Aleksey Tetenov (Collegio Carlo Alberto)

“Equality-Minded Treatment Choice”

ABSTRACT

Empirical studies in program evaluation often concern policies that aim to reduce economic inequality in the population. A utilitarian policy maximizing the sum of individual outcomes in the population may not be the best choice if it magnifies economic inequality and post-treatment redistribution of income among the subjects is infeasible. This paper develops a method to estimate the optimal treatment assignment policy based on observable individual covariates when the policy objective is to maximize an equality-minded rank-dependent social welfare criterion, which puts higher weight on individuals with lower-ranked outcomes. We estimate the optimal policy by maximizing a sample analogue of the social welfare over a properly constrained set of policies. Although an analytical characterization of the optimal policy is not available even with the knowledge of the potential outcome distributions, we show that the average social welfare attained by our estimated policy converges to the maximal attainable welfare at n^(-1/2) rate uniformly over a large class of data distributions. We also show that this rate is minimax optimal. We provide an application of our method using the data from the National JTPA Study.