Title: Distributional Treatment Effect with Finite Mixture

Abstract: Treatment effect heterogeneity is of a great concern when evaluating the treatment. However, even with a simple case of a binary treatment, the distribution of treatment effect is difficult to identify due to the fundamental limitation that we cannot observe both treated potential outcome and untreated potential outcome for a given individual. This paper assumes a finite mixture model on the potential outcomes and a vector of control covariates to address treatment endogeneity and imposes a Markov condition on the potential outcomes and covariates within each type to identify the treatment effect distribution. The mixture weights of the finite mixture model are consistently estimated with a nonnegative matrix factorization algorithm, thus allowing us to consistently estimate the component distribution parameters, including ones for the treatment effect distribution.