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.