Corrective regulation with imperfect instruments

This paper studies optimal second-best corrective regulation, when some agents/activities cannot be perfectly regulated. We show that policy elasticities and Pigouvian wedges are sufficient statistics to characterize the marginal welfare impact of regulatory policies in a large class of environments. We show that a subset of policy elasticities, leakage elasticities, determine optimal second-best policy, and characterize the marginal value of relaxing regulatory constraints. We apply our results to scenarios with unregulated agents/activities, uniform regulation across agents/activities, and costly regulation. We illustrate our results in applications to financial regulation with environmental externalities, shadow banking, behavioral distortions, asset substitution, and fire sales.