Since the seminal introduction of the propensity score by Rosenbaum and Rubin, propensity-score-based (PS-based) methods have been widely used for drawing causal inferences in the behavioral and social sciences. However, the propensity score approach depends on the ignorability assumption: there are no unobserved confounders once observed covariates are taken into account. For situations where this assumption may be violated, Heckman and his associates have recently developed a novel approach based on marginal treatment effects (MTE). In this paper, we (1) explicate consequences for PS-based methods when aspects of the ignorability assumption are violated; (2) compare PS-based methods and MTE-based methods by making a close examination of their identification assumptions and estimation performances; (3) apply these two approaches in estimating the economic return to college using data from NLSY 1979 and discuss their discrepancies in results. When there is a sorting gain but no systematic baseline difference between treated and untreated units given observed covariates, PS-based methods can identify the treatment effect of the treated (TT). The MTE approach performs best when there is a valid and strong instrumental variable (IV). In addition, this paper introduces the “smoothing-difference PS-based method,” which enables us to uncover heterogeneity across people of different propensity scores in both counterfactual outcomes and treatment effects.
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