METHODOLOGY 21
suitable instruments. Another method is the fixed-effect method from panel data analysis, where the assumption is that unobserved differences between the two groups are constant over time and are correlated with the indepen-
dent variables xj, which are also correlated with the unobserved individual specific effect αj. More recent methods, such as experimental and quasi- experimental methods, try to establish alternative scenarios that represent
the counterfactual situation by ensuring that the composition of the two groups remains the same over the course of the treatment. Each method has its advantages and disadvantages given the practical difficulties of testing the validity of the assumptions and cost implications and the quantitative requirements, among others, that are associated with using the different methods. In this study we use a combined matching and panel regression approach within a two-stage procedure to estimate the impact of the NAADS program on several outcome indicators. To generate greater confidence in the policy implications of our results, however, we also present results from using some of the other individual methods. We next present the individual methods to set the context, followed by our combined matching and panel regression approach.
Difference-in-Differences Method
Assuming that the outcome indicator of interest was growing or changing at the same rate between the treatment group and the control group prior to the treatment, the difference-in-differences (DID) or double differencing method, which measures the average gain or change in the outcome y over time in the treatment group less the average gain or change in the outcome y over time in the control group, can be used (Ravallion 2008). Albeit simple, this method removes biases in the comparison between the two groups that may be due to permanent differences between the two groups (e.g., location effect), as well as biases from comparison over time in the treatment group that may be due to time trends unrelated to the treatment. The impact of the NAADS program using this method can be obtained by estimating a difference equation of Equation 3.2 by OLS methods simply without the covariates, xj, as follows:
Δyj = α ˆ + δ ˆDIDNAADSj + yjt0 + ej, (3.4)
where Δyj = yt1 - yt0, and yt0 and yt1 are the outcomes in the initial and later periods, respectively. The method can be extended to include the covariates,
xj, as shown in Equation 3.5: Δyj = α
ˆ + β ˆ′DIDTΔxj + δ ˆDIDTNAADSj + yjt0 + ej. (3.5)
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