SELECTION BIAS: Our Data 2

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Table 3 presents the estimated coefficients of the logit model P(X). Variables are included in the model on the basis of two criteria: (a) minimization of classification error when P(X) > Pc is used to predict D = 1 and P{X)
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Figure 2 presents the distributions of the estimated P{X) in the {D = 0} and {D = 1} groups. We obtain similar distributions for P(X) using alternative sets of regressors.32 This figure indicates the potential importance of defining bias on a common support of P(X). For the sample of controls, the histogram of P(X) values has support over the entire [0,1] interval. Surprisingly, however, the mode of the distribution of P(X) for controls is near zero. Many controls have a low estimated probability of participation. In the sample of ENPs, the support of P(X) is concentrated in the interval [0,0.225]. Thus, the bias measure BsP, which is the bias defined conditional on P(X) rather than X, is defined only over a fairly limited interval. As a result of this restriction on the support, any nonexperimental evaluation can nonparametrically estimate program impacts defined only over this interval. As we demonstrate below, the difference between the distributions of the estimated values of P has important implications for understanding the sources of selection bias as conventionally measured. Before presenting this decomposition, we first develop some econometric tools that are used in the empirical results reported in this paper.