JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact support@jstor.org.. Oxford University Press and The Review of Economic Studies, Ltd. are collaborating with JSTOR to digitize, preserve and extend access to The Review of Economic Studies. This paper considers whether it is possible to devise a nonexperimental procedure for evaluating a prototypical job training programme. Using rich nonexperimental data, we examine the performance of a two-stage evaluation methodology that (a) estimates the probability that a person participates in a programme and (b) uses the estimated probability in extensions of the classical method of matching. We decompose the conventional measure of programme evaluation bias into several components and find that bias due to selection on unobservables, commonly called selection bias in econometrics, is empirically less important than other components, although it is still a sizeable fraction of the estimated programme impact. Matching methods applied to comparison groups located in the same labour markets as participants and administered the same questionnaire eliminate much of the bias as conventionally measured, but the remaining bias is a considerable fraction of experimentally-determined programme impact estimates. We test and reject the identifying assumptions that justify the classical method of matching. We present a nonparametric conditional difference-in-differences extension of the method of matching that is consistent with the classical index-sufficient sample selection model and is not rejected by our tests of identifying assumptions. This estimator is effective in eliminating bias, especially when it is due to temporallyinvariant omitted variables.

This paper develops the method of matching as an econometric evaluation estimator. A rigorous distribution theory for kernel-based matching is presented. The method of matching is extended to more general conditions than the ones assumed in the statistical literature on the topic. We focus on the method of propensity score matching and show that it is not necessarily better, in the sense of reducing the variance of the resulting estimator, to use the propensity score method even if propensity score is known. We extend the statistical literature on the propensity score by considering the case when it is estimated both parametrically and nonparametrically. We examine the benefits of separability and exclusion restrictions in improving the efficiency of the estimator. Our methods also apply to the econometric selection bias estimator.

JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact support@jstor.org.Semiparametric methods are developed to estimate the bias that arises from using nonexperimental comparison groups to evaluate social programs and to test the identifying assumptions that justify matching, selection models, and the method of differencein-differences. Using data from an experiment on a prototypical social program and data from nonexperimental comparison groups, we reject the assumptions justifying matching and our extensions of it. The evidence supports the selection bias model and the assumptions that justify a semiparametric version of the method of difference-in-differences. We extend our analysis to consider applications of the methods to ordinary observational data. This content downloaded from 138.38.44.95 on Mon, 20 Jun 2016 12:01:09 UTC All use subject to http://about.jstor.org/terms 2 These estimators and the identifying assumptions that justify them are summarized in Heckman

For the class of single-index models, I construct a semiparametric estimator of coefficients up to a multiplicative constant that exhibits 1/ v'n-consistency and asymptotic normality. This class of models includes censored and truncated Tobit models, binary choice models, and duration models with unobserved individual heterogeneity and random censoring. I also investigate a weighting scheme that achieves the semi parametric efficiency bound. •1 thank Professors Daniel McFadden and James Powell fovadvice and Professor Charles Manski for encouragement. I have benefited from many comments I received from Professors Jonathan Feinstein, Robert Gertner, Peter Hall, Lung-Fei Lee, Daniel McFadden, and Kazumitsu Nawata. The points lowe to them are indicated in the paper. I also received extensive editorial suggestions from Dr. Steven Herzenberg on a very early version and professional editorial help from Patricia Haswell on this version. I am grateful to all of these individuals. This paper supersedes three earlier papers, "Single Index Models and their Consistent Semi parametric Estimation" (October 1985), "Estimation of Single Index Models" (September 1987) (Ph.D. thesis), and "Semi parametric Least Squares Estimation of Single Index Models" (August 1988).

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