Stock Market Volatility and Learning1

We study a standard consumption based asset pricing model with rational investors who entertain subjective prior beliefs about price behavior. Optimal behavior then dictates that investors learn about price behavior from past price observations. We show that this imparts momentum and mean reversion into the equilibrium behavior of the price dividend ratio, similar to what can be observed in the data. Estimating the model on U.S. stock price data using the method of simulated moments, we show that it can quantitatively account for the observed stock price volatility, the persistence of the price-dividend ratio, and the predictability of long-horizon returns. For reasonable degrees of risk aversion, the model also passes a formal statistical test for the overall goodness of …t, provided one excludes the equity premium from the set of moments to be matched. JEL Class. No.: G12, D84 "Investors, their con…dence and expectations buoyed by past price increases, bid up speculative prices further, thereby enticing more investors to do the same, so that the cycle repeats again and again.” Irrational Exuberance, Shiller (2005, p. 56)