The purpose of this paper is to show that a very simple asset pricing model is able to reproduce a variety of stylized facts if one allows for very small departures from rationality.
The result is somehow remarkable, since the literature in empirical finance has had a very hard time in developing dynamic equilibrium rational expectations models that can account for some of those facts. For example, Campbell and Cochrane (1999) show that a habit-persistence model is able to match US data only after imposing a multiple-parameter complex specification for the formation of habit in preferences.
It has long been recognized that stock prices exhibit movements that cannot be reproduced within the realm of rational expectation models: the risk premium is too high, stock prices are too volatile, the price/dividend ratio is too persistent and volatile, stock returns are unpredictable in the short run but negatively related to the price/dividend ratio in the long run, and there are stock market crashes.
A very large body of literature has been devoted to documenting these empirical observations and to finding extensions of the standard model that will improve its empirical performance. A quick (and, therefore, unfair) summary is that it is not possible to find reasonable extensions of the basic model that will get close to explaining all these facts2, unless a large number of parameter is added to the model, as in Campbell and Cochrane (1999). Instead, we follow a different approach: we replace the full rationality assumption by the most standard scheme used in the learning literature3: least squares learning (OLS). We show that with this modification, the model can replicate the data surprisingly well.
In this model, least squares learning has the property that in the long run the equilibrium converges to rational expectations,but this process takes a very long time, and the dynamics generated by learning along the transition cause prices to be very different from the rational expectations (RE) prices.
The reason is that if expectations about stock price growth have increased, the actual growth rate of prices has a tendency to increase beyond the growth of fundamentals, thereby reinforcing the belief in a higher stock price growth. Learning thus imparts ‘momentum’ on stock prices and beliefs and produces large and sustained deviations of the price/dividend ratio, as they are observed in the data. Our model also produces not rational ‘bubbles’, meaning large increases in stock prices that do not seem justified by increases in fundamentals. Stock prices can be very high precisely because agents believe in higher stock price growth and the market behavior reinforces this belief.
The high volatility of stock price growth and the predictability of stock returns in the long run follow from this behavior. We also find that once price embarks on a ‘bubble’ path, small changes in fundamentals (dividends) can trigger a market ‘crash’ that will end the bubble, meaning a sudden-large drop in stock prices.
