Supporting weakly Pareto optimal allocations in infinite dimensional nonconvex economies

In this paper, we prove a new version of the Second Welfare Theorem for economies with a finite number of agents and an infinite number of commodities, when the preference correspondences are not convex-valued and/or when the total production set is not convex. For this kind of nonconvex economies, a recent result, obtained by one of the authors, introduces conditions which, when applied to the convex case, give for Banach commodity spaces the well-known result of decentralization by continuous prices of Pareto-optimal allocations under an interiority condition. In this paper, in order to prove a different version of the Second Welfare Theorem, we reinforce the conditions on the commodity space, assumed here to be a Banach lattice, and introduce a nonconvex version of the properness assumptions on preferences and the total production set. Applied to the convex case, our result becomes the usual Second Welfare Theorem when properness assumptions replace the interiority condition. The proof uses a Hahn-Banach Theorem generalization by Borwein and Jofré (in Joper Res Appl Math 48:169–180, 1997) which allows to separate nonconvex sets in general Banach spacesThis work was partially supported by Nucleo Complex Engineering System. The successive versions of the paper were partly prepared during visits of Alejandro Jofré to CERMSEM and of Monique Florenzano and Pascal Gourdel to the Centro de Modelamiento Matematico. The hospitality of both institutions and the support of the french Coopération régionale Cone Sud are gratefully aknowledged. The authors thank Ali Khan for stimulating exchange of ideas and literature, Roko Aliprantis, Jean-Marc Bonnisseau, Alain Chateauneuf, Roger Guesnerie, Filipe Martins Da Rocha, Moncef Meddeb, B. Mordukovich, Lionel Thibault and Rabee Tourky for valuable discussions     

Pareto improving price regulation when the asset market is incomplete

Summary. Incomplete asset markets cause competitive equilibria to be constrained suboptimal and provides scope for Pareto improving interventions. In this paper, we examine how intervention in prices in asset or spot commodity markets serves this purpose. We show that, if fix-price equilibria behave sufficiently regularly near Walrasian equilibria, Pareto improving price regulation is generically possible. An advantage of price regulation, contrasted with interventions in individuals asset portfolios, is that it operates anonymously, on market variables.Received: 12 August 2002, Revised: 10 July 2003, JEL Classification Numbers: D45, D52, D60.Earlier and longer versions were circulated as Discussion Paper No. 9841 (June, 1998), CORE, Université Catholique de Louvain, and Working Paper No. 01-31 (2001), Department of Economics, Brown University.The research of Herings was made possible by a fellowship of the Royal Netherlands Academy of Arts and Sciences and a grant of the Netherlands Organization for Scientific Research (NWO); while this paper was being written, he enjoyed the generous hospitality of the Cowles Foundation.John Geanakoplos and Hamid Sabourian asked questions that clarified a number of points in earlier drafts of the paper. An anonymous referee made comments that were insightful and helpful.     

Edgeworth and Lindahl–Foley equilibria of a General Equilibrium Model with Private Provision of Pure Public Goods

In this paper, we propose a definition of Edgeworth equilibrium for a private ownership production economy with (possibly infinitely) many private goods and a finite number of pure public goods. We show that Edgeworth equilibria exist whatever be the dimension of the private goods space and can be decentralized, in the finite and infinite dimensional cases, as Lindahl–Foley equilibria. Existence theorems for Lindahl–Foley equilibria are a by‐product of our results.     

Are incomplete markets able to achieve minimal efficiency?

Summary. We consider economies with incomplete markets, one good per state, two periods, t = 0,1, private ownership of initial endowments, a single firm, and no assets other than shares in this firm. In Dierker, Dierker, Grodal (2002), we give an example of such an economy in which all market equilibria are constrained inefficient. In this paper, we weaken the concept of constrained efficiency by taking away the planners right to determine consumers investments. An allocation is called minimally constrained efficient if a planner, who can only determine the production plan and the distribution of consumption at t = 0, cannot find a Pareto improvement. We present an example with arbitrarily small income effects in which no market equilibrium is minimally constrained efficient.Received: 26 November 2002, Revised: 28 May 2003, JEL Classification Numbers: D2, D52, D61, G1.We are grateful to an anonymous referee for very valuable comments. E. and H. Dierker would like to thank the Institute of Economics, University of Copenhagen, for its hospitality and its financial support.     

Neutrality in arrow and other impossibility theorems

Summary. Although not assumed explicitly, we show that neutrality plays an important role in Arrow and other impossibility theorems. Applying it to pivotal voters we produce direct proofs of classical impossibility theorems, including Arrow's, as well as extend some of these theorems. We further explore the role of neutrality showing that it is equivalent to Pareto or reverse Pareto, and to effective dictatorship for non-null social welfare functions satisfying the principle of independence of irrelevant alternatives. It is also equivalent to Wilson's Citizens' Sovereignty--which is related to the intuition that symmetry over alternatives makes social preference depend only on citizens' preferences. We show that some of these results are more fundamental than others in that they extend both to infinite societies and to considerably smaller domains of preferences. Finally, as an application of Arrow's theorem, we provide a simple proof of the Gibbard-Satterthwaite theorem.Received: 13 April 2000, Revised: 6 December 2002, JEL Classification Numbers: D71, C70.I thank Salvador Barberá, Luis Corchón, Cesar Martinelli, Eric Maskin, Tomas Sjöström, Ricard Torres, José Pedro Ubeda, and an anonymous referee for feedback. The proofs of Arrow's theorem and two Wilson's theorems come from a note I wrote in 1987 at Universitat Autónoma de Barcelona (Ubeda [16]). In 1996 Geanakoplos [7] wrote a proof of Arrow's theorem similar but not identical to mine. All work in this paper is independent of his.     

Creditworthiness and thresholds in a credit market model with multiple equilibria

Summary. The paper studies creditworthiness in a model with endogenous credit cost and debt constraints. Such a model can give rise to multiple candidates for steady state equilibria. We use new analytical techniques such as dynamic programming (DP) with flexible grid size to find solutions and to locate thresholds that separate different domains of attraction. More specifically, we (1) compute present value borrowing constraints and thus creditworthiness, (2) locate thresholds where the dynamics separate to different domains of attraction, (3) show jumps in the decision variable, (4) distinguish between optimal and non-optimal steady states, (5) demonstrate how creditworthiness and thresholds change with change of the credit cost function of the debtor and (6) explore the impact of debt ceilings and consumption paths on creditworthiness.JEL Classification Numbers: C61, C63, D91, D92, E51, G12, G32.An earlier version of this paper has been prepared for the 1998 North American Winter Meeting of the Econometric Society, January 1998, Chicago. We want to thank Jess Benhabib, Buz Brock, Gustav Feichtinger, Franz Wirl, Michael Woodford, Wolf-Jürgen Beyn and Thorsten Pampel for helpful discussions and comments on various versions of the paper. We also want to thank participants in a workshop at the University of Technology, Vienna, the Macroeconomic Workshop at Columbia University, and the SCE conference, at Yale University, June 2001. We are also grateful for comments from a referee of the journal.     

Communication equilibrium payoffs in repeated games with imperfect monitoring

We characterize the set of communication equilibrium payoffs of any undiscounted repeated matrix-game with imperfect monitoring and complete information. For two-player games, a characterization is provided by Mertens, Sorin, and Zamir (Repeated games, Part A (1994) CORE DP 9420), mainly using Lehrer's (Math. Operations Res. (1992) 175) result for correlated equilibria. The main result of this paper is to extend this characterization to the n-player case. The proof of the characterization relies on an analogy with an auxiliary 2-player repeated game with incomplete information and imperfect monitoring. We use Kohlberg's (Int. J. Game Theory (1975) 7) result to construct explicitly a canonical communication device for each communication equilibrium payoff.     

A simple search model of money with heterogeneous agents and partial acceptability

Summary. Simple search models have equilibria where some agents accept money and others do not. We argue such equilibria should not be taken seriously. This is unfortunate if one wants a model with partial acceptability. We introduce heterogeneous agents and show partial acceptability arises naturally and robustly. There can be multiple equilibria with different degrees of acceptability. Given the type of heterogeneity we allow, the model is simple: equilibria reduce to fixed points in [0,1]. We show that with other forms of heterogeneity equilibria are fixed points in set space, and there is no method to reduce this to a problem in R¹.Received: 4 September 2002, Revised: 23 September 2002JEL Classification Numbers: C78, E40.A. Shevchenko, R. Wright: We thank seminar participants at the Federal Reserve Bank of Cleveland, Indiana University, Purdue University, University of Toronto, the 2002 Midwest Macroeconomics Conference at Vanderbilt University, and the 2001 Conference on Economic Dynamics at the University of Essex. The National Science Foundation and the Federal Reserve Bank of Cleveland provided financial support. Braz Ministerio de Camargo and Gabriel Camera provided some helpful suggestions. Correspondence to: R. Wright     

Book Review

Centro Latinoamericano de Documentación Económica Y Social : Bibliografia sobre empresas públicas (Bibliography of Public Enterprise), Naciones Unidas/CEPAL, Santiago, 1972, 248 pages + statistical annex. Public Enterprise, edited by R. Turvey, Penguin Modern Economics Readings, re-issued 1971. Balbir S. Sahni : Public Expenditure Analysis Selected Readings, Rotterdam University Press, 1972, 269 pages. Angelos Angelopoulos : Le Tiers-Monde face aux pays riches (The Third World and the Rich Countries), Presses Universitaires de France, Paris, 1972, 222+xv1 pages. International Cooperative Alliance : The Needs Of the Cooperative Movement of Bangla Desh, New Delhi, 1972, 115 pp. R.N. Tewari : Agricultural Planning and Cooperatives, Sultan Chand & Sons, Delhi, 100 pp. Albert Masnata : Le destin des échanges Ouest-Est (The Future of East-West Trade), La Baconnière, Neuchǎtel, 1972, 173 pages.     

Discounting long run average growth in stochastic dynamic programs

Summary. Finding solutions to the Bellman equation often relies on restrictive boundedness assumptions. In this paper we develop a method of proof that allows to dispense with the assumption that returns are bounded from above. In applications our assumptions only imply that long run average (expected) growth is sufficiently discounted, in sharp contrast with classical assumptions either absolutely bounding growth or bounding each period (instead of long run) maximum (instead of average) growth. We discuss our work in relation to the literature and provide several examples. Received: July 26, 2000; revised version: July 10, 2002 RID="*" ID="*" I am specially grateful to Cuong Le Van and to anonymous referee for detecting an error in a previous version of this paper and for suggestions that sensibly improved the paper. Comments and suggestions are also acknowledged to Michele Boldrin, Raouf Boucekkine, Fabrice Collard, Tim Kehoe, Omar Licandro, and Luis Puch. I am also indebted to participants to the III Summer School on Economic Theory held at the Universidade de Vigo, the Macroeconomics Workshop at the Universitat Autò}noma de Barcelona, and the Econometrics Seminar at Tilburg University. Financial support from the Belgian government, under project PAI P4/01, at the IRES-UCL, from a European Marie Curie fellowship, Grant HPMF-CT-1999-00410, at the CEPREMAP, and from IVIE and Spanish Ministerio de Ciencia y Tecnología and FEDER, under project BEC2001-0535, at the Universidad de Alicante, is gratefully acknowledged.     

Pooling and endogenous market incompleteness

Summary. We study a financial market economy with a continuum of borrowers and pooling of borrowers promises. Under these conditions and in the absence of designing costs, utility-maximizing decisions of price-taking borrowers may lead to financial market incompleteness. Parametrizing equilibria through the borrowers no-arbitrage beliefs, we link expectations to the financial market structure. Markets are complete if and only if borrowers beliefs are homogeneous. Price-taking behavior causes a coordination problem which in turn yields indeterminacy and inefficiency of equilibrium allocations.Received: 29 May 2003, Revised: 13 February 2004, JEL Classification Numbers: D50, D52.Correspondence to: Alessandro CitannaWe would like to thank David Cass, John Geanakoplos, Thorsten Hens, Atsushi Kajii, and an anonymous referee for their comments. The first author also thanks CERMSEM (Paris I) and Columbia University Graduate School of Business for the hospitality. A first version of this paper has appeared as GSIA Working Paper #1997-E137, Carnegie Mellon University, which itself revised Citanna and Villanacci (1995).     

The limit theorem on the core of a production economy in vector lattices with unordered preferences

Summary. We prove Aliprantis, Brown, and Burkinshaw's (1987) theorem on the equivalence of Edgeworth production equilibria and pseudo-equilibria in a more general setting. We consider production economies with unordered preferences and general consumption sets in a vector lattice commodity space. We adapt the approach of Mas-Colell and Richard (1991) and prove our theorem by applying a separating hyperplane argument in the space of all allocations. We also generalize Podczeck's (1996) important result on the relationship between continuous and discontinuous equilibrium prices to the case of production. Received: April 18, 1997; revised version: February 6, 1998     

Existence of Edgeworth equilibria for economies with asymmetric information

We analyze a general equilibrium model with asymmetrically informed agents. A basic and well-known consequence of asymmetric information is the failure of equal treatment property. Despite of this, we show that in every replica economy a private core allocation, which treats agents of the same type equally, exists. This result is provided in the framework of two different models, with and without expectations, and it suffices to guarantee in both cases the existence of a private Edgeworth equilibrium. The author is grateful to an anonymous referee for his/her careful reading and helpful comments and acknowledges support by Research Grant no. 2006132713-005 (Ministero Italiano dell’Università e della Ricerca).     

Outliers - robust ECM cointegration tests based on the trend components

The main goal of this paper is to analyze the behavior of the ECM non-cointegration test when there are additive outliers in the time series under different co-breaking situations. We show that the critical values of the usual ECM test are not robust to the presence of transitory shocks and we suggest a procedure based on signal extraction to bypass this problem. These procedure renders ECM tests with a left tail of distribution under the null that is robust to the presence of additive outliers in the series. The small sample critical values and the empirical power of the test are analyzed by Monte Carlo simulations for several low frequency filters. The proposed empirical methodology is applied to the CPI-based US/Finland real exchange rate.JEL Classification: C22, C12, C15, C52, C51 Corresponding author: Alvaro EscribanoWe thank A. Lucas for kindly providing us with the data for the empirical example. Previous drafts of this paper have greatly improved thanks to the comments of two anonymous referees and the Associate Editor. The first author wishes to thank members of Department of Statistics and Econometrics, Universidad Carlos III de Madrid, and Department of Economics, University of Maryland at College Park. The second author acknowledeges support from the following grants: Spanish MCyT BEC2002-00279, The European TMR-ERB-40618C97-0994 and the Secretaría de Estado de Universidades PR2003-0305. This paper was finished while Alvaro Escribano was visiting the Department of Economics, Georgetwon University, Washington DC, USA.     

Brown's original fictitious play

What modern game theorists describe as “fictitious play” is not the learning process George W. Brown defined in his 1951 paper. Brown's original version differs in a subtle detail, namely the order of belief updating. In this note we revive Brown's original fictitious play process and demonstrate that this seemingly innocent detail allows for an extremely simple and intuitive proof of convergence in an interesting and large class of games: nondegenerate ordinal potential games.     

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.     

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)     

Coalitional instability of the distributive Lindahl equilibrium

Summary Bergstrom [3] has showed that the Lindahlian approach to the analysis of public goods may also be used to analyze a model of wide-spread externalities in which agents have preferences defined on allocations rather than on individual commodity bundles. He has provided versions of the first and second welfare theorem for adistributive Lindahl equilibrium and also presented sufficient conditions for its existence. However, we shall show that, in contrast to Foley's [4] result on the core stability of a Lindahl equilibrium, a distributive Lindahl equilibrium need not satisfy coalitional stability. We will provide a robust example in which the unique, distributive Lindahl equilibrium does not belong to the -core defined either as in Scarf [11] or as in Yannelis [12].I would like to thank F. Canova, R. Serrano, M. Spagat, R. Vohra at Brown University, P. C. Padoan at University of Rome and an anonymous referee for their comments. I am also grateful to the participants at the Third Annual MeetingColloquia on Economic Research at I.G.I.E.R. in Milan, Italy, and to the participants at the Citibank Workshop in Economic Theory at Brown University.     

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.