SITE workshop at Stanford University for discussions.     

A short proof of the Bulow-Klemperer auctions vs. negotiations result

Summary. Bulow and Klemperer [1] have provided an upper bound on the value of bargaining power for a seller of an indivisible object. Specifically, negotiating optimally with N buyers yields lower revenue than an English auction with N + 1 buyers. In this paper, a short and intuitive proof of this result is presented.Received: 2 August 2004, Revised: 6 December 2004, JEL Classification Numbers: C78, D44, D82.I would like to thank Per B. Overgaard and an anonymous referee for many valuable comments.