20 CHAPTER 4
reflect common trends affecting project participants and nonparticipants equally (such as changes in prices or weather) (Ravallion 2005). For example, if project participants and nonparticipants are different in their asset endow- ments (mostly observable) or in their abilities (mostly unobservable), and if those differences have an additive and fixed effect on outcomes during the period studied, such differences will have no confounding effect on the esti- mated ATT. Given that a large share of observations did not match, we sought to understand the impact of Fadama II on the unmatched beneficiaries. We did this evaluation by comparing the change in income and value of asset of beneficiaries and nonbeneficiaries, both of whom did not match; that is, we estimated DD using the straightforward equation (3), because these observa- tions did not match. This comparison helps us to better understand the varia- tion of the impact of the program across a wide range of beneficiaries. In principle, the double-difference approach can be used to assess project impacts without using PSM and will produce unbiased estimates of impact as long as these assumptions hold. However, if the project has differential effects on people with different levels of wealth or other observable characteristics, the simple double-difference estimator will produce biased estimates if par- ticipant and nonparticipant households differ in those characteristics (Raval- lion 2005). By combining PSM with the double-difference estimator, controls for differences in preproject observable characteristics can be established. A bias could still result from the heterogeneous or time-variant impacts of the unobservable differences between participants and nonparticipants. For example, communities and households that participated in Fadama I may have different responses to Fadama II than those that did not because of the cumulative effects of social capital developed under Fadama I, favorable or adverse experiences under Fadama I, or other factors.9 Such shortcomings are unfortunately inherent in all nonexperimental methods of impact assess- ment (Duflo, Glennerster, and Kremer 2006). Although no solution to these potential problems is perfect, we believe the method we have used addresses these issues as well as possible in this case.
The standard errors estimated by the double-difference method may be inconsistent because of serial correlation or other causes of a lack of in- dependence among the errors. In ordinary regression models, serial correla- tion can result from unobserved fixed effects, but by taking first differences, the double-difference method eliminates that source of serial correlation. However, serial correlation may still be a problem if more than two years of panel data are used (Duflo, Mullainathan, and Bertrand 2004). In our study,
9 Unfortunately, we did not collect information on respondents’ participation in Fadama I and thus could not try to test or control directly for such effects.
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