How should one use (quasi-)experimental evidence when choosing policies such as top tax rates, health insurance coinsurance rates, unemployment benefit levels, class sizes in schools, etc.? This paper provides an answer that combines insights from (i) optimal policy theory as developed in the field of public finance, and (ii) machine learning using Gaussian process priors. We propose to choose policies which maximize posterior expected social welfare. We provide explicit formulas for posterior expected social welfare and optimal policies in a wide class of policy problems.
The proposed methods are applied to the choice of coinsurance rates in health insurance, using the data of the RAND health insurance experiment. The key tradeoff in this setting is between redistribution toward the sick and insurance revenues. The key empirical relationship the policymaker needs to learn about is the response of health care expenditures to coinsurance rates. Holding everything constant except the estimation method, we obtain much smaller estimates of the optimal coinsurance rate (18% vs. 50%) than those obtained using a conventional ``sufficient statistic'' approach.