. We thank Jaap Abbring, Richard Blundell and two anonymous referees for helpful comments on the first round reports. We benefited from the close reading of Ricardo Avelino, Jean-Marc Robin, Sergio Urzua, and Weerachart Kilenthong on the second draft. We have benefited from a close reading by Jora Stixrud and Sergio Urzua on the third draft. We have also benefited from comments by an anonymous referee on the second draft of this paper. Sergio Urzua provided valuable research assistance in programming the simulations reported in this paper and was assisted by Hanna Lee. Urzua made valuable contributions to our understanding of the random coefficient case and cases with negative weights and made numerous valuable comments on this draft, as did Weerachart Kilenthong. See our companion paper (Heckman, Urzua, and Vytlacil, 2004) where these topics are developed further.

This paper examines the properties of instrumental variables (IV) applied to models with essential heterogeneity, that is, models where responses to interventions are heterogeneous and agents adopt treatments (participate in programs) with at least partial knowledge of their idiosyncratic response. We analyze two-outcome and multiple-outcome models, including ordered and unordered choice models. We allow for transition-specific and general instruments. We generalize previous analyses by developing weights for treatment effects for general instruments. We develop a simple test for the presence of essential heterogeneity. We note the asymmetry of the model of essential heterogeneity: outcomes of choices are heterogeneous in a general way; choices are not. When both choices and outcomes are permitted to be symmetrically heterogeneous, the method of IV breaks down for estimating treatment parameters. Copyright by the President and Fellows of Harvard College and the Massachusetts Institute of Technology.

This paper examines the relationship between various treatment parameters within a latent variable model when the effects of treatment depend on the recipient's observed and unobserved characteristics. We show how this relationship can be used to identify the treatment parameters when they are identified and to bound the parameters when they are not identified.

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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. KeywordsReturns to Schooling; Marginal Return; Average Return; Marginal Treatment Effect Estimating the marginal return to policies is a central task of economic cost-benefit analysis. A comparison between marginal benefits and marginal costs determines the optimal size of a social program. For example, to evaluate the optimality of a policy that promotes expansion in college attendance, analysts need to estimate the return to college for the marginal student, and compare it to the marginal cost of the policy. This is a relatively simple task (a) if the effect of the policy is the same for everyone (conditional on observed variables) or (b) if the effect of the policy varies across individuals given observed variables but agents either do not know their idiosyncratic returns to the policy, or if they know them, they do not act on them. In these cases, individuals do not choose their schooling based on their realized idiosyncratic individual returns, and thus the marginal and average ex post returns to schooling are the same. 1 * edward.vytlacil@yale.edu. . The Web Appendix for this paper is http://jenni.uchicago.edu/estimating_returns_ed/. 1 See James J. Heckman and Edward J. Vytlacil (2007b). NIH Public Access Author ManuscriptAm Econ Rev. Author manuscript; available in PMC 2014 August 08. NIH-PA Author Manuscript NIH-PA Author Manuscript NIH-PA Author ManuscriptUnder these conditions, the mean marginal return to college can be estimated using conventional methods applied to the following Mincer equation: (1) where Y is the log wage, S is a dummy variable indicating college attendance, β is the return to schooling (which may vary among persons) and ε is a residual. The standard problem of selection bias (S correlated with ε) may be present, but this problem can be solved by a variety of conventional methods (instrumental variables, regression discontinuity, and selection models).The recent literature shows how to empirically test the conditions that justify conventional methods (James J. Sergio Urzua 2010 andHeckman and. Applying these methods on data from the National Longitudinal Survey of Youth of 1979 (NLSY), we find that returns vary (i.e. β is random) and furthermore agents act as if they possess some knowledge of their idiosyncratic return (i.e., β is correlated with S). Selection on gains complicates the estimation of marginal returns.Under assumption...

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provided helpful comments on various drafts. Supplementary material for this paper is available at the website http;//jenni.uchicago.edu/underiv. The views expressed herein are those of the author(s) and do not necessarily reflect the views of the National Bureau of Economic Research.