METHODOLOGICAL FRAMEWORK 19
comes between the two matched groups can be interpreted as the impact of the project on the beneficiaries (Smith and Todd 2001). We used this method to estimate the ATT for impacts of Fadama II on household productive assets, incomes, and indicators of access to and impact of rural infrastructure. The PSM method matches project beneficiaries with comparable non- beneficiaries using a propensity score, which is the estimated probability of being included in the project. Only beneficiaries and nonbeneficiaries with comparable propensity scores are used to estimate the ATT. Those who do not have comparable propensity scores are dropped from the comparison groups. In our study, 1,728 of 3,758 observations matched. Therefore we used only the matched observations to analyze the impact of Fadama II. Among the advantages of PSM over econometric regression methods is that it compares only comparable observations and does not rely on para- metric assumptions to identify the impacts of projects. However, PSM is sub- ject to the problem of selection on unobservables, meaning that the benefi- ciary and comparison groups may differ in unobservable characteristics, even though they are matched in terms of observable characteristics (Heckman et al. 1998). Econometric regression methods devised to address this problem suf- fer from the problems previously noted. As Heckman et al. (1998) further note, the bias resulting from comparing noncomparable observations can be much larger than that resulting from selection on unobservables, although this comparison may not be conclusively generalized.
In this study, we address the problem of selection on unobservables by combining PSM with the use of the double-difference estimator.8 This estima- tor compares changes in outcome measures (the change from before to after the project) between project participants and nonparticipants, rather than simply comparing outcome levels at one point in time:
DD = (Yp1 – Yp0) – (Ynp1 – Ynp0), (3)
where DD is the double-difference estimator; Yp0 and Yp1 are the outcomes of participants before and after project start, respectively; and Ynp0 and Ynp1 are the outcomes of nonparticipants before and after project start, respectively.
The advantage of the double-difference estimator is that it nets out the effects of any additive factors (whether observable or unobservable) that have fixed (time-invariant) impacts on the outcome indicator (such as the abilities of farmers or the inherent quality of natural resources) or that
8 The double-difference method is also known as the difference-in-difference method (Duflo, Mullainathan, and Bertrand 2004).
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