Identification and Estimation of Unconditional Policy Effects of an Endogenous Binary Treatment: an Unconditional MTE Approach

This paper studies identification and estimation of unconditional policy effects when treatment status is binary and endogenous. We introduce a new class of unconditional marginal treatment effects (MTE) based on the influence function of the functional underlying the policy target. We show that an unconditional policy effect can be represented as a weighted average of the newly defined unconditional MTEs over the individuals who are indifferent about their treatment status. We provide conditions for point identification of the unconditional policy effects. When a quantile is the functional of interest, we characterize the asymptotic bias of the unconditional quantile regression (UQR) estimator that ignores the endogeneity of the treatment and elaborate on the channels that the endogeneity can render the UQR estimator inconsistent. We show that, even if the treatment status is exogenous, the UQR estimator can still be inconsistent when there are common covariates affecting both the treatment status and the outcome variable. To overcome the inconsistency of the UQR estimator, we introduce the UNconditional Instrumental Quantile Estimator (UNIQUE) and establish its consistency and asymptotic distri- bution. In the empirical application, we estimate the effect of changing college enrollment status, induced by higher tuition subsidy, on the quantiles of the wage distribution.