Estimating Marginal Treatment Effects under Unobserved Group Heterogeneity

Document pages: 39 pages

Abstract: This paper studies endogenous treatment effect models in which individualsare classified into unobserved groups based on heterogeneous treatment choicerules. Such heterogeneity may arise, for example, when multiple treatmenteligibility criteria and different preference patterns exist. Using a finitemixture approach, we propose a marginal treatment effect (MTE) framework inwhich the treatment choice and outcome equations can be heterogeneous acrossgroups. Under the availability of valid instrumental variables specific to eachgroup, we show that the MTE for each group can be separately identified usingthe local instrumental variable method. Based on our identification result, wepropose a two-step semiparametric procedure for estimating the group-wise MTEparameters. We first estimate the finite-mixture treatment choice model by amaximum likelihood method and then estimate the MTEs using a seriesapproximation method. We prove that the proposed MTE estimator is consistentand asymptotically normally distributed. We illustrate the usefulness of theproposed method with an application to economic returns to college education.