Forecasts as repeated cheap talk from an expert of unknown statistical bias

Abstract

For two periods an expert $E$ announces his forecast of the state to a decision-maker $D$. $E$ and $D$ disagree about the precision of the probability assessments that $E$ makes. At the end of period 1 the state is observed, and $D$ updates his opinion about $E$ as a forecaster. In period 2 $E$ tends to make announcements more extreme than his forecasts. Despite no upper bound to the cardinality of the final equilibrium partition, full revelation is never realized. In period 1 $E$ takes into account that his report affects his reputation. This consideration can mitigate $E$’s incentive to exaggerate. However, full revelation is impossible and the equilibria are partitional.