Estimating Marginal Treatment Effects under Unobserved Group Heterogeneity

This paper studies endogenous treatment effect models in which individuals are classified into unobserved groups based on heterogeneous treatment choice rules. Such heterogeneity may arise, for example, when multiple treatment eligibility criteria and different preference patterns exist. Using a finite mixture approach, we propose a marginal treatment effect (MTE) framework in which the treatment choice and outcome equations can be heterogeneous across groups. Under the availability of valid instrumental variables specific to each group, we show that the MTE for each group can be separately identified using the local instrumental variable method. Based on our identification result, we propose a two-step semiparametric procedure for estimating the group-wise MTE parameters. We first estimate the finite-mixture treatment choice model by a maximum likelihood method and then estimate the MTEs using a series approximation method. We prove that the proposed MTE estimator is consistent and asymptotically normally distributed. We illustrate the usefulness of the proposed method with an application to economic returns to college education.