Equality-minded treatment choice

The goal of many randomized experiments and quasi-experimental studies in economics is to inform policies that aim to raise incomes and reduce economic inequality. A policy maximizing the sum of individual incomes may not be desirable if it magnifies economic inequality and post-treatment redistribution of income 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 function, which puts higher weight on individuals with lower-ranked outcomes. We estimate the optimal policy by maximizing a sample analog of the rank-dependent welfare over a properly constrained set of policies. Although an analytical characterization of the optimal policy under a rank-dependent social welfare is not available even with the knowledge of 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.