Column (1) of our Table 10 presents the baseline PK estimates as re-estimated with Roodman’s _cmp_ program and presented in Pitt (2011a), Table 1, column (3).<sup>33</sup> Column (2) of the table, labeled “No instruments,”<sup>34</sup> presents new estimates dropping all of the slope variables X and all of the village fixed effects from each first-stage equation (4) and (5), leaving only a constant term.<sup>35</sup> What is striking about a comparison of column (2) with column (1) is how little the parameter estimates have changed. Leaving out instruments that RM believe to be troublesome alters the points estimates hardly at all, improves the precision of the estimates, and leaves fully intact the PK conclusion that microcredit provided women positively affects household consumption while microcredit provided men has no statistically discernible effect.<sup>36</sup> In column (2) of our Table 10 we eliminated exclusion restrictions by dropping all of the exogenous variables, X, plus the village fixed effects (leaving only a constant term) from the first-stage. The polar opposite method to eliminate exclusion restrictions is to retain all of these variables in the first-stage equations and just add them to the second-stage equation. To implement this method, we include interactions between the dummy variable indicating a nontarget (ineligible) household with all of the slope variables X plus _thana_ (sub-district) fixed effects in column (3) of Table 10, and, alternatively, we include these variables separately interacted with male and female choice in column (4) of Table 10.<sup>37</sup> Once again, these estimates, labeled “No exclusion restrictions” in Table 10,<sup>38</sup> demonstrate the robustness of the PK results to the exclusion restrictions that RM believe are not credible.<sup>39</sup> To demonstrate that identification in the “no instruments” and “no exclusion restrictions” case does not depend on the Tobit nature of the first-stage equations, we re-estimate these models replacing the Tobit part of the pseudo-log-likelihood function in the first-stage with linear OLS. These estimates are presented in our Table 11. The first column of Table 11 just reproduces the “baseline” PK results of Table 10 and Pitt (2011a). Column (2) of the our Table 11 replaces Tobit with linear OLS with only a slight loss of precision as compared to the model

> 33 To remain consistent with the estimates of Pitt (2011a) and (2011b), we continue to use all three rounds of credit data in estimating the first-stage equation.

> 34 “No Instruments” means that the first-stage equations ((3) and (4)) have no slope terms.

> 35 This looks very much like a Wald estimator as there is a single binary instrument corresponding to each endogenous variable.  Because there are two correlated endogenous variables, the credit effect parameter is not given by the ratio of the difference in the means of the dependent variable over the difference in the means of the endogenous variable for each sub-sample as it is in the single endogenous variable case.

> 36 The log-likelihood function in the “no instruments” case is bimodal.

> 37 There are three villages in a _thana_ (sub-district) in the sample frame.  Using all villages interacted with both female and male choice yields very similar estimates.

> 38 “No exclusion restrictions” means that the second-stage equation contains the full set of slope interactions.

> 39 RM have done something similar in their Table 1 of RM (2011).  They present two sets of estimates, labeled “ _De facto_ ” and “ _De jure_ ” each in which just the choice dummy variables and then all of the instruments are included, in turn, into the second stage.  RM suggest that it is the nonlinearity of the Tobit instrumenting equations that permits model identification in this case.  They are mistaken.  The model is identified even if the first-stage instrumenting equations are linear OLS.  More importantly, even RM report that women’s credit effects are positive and significant under both the _de facto_ and _de jure_ rule when there are “no exclusion restrictions” in their Table 1, and that men’s effects are insignificantly different from zero.

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