Speed, Accuracy, and Complexity

This paper studies when response time is informative about problem complexity. It revisits a canonical sequential-sampling model in which a decision-maker chooses when to stop acquiring costly information. Problem complexity is measured by the noise-to-signal ratio of the evidence process. Under exogenous stopping rules — as when the decision-maker does not optimally adjust to problem complexity — response time increases with complexity. By contrast, this monotonicity breaks down when the decision-maker observes problem complexity ex ante and optimally adjusts to it. Expected stopping time is then inverse-U-shaped in complexity, so choices are fast in both very simple and very complex problems. Ability and response time are similarly ambiguously related: more able decision-makers are faster on simple problems but slower on complex ones. Finally, this paper shows that complexity and ability can be inferred from the sensitivity of choices to subsidies, which is greater in more complex problems and for less able decision-makers.