Accounting for individual-level heterogeneity in the response to treatment is a major development in the econometric literature on program evaluation. A substantial body of empirical evidence demonstrates that econometric models fit on individual-level data manifest heterogeneity in treatment effects that is present even after conditioning on observables. An important distinction is the one between evaluation models where participation in the program being evaluated is based, at least in part, on unobserved idiosyncratic responses to treatment and models where participation is not based on unobserved idiosyncratic responses. This is the distinction between selection on unobservables and selection on observables. The validity of entire classes of evaluation estimators hinges on whether or not they allow agents to act on unobserved idiosyncratic responses. In a wide variety of applications, the available evidence suggests that not only are ex post (postenrollment) responses heterogeneous, but that ex ante decisions to participate in programs are based, in part, on these heterogeneous responses (Heckman and Vytlacil, 2000b, 2001).

Treatment Effect Bounds under Monotonicity Assumptions: An Application to Swan-Ganz Catheterization by Jay Bhattacharya, Azeem M. Shaikh and Edward Vytlacil. Published in volume 98, issue 2, pages 351-56 of American Economic Review, May 2008

This paper estimates marginal returns to college for individuals induced to enroll in college by different marginal policy changes. The recent instrumental variables literature seeks to estimate this parameter, but in general it does so only under strong assumptions that are tested and found wanting. We show how to utilize economic theory and local instrumental variables estimators to estimate the effect of marginal policy changes. Our empirical analysis shows that returns are higher for individuals with values of unobservables that make them more likely to attend college. We contrast our estimates with IV estimates of the return to schooling.