The Limits of Learning

In this paper, we criticize the current adaptive or statistical learning literature. Instead of emphasizing asymptotical results, we focus on the short run forecasting performance of the different algorithms before convergence to rational expectation solution occurs. First, we suggest that the literature should drop ordinary least squares techniques in favor of the more efficient Bayesian estimation. Second, we cast doubt on the rationality of the behavior implied by the theory. We argue that agents do not use all available information in these models. Past prices carry some information about expectations of others and some algorithms are able to exploit this information. In a very simple case, this algorithm is simply naive expectations. In more complex one, we augment the usual learning with an estimation of past expectation errors using Kalman Filter. Interestingly, we find that some of these algorithms are divergent and may beat convergent ones in the short run. For a large set of parameters, their dominance is too short to be significant. However, when the sensitivity of the actual price to the expected one is close to one, divergent algorithms should be considered.