Dynamic beliefs

•Evidence shows beliefs about future success decrease with time.•This is consistent with reference-dependent agents who experience anticipatory utility and choose beliefs optimally.•A decreasing path of beliefs helps setting incentives and defines the optimal length of productivity bonuses.

This paper studies the temporal path of subjective probability assessments. A reference-dependent agent who experiences utility from anticipation and from changes in this anticipatory emotion makes utility-maximizing assessments about his likelihood of success in a future lottery. Consistent with the empirical evidence, the model predicts that if the lottery is sufficiently valuable, optimism decreases as the payoff date approaches. Intuitively, as time goes by, last-period expected disappointment becomes increasingly important relative to the joy of anticipating a favorable outcome. Applying the model to the optimal timing of productivity bonuses, I find that a decreasing path of beliefs reduces the cost of providing incentives. Thus, optimal bonuses are sizable and are not frequently offered.