A Model of Financial Markets with Endogenously Correlated Rational Beliefs

This paper studies how communication amongst agents influences the equilibria of a financial economy. We set up a standard overlapping generations model with assets, while allowing for heterogeneous beliefs. The paper explicitly describes how communication causes the beliefs of the agents to be correlated. In particular, it is shown that communication may generate large fluctuations even if the unconditional probability beliefs themselves are independent. Because of the complex nature of the problem, we use simulations to examine the characteristics of the equilibria Part of the results presented in this paper is based on my Ph.D. thesis at Stanford University. I gratefully acknowledge the inspiration obtained from innumerable discussions with Mordecai Kurz about this subject over the years. Also, I appreciate comments from Kenneth J. Arrow and Peter J. Hammond as well as from the participants of the workshop at Stanford University, University of Tokyo and the 1st Illinois workshop in Economic Theory (University of Illinois at Urbana-Champaign) and the anonymous referee     

Floating exchange rates versus a monetary union under rational beliefs: the role of endogenous uncertainty

Using the concept of ex-post optimality, we compare different exchange rate regimes, including floating exchange rates and fixed exchange rates with a Monetary Union in a two country OLG model with stochastic endowments. The emphasis of this comparison is on the welfare consequences of agents having incorrect beliefs. We do not assume that agents can hold any beliefs, but rather that their beliefs are rational that is consistent with the observed empirical behavior of the economy. We study a large set of possible policies, but two of them have our particular interest. The first policy implies devaluations in reaction to a negative shock, while the other implies a fixed exchange rate. These policies have very different consequences. The first will for generic beliefs not result in an ex-post optimal allocation. The other policy is on the other hand always feasible and results in an ex-post optimal allocation. When the two countries form a Monetary Union, the ex-post optimal allocation is also achieved. The meaning of “endogenous uncertainty” as an institutionally induced uncertainty is illustrated. Received: September 1, 2001; revised version: 24 June 2002 RID="*" ID="*" I would like to thank Horace W. Brock, Gianluca Cassese, Paula Orlando, Ho-Mou Wu as well as seminar participants at Copenhagen Business School, ESEM98, Keio University, Kyoto University, Osaka University, SITE (Stanford) and University of Copenhagen for many useful comments on the paper. I am also grateful to Mark J. Garmaise, Takako Fujiwara-Greve, and an anonymous referee for many helpful suggestions for improving the paper. Without the many discussions about Rational Beliefs and related issues I have had with Mordecai Kurz over the years, the research presented here would not have been possible. Financial support from The Carlsberg Foundation, Danish Social Research Council, University of Copenhagen and SITE is gratefully acknowledged.     

Speculative trading with rational beliefs and endogenous uncertainty

Summary. This paper introduces the framework of rational beliefs of Kurz (1994), which makes the assumptions of heterogeneous beliefs of Harrison and Kreps (1978) and Morris (1996) more plausible. Agents hold diverse beliefs that are “rational” in the sense of being compatible with ample observed data. In a non-stationary environment the agents only learn about the stationary measure of observed data, but their beliefs can remain non-stationary and diverse. Speculative trading then stems from disagreements among traders. In a Markovian framework of dividends and beliefs, we obtain analytical results to show how the speculative premium depends on the extent of heterogeneity of beliefs. In addition, we demonstrate that there exists a unique Rational Belief Equilibrium (RBE) generically with endogenous uncertainty (as defined by Kurz and Wu, 1996) and that the RBE price is higher than the rational expectation equilibrium price (REE) under some general conditions Received: March 15, 2001; revised version: April 26, 2002 RID="*" ID="*" We are deeply grateful to Mordecai Kurz for his constant encouragement and inspiring guidance over the years. We wish to express our gratitude to an anonymous referee for the very valuable comments provided. We also thank Kenneth Arrow, Peter Hammond, Roko Aliprantis and Nicholas Yannelis for their helpful suggestions and Academia Sinica and the National Science Council of the R.O.C. for their indispensable support. Correspondence to: H.-M. Wu     

Endogenous uncertainty and the non-neutrality of money

Summary. We study some implications of the Theory of Rational Beliefs to monetary policy. We show that monetary policy in a Rational Beliefs environment can have an important effect on the characteristics of economic fluctuations. In Rational Beliefs Equilibria money is generically non-neutral unlike Rational Expectations Equilibria in which money is neutral and monetary policy is ineffective. Under Rational Beliefs Equilibria nominal prices and real output change not only in response to changes in the exogenous growth rate of money but also in response to changes in the state of beliefs. In Rational Beliefs Equilibria monetary shocks have real effects even when they are observed but are not fully anticipated. Furthermore, the non-neutrality of money results in a short run Phillips curve. When money “flutters, real output sputters” [8]. We show that Endogenous Uncertainty and the distribution of market beliefs are the major explanatory variables of such fluctuations. Under Rational Expectations monetary policy is ineffective because agents neutralize it by predicting correctly the effect of the policy. Under Rational Beliefs it is shown instead that inflation and recessions can be substantially aggravated by the distribution of market beliefs. Received: January 14, 2002; revised version: April 5, 2002 RID="*" ID="*" I would like to thank Mordecai Kurz for his constant help and support. Most of the ideas developed hereby have been inspired by innumerable and fruitful discussions with him. I have also greatly benefited from helpful comments by Stanley Black, Luigi Campiglio, Carsten Nielsen and Ho-Mou Wu. I also received valuable remarks from participants at the V meeting of “The Society for the Advancement of Economic Theory” held in Ischia, Italy, on July 2-8, 2001, where an initial draft of the present work was presented.     

Learning,non-equilibrium beliefs,and non-pecuniary payoffs in an experimental game

Summary. We present a parametric learning model of players' dynamic and possibly out-of-equilibrium beliefs about other players' preferences that also incorporates random utility (noise). We estimate the model using the data from the four-country ultimatum game experiments of Roth et al. (1991). We find evidence that in the US and in Israel, the estimated beliefs of proposers are stationary and out-of-equilibrium, that in Slovenia, they are in equilibrium, and that in Japan, they are out-of-equilibrium, change from period to period and move away from equilibrium over time. In Japan and in the US, the estimated proposers' beliefs are further away from the uniform prior than the estimated equilibrium beliefs. The results seem to provide support for a non-pecuniary payoff explanation in all countries. Received: May 16, 2000; revised version: December 15, 2001 RID="*" ID="*" We thank Alvin Roth for providing us with the data sets of Roth, Prasnikar, Okuno-Fujiwara, and Zamir (1991). We are very grateful to Vincent Crawford, Joel Sobel, and an anonymous referee for all their comments and feedback. We are also grateful to J?rg Borrmann, Bruno Broseta, Jimmy Chan, Liran Einav, Bernd Engelmann, Drew Fudenberg, Oscar Jorda, Muriel Niederle, Pedro Pereira, Georg Weizs?cker, and audiences at the California Institute of Technology, Harvard University, Universidade Nova de Lisboa, University of Nevada, Las Vegas, and at the European Summer Meetings of the Econometric Society in Lausanne for their comments. Costa-Gomes was affiliated with the Harvard Business School during part of his work on this project. The usual disclaimer applies. Correspondence to:M.A. Costa-Gomes and K.G. Zauner     

Speculative trade, asset prices and investment levels

Summary. In this paper I consider a dynamically complete market model without intrinsic uncertainty. Agents' beliefs are different, but correct in the limit. Some agents are more patient than others. I show that infinitely often share prices are low and the economy stagnates. Also, infinitely often share prices are high and the economy grows. The changes from growth to stagnation and from stagnation to growth are not caused by exogenous shocks. They are caused by speculative trade among agents with different propensities to save and invest. Received: January 8, 2001; revised version: April 11, 2002 RID="*" ID="*" I thank an anonymous referee for helpful comments. I gratefully acknowledge financial support from the National Science Foundation.     

Effect of credible quality investment with Bertrand and Cournot competition

We show how credible revelation and ability to commit to quality choice effect equilibrium qualities and welfare when product market is either Bertrand or Cournot competition. We show that results depend on the type of competition but not generally on the cost of quality function. We show that with Bertrand competition, the equilibrium qualities are lower with credible commitment. Competition is moderated and producer surplus is higher and consumer surplus lower. With Cournot competition, higher quality will be better but lower quality will be worse with credible commitment. Consumer surplus is always greater with credible commitment and if cost does not increase too quickly with quality, producer surplus will also increase. Thus credible commitment is a collusive device with Bertrand competition but it can improve social welfare with Cournot competition. Received: February 8, 2000; revised version: February 14, 2002 RID="*" ID="*" The idea of this paper originated in the weekly workshops of Mordecai Kurz at Stanford. I am forever in debted to Mordecai and fellow students – Luis Cabral, Peter DeMarzo, John Hillas, Michihiro Kandori, Steve Langois, Patrick McAllister, Steve Sharpe, Peter Streufert, Steve Turnbull and Gyu-Ho Wang – for their criticism and encouragement. I also benefited from comments from Yi-Heng Chen, Jin-Li Hu, Kala Krishna, Jinji Naoto, Thomas J. Prusa, and Shyh-Fang Ueng at various later stages of this work. Last but not least, I am grateful for the detailed comments of the referee.     

Monte Carlo simulation of macroeconomic risk with a continuum of agents: the symmetric case

Summary. Suppose a large economy with individual risk is modeled by a continuum of pairwise exchangeable random variables (i.i.d., in particular). Then the relevant stochastic process is jointly measurable only in degenerate cases. Yet in Monte Carlo simulation, the average of a large finite draw of the random variables converges almost surely. Several necessary and sufficient conditions for such “Monte Carlo convergence” are given. Also, conditioned on the associated Monte Carlo -algebra, which represents macroeconomic risk, individual agents' random shocks are independent. Furthermore, a converse to one version of the classical law of large numbers is proved. Received: October 29, 2001; revised version: April 24, 2002 RID="*" ID="*" Part of this work was done when Yeneng Sun was visiting SITE at Stanford University in July 2001. An early version of some results was included in a presentation to Tom Sargent's macro workshop at Stanford. We are grateful to him and Felix Kübler in particular for their comments. And also to Marcos Lisboa for several discussions with Peter Hammond, during which the basic idea of the paper began to take shape. Correspondence to: P.J. Hammond     

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     

Quasi-fundamental exchange rate variation

Summary. This paper uses a general equilibrium model to study the determination of the exchange rate in an economy with fundamental uncertainty. The model has steady state equilibria in which the exchange rate is constant. These equilibria may coexist with “quasi-fundamental” equilibria – nonstationary equilibria in which the exchange rate displays stochastic fluctuations that are correlated with the fluctuations in fundamental random variables. The quasi-fundamental equilibria are Pareto dominated by the corresponding constant-exchange-rate steady states. They also converge to these steady states, inevitably or with positive probability. Received: October 2, 1999; revised version: March 26, 2002 RID="*" ID="*" This paper began as a joint project with Alex Mourmouras, who has made many helpful comments and suggestions but is not responsible for any errors or deficiencies. In addition, I thank an anonymous referee for helpful comments.     

Robust estimation of models of Engel curves

Both standard and robust methods are used here to estimate models of Engel curves for three household commodities, namely, food, transport, and tobacco and alcohol in Canada. The income elasticities of demand computed from the various methods differ significantly for the transport and tobacco-alcohol consumption where there are obvious outliers and zero expenditures problem. Robust estimators point to lower income elasticities and have better performance than the standard LS and Tobit estimator. These results are analyzed in the light of the information on finite-sample performance obtained in a previous Monte Carlo study. First version received: July 2000/Final version received: July 2001 RID="*" ID="*"  I wish to thank Victoria Zinde-Walsh, John Galbraith, Clint Coakley, two anonymous referees and an associate editor for helpful comments. I would also like to thank Anastassia Khouri for kindly providing the 1992 Family Expenditure Survey of Canada data.     

Pooling surveys in the estimation of income and price elasticities: An application to Tunisian households

This paper presents a methodological extension of Deaton's (1990) model for estimating price elasticities, by pooling Tunisian data from several surveys to improve the inter-cluster variability of unit values which is one of the key elements used in the derivation of these elasticities. Since the surveys cover a relatively long period, possible structural changes in consumption behaviour occurring over time are accounted for by postulating that certain response coefficients of the basic model vary from one survey to the other. The own price and cross price elasticities calculated using appropriate estimates of the extended model are satisfactory both from the economic point of view of their sign and the statistical point of view of their significance and superior to those obtained using a single survey. First version received: April 2000/Final version received: June 2001 RID="*" ID="*"  The authors would like to thank Angus Deaton and anonymous referees for useful comments and suggestions.     

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”.     

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.     

Cournot-Nash and Lindahl equilibria in pure public “bad” economies

Summary. Using a general equilibrium framework, this paper analyzes the equilibrium provision of a pure public bad commodity (for example pollution). Considering a finite economy with one desired private good and one pure public “bad” we explicitly introduce the concept of Lindahl equilibrium and the Lindahl prices into a pure public bad economy. Then, the Lindahl provision is analyzed and compared with the Cournot-Nash provision. The main results for economies with heterogeneous agents state that the asymptotic Lindahl allocation of the pure public bad is the null allocation. In contrast, the asymptotic Cournot-Nash provision of the public bad might approach infinity. Other results were obtained in concert with the broad analysis of the large finite economies with pure public bad commodities. Received: July 26, 2001; revised version: March 12, 2002 RID="*" ID="*" We are indebt to Nicholas Yannelis and anonymous referee for their valuable comments and suggestions. Correspondence to: B. Shitovitz     

Firm reputation with hidden information

Summary. An adverse selection model of firm reputation is developed in which short-lived clients purchase services from firms operated by overlapping generations of agents. A firm's only asset is its name, or reputation, and trade of names is not observed by clients. As a result, names are traded in all equilibria regardless of the economy's horizon The general equilibrium analysis links the value of a name to the market for services. This causes a non-monotonicity that precludes higher types from sorting themselves through the market for names, and leads to “sensible” dynamics: reputations, and name prices, increase after success and decrease after failure. Received: July 31, 2001; revised version: December 20, 2001 RID="*" ID="*" I thank Jon Levin, Eric Maskin and Drew Fudenberg for valuable discussions, and Heski Bar-Isaac for comments on an earlier draft. Financial support from the National Science Foundation (NSF grants SBR-9818981 and SES-0079876) is gratefully acknowledged. This paper replaces an older (and incomplete) working paper titled “Reputation with Hidden Information”.     

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)     

Inefficient Markov perfect equilibria in multilateral bargaining

We study a complete-information alternating-offer bargaining game in which one “active” player bargains with each of a number of other “passive” players one at a time. In contrast to most existing models, the order of reaching agreements is endogenously determined, hence the active player can “play off” some passive players against others by m oving back and forth bargaining with the passive players. We show that this model has a finite number of Markov Perfect Equilibria, some of which exhibiting wasteful delays. Moreover, the maximum number of delay periods that can be supported in Markov Perfect Equilibria increases in the order of the square of the number of players. We also show that these results are robust to a relaxing of the Markov requirements and to more general surplus functions. Received: November 19, 2001; revised version: August 20, 2002 RID="*" ID="*"This paper grew out of my dissertation submitted to Stanford University. I am deeply indebted to my advisor, Paul Milgrom, for his insights and guidance. I would also like to thank Douglas Bernheim, Sushil Bikhchandani, Harold Demsetz, Bryan Ellickson, Avner Greif, Peter Hammond, David Levine, Bentley Macleod, Joe Ostroy, John Pencavel, Jean-Laurent Rosenthal, David Starrett, Robert Wilson, Bill Zame and especially John Riley and Jeff Zwiebel for their helpful comments. I am grateful to an anonymous referee for extremely constructive suggestions.     

Endogenous fluctuations in the demand for education

Abstract. Enrollment rates to higher education reveal a quite large variation over time which cannot be explained by productivity shocks alone. We develop a human capital investment model in an overlapping generations framework that features endogenous fluctuations in the demand for education. Agents are heterogeneous in their beliefs about future wage differentials. An evolutionary competition between the heterogeneous beliefs determines the fraction of the newborn generation having a certain belief. Costly access to information on the returns to education induces agents to use potentially destabilizing backward looking prediction rules. Only if previous generations experience regret about their human capital investment decisions, will agents choose a more sophisticated prediction rule that dampens the cycle. Access to information becomes key for stable flows to higher education. RID="*" ID="*"We would like to thank Cars Hommes, Florian Wagener, seminar participants at the University of Amsterdam, participants of the workshop on ‘Skill Needs and Labor Market Dynamics’ at the Wissenschaftszentrum Berlin für Sozialforschung (WZB) for helpful discussions, and an editor of this Journal and three anonymous referees for their comments. Tuinstra's research is supported by the Netherlands Organisation for Scientific Research (NWO) under a MaG-Pionier grant. Neugart acknowledges financial support from the German Ministry of Education. Parts of the research were done while Tuinstra was visiting the WZB and when Neugart was visiting CeNDEF. Correspondence to: The research for this paper was done while the first author was affiliated with the Wissenschaftszentrum Berlin für Sozialforschung.     

Common priors under incomplete information: a unification

Summary. While the meaningfulness of the common prior assumption (CPA) under incomplete information has been established recently by various authors, its epistemic rationale has not yet been adequately clarified. To do so, we provide a characterization of the CPA in terms of a new condition called “Mutual Calibration”, and argue that it constitutes a more transparent and more primitive formalization of the Harsanyi Doctrine than the existing characterizations. Our analysis unifies the understanding of the CPA under incomplete information and clarifies the role of higher-order expectations and of the difference between situations with only two and those with at least three agents. In the concluding section, the analysis is applied to the problem of defining Bayesian consistency of the intertemporal beliefs of a single-agent with imperfect memory. The CPA yields a notion of “Bayesian updating without a prior”. Received: March 24, 2000; revised version: April 27, 2000