METHODOLOGY 25
acteristics can be tested with the omitted variable test (Greene 1993), but this is useful only to the extent that potential omitted variables or their proxies are available to be included in the participation decision model. The tests for com- mon support (i.e., histograms of the propensity scores and balancing test) also depend on the participation decision model’s being correctly specified and estimated. Careful selection of covariates that include several variables mea- sured at different levels (farm, household, community, and region) can be used to minimize the omitted-variable problem and improve common support. Another limitation with using the matching method is that, unlike the DID esti- mator shown in Equation 3.5, the contribution of other factors (x) to achieving the outcomes and impacts cannot be analyzed. Thus it seems that combining the two methods, the preferred approach used in this study, will yield more consistent estimates of the treatment effect than using either method alone. This issue is taken up next.
Two-Stage Weighted Regression (or Combined Matching and Panel Regression) Method
To net out the effect of time-variant factors on the outcome over the period of treatment, a regression method is necessary. Because of the potential
correlation between the covariates (xj) and the treatment variable (NAADSj), however, conventional regression methods including instrumental variables may not be sufficient. This problem can be interpreted as a multicollinear- ity problem the severity of whose consequences increases with increasing differences in the covariate distribution or with decreasing common support between participants and nonparticipants of the program (Imbens and Wool- dridge 2009). Given the merits of the matching estimator, particularly in reducing the bias between the two groups, we combine matching and regres- sion in a two-stage estimation procedure (Robins and Rotnitzky 1995; Robins, Rotnitzky, and Zhao 1995; Imbens and Wooldridge 2009). Equation 3.3 is first estimated by probit to obtain the propensity scores, which are then used as weights in a second-stage estimation of Equation 3.2. Basically, we apply a two-stage weighted regression (2SWR) method, using the propensity scores from the matching estimator as weights in the DID estimators as follows:
Δyj = α and Δyj = α ˆ + β ˆ′2SWRTΔxj + δ ˆ2SWRTNAADSj + yjt0 + ej. The impact of the NAADS program or the ATT is measured by δ (3.9) ˆ2SWR and δ ˆ2SWRT
for the two model specifications, respectively. The weighting can be inter- preted as removing the bias due to any correlation between xj and NAADSj
ˆ + δ ˆ2SWRNAADSj + yjt0 + ej, (3.8)
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