Optimal Indirect Regulation of Externalities

Abstract

This paper studies the regulation of a good that generates different amounts of an externality on consumption, but direct taxation of the externality is infeasible. Under certain conditions, I show that the deadweight loss due to any (possibly nonlinear) tax on the good is equal to the Bregman divergence between the allocation that the tax induces and the first-best allocation. This yields a regression-based method to derive the tax that minimizes deadweight loss in any family of taxes. I use this method to characterize the second-best nonlinear tax and show that quantity restrictions, such as bans and mandates, can be optimal. I quantify the welfare gains of using a nonlinear tax over a linear tax. Finally, I illustrate policy implications by applying my results to the taxation of vehicle miles traveled to regulate automobile externalities.

Keywords: externalities, mechanism design, regression, non-market policy, sufficient statistics

JEL Classification: D47, D62, D63, D82, H23