Rational inattention when decisions take time

Decisions take time, and the time taken to reach a decision is likely be informative about cost of more precise judgments. We formalize this insight using dynamic model optimal evidence accumulation. provide conditions under which resulting belief dynamics resemble either diffusion processes or with large jumps. then consider in discounting effects are small relative opportunity show that state-contingent choice probabilities predicted by our identical those static rational inattention model, providing micro-foundation for such models. In case, provides normative foundation variant drift-diffusion from mathematical psychology.