LAUSR

Abstract Donald and Hsu (2014) studied the estimation and inference for the counterfactual distribution and quantile functions in a binary treatment model. We extend their work to the continuous treatment model. Specifically, we propose a weighted regression estimator for the counterfactual distribution but we estimate the weighting function from a covariate balancing equation by maximizing a globally concave criterion function. We estimate the quantile function by inverting the estimated counterfactual distribution. To test the distributional effect, we consider the (uniform) confidence bands, the sup and L 2 distance, and the Mann–Whitney test. We also consider the stochastic dominance test for the distributional effect and the L 2 test for constant quantiles. A simulation study reveals that our tests exhibit a satisfactory finite-sample performance, and an application shows their practical value.