26 CHAPTER 3
(Imbens and Wooldridge 2009), while the regression isolates the effect of xj over time.
In a typical two-stage estimation procedure, it is important to address the identification of the second-stage regression or the endogeneity of the first- stage regression. A procedure commonly used is the imposition of exclusion restrictions in the sense of excluding some of the explanatory variables used in estimating the first-stage probit from the second-stage regression (i.e., having x ⊂ w or x ≠ w and corr (w, ε/x) = 0), which is similar to finding appro- priate instruments or predictors for treatment or participation in the NAADS program. In general, nonlinearity of the first-stage probit model, as here, renders exclusion restrictions unnecessary for identification (Wilde 2000). Furthermore, because we apply a fixed-effect or difference estimator in the second-stage regression, the condition is satisfied in the sense that Δx ≠ w. However, we still used exclusion restrictions to improve identification of the second-stage regression and tested the validity of the excluded variables using Hansen’s (1982) chi-squared test of identification. A critical feature of this combined estimator is that the sample of treated and comparison observations is restricted to be the same as in the matching estimator. Therefore, the 2SWR is estimated using the propensity scores (as weights) and samples associated with the different matching procedures, i.e., one, three, and five nearest-neighbor matches. The 2SWR estimator was used to estimate the impact of the NAADS program on several outcome indicators
mentioned earlier as well as to analyze the contribution of various factors (xj) on the different outcome indicators. Two different types of regressions were employed in the second-stage estimation depending on the type of dependent variable, how it was measured, and whether it was measured in both time periods. For dichotomous variables measured in both 2004 and 2007 (e.g., adoption of new crop and livestock enterprises and adoption of selected crop and livestock technologies and practices), we used the fixed-effects probit; otherwise (e.g., for demand of advisory services measured in 2007 only) we used the random-effects specification. For the other indicators that were measured as continuous variables, including crop and livestock productivity, market participation, and agricultural revenue, we used the first-difference fixed-effect regression.
The conceptual framework presented in Chapter 2 shows that change in some outcome indicators can affect change in other outcome indicators. For example, change in agricultural productivity (Q) can cause change in market participation (MKT), which together with change in agricultural productivity can cause change in income (INC). This means that the issue of simultaneity is important in estimating the structural model for each outcome variable. We avoid this problem by using the reduced-form single-equation approach,
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