A Synthetic Control Approach to Conditional Distributional Treatment Effects

Abstract

This paper proposes a synthetic control (SC) framework for the estimation of conditional distributional treatment effects. Identification rests on a parallel trends condition formulated in the parameter space of the semiparametric distribution regression (DR) model, which keeps the counterfactual conditional distribution within the model class. The weights solve a least-squares problem subject to an adding-up constraint, yielding a closed-form estimator. We derive the asymptotic distribution of the counterfactual estimator, with DR estimation error and weight estimation error contributing at the same rate to the asymptotic variance. Moreover, we propose a supremum test for the null of no treatment effect, whose limit is the supremum of a Gaussian process. Simulations illustrate that conditioning on covariates can reveal effects being difficult to detect from the unconditional distribution alone. An application to the 1992 New Jersey minimum wage increase using CPS data finds effects concentrated in the minimum-wage corridor for low-education, low-experience workers.