Persistence, patience and costly information acquisition

TL;DR

This paper analyzes how an agent optimally acquires costly information about a persistent Gaussian process, revealing effects of persistence and patience on beliefs and costs.

Contribution

It characterizes the optimal information acquisition policy and examines how persistence and patience influence steady-state beliefs and costs.

Findings

Higher persistence non-monotonically affects belief precision.

Increased patience leads to more precise beliefs and lower costs.

Steady-state costs depend on the persistence and patience parameters.

Abstract

A forward-looking agent observes signals of a state that follows a Gaussian AR(1) process. He balances the cost of having imprecise beliefs with the cost of acquiring more precise signals. I characterize his optimal information acquisition policy, and analyze how his steady-state beliefs and costs depend on persistence (the AR(1) parameter) and patience (the agent's discount factor). Higher persistence has a non-monotone effect on belief precision and raises overall costs. Higher patience makes beliefs more precise and lowers overall costs.