Inertia in social learning from a summary statistic

We model normal-quadratic social learning with agents who observe a summary statistic over past actions, rather than complete action histories. Because an agent with a summary statistic cannot correct for the fact that earlier actions influenced later ones, even a small presence of old actions in the statistic can introduce very persistent errors. Depending on how fast these old actions fade from view, social learning can either be as fast as if agents’ private information were pooled (rate n) or it can slow to a crawl (rate ln n). We also examine extensions to learning from samples of actions, learning about a moving target, heterogeneous preferences, and biases toward own information.