the full sample – choice and nonchoice – and apply that level of skewness to all of the residuals in their simulation exercise.<sup>24</sup> In addition, as noted above, they motivate dropping the high consumption observations from the PK Bangladesh data set, the 16 observations with the highest consumption in particular, that they call “the ones most responsible for the model-violating skew in the error,” in an effort to reduce the “bias” from skewness. However, a (weighted) 86 percent of these 16 observations are non-choice observations and thus cannot be implicated in any bias arising from skewness. These high consumption (i.e., non-poor) observations are primarily non-choice because they are so well off they are ineligible for microcredit, and thus it is expected that their consumption would be at the righttail of the distribution. It also suggests that the level of skewness and excess kurtosis is much lower in the sub-sample that matters, those with choice, than in the sub-sample most affected by the trimming strategy of RM – those without choice. Moreover, even if the errors in the choice sub-sample have skewness and excess kurtosis, we have shown that identification that arises from the inclusion of covariates in the model swamps any possibly faulty additional identification that may arise from specifying error distributions when the first-stage is Tobit, and which is demonstrated below with the actual Bangladesh data.<sup>25</sup> Readers of RM may incorrectly form the view that the positive female effects estimated by PK are the result of up to 16 observations having both female borrowers and very large values of household consumption, a combination that one might expect to make female credit effects more positive. That is, it might be expected that a very few program participants who report doing extraordinarily well can make a program look more effective than it is for most other participants. Conversely, if most of the observations with the very best outcomes were not treated by a credit program, then credit would look less effective in a regression. So it may seem surprising that in fact only one of the 16 high consumption observations has a female borrower, and that that one observation accounts for only a weighted 3.5 percent of the 16“outlier” observations that RM highlight, equivalent to about one-half of an observation. If 96.5 percent of the highest consumption observations have no female borrowing, then the standard outlier story suggests that this would make the estimated female credit effect smaller (less positive) since households having the very best household consumption outcomes were able to do so without female participation in a credit program. The standard intuition about the estimated effect of an independent variable on the dependent variable when there are “outliers” is wrong in this case as a consequence of the non-standard way in which parameter identification is achieved in the instrumental variables model of PK, a model in which (i) nonchoice observations are the source of identification, and (ii) households that are wealthy (consumption outliers) are denied choice by design. It is hard to understand why RM say nothing about the fact that the household consumption outliers they highlight are overwhelmingly not participating in female microcredit, even though their papers and posts going

> 24 PK (1998) estimate a single (second-stage) error variance for the choice observations and the nonchoice observations. The test statistic for the null hypothesis that the variance is equal across subsamples is χ<sup>2</sup> (1)=0.71, p=0.398.  This test statistic was obtained by directly adding an extra variance term into PK’s IV-ML estimation.

> 25 In the PK model, when the first-stage is linear the only source of identification is covariates and model is more robust to error distribution (Table 2, row 2).  The RM model is biased whatever the distribution of the errors.

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