Existence of a competitive equilibrium in a one sector growth model with heterogeneous agents and irreversible investment

Summary. We prove existence of a competitive equilibrium in a version of a Ramsey (one sector) model in which agents are heterogeneous and gross investment is constrained to be non negative. We do so by converting the infinite-dimensional fixed point problem stated in terms of prices and commodities into a finite-dimensional Negishi problem involving individual weights in a social value function. This method allows us to obtain detailed results concerning the properties of competitive equilibria. Because of the simplicity of the techniques utilized our approach is amenable to be adapted by practitioners in analogous problems often studied in macroeconomics. Received: September 13, 2001; revised version: December 9, 2002 RID="*" ID="*" We are grateful to Tapan Mitra for pointing out errors as well as making very valuable suggestions. Thanks are due to Raouf Boucekkine and Jorge Duran for additional helpful discussions. We also thank an anonymous referee for his/her helpful comments. The second author acknowledges the financial support of the Belgian Ministry of Scientific Research (Grant ARC 99/04-235 “Growth and incentive design”) and of the Belgian Federal Goverment (Grant PAI P5/10, “Equilibrium theory and optimization for public policy and industry regulation”). Correspondence to: C. Le Van     

On bubbling dynamics generated by a stochastic model of herd behavior

This paper suggests a class of stochastic collective learning processes exhibiting very irregular behavior. In particular, there are multimodal long run distributions. Some of these modes may vanish as the population size increases. This may be thought of as “bubbles” persistent for a finite range of population sizes but disappearing in the limit. The limit distribution proves to be a discontinuous function of parameters determining the learning process. This gives rise to another type of “bubbles”: limit outcomes corresponding to small perturbations of parameters are different. Since an agent's decision rule involves imitation of the majority choice in a random sample of other members of the population, the resulting collective dynamics exhibit “herding” or “epidemic” features. RID="*" ID="*" We are grateful to two anonymous referees for the comments and suggestions. Correspondence to: L. Gaio     

Estimating the stationary distribution of a Markov chain

Summary. Let be a Markov chain with a unique stationary distribution . Let h be a bounded measurable function. Write and . This paper explores conditions for the consistency and asymptotic normality of the estimate of of assuming the existence of a solution to the Poisson equation . Our framework covers the case of nonirreducible Markov chains arising in many growth models in economics. Received: October 8, 2001; revised version: April 8, 2002 RID="*" ID="*" Thanks are due to Professors Rabi Bhattacharya, Nicholas Kiefer and Timothy Vogelsang on an earlier draft for helpful conversations, and a referee for insightful comments. Correspondence to: M.Majumdar     

Rationalizable implementation

We consider the implementation of social choice functions under complete information in rationalizable strategies. A strict version of the monotonicity condition introduced by Maskin is necessary under the solution concept of rationalizability. Assuming the social choice function is responsive, i.e. in distinct states it selects distinct outcomes, we show that strict Maskin monotonicity is also sufficient under a mild “no worst alternative” condition. In particular, no economic condition is required. We discuss how our results extend when the social choice function is not responsive.     

Economic policy making in evolutionary perspective

Economic policy making is discussed from three different angles: the political economy of actual policy making (“what policy does do”), the analysis of policy instruments for given ends (“what policy could do”), and the debate on policy goals and their legitimization (“what policy ought to do”). Center stage in the evolutionary perspective is new, positive and normative knowledge which is unfolding during the policy making process and in its aftermath. It is argued that this implies regularities and constraints which extend and modify the comparative-static interpretations of public choice theory, economic policy making theory, and social philosophy. RID="*" ID="*" The author should like to thank three anonymous referees of this journal and the editor for helpful comments on an earlier version of the paper.     

Extensive Form Implementation in Incomplete Information Environments

We study the implementation of social choice rules in incomplete information environments. A sufficiency condition calledposterior reversalis given for extensive form implementation. The condition has a natural interpretation in signaling terms: Consistent posterior distributions under truth-telling are different from consistent posteriors under deception. This variation in the distribution over player types leads to variation in the distribution over actions and outcomes (comparing truth-telling and deception). We exploit this feature to implement social choice rules.Journal of Economic LiteratureClassification Numbers: D78, D82.     

Interactive expectations

In modeling expectation formation, economic agents are usually viewed as forming expectations adaptively or in accordance with some rationality postulate. We offer an alternative nonlinear model where agents exchange their opinions and information with each other. Such a model yields multiple equilibria, or attracting distributions, that are persistent but subject to sudden large jumps. Using German Federal Statistical Office economic indicators and German IFO Poll expectational data, we show that this kind of model performs well in simulation experiments. Focusing upon producers' expectations in the consumption goods sector, we also discover evidence that structural change in the interactive process occurred over the period of investigation (1970–1998). Specifically, interactions in expectation formation seem to have become less important over time. RID="*" ID="*"We would like to thank Ulrich Witt, Director of the Evolutionary Economics Unit, The Max Planck Institute for Research into Economic Systems, Jena, Germany, for providing the intellectual stimulus for this project and arranging the necessary financial support from the Max Planck Society to facilitate our collaboration. Thanks are also due to the IFO Institute for providing the data for this study. However, the usual caveat applies.     

Core and Walrasian equilibria when agents' characteristics are extremely dispersed

Summary. It is shown that core-Walras equivalence fails whenever the commodity space is a non-separable Banach space. The interpretation is that a large number of agents guarantees core-Walras equivalence only if there is actually a large number of agents relative to the size of the commodity space. Otherwise a large number of agents means that agents' characteristics may be extremely dispersed, so that the standard theory of perfect competition fails. Supplementing the core-Walras non-equivalence result, it is shown that in the framework of economies with weakly compact consumption sets – as developed by Khan and Yannelis (1991) – the core is always non-empty, even if consumption sets are non-separable. December 12, 2001; revised version: December 6, 2002 RID="*" ID="*" Thanks to E. Dierker, M. Nermuth, R. Tourky, and N. C. Yannelis for helpful discussions and suggestions, and thanks to a referee for comments which helped to improve the final version.     

The robustness of robust implementation

We show that a mechanism that robustly implements optimal outcomes in a one-dimensional supermodular environment continues to robustly implement ε-optimal outcomes in all close-by environments. Robust implementation of ε-optimal outcomes is thus robust to small perturbations of the environment. This is in contrast to ex-post implementation which is not robust in this sense as only trivial social choice functions are ex-post implementable in generic environments.     

Dictatorial domains

Summary. In this paper, we introduce the notion of a linked domain and prove that a non-manipulable social choice function defined on such a domain must be dictatorial. This result not only generalizes the Gibbard-Satterthwaite Theorem but also demonstrates that the equivalence between dictatorship and non-manipulability is far more robust than suggested by that theorem. We provide an application of this result in a particular model of voting. We also provide a necessary condition for a domain to be dictatorial and use it to characterize dictatorial domains in the cases where the number of alternatives is three. Received: July 12, 2000; revised version: March 21, 2002 RID="*" ID="*" The authors would like to thank two anonymous referees for their detailed comments. Correspondence to: A. Sen     

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.     

On the constancy of bribe-proof solutions

Summary. We consider the problem of choosing one point in a set of alternatives when monetary transfers are possible. In this context, Schummer (2000) shows that a social choice function must be a constant function if manipulation through bribes is ruled out. But he requires two kinds of domain-richness conditions. One is either smooth connectedness or the finiteness of the set of alternatives and the other is monotonical closedness. However, dispensing with the former condition, we alternatively prove the same result under a weaker condition than monotonical closedness. Received: April 11, 2000; revised version: February 25, 2002 RID="*" ID="*" This paper received the Osaka University Institute of Social and Economic Research Moriguchi Prize in January 2001. I am grateful to Prof. Ryoichi Nagahisa, Prof. Tatsuyoshi Saijo, Prof. Ken-ichi Shimomura, Prof. Ken Urai, and especially two anonymous referees for their useful and helpful comments and suggestions. I am a Research Fellow of the Japan Society for the Promotion of Science.     

On the choice of functional form in stochastic frontier modeling

This paper examines the effect of functional form specification on the estimation of technical efficiency using a panel data set of 125 olive-growing farms in Greece for the period 1987–93. The generalized quadratic Box-Cox transformation is used to test the relative performance of alternative, widely used, functional forms and to examine the effect of prior choice on final efficiency estimates. Other than the functional specifications nested within the Box-Cox transformation, the comparative analysis includes the minflex Laurent translog and generalized Leontief that possess desirable approximation properties. The results indicate that technical efficiency measures are very sensitive to the choice of functional specification. Perhaps most importantly, the choice of functional form affects the identification of the factors affecting individual performance – the sources of technical inefficiency. The analysis also shows that while specification searches do narrow down the set of feasible alternatives, the identification of the most appropriate functional specification might not always be (statistically) feasible. First version received: November 1999/Final version received: July 2001 RID="*" ID="*"  The authors wish to thank Almas Heshmati, Robert Romain, and an anonymous referee for insightful comments and suggestions. Special thanks go to the associate editor who handled the paper, and whose careful reading and suggestions have improved the paper substantially. The second author wishes to acknowledge the financial support from “President SSHRC” from the University of Saskatchewan. The usual caveats with respect to opinions expressed in the paper apply. Senior authorship is shared. This is University of Nebraska-Lincoln Agricultural Research Division Article No. 13270.     

A strategy-proofness characterization of majority rule

Summary. A feasible alternative x is a strong Condorcet winner if for every other feasible alternative y there is some majority coalition that prefers x to y. Let (resp., denote the set of all profiles of linear (resp., merely asymmetric) individual preference relations for which a strong Condorcet winner exists. Majority rule is the only non-dictatorial and strategy-proof social choice rule with domain , and majority rule is the only strategy-proof rule with domain . Received: August 29, 2000; revised version: November 13, 2002 RID="*" ID="*"We are grateful to Wulf Gaertner and our two referees for insightful comments on a previous draft. Correspondence to: D. E. Campbell     

Robust Implementation in Direct Mechanisms

A social choice function is robustly implementable if there is a mechanism under which the process of iteratively eliminating strictly dominated messages lead to outcomes that agree with the social choice function for all beliefs at every type profile. In an interdependent-value environment with single-crossing preferences, we identify a contraction property on the preferences which together with strict ex post incentive compatibility is sufficient to guarantee robust implementation in the direct mechanism. Strict ex post incentive compatibility and the contraction property are also necessary for robust implementation in any mechanism, including indirect ones. The contraction property requires that the interdependence is not too high. In a linear signal model, the contraction property is equivalent to an interdependence matrix having all eigenvalues smaller than one.     

Nash implementation with partially honest individuals

We investigate the problem of Nash implementation in the presence of “partially honest” individuals. A partially honest player is one who has a strict preference for revealing the true state over lying when truthtelling does not lead to a worse outcome than that which obtains when lying. We show that when there are at least three individuals, all social choice correspondences satisfying No Veto Power can be implemented. If all individuals are partially honest and if the domain is separable, then all social choice functions can be implemented in strictly dominant strategies by a mechanism which does not use “integer/modulo games”. We also provide necessary and sufficient conditions for implementation in the two-person case, and describe some implications of these characterization conditions.     

Implementation in teams

Summary. This paper considers a team production model in which the final output is a function of one or more observable intermediate variables that are functions of the actions of the team members. When there is only one intermediate variable, our model essentially reduces to the standard models in which only the final output is observable. We provide a necessary and sufficient condition for implementing an outcome. This condition imposes restrictions on the possible deviations from the outcome that can be caused by every member of the team unilaterally. As a consequence of this characterization, when there are more than one intermediate variable, we are able to show that in a broad class of problems these intermediate variables may be sufficiently informative to allow sharing rules that implement efficient outcomes. Received: March 26, 2001; revised version: August 12, 2002 RID="*" ID="*"I would like to thank Parimal Bag, Craig Brett, Greg Dow, Hugo Hopenhayn, Ashok Kotwal, Dilip Mookherjee, Santanu Roy, Sudhir Shah, Guofu Tan and John Weymark for helpful discussions on earlier versions of this paper. The usual disclaimer applies.     

Ten-year forecasts of real stock price changes

This paper provides the strongest evidence to-date on the predictability of real stock prices over long horizons. Ex ante forecasts account for over two-thirds of the variation of the growth rate of real stock prices over ten year spans from 1940 through 2001. The paper forecasts negative growth rates of real stock prices over the next ten years. This bearish long-run outlook is buttressed by the long-run relationship between the growth rates of real stock prices, inflation, dividends, and productivity. First version received: June 2000/Final version received: June 2001 RID="*" ID="*"  Special thanks to an anonymous referee for helpful comments.     

Robust implementation in general mechanisms

A social choice function is robustly implemented if every equilibrium on every type space achieves outcomes consistent with it. We identify a robust monotonicity condition that is necessary and (with mild extra assumptions) sufficient for robust implementation.Robust monotonicity is strictly stronger than both Maskin monotonicity (necessary and almost sufficient for complete information implementation) and ex post monotonicity (necessary and almost sufficient for ex post implementation). It is equivalent to Bayesian monotonicity on all type spaces.     

An impossibility result for virtual implementation with status quo

In this paper, virtual implementation is restricted to deliver, on the equilibrium path, either a socially optimal outcome or a status quo: an outcome fixed for all preference profiles. Under such a restriction, for any unanimous and implementable social choice function there is a dictator, who obtains her most preferable outcome as long as all agents prefer this outcome to the status quo. Further restrictions on the lottery space and the range of social choice functions allow the dictator to impose her most preferred outcome even when other agents prefer the status quo to this outcome.