Internal Rationality and Asset Prices

We present a decision theoretic framework with agents that are learning about the behavior of market determined variables. Agents are 'internally rational', i.e., maximize discounted expected utility under uncertainty given consistent beliefs about the future, but may not be 'externally rational', i.e., may not know the true stochastic process for market determined variables (asset prices) and fundamentals (dividends). We apply this approach to a simple asset pricing model with heterogeneity and incomplete markets. We show how knowledge about dividends and optimal behavior alone fail to fully inform agents about equilibrium prices, so that learning about price behavior, as in Adam, Marcet and Nicolini (2008), is fully consistent with internal rationality. We also show that equilibrium prices depend on expectations of the discounted price and dividend in the next period only, rather than on the expected discounted sum of future dividends. Discounted sums emerge only after making very strong assumptions about agents' knowledge and prove extremely sensitive to the details about agents' prior beliefs about the dividend process.