22 CHAPTER 3
With the DID method, possible serial correlation (i.e., cov(εt, εt–1) ≠ 0) is not considered. Although we do not have historical data on the outcome indica-
tors prior to treatment to test the validity of the underlying assumption, we minimize the effects of violating the assumption by estimating Equations 3.4 and 3.5 using a matched sample of the treatment and control groups (dis- cussed in the next two subsections). In general, the DID method, especially the specification without the covariates, is one that many policymakers can identify with, and the results can be used as a basis to compare the results obtained using other more complex methods.
Propensity Score Matching Method
The fundamental problem in applying the DID and other conventional evalu- ation methods is lack of overlap in the covariate distributions or common support between the treatment and control observations (Imbens and Wool- dridge 2009). This problem is what is usually referred to as comparing apples and oranges. The propensity score matching (PSM) method, which is a quasi- experimental method now commonly used in program evaluation, tries to address this problem by selecting program participants (treatments) and non- participants (controls) that are as similar as possible in terms of pre-treatment observable characteristics that are expected to affect the decision and extent of participation in the program as well as the outcomes due to participation.6 The difference in outcomes between the two matched groups can be inter- preted as the impact of the program on the participants (Smith and Todd 2005). In practice, the PSM method matches subgroups of program partici- pants with comparable subgroups of nonparticipants using a propensity score, which is the estimated conditional probability of participation in the pro- gram.7 In this case, only participants who have comparable propensity scores or have matches are used in the estimation. Those who do not have compa- rable propensity scores or have no matches are dropped prior to the estima- tion. After selecting the comparable subgroups, the counterfactual of each participant, that is, the value of the outcome if the participant had not participated in the program (y
ˆ0j|NAADSj = 1), is imputed as the average of
the observed outcomes of the participant’s nonparticipant matches. Assuming i = 1, 2, . . . M matches for the jth observation,
6 This method is referred to as a quasiexperimental method because it seeks to mimic the approach of experiments in identifying similar “treatment” and “control” groups. However, because the comparison groups identified in the PSM method are not selected by random assign- ment, they may differ in unobserved characteristics even though they are matched in terms of
observable characteristics. See Imbens and Wooldridge (2009) for a review. 7 See Becker and Ichino (2002) on how to implement the PSM method.
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