Identifying Present Bias from the Timing of Choices

A (partially naïve) quasi-hyperbolic discounter repeatedly chooses whether to complete a task. Her net benefits of task completion are drawn independently between periods from time-invariant distribution. We show that the probability completing conditional on not having done so earlier increases towards deadline. Conversely, we establish nonidentifiability by proving for any time-preference parameters and dataset with such (weakly increasing) task-completion probabilities, there exists stationary payoff distribution rationalizes agent’s behavior if she is either sophisticated or fully naïve. Additionally, provide sharp partial identification case observable continuation values. (JEL C14, D11, D15, D90, D91)