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

The content of this paper is solely the responsibility of the authors and does not necessarily represent the official views of the National Institutes of Health. [...] The methodological rationale for this approach is that under the assumption of ignorability, the interaction between treatment status and the propensity score captures all of the treatment effect heterogeneity that is consequential for selection bias (Rosenbaum and Rubin 1983). [...] In a series of papers, Heckman and his col- leagues have also established the key roles of the propensity score in a variety of econometric methods, including control functions, instrumental variables, and the MTE approach (Heckman and Robb 1986; Heckman and Hotz 1989; Heckman and Navarro-Lozano 2004; Heckman 2010).1 In the MTE approach, for example, incremental changes in the propensity score ser. [...] (2011), we use the following instrumental variables (Z\X): (a) the presence of a four-year college in the county of residence at age 14, (b) local wage in the county of residence at age 17, (c) local unemployment rate in the state of residence at age 17, and (d) average tuition in public four-year colleges in the county of residence at age 17, as well as their interactions with mother’s years of s. [...] In this case, the unconditional approach can partly exploit the variation of treatment effect by X (through the first component of equation (16)) whereas the conditional approach cannot (since it focuses exclusively on the second component of equation (16)).