10 improve comparability. The approach adopted in this paper is that suggested by Crump et al. (2006), who suggest trimming the sample in such a way as to minimize the variance of the estimated average treatment effects. The implications of this for the sample used are discussed further below. _All_ the control group cases retained in the analysis are used to construct the counterfactual outcome for the treated individuals (i.e. the HCFP beneficiaries) via kernel matching.<sup>9</sup> This can be thought of as a weighted regression of the outcome on the treatment indicator variable, the kernel weights being a decreasing function of the absolute difference in propensity score between the treated and untreated unit (Smith and Todd 2005).<sup>10</sup> The sensitivity of the results to the choice of estimator are checked by matching treated and untreated cases via weights based directly on the propensity score. This estimator can also be implemented as a weighted regression of the outcome on the treatment indicator, where the weight is one for a treated unit, and _P_ /(1- _P_ ) for the untreated unit, _P_ being the (estimated) propensity score (cf. Imbens 2004). The regression implementation reduces the computational burden, substantially in the case where there are many outcome indicators.<sup>11</sup> A further attraction is that it facilitates estimates of differences in impact across subsamples. In the present context, given the specific focus of the program on the poor, an obvious dimension along which to explore differential impact is income. By regressing the outcome on the treatment indicator, income (or, more accurately, consumption) category dummies, and interactions between the two, weighting the regression by the kernel or propensity score weights, one can obtain estimates of the impacts for the different income groups.<sup>12</sup> The regression using propensity score weights leads directly to robust standard errors. In the case of kernel matching, standard errors are obtained through bootstrapping with 100 replications.<sup>13</sup>

> 9  Cf. nearest-neighbor matching which results in a further dropping of cases that are not close enough in terms of their propensity scores.

> 10 A normal (Gaussian) kernel was used with a bandwidth of 0.06.

> 11 The regression routine in Stata is much faster than psmatch2 or other matching routines. The kernel weights need be estimated just for one outcome (which can be done using psmatch2), and then used in regressions for the other outcomes.

> 12  This method also provides a simple way to obtain impacts for different income groups using the DD _without_ matching. With or without matching (i.e. weighting), the impact for a particular income group is the sum of the coefficient on the NCMS treatment indicator plus the coefficient on the interaction between the treatment dummy and the income group dummy.

> 13  These turn out to be similar in fact to those obtained from the regression. The reservations that have been expressed about bootstrapping standard errors in matching do not apply to the kernel method, because it does not run into the discontinuities that arise in nearest-neighbor matching (see e.g. Imbens 2004).