  This paper considers estimation and inference for heterogeneous
counterfactual effects with high-dimensional data. We propose a novel robust
score for debiased estimation of the unconditional quantile regression (Firpo,
Fortin, and Lemieux, 2009) as a measure of heterogeneous counterfactual
marginal effects. We propose a multiplier bootstrap inference and develop
asymptotic theories to guarantee the size control in large sample. Simulation
studies support our theories. Applying the proposed method to Job Corps survey
data, we find that a policy which counterfactually extends the duration of
exposures to the Job Corps training program will be effective especially for
the targeted subpopulations of lower potential wage earners.
