Optimal Memory with Sequential Learning: Signals or Posterior Beliefs

Abstract

Agents with memory constraints must make trade-offs as to what information to remember over time. They may choose to remember signals, and form posterior beliefs only when asked; or alternatively, they may only remember posterior beliefs, and neglect to remember past signals. We demonstrate that memory constrained agents who can flexibly and optimally choose what information to remember will alter their choices in response to changes in the decision-making environment. When there is more uncertainty about which states are relevant for a decision, or when there are fewer signals, agents will tend to remember signals, and only form posteriors from signals when required. In contrast, when there is little uncertainty about the decision-relevant states or many signals, agents choose to remember posterior beliefs over the relevant states, and neglect to remember signals.

Keywords: Sequential learning, information processing, memory constraint

JEL Classification: D83, D91, C91