Excess volatility and predictability of stock prices in autoregressive dividend models with learning

To what extent can agents' learning and incomplete information about the ''true'' underlying model generating stock returns explain findings of excess volatility and predictability of returns in the stock market? In this paper we analyse two models of recursive learning in the stock market when dividends follow a (trend-)stationary autoregressive process. The asymptotic convergence properties of the models are characterized and we decompose the variation in stock prices into rational expectations and recursive learning components with different rates of convergence. A present-value learning rule is found to generate substantial excess volatility in stock prices even in very large samples, and also seems capable of explaining the positive correlation between stock returns and the lagged dividend yield. Self-referential learning, where agents' learning affect the law of motion of the process they are estimating, is shown to generate some additional volatility in stock prices, though of a magnitude much smaller than present value learning.