Pigouvian taxes can fully correct for market failures due to externalities, but actual policies are commonly forced to deviate from the Pigouvian ideal due to administrative or political constraints. This paper derives sufficient statistics, which require a minimum of market information, that quantify the efficiency costs of such constraints on policy design. We demonstrate that, under certain intuitive conditions, standard output from a regression of true externalities on policy variables, including the R-squared and the sum of squared residuals, have immediate welfare interpretations – they are sufficient statistics that compare alternative policies. We utilize our approach in three diverse empirical applications: random mismeasurement in externalities, imperfect spatial policy differentiation, and heterogeneity in the longevity of energy-consuming durable goods. Regarding the latter, we use our method and a novel data set and find that policies that regulate vehicle fuel-economy, but ignore the differences in average longevity across types of automobiles, recover only about one-quarter to one-third of the welfare gains achievable by a policy that also takes product longevity into account. In contrast, our other two empirical applications suggest that policy imperfections have only small welfare costs.