18 CHAPTER 4
The expression in the first set of square brackets is observable, because it is the difference between the incomes of the beneficiaries and nonbeneficia-
ries. The second bracketed expression is unobservable, because E(Y0|p = 1) is unobservable and thus represents the bias resulting from estimating ATT as the first expression. This bias results because the incomes that non- beneficiaries receive without the project may not be equal to the incomes that
beneficiaries would have received without the project; that is, E(Y0|p = 1) may not equal E(Y0|p = 0).
Two common sources of bias are (1) project placement or targeting bias, in which the location or target population of the project is not random (such as when some subprojects of Fadama II are targeted to the poor and vulner- able, so that wealthier groups do not have an equal chance of participating), and (2) self-selection bias, in which households choose whether to participate and thus may be different in their experiences, endowments, and abilities.6 The most widely accepted method to address these biases is to use an experimental approach to construct an estimate of the counterfactual situa- tion by randomly assigning households to treatment (beneficiary) and control (nonbeneficiary) groups. Random assignment ensures that both groups are statistically similar (that is, that they are drawn from the same distribution) in both observable and unobservable characteristics, thus avoiding project placement and self-selection biases. Such an approach is not feasible in the present study, because project placement and participation decisions were already made before the design of the study and were probably not random. The notion of random assignment also conflicts with the nature of this CDD project, in which communities and households make their own decisions about whether to participate and what activities they will pursue, thus limit- ing the ability to use a randomized approach at the outset. Various quasi-experimental and nonexperimental methods have been used to address the bias problem (for details, see Rosenbaum and Rubin 1983; Heck- man, Ichimura, and Todd 1998; Heckman et al. 1998; Smith and Todd 2001). One of the most commonly used quasi-experimental methods is propensity score matching (PSM), which selects project beneficiaries and nonbeneficia- ries who are as similar as possible in terms of those observable characteristics expected to affect project participation and outcomes.7 The difference in out-
6 For example, a pastoralist in the state of Niger reported that he did not want to participate in
Fadama II because similar projects in the past had failed. 7 This method is referred to as quasi-experimental because it seeks to mimic the approach of experiments in identifying similar treatment and control groups. However, because the compari- son groups identified by PSM are not selected by random assignment, they may differ in un- observed characteristics.
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