When and what to learn in a changing world

Abstract

A decision-maker periodically acquires information about a changing state, controlling both the timing and content of updates. I characterize optimal policies using a decomposition of the dynamic problem into optimal stopping and static information acquisition. Eventually, information acquisition either stops or follows a simple cycle in which updates occur at regular intervals to restore prescribed levels of relative certainty. This enables precise analysis of long run dynamics across environments. As fixed costs of information vanish, belief changes become lumpy: it is optimal to either wait or acquire information so as to exactly confirm the current belief until rare news prompts a sudden change. The long run solution admits a closed-form characterization in terms of the "virtual flow payoff". I highlight an illustrative application to portfolio diversification.