If You’re So Smart, Why Aren’t You Rich? Market Selection Hypothesis

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Belief Selection In Complete And Incomplete Markets

Lawrence Blume and David Easley
Department of Economics
Cornell University

July 2002

Abstract: This paper provides an analysis of the asymptotic properties of Pareto optimal consumption allocations in a stochastic general equilibrium model with heterogeneous consumers. In particular we investigate the market selection hypothesis, that markets favor traders with more accurate beliefs. We show that in any Pareto optimal allocation whether each consumer vanishes or survives is determined entirely by discount factors and beliefs. Since equilibrium allocations in economies with complete markets are Pareto optimal, our results characterize the limit behavior of these economies. We show that, all else equal, the market selects for consumers who use Bayesian learning with the truth in the support of their prior and selects among Bayesians according to the size of their parameter space. Finally, we show that in economies with incomplete markets these conclusions may not hold. With incomplete markets payoff functions can matter for long run survival, and the market selection hypothesis fails.

If You’re So Smart, Why Aren’t You Rich? Market Selection Hypothesis – Introduction

General equilibrium models of macroeconomic and financial phenomena commonly assume that traders maximize expected utility with rational, which is to say, correct, beliefs. The expected utility hypothesis places few restrictions on traders’ behavior in the absence of rational expectations, and so much attention has been paid to the validity of assuming accurate beliefs. However, an adequate explanation of how traders come to correctly forecast endogenous equilibrium rates of return is lacking.

Two explanations have been offered. One proposes that correct beliefs can be learned. That is, rational expectations are stable steady states of learning dynamics | Bayesian or otherwise. In our view learning cannot provide a satisfactory foundation for rational expectations. In models where learning works, the learning rule is tightly coupled to the economy in question. Positive results are delicate. Robust results are mostly negative. See Blume, Bray, and Easley (1982), Blume and Easley (1998) and Marimon (1997) for more on learning and its limits.

The other explanation posits “natural selection” in market dynamics. The market selection hypothesis, that markets favor rational traders over irrational traders, has a long tradition in economic analysis. Alchian (1950) and Friedman (1953) believed that market selection pressure would eventually result in behavior consistent with maximization; those who behave irrationally will be driven out of the market by those who behave as if they are rational. Cootner (1964) and Fama (1965) argued that in financial markets, investors with incorrect beliefs will lose their money to those with more accurate assessments, and will eventually vanish from the market. Thus in the long run prices are determined by traders with rational expectations. This argument sounds plausible, but until recently there has been no careful analysis of the market selection hypothesis; that wealth dynamics would select for expected utility maximizers, or, within the class of expected utility maximizers, select for those with rational expectations.

In two provocative papers, DeLong, Shleifer, Summers and Waldman (1990, 1991) undertook a formal analysis of the wealth flows between rational and irrational traders. They argue that irrationally overconfident noise traders can come to dominate an asset market in which prices are set exogenously; a claim that contradicts Alchian’s and Friedman’s intuition. Blume and Easley (1992) address the same issue in a general equilibrium model. We showed that if savings rates are equal across traders, general equilibrium wealth dynamics need not lead to traders making portfolio choices as if they maximize expected utility using rational expectations. We did not study the emergence of fully intertemporal expected utility maximization, nor did we say much about the emergence of beliefs. Sandroni (2000) addressed the latter question. He built economies with intertemporal expected utility maximizers and studied selection for rational expectations. He showed in a Lucas trees economy with some rational-expectations traders that, controlling for discount factors, only traders with rational expectations, or those whose forecasts merge with rational expectations forecasts, survive. He also showed that if even if no such traders are present, no trader whose forecasts are persistently wrong survives in the presence of a learner.

Sandroni’s (2000) analysis stands in sharp contrast to that of DeLong, Shleifer, Summers and Waldman (1990,1991). Why is it that in one setting traders with rational expectations are selected for and in the other setting they are driven out of the market by those with irrational expectations? Answering this question, and in general understanding more completely when selection for rational traders occurs and when it does not, requires a more general analysis than that in the earlier papers. DeLong, Shleifer, Summers and Waldman do not undertake a full equilibrium analysis.1 In their model attitudes toward risk and beliefs both matter in determining who will survive. Sandroni (2000) analyses a full general equilibrium model, with only Lucas trees for assets. In his world attitudes toward risk have no effect on survival.2

We show here that Pareto optimality is the key to understanding selection for or against traders with rational expectations. For any optimal allocation, the survival or disappearance of a trader is determined entirely by discount factors and beliefs. Attitudes toward risk are irrelevant to the long run fate of traders in optimal allocations. In particular, controlling for discount factors, only those traders with correct expectations survive. The rst theorem of welfare economics implies that correct beliefs are selected for whenever markets are complete. This conclusion is robust to the asset structure, of course, so long as markets are complete at the equilibrium prices. Sandroni’s (2000) analysis thus fits into this setting.3 Evidently too, DeLong, Shleifer, Summers and Waldman’s allocations are not Pareto optimal.

In economies with incomplete markets, opportunities for trade may be restricted; consequently, equilibrium allocations need not be Pareto optimal. We show that when markets are incomplete, the market selection hypothesis may fail. Discount factors, attitudes toward risk and beliefs all matter. Even when there is a common discount factor, traders with incorrect beliefs may drive out those with more accurate beliefs. We show that with incomplete markets, a trader who is overly optimistic about the return on some asset in some state can choose to save enough to more than overcome the poor asset allocation decision that his incorrect expectations create. We also show that a trader who is overly pessimistic about the return on some asset in some state can choose to save enough to more than overcome the poor asset allocation decision that his incorrect expectations create. Whether optimism or pessimism leads to greater savings depends on the individual’s utility function so there is no general result about selection for one type or the other.

See full PDF below.

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