Welfare Comparisons for Biased Learning

We study robust welfare comparisons of learning biases (misspecified Bayesian and some forms of non-Bayesian updating). Given a true signal distribution, we deem one bias more harmful than another if it yields lower objective expected payoffs in all decision problems. We characterize this ranking in static and dynamic settings. While the static characterization compares posteriors signal by signal, the dynamic characterization employs an "efficiency index" measuring how fast beliefs converge. We quantify and compare the severity of several well-documented biases. We also highlight disagreements between the static and dynamic rankings, and that some "large" biases dynamically outperform other "vanishingly small" biases.