Nonparametric identification and estimation of heterogeneous causal effects under conditional independence

Abstract

In this article, I propose a nonparametric strategy to identify the distribution of heterogeneous causal effects. A set of identification restrictions proposed in this article differs from existing approaches in three ways. First, it extends the random coefficient model by allowing potentially nonlinear interactions between distributional parameters and the set of covariates. Second, the causal effect distributions identified in this article give an alternative to those under the rank invariance assumption. Third, identified distribution lies within the sharp bound of distributions of the treatment effect. I develop a consistent nonparametric estimator exploiting the identifying restriction by extending the conventional statistical deconvolution method to the Rubin causal framework. Results from a Monte Carlo experiment and an application to wage loss of displaced workers suggest that the method yields robust estimates under various scenarios.