Self-reporting in optimal law enforcement when violators have heterogeneous probabilities of apprehension

Laws often encourage violators to self-report their crimes rather than subject themselves to probabilistic law enforcement. This paper studies the merits of self-reporting when Violators otherwise face heterogeneous probabilities of apprehension. In this setting, an optimal enforcement regime does not elicit self-reporting by all violators. However, even when self-reporting enjoys none of the advantages identified elsewhere, efficiency can often be enhanced by inducing some violators - those with a sufficiently high risk of apprehension - to self-report. By offering a lower sanction to violators who are excessively penalized, the self-reporting option provides more efficient incentives for these individuals to avoid criminal conduct.