Sharp Bounds and Inference in Sample Selection Models with Treatment Endogeneity

This paper provides partial identification and inference for treatment effects in nonparametric sample selection models with endogenous treatment and (weak) sample selection monotonicity. Outcomes are observed only for a non-randomly selected subsample and treatment is endogenous because of noncompliance with assignment. The proposed bounds for intensive margin treatment effects among compliers are sharp and tighter than those of Chen and Flores (2015). For inference, we develop semiparametrically efficient orthogonal moments and a debiased machine learning procedure that permits valid root-$n$ inference under high-dimensional covariates and/or flexible functional forms. Simulation results indicate good finite sample performance. Applications to Job Corps and the Oregon Health Insurance Experiment show that the method can deliver substantially tighter effect bounds and confidence intervals than existing alternatives.