The goal of this paper is to use a semiparametric reduced form model to estimate the effects of various tuition subsidies. This approach expands on the tuition subsidy example in Ichimura and Taber (2000) in a number of dimensions. It has become common practice in the empirical literature to refer to any nonstructural empirical analysis as "reduced form." This is not the traditional sense of the phrase. A classic reduced form analysis (see e.g. Marschak, 1953) first specifies a structural model and then derives the reduced form parameters in terms of the structural parameters. While many recent studies have asserted to taking a reduced form approach, the structural parameters. While many recent studies have asserted to taking a reduced form approach, the structural model which the reduced form model should correspond is rarely specified. We explicitly specify a structural model and use the implied reduced form structure to estimate the effect of tuition subsidy policies. Specifying the underlying model has the advantage of being explicit about the assumptions that justify the analysis. This avoids Rosenzweig and Wolpin's (2000) criticism of work on natural 'natural experiments' that often leaves these conditions implicit. Our structural model is based on the model studied by Keane and Wolpin (1999). It is highly nonlinear and allows for more unobserved heterogeneity than the typical simultaneous equations framework that most previous work has used in reduced form estimation. Using hte specified structural model, we examine the assumptions discussed in Ichimura and Taber (2000) to justify reduced form estimation of the policy effects

Propensity-score matching is a nonexperimental method for estimating the average effect of social programs (see William Cochran, 1968; Paul Rosenbaum and Donald Rubin, 1983; James Heckman et al., 1998b). The method compares average outcomes of participants and nonparticipants, conditioning on the propensityscore value. The average comparison measures the average impact of a program. This methodology has received much attention recently in econometrics (see Heckman et al., 1996, 1997, 1998a, b; Jinyong Hahn, 1998; Rajeev Dehejia and Sadek Wahba, 1999; Jeffrey Smith and Petra Todd, 2000; Keisuke Hirano et al., 2000). The underlying identification requirement of the matching methodology is that the program choice is independent of outcomes conditional on a certain set of observables. While intuitively attractive in that the method replicates features of randomized experiments within observational data, the identification requirement excludes a possibility that the program-choice decision could be correlated with the outcomes given the set of observables (see Heckman et al., 1997, 1998b). Unobservables that are correlated both with an outcome and the program choice are not allowed. There are some efforts to estimate more general models using nonparametric methods (see Whitney Newey and James Powell, 1989; Heckman, 1997; Alberto Abadie, 2000; Serge Darolles et al., 2000; Matali Das, 2000; JeanPierre Florens, 2000; Ichimura and Taber, 2000). One such effort is the use of the instrumental-variable methods. Heckman (1997) has shown that the set of assumptions to justify instrumental-variable methods are very restrictive from the perspective of behavioral models of program participation. We show that his conditions justifying instrumental-variable methods actually justify the matching method as a special case.1 This observation ties the limitations of the matching method in line with those of instrumental-variable methods and also is useful in constructing specification tests for matching methods when valid instrumental variables are available. This is analogous to testing the validity of the identification conditions for ordinary least-squares (OLS) estimators when there are overidentifying instrumental variables. We then present two different propensityscore methods that are based on instrumental variables. Both methods include standard propensity-score matching as special cases. They help reduce the dimension of the conditioning variables without invoking functional-form assumptions in the same way that the standard propensity-score matching helps reduce the dimension of the conditioning variables. We show how to use these ideas to construct estimators that can be easily implemented.

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.

We present a simple way to estimate the effects of changes in a vector of observable variables X on a limited dependent variable Y when Y is a general nonseparable function of X and unobservables, and X is independent of the unobservables. We treat models in which Y is censored from above, below, or both. The basic idea is to first estimate the derivative of the conditional mean of Y given X at x with respect to x on the uncensored sample without correcting for the effect of x on the censored population. We then correct the derivative for the effects of the selection bias. We discuss nonparametric and semiparametric estimators for the derivative. We also discuss the cases of discrete regressors and of endogenous regressors in both cross section and panel data contexts.

This paper develops and applies semiparametric econometric methods to estimate the form of selection bias that arises from using nonexperimental comparison groups to evaluate social programs and to test the identifying assumptions that justify three widely-used classes of estimators and our extensions of them: (a) the method of matching; (b) the classical econometric selection model which represents the bias solely as a function of the probability of participation; and (c) the method of difference-in-differences. Using data from an experiment on a prototypical social program combined with unusually rich data from a nonexperimental comparison group, we reject the assumptions justifying matching and our extensions of that method but find evidence in support of the index-sufficient selection bias model and the assumptions that justify application of a conditional semiparametric version of the method of difference-in-difference. Fa comparable people and to appropriately weight participants and nonparticipants a sources of selection bias as conveniently measured. We present a rigorous defin bias and find that in our data it is a small component of conventially meausred it is still substantial when compared with experimentally-estimated program impa matching participants to comparison group members in the same labor market, givi same questionnaire, and making sure they have comparable characteristics substan the performance of any econometric program evaluation estimator. We show how t analysis to estimate the impact of treatment on the treated using ordinary obser

This paper examines changes in the distribution of wages using bounds to allow for the impact of nonrandom selection into work. We show that worst case bounds can be informative. However, because employment rates in the United Kingdom are often low, they are not informative about changes in educational or gender wage differentials. Thus we explore ways to tighten these bounds using restrictions motivated from economic theory. With these assumptions, we find convincing evidence of an increase in inequality within education groups, changes in educational differentials, and increases in the relative wages of women.