Dynamic Amnesty Programs

A regulator faces a stream of agents engaged in crimes with stochastic returns. The regulator designs an amnesty program, committing to a time path of punishments for criminals who report their crimes. In an optimal program, time variation in the returns from crime can generate time variation in the generosity of amnesty. I construct an optimal time path and show that it exhibits amnesty cycles. Amnesty becomes increasingly generous over time until it hits a bound, after which the cycle resets. Agents engaged in high return crime report at the end of each cycle, while agents engaged in low return crime report always. (JEL D82, D86, K42)