Nash and Walras equilibrium via Brouwer

Summary. The existence of Nash and Walras equilibrium is proved via Brouwer's Fixed Point Theorem, without recourse to Kakutani's Fixed Point Theorem for correspondences. The domain of the Walras fixed point map is confined to the price simplex, even when there is production and weakly quasi-convex preferences. The key idea is to replace optimization with “satisficing improvement,” i.e., to replace the Maximum Principle with the “Satisficing Principle.” Received: July 9, 2001; revised version: February 25, 2002 RID="*" ID="*" I wish to thank Ken Arrow, Don Brown, and Andreu Mas-Colell for helpful comments. I first thought about using Brouwer's theorem without Kakutani's extension when I heard Herb Scarf's lectures on mathematical economics as an undergraduate in 1974, and then again when I read Tim Kehoe's 1980 Ph.D dissertation under Herb Scarf, but I did not resolve my confusion until I had to discuss Kehoe's presentation at the celebration for Herb Scarf's 65th birthday in September, 1995. RID="*" ID="*"Correspondence to: C. D. Aliprantis     

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.     

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.     

On strategic complementarity conditions in Bertrand oligopoly

Summary. For Bertrand duopoly with linear costs, we establish via a single (counter-)example that: (i) A new monotone transformation of the firms' profit functions may lead to the supermodularity of transformed profits when the standard log and identity transformations both fail to do so, and (ii) Topkis's notion of critical sufficient condition for monotonicity of a Bertrand firm's best-reply correspondence cannot be extended to rely only on positive unit costs. Received: January 16, 2001; revised version: March 20, 2002 RID="*" ID="*" This work was completed while the first author was visiting the Institute for Industrial Economics at the University of Copenhagen during Spring 2000. Their financial support and stimulating research environment are gratefully acknowledged. The views expressed here are those of the authors and should not be attributed to the European Commission. Correspondence to: R. Amir     

Endogenous market segmentation with heterogeneous agents

Summary. An explanation is provided for the evolution of segmented marketplaces in a pairwise exchange economy. Large traders operating in a pairwise exchange market prefer to meet other similar traders, because this enables them to trade their endowments in a smaller number of encounters. Large and small traders, however, cannot be distinguished a priori, and the existence of the small traders imposes a negative externality on the large traders. We show that, under conditions which are not very restrictive, establishing a separate market (perhaps with an entry fee) designated for the large traders induces the two types of traders to segment themselves. However, this segmentation is not necessarily welfare improving. Received: January 12, 2001; revised version: July 17, 2002 RID="*" ID="*" I wish to thank the participants in the Friday Theory Workshop at the University of Sydney, and the participants at the 17th Australian Theory Workshop at the University of Melbourne for comments and discussion. John Hillas and Stephen King pointed out an omission in an earlier version, and Catherine de Fontenay and Hodaka Morita made extensive comments on earlier drafts. This work was initiated while I was a short-term visitor at the University of Southern California.     

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     

Indeterminacy in a small open economy with endogenous labor supply

Summary. We establish conditions under which indeterminacy can occur in a small open economy business cycle model with endogenous labor supply. Indeterminacy requires small externalities in technologies with social constant returns to scale, independently of the intertemporal elasticities in both consumption and labor. Received: December 12, 2001; revised version: May 17, 2002 RID="*" ID="*"The paper has benefited from discussions with Jess Benhabib and Mark Weder, as well as from the comments of an anonymous referee. Correspondence to: Q. Meng     

Incentive compatible contractible information

Summary. The paper seeks to characterize what information is always available for contracting, independent of the form of the contract and the probabilities of different states of nature. The paper denotes such information as contractible. It is established that it is possible to speak uniquely of maximal contractible information. Several characterizations are exhibited. In particular, it is shown that if either (a) punishments are bounded everywhere, or (b) deviations from truth-telling are either always or never detected, then maximum contractible information coincides with where is the information partition of agent j. An argument is given for why (b) may be expected to hold. Received: August 7, 2000; revised version: December 21, 2001 RID="*" ID="*" I thank Michael Chwe, Douglas Diamond, Lars Stole, Robert Townsend, Nicholas Yannelis and an anonymous referee for helpful comments.     

A simple axiomatization and constructive representation proof for choquet expected utility

>P>Summary. We provide a set of simple and intuitive set of axioms that allow for a direct and constructive proof of the Choquet Expected Utility representation for decision making under uncertainty. Received: October 29, 2002; revised version: November 13, 2002 RID="*" ID="*" We thank Matthew Ryan for very useful comments and suggestions on related work and for encouraging us to write this note. Correspondence to: S. Grant     

Relative backwardness and technology catching up with scale effects

Controlling for capital accumulation from per capita income growth, this paper shows robust scale effects on total factor productivity growth. The estimated speeds of technology catching up are around 2 percent per year. In addition, the empirical analysis confirms the catching up theory, in which the initial relative backwardness and policy variables conducive to technology adoption are statistically significant. RID="*" ID="*" This is a revised part of Ph.D. thesis at Stanford University. I would like to thank the committee members, Charles I. Jones, Anne O. Krueger, and Paul Romer as well as Ronald Findlay, Ronald I. Mckinnon, Yasuyuki Sawada, Robert Sinclair, a referee and seminar participants at Stanford University, the Pacific Rim Allied Economic Organizations Conference, the East Asian Economic Association Conference, and the 8th World Congress.     

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.     

Real exchange rate determination: Empirical observations from East-Asian countries

In this paper the models for the real exchange rate determination are re-examined between Japan and five East-Asian countries. Two important findings are reported. First, the real interest rate-bias model is valid for Korea-, Malaysia-, Indonesia-, and Philippines-Japan, and the productivity-bias model is valid for Indonesia-, and Philippines-Japan: that is, the coefficients of relative variables are stable and statistically significant. Second, there is no evidence that the political risk premium model is valid. First version received: September 2000/Final version received: April 2001 RID="*" ID="*"  This paper was presented at the Tohoku University Economics Conference April 1999. I acknowledge Yoshihiko Tsukuda, Hiroya Akiba, Tadashi Kuriyama, Jiro Akita and Hiroyuki Ozaki for their helpful comments. Also, I am very grateful to two referees of this journal for many valuable comments. The research was supported by the Nomura foundation for Social Science in 2000.     

Inefficient ex-post equilibria in efficient auctions

Summary. I consider a single-object English auction with two asymmetric bidders and show that it has a continuum of inefficient undominated ex-post equilibria. The result extends for the generalized VCG mechanism, Dasgupta-Maskin auction and, generally, for every auction that has an efficient ex-post equilibrium. Received: November 5, 2001; revised version: June 10, 2002 RID="*" ID="*"I am grateful to Vijay Krishna, Sergei Izmalkov and anonymous referee for many important comments.     

A modified logit model for time series with an application to the pricing behaviour of manufacturing firms in Australia

The modified logit model (Amemiya and Nold, 1975) is generalised to the case where the error term is autocorrelated. The asymptotic distribution (as n →∞ and T →∞) of a feasible GLS estimator of β is derived. Tests of linear restrictions on β and the significance of ρ are presented. The results of the applied work suggest that the factors which explain the pricing behaviour of manufacturing firms, as reported in the tendency survey conducted by the Australian Chamber of Commerce and Industry and the Westpac Banking Corporation, include historical inflation rates of up to 7 quarters and capacity utilisation. First version received: March 2001/Final version received: July 2002 RID="*" ID="*"  The first draft of this paper was written while the author was on study leave at the Department of Econometrics, University of Sydney, Australia.     

Recursive structure and equilibria in games with private monitoring

Summary. In each stage of a repeated game with private monitoring, the players receive payoffs and privately observe signals which depend on the players' actions and the state of world. I show that, contrary to a widely held belief, such games admit a recursive structure. More precisely, I construct a representation of the original sequential problem as a sequence of static games with incomplete information. This establishes the ground for a characterization of strategies and, hence, of behavior in interactive-decision settings where private information is present. Finally, the representation is used to give a recursive characterization of the equilibrium payoff set, by means of a multi-player generalization of dynamic programming. Received: February 11, 2002; revised version: July 22, 2002 RID="*" ID="*" I am very grateful to In-Koo Cho, Larry Epstein, Denis Gromb, Stephen Morris, Paolo Siconolfi, Lones Smith and Max Stinchcombe for several insights and suggestions. A referee's comments helped improving the exposition. Finally, I wish to thank the participants to the seminars at MEDS, NYU, Columbia University, Caltech, UCLA, University of Rochester, University of Texas-Austin, Northwestern Summer Microeconomics Conference 98, Summer in Tel Aviv 98, and NASM98.     

A note on control costs and logit rules for strategic games

We consider best response dynamics with endogenous noise based on a finite game in strategic form. A player can reduce the noise level by expending an extra effort and incurring some disutility or control costs. We specify control costs that result in logit adjustment rules. The stochastically stable states of the dynamic process are partial Nash configurations, that is, states where at least one player plays a best response against the others. If the game has a potential, then the stochastically stable states coincide with the Nash equilibria on which the potential is maximized. RID="*" ID="*" Instructive comments of a referee are gratefully acknowledged. Correspondence to:H. Haller     

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     

Modelling exchange of probabilistic opinions

Summary. This paper studies how communication or exchange of opinions influences correlation of beliefs. The paper focuses on a situation in which agents communicate with each other infinitely many times without observing data. It is an extension to the ‘Expert Problem’ in Bayesian theory, where the informational flow is asymmetric. Moreover, this paper generalizes the existing literature of communication that employs the common prior assumption (CPA) by allowing for heterogeneous beliefs. Some basic convergence results are shown in contrast with the results obtained under the CPA. Furthermore, several economic implications of the basic results are provided. Received: August 27, 2001; revised version: April 16, 2002 RID="*" ID="*" The results presented in this paper are taken from my Ph.D. thesis at Stanford University. I gratefully acknowledge the inspiration obtained from innumerable discussions with Mordecai Kurz about this subject. Also, I appreciate comments from Kenneth J. Arrow, Peter J. Hammond, Maurizio Motolese, Carsten K. Nielsen, Ho-Mou Wu and the anonymous referee.     

The sale of small firms: a multidimensional analysis

Summary. This paper endogeneizes the security voting structure in an auction mechanism used to sell a small firm. The design of security voting structure allows the seller to choose between two objectives which are not mutually consistent. If the seller wants to maximize his revenue, he should retain some shares to benefit from the future dividends generated by the acquirer. At the opposite, if he wants to sell his firm to the most efficient candidate, he should sell all the shares. Received: July 4, 2001; revised version: October 31, 2002 RID="*" ID="*" The paper has benefited from a number of comments from the anonymous referees. Correspondence to: C. At     

Stochastic growth: asymptotic distributions

Summary. This note studies conditions under which sequences of state variables generated by discrete-time stochastic optimal accumulation models have law of large numbers and central limit properties. Productivity shocks with unbounded support are considered. Instead of restrictions on the support of the shock, an “average contraction” property is required on technology. Received: August 27, 2001; revised version: January 9, 2002 RID="*" ID="*"The author thanks John Creedy and Rabee Tourky for helpful comments, and the Economic Theory Center, University of Melbourne for financial support.