Distributional Treatment Effect with Latent Rank Invariance

Abstract

Treatment effect heterogeneity is of a great concern when evaluating policy impact: "is the treatment Pareto-improving?", "what is the proportion of people who are better off under the treatment?", etc. However, even in the simple case of a binary random treatment, existing analysis has been mostly limited to an average treatment effect or a quantile treatment effect, due to the fundamental limitation that we cannot simultaneously observe both treated potential outcome and untreated potential outcome for a given unit. This paper assumes a conditional independence assumption that the two potential outcomes are independent of each other given a scalar latent variable. With a specific example of strictly increasing conditional expectation, I label the latent variable as 'latent rank' and motivate the identifying assumption as 'latent rank invariance.' In implementation, I assume a finite support on the latent variable and propose an estimation strategy based on a nonnegative matrix factorization. A limiting distribution is derived for the distributional treatment effect estimator, using Neyman orthogonality.