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Heterogeneous Treatment Effects in the Presence of Self-Selection: A Propensity Score Perspective

An essential feature common to all empirical social research is variability across units of analysis. Individuals differ not only in background characteristics but also in how they respond to a particular treatment, intervention, or stimulation. Moreover, individuals may self-select into treatment on the basis of anticipated treatment effects. To study heterogeneous treatment effects in the presence of self-selection, Heckman and Vytlacil developed a structural approach that builds on the marginal treatment effect (MTE). In this article, we extend the MTE-based approach through a redefinition of MTE. Specifically, we redefine MTE as the expected treatment effect conditional on the propensity score (rather than all observed covariates) as well as a latent variable representing unobserved resistance to treatment. As with the original MTE, the new MTE also can be used as a building block for evaluating standard causal estimands. However, the weights associated with the new MTE are simpler, more intuitive, and easier to compute. Moreover, the new MTE is a bivariate function and thus is easier to visualize than the original MTE. Finally, the redefined MTE immediately reveals treatment-effect heterogeneity among individuals who are at the margin of treatment. As a result, it can be used to evaluate a wide range of policy changes with little analytical twist and design policy interventions that optimize the marginal benefits of treatment. We illustrate the proposed method by estimating heterogeneous economic returns to college with National Longitudinal Study of Youth 1979 data.