Rational Inattention when Decisions Take Time

Rational Inattention when Decisions Take Time

By Benjamin Hébert, Michael Woodford
March 25,2020Working Paper No. 3457

Decisions take time, and the time taken to reach a decision is likely to be informative about the cost of more precise judgments. We formalize this insight in the context of a dynamic rational inattention (RI) model. Under standard conditions on the flow cost of information in our discrete-time model, we describe the continuous-time limit. We next provide conditions under which the resulting belief dynamics resemble either diffusion processes or processes with large jumps. We then demonstrate that the state-contingent choice probabilities predicted by our model are identical to those predicted by a static RI model, providing a micro-foundation for such models. In the diffusion case, our model provides a normative foundation for a variant of the DDM models studied in mathematical psychology.