Propensity-Score Matching with Instrumental Variables
证明工具变量方法的假设条件实际上也支持倾向得分匹配，并提出了两种基于工具变量的倾向得分匹配方法，有助于在减少条件变量维度的同时进行更稳健的因果效应估计。
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.