Model Selection by Market Selection

Abstract

We define the concept of market beliefs in an economy with disagreement, such that equilibrium in a representative agent economy with market beliefs is equivalent to equilibrium in the disagreement economy. In general, the mapping from individual agent beliefs to market beliefs is complex and nonlinear, suggesting that several puzzles that arise in the representative agent setting may in fact be due to disagreement, and limiting the possibility of drawing inferences about the pricing kernel and beliefs from asset prices alone. Nevertheless, market beliefs are often highly informative about objective probabilities. We analyze the properties of the market belief process, viewed as an estimator, and show that it satisfies several remarkable properties, nesting Bayesian updating, frequentist estimators, and allowing for shrinkage estimation. We relate these properties to the literature on market selection and to the adaptive market hypothesis.

Keywords: Market Selection, Model Selection, Estimation, Heterogeneous Beliefs

JEL Classification: C10, C11, C13, D51, G10