Two-Way Exclusion Restrictions in Models with Heterogeneous Treatment Effects

Abstract

This paper discusses identification and estimation of nonparametric structural functions in models with discrete endogenous regressors (treatment) and additive treatment-specific error terms. We do not make functional form assumption or impose shape restrictions on the selection equation, which is also allowed to contain multi-dimensional error vectors. We focus on applications in which there exists two-way exclusive variables: (i) an outcome-exclusive variable which affects the treatment but is excluded from the potential outcome equation, (ii) another treatment-exclusive exogenous variable which affects the potential outcome but excluded from the selection equation. We nonparametrically identify the derivative of conditional average treatment effect and (up to a location normalization) the conditional average treatment effect. We also propose an asymptotically normal two-step estimator.