Learning about informativeness

TL;DR

This paper examines how agents learn about the informativeness of signals in a sequential social learning setting, revealing that asymptotic learning is not guaranteed and depends on the distribution of private beliefs, with perpetual disagreement playing a key role.

Contribution

It introduces a model where agents learn about signal informativeness, highlighting the conditions under which asymptotic learning fails due to perpetual disagreement.

Findings

Asymptotic learning depends on tail distributions of private beliefs.

Perpetual disagreement prevents convergence to true informativeness.

Learning behavior is characterized in Gaussian environments.

Abstract

We study a sequential social learning model in which there is uncertainty about the informativeness of a common signal-generating process. Rational agents arrive in order and make decisions based on the past actions of others and their private signals. We show that, in this setting, asymptotic learning about informativeness is not guaranteed and depends crucially on the relative tail distributions of the private beliefs induced by uninformative and informative signals. We identify the phenomenon of perpetual disagreement as the cause of learning and characterize learning in the canonical Gaussian environment.