Time-Consistent Criminal Sanctions

A classic argument in the theory of crime is that optimal enforcement policy should involve maximal sanctions combined with minimal detection costs. Yet this is rarely observed in the real world. We argue that reson for this has to do with the time inconsistency of such a policy. If sanctions are only applied after a crime has been committed, the enforcement authority are only reluctant to impose a high sanction since it will no longer have any deterrent effect. We show in a simple one period setting that if the enforcement authority can commit to its announced sanctions, the classic result is obtained. However, if the enforcement authority cannot commit, a minimal sanction with no enforcement effort is obtained. These extreme outcomes can be avoided in a setting in which crimes and enforcement occur repeatedly and the authority is able to build a reputation.