Inefficiency caused by random matching and heterogeneity

I study an economy with sellers and buyers with unit supplies and unit demands. Both parties have valuations uniformly distributed on a unit interval. I quantify the inefficiency, compared to the Walrasian markets, when the agents meet randomly. There are several causes of inefficiency that I deal with separately. First, even if there is perfect information about valuations it makes a difference whether all agents participate in the markets or whether only those who would trade in the Walrasian market participate. The same applies when there is private information about valuations.     

Coordination and correlation in Markov rational belief equilibria

Summary This paper studies the effect of correlation in the rational beliefs of agents on the volatility of asset prices. We use the technique of generating variables to study stable and non-stationary processes needed to characterize rational beliefs. We then examine how the stochastic interaction among such variables affects the behavior of a wide class of Rational Belief Equilibria (RBE). The paper demonstrates how to construct a consistent price state space and then shows the existence of RBE for any economy for which such price state space is constructed. Next, the results are used to study the volatility of asset prices via numerical simulation of a two agents model. If beliefs of agents are uniformly dispersed and independent, we would expect heterogeneity of beliefs to have a limited impact on the fluctuations of asset prices. On the other hand, our results show that correlation across agents can have a complex and dramatic effect on the volatility of prices and thus can be the dominant factor in the fluctuation of asset prices. The mechanism generating this effect works through the clustering of beliefs in states of different levels of agreement. In states of agreement the conditional forecasts of the agents tend to fluctuatetogether inducing more volatile asset prices. In states of disagreement the conditional forecasts fluctuatein diverse directions tending to cancel each other's effect on market demand and resulting in reduced price volatility.This research was supported, in part, by the Fondazione Eni Enrico Mattei of Milan, Italy, and by the Research Incentive Fund of Stanford University. The authors thank Carsten K. Nielsen and Ho-Mou Wu for valuable discussions on an earlier draft. Carsten K. Nielsen also made an important contribution to the development of Section 3.     

Learning to bid: The design of auctions under uncertainty and adaptation

We examine auction design in a context where symmetrically informed adaptive agents with common valuations learn to bid for a good. Despite the absence of private valuations, asymmetric information, or risk aversion, bidder strategies do not converge to the Bertrand–Nash equilibrium strategies even in the long run. Deviations from equilibrium strategies depend on uncertainty regarding the value of the good, auction structure, the agents? learning model, and the number of bidders. Although individual agents learn Nash bidding strategies in isolation, the learning of each agent, by flattening the best-reply correspondence of other agents, blocks common learning. These negative externalities are more severe in second-price auctions, auctions with many bidders, and auctions where the good has an uncertain value ex post.     

Combinatorial auctions with decreasing marginal utilities

In most of microeconomic theory, consumers are assumed to exhibit decreasing marginal utilities. This paper considers combinatorial auctions among such submodular buyers. The valuations of such buyers are placed within a hierarchy of valuations that exhibit no complementarities, a hierarchy that includes also OR and XOR combinations of singleton valuations, and valuations satisfying the gross substitutes property. Those last valuations are shown to form a zero-measure subset of the submodular valuations that have positive measure. While we show that the allocation problem among submodular valuations is NP-hard, we present an efficient greedy 2-approximation algorithm for this case and generalize it to the case of limited complementarities. No such approximation algorithm exists in a setting allowing for arbitrary complementarities. Some results about strategic aspects of combinatorial auctions among players with decreasing marginal utilities are also presented.     

Informational efficiency: ranking markets

Summary. The paper studies informational properties of three types of imperfectly competitive markets: a one-signal speculative market (OSS market) in which agents have only private information about the fundamental value (v) of the risky asset traded, a two-signal speculative market (TSS market) in which agents have private information about both v and the asset supply, and a market in which agents are endowed with both information about v and shares of the risky asset traded. In this last market (JA market), agents have joint activities: they trade for both speculative and hedging purposes. It is shown that (i) the JA market and the OSS market are the most and the least efficient, respectively, and (ii) the levels of informational efficiency in the three markets are inversely correlated with the intensities with which traders use their private information about the fundamental value of the asset. Received May 28, 1999; revised version: May 28, 1999     

The relative contributions of private information sharing and public information releases to information aggregation

We calculate learning rates when agents are informed through public and private observation of other agents' actions. We characterize the evolution of the distribution of posterior beliefs. If the private learning channel is present, convergence of the distribution of beliefs to the perfect-information limit is exponential at a rate equal to the sum of the mean arrival rate of public information and the mean rate at which individual agents are randomly matched with other agents. If, however, there is no private information sharing, then convergence is exponential at a rate strictly lower than the mean arrival rate of public information.     

Insecure property rights and growth: the role of appropriation costs, wealth effects, and heterogeneity

Summary. We extend the model from Tornell and Velasco [13] and Tornell and Lane [12] by adding three features: (i) extracting the common property asset involves a private appropriation cost, (ii) agents derive utility from wealth as well as from consumption, and (iii) agents can be heterogeneous. We show that both an increase in the appropriation cost and, when appropriation costs vary across agents, an increase in the degree of heterogeneity of these costs reduce the growth rate of the public capital stock. We also show that, in the interior equilibrium, the private asset can have either a lower or a higher money rate of return than the common property asset.Received: 22 June 2004, Revised: 20 April 2005, JEL Classification Numbers: C73, O40.This research is supported by SSHRC, FQRSC, and the Austrian Science Fund (FWF). Thanks are due to Hassan Benchekroun, Parkash Chander, Gerard Gaudet, Basant Kapur, Kim Long, Colin Rowat, Koji Shimomura, and an anonymous referee for comments and discussions.     

Group decision-making in the shadow of disagreement

A model of group decision-making is studied, in which one of two alternatives must be chosen. While agents differ in their preferences over alternatives, everybody prefers agreement to disagreement. Our model is distinguished by three features: private information regarding valuations, differing intensities in preferences, and the option to declare neutrality to avoid disagreement. There is always an equilibrium in which the majority is more aggressive in pushing its alternative, thus enforcing their will via both numbers and voice. However, under general conditions an aggressive minority equilibrium inevitably makes an appearance, provided that the group is large enough. Such equilibria invariably display a “tyranny of the minority”: the increased aggression of the minority always outweighs their smaller number, leading to the minority outcome being implemented with larger probability than the majority alternative. We fully characterize the asymptotic behavior of this model as group size becomes large, and show that all equilibria must converge to one of three possible limit outcomes.     

Spring cleaning: rural water impacts, valuation, and property rights institutions

Using a randomized evaluation in Kenya, we measure health impacts of spring protection, an investment that improves source water quality. We also estimate households' valuation of spring protection and simulate the welfare impacts of alternatives to the current system of common property rights in water, which limits incentives for private investment. Spring infrastructure investments reduce fecal contamination by 66%, but household water quality improves less, due to recontamination. Child diarrhea falls by one quarter. Travel-cost based revealed preference estimates of households' valuations are much smaller than both stated preference valuations and health planners' valuations, and are consistent with models in which the demand for health is highly income elastic. We estimate that private property norms would generate little additional investment while imposing large static costs due to above-marginal-cost pricing, private property would function better at higher income levels or under water scarcity, and alternative institutions could yield Pareto improvements.     

An Incentive‐Compatible Condorcet Jury Theorem*

We consider a group of individuals who face a binary collective decision. Each group member holds some private information, and all agree about what decision should be taken in each state of nature. However, the state is unknown, and members can differ in their valuations of the two types of mistakes that might occur, and in their prior beliefs about the true state. For a slightly randomized majority rule, we show that informative voting by all voters is the unique Nash equilibrium, that this equilibrium is strict, and that the Condorcet asymptotic efficiency result holds in this setting.     

DIMENSIONALITY AND DISAGREEMENT: ASYMPTOTIC BELIEF DIVERGENCE IN RESPONSE TO COMMON INFORMATION

We provide a model of boundedly rational, multidimensional learning and characterize when beliefs will converge to the truth. Agents maintain beliefs as marginal probabilities instead of joint probabilities, and agents' information is of lower dimension than the model. As a result, for some observations, agents may face an identification problem affecting the role of data in inference. Beliefs converge to the truth when these observations are rare, but beliefs diverge when observations presenting an identification problem are frequent. Robustly, two agents with differing priors who observe identical, unambiguous information may disagree forever, with stronger disagreement the more information received.     

Asset pricing and institutional investors with disagreements

We develop a dynamic asset pricing model with two institutional investors who have benchmark incentives and who disagree about the underlying economy. We derive semi-closed form expressions for all equilibrium quantities. We find that the benchmark stock price increases and the non-benchmark stock price decreases with the benchmark incentives. Furthermore, each stock price decreases with its own disagreement and increases with the other stock disagreement. We also show that there is a positive relationship between the co-movement of the stocks and the benchmark incentives, but that this co-movement is negative with the disagreements, owing to the endogenous risk-sharing mechanisms. Moreover, we find that, when one stock disagreement increases, the optimistic institutional investor always takes positions on this stock by shorting the other stock and the bond in order to hedge against the risk of market changes, in line with the pessimistic investor's beliefs.     

Endogenous uncertainty and market volatility

We advance the theory that the distribution of beliefs in the market is the most important propagation mechanism of economic volatility. Our model is based on the theory of Rational Beliefs (RB) and Rational Belief Equilibrium (RBE) developed by Kurz (1994, 1997). We argue that the diverse market puzzles which are examined, such as the equity premium puzzle, are all driven by the structure of market expectations. In support of our view, we present an RBE model with which we study financial markets. The model is able to simulate the correct order of magnitude of: (i) the long term mean and standard deviation of the price\dividend ratio; (ii) the long term mean and standard deviation of the risky rate of return on equities; (iii) the long term mean and standard deviation of the riskless rate; (iv) the long term mean equity premium. In addition, the model predicts (v) the GARCH property of risky asset returns; (vi) the observed pattern of the predictability of long returns on assets, and (vii) the Forward Discount Bias in foreign exchange markets. The common economic explanation for these phenomena is the existence of heterogenous agents with diverse but correlated beliefs such that some agents are optimistic and some pessimistic about future capital gains. The model has a unique parameterization under which the model makes all the above predictions simultaneously. The parameterization requires the optimists to be in the majority but the rationality of belief conditions of the RBE require the pessimists to have a higher intensity level. In simple terms, the large equity premium and the low equilibrium riskless rate are the result of the fact that at any moment of time there are agents who hold extreme pessimistic beliefs and they have a relatively stronger impact on the market. The paper also studies the effect of correlation of beliefs among investors. It shows that the main effect of such correlation is on the dynamic patterns of asset prices and returns and is hence important for studying such phenomena as stochastic volatility. Received: May 16, 2000; revised version: November 15, 2000     

The dynamics of efficient asset trading with heterogeneous beliefs

This paper analyzes the dynamic properties of portfolios that sustain dynamically complete markets equilibrium when agents have heterogeneous priors. We argue that the conventional wisdom that belief heterogeneity generates continuous trade and significant fluctuations in individual portfolios may be correct but it needs some qualifications. We consider an infinite horizon stochastic endowment economy populated by many Bayesian agents with heterogeneous priors over the stochastic process of the states of nature. Our approach hinges on studying the portfolios that decentralize Pareto optimal allocations. Since these allocations are typically history dependent, we propose a methodology to provide a complete recursive characterization when agents believe that the process of states of nature is i.i.d. but disagree about the probability of the states. We show that even though heterogeneous priors within that class can indeed generate genuine changes in the portfolios of any dynamically complete markets equilibrium, these changes vanish with probability one if the true process consists of i.i.d. draws from a common distribution and the support of some agent's prior belief contains the true distribution. Finally, we provide examples in which asset trading does not vanish because either (i) no agent learns the true conditional probability of the states or (ii) some agent does not know the true process generating the data is i.i.d.     

基于投资者异质性信念的证券定价模型——对我国股票市场价格的实证检验

投资者异质性信念的相互作用影响着证券价格,证券市场上的各种证券需求与供给关系,往往表现为投资者各种不同信念的对抗和交融。本文以悲观信念（看多）和乐观信念（看空）之间的相互作用为例,研究了异质性信念对资产均衡定价的影响,并以我国股票市场的机构投资者信念为对象进行了实证检验,得出我国股票市场投资者信念与证券价格相互作用的结论。本文的建议是在投资过程中,准确分析市场中投资者的异质性信念结构,尤其是资金雄厚的机构投资者的信念结构至关重要。     

Internet auctions with many traders

We study a multi-unit auction environment similar to eBay. Sellers, each with a single unit of a homogeneous good, set reserve prices at their own second-price auctions. Each buyer has private value for the good and wishes to acquire a single unit. Buyers can bid as often as they like and move between auctions. We characterize a perfect Bayesian equilibrium for this decentralized dynamic mechanism in which, conditional on reserve prices, an efficient set of trades occurs at a uniform price. In a large but finite market, the sellers set reserve prices equal to their true costs under a very mild distributional assumption, so ex post efficiency is achieved. Buyers’ strategies in this equilibrium are simple and do not depend on their beliefs about other buyers’ valuations, or the number of buyers and sellers.     

MARRIAGE,DIVORCE, AND ASYMMETRIC INFORMATION

We use data on people's valuations of options outside marriage and beliefs about spouses' options. The data demonstrate that, in some couples, one spouse would be happier and the other spouse unhappier outside of some marriages, suggesting that bargaining takes place and that spouses have private information. We estimate a bargaining model with interdependent utility that quantifies the resulting inefficiencies. Our results show that people forgo some utility in order to make their spouses better off and, in doing so, offset much of the inefficiency generated by their imperfect knowledge. Thus, we find evidence of asymmetric information and interdependent utility in marriage.     

Comment on “Correlated information, mechanism design and informational rents” [J. Econ. Theory 123 (2) (2005) 210–217]

We amend an error in [S. Parreiras, Correlated information, mechanism design and informational rents, J. Econ. Theory 123 (2005) 210–217]. Consequently, it is in general not possible to reinterpret a mechanism design model that violates the spanning condition of Crémer and McLean [J. Crémer, R. McLean, Full extraction of the surplus in bayesian, dominant strategy auctions, Econometrica 56 (1988) 1247–1258] as one in which agents hold private information about the informativeness of their signals about other agents? types. Instead, such an interpretation is warranted only when the weights used to span an agent?s set of beliefs stand in a singular relation with the prior type distribution that is known as an alternative characterization of Blackwell dominance.     

Heterogeneous quantal response equilibrium and cognitive hierarchies

We explore an equilibrium model of games where behavior is given by logit response functions, but payoff responsiveness and beliefs about others' responsiveness are heterogeneous. We study two substantively different ways of extending quantal response equilibrium (QRE) to this setting: (1) Heterogeneus QRE, where players share identical correct beliefs about the distribution of payoff responsiveness; and (2) Truncated QRE, where players have downward looking beliefs, systematically underestimating others' responsiveness. We show that the cognitive hierarchy model is a special case of Truncated QRE. We conduct experiments designed to differentiate these approaches. We find significant evidence of payoff responsive stochastic choice, and of heterogeneity and downward looking beliefs in some games.     

A TWO FACTOR MODEL OF INCOME DISTRIBUTION DYNAMICS

This paper analyzes empirical income distributions and proposes a simple stochastic model to explain the stationary distribution and deviations from it. Using the individual tax returns data in the U.S. and Japan for 40 years, we first summarize the shape of the income distribution by an exponential decay up to about the 90th percentile and a power decay for the top 1 percent. We then propose a minimal stochastic process of labor and asset income to reproduce the empirical characteristics. In particular, the Pareto exponent is derived analytically and matched with empirical statistics.