Identifying Present-Bias from the Timing of Choices

Timing decisions are common: when to file your taxes, finish a referee report, or complete a task at work. We ask whether time preferences can be inferred when only task completion is observed. To answer this question, we analyze the following model: each period a decision maker faces the choice whether to complete the task today or to postpone it to later. The cost and benefits of task completion cannot be directly observed by the analyst, but the analyst knows that the net benefits are drawn independently between periods from a time-invariant distribution and that the agent has time-separable utility. Furthermore, we suppose—-either because there is a continuum of agents or because the analyst sees the agent facing the same choice (infinitely) often—-that the analyst can observe the exact stopping probability of the agent. We establish that for any agent with quasi-hyperbolic preferences and given level of partial naivete, the probability of completing the task conditional on not having done it earlier increases towards the deadline. And conversely, for any given preference parameters (beta,delta) and weakly increasing profile of task completion probability, there exists a stationary payoff distribution that rationalizes her behavior as long as the agent is either sophisticated or fully naive. An immediate corollary being that it is impossible to rule out time-consistency even when imposing a priori assumption on the permissible discount factors.

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