Estimation of Heterogeneous Treatment Effects Using a Conditional Moment Based Approach

Abstract: We propose a new estimator for heterogeneous treatment effects in a partially linear model (PLM) with multiple exogenous covariates and a potentially endogenous treatment variable. Our approach integrates a Robinson transformation to handle the nonparametric component, the Smooth Minimum Distance (SMD) method to leverage conditional mean independence restrictions, and a Neyman-Orthogonalized first-order condition (FOC). By employing regularized model selection techniques like the Lasso method, our estimator accommodates numerous covariates while exhibiting reduced bias, consistency, and asymptotic normality. Simulations demonstrate its robust performance with diverse instrument sets compared to traditional GMM-type estimators. Applying this method to estimate Medicaid's heterogeneous treatment effects from the Oregon Health Insurance Experiment reveals more robust and reliable results than conventional GMM approaches.