Estimating 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 and outcomes of interest, but also in how they respond to a particular treatment, intervention, or stimulation. Moreover, individuals may self-select into treatment on the basis of their anticipated treatment effects. To study heterogeneous treatment effects in the presence of self-selection, Heckman and his colleagues have developed a structural approach that builds on the marginal treatment effect (MTE). In this paper, we propose a revision of the MTE-based approach through a redefinition of the MTE. Specifically, we redefine MTE as the expected treatment effect conditional on the propensity score (instead of the vector of observed covariates) as well as a latent variable representing unobserved resistance to treatment. The redefined MTE is superior to the original MTE in a number of aspects. First, while it is conditional on a unidimensional summary of covariates, it is sufficient to capture all of the treatment effect heterogeneity that is consequential for selection bias. Second, the new MTE is a bivariate function, thus much easier than the original MTE to be visualized. Third, as with the original MTE, the new MTE can also be used as a building block with which to estimate causal effects in the aggregate. However, the weights associated with the new MTE are simpler, more intuitive, and much easier to implement. Finally, the newly defined MTE allows us to directly assess 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 effort, and to design policy interventions that maximize the marginal benefits of treatment.