Optimal Sanctions for Imperfect Rules

This paper analyzes rules that are imperfect in that they are either overinclusive-prohibiting an action that in some circumstances is beneficial-or underinclusive-allowing agents to undertake alternative conducts that are harmful-or both. This concept of imperfection differs from that of over- and underdeterrence and from that of legal errors. We examine how the optimal sanction changes due to the imperfection of the rules, identify the factors that affect its level, and discuss conditions that make the enforcement of the rule desirable even if it is imperfect. We show that when a rule is imperfect the optimal sanction is lower than for a perfect rule, both when it is overinclusive and-more surprisingly-when it is underinclusive. This contrasts with the way the expected sanction needs to be adjusted to restore optimality when the level of deterrence is inadequate or when legal errors are possible. (JEL K14, K40, K42)