replicators is important and it is their responsibility to take extra care in the quality of their methods and the claims they make (e.g. Pitt 2012).

# **5.  Summary**

This response paper refutes the claims of Roodman and Morduch that were not addressed in the earlier World Bank working paper of Pitt and Khandker (2012). This response paper, like the Pitt and Khandker (2012) paper and others that preceeded it, shows that many of the Roodman and Morduch claims are based on a flawed econometric understanding and a lack of due diligence in formulating and interpreting statistical models.

One claim highlighted by RM is that the PK results are not robust to deviations from normality of the second-stage errors, and that this non-normality is an important source of bias in PK. The determinants of the outcome (household consumption) for those without choice to participate in a credit program is simply estimated by PK using ordinary least squares and, as is well known, does not require normality. Roodman and Morduch, having improperly stated the distributional requirements of the errors, proceed to drop high consumption observations as a _cure_ even though they are predominately in the OLS part of the model and thus are not part of the error term that matters – the error associated with observations that have a choice to join a credit program. Furthermore, this paper demonstrates that symmetrically dropping 2.5 percent of the sample with choice from each tail of household consumption (i) actually strengthens the PK results, and (ii) cannot reject normality of the error for those with choice.

RM provide evidence from simulations that seemingly demonstrate the consistency of their approach as compared to that of Pitt and Khandker. Their simulation is for the unrealistic special case in which there are no exogenous variables at all in the model, only a constant. In Pitt and Khandker it is the exogenous variables that, coupled with non-choice observations, are ultimately the source of identification and since there are about 80 exogenous independent variables in every equation PK estimate, this is a very peculiar specification by RM with which to examine the econometric properties of the PK results. This peculiar choice is better understood by knowing that it is the independent variables that are the source of bias in the Roodman and Morduch specification. It is the existence of exogenous covariates that generates the plethora of interaction terms in the misspecified 2SLS setup of RM that make the RM instrument set weak and the linear LIML estimates invalid. This was discussed at length in Pitt and Khandker (2012) and yet RM continue to ignore the issue. This issue is key in that using the asymptotically correct standard 2SLS formula to compute t-ratios for the credit effects parameters that <u>RM estimate by linear LIML and report in column (2) of Table 5 of RM yields statistically significant and</u> large positive effect of women’s credit on household consumption.

Although RM follow an incorrect strategy to deal with non-normal second-stage errors, their dropping (“trimming”) of high consumption observations does alter the IV-ML results of PK but does not follow the PK protocol. The RM approach of deleting a single selected set of observations and then obtaining estimates that do not follow the protocol clearly described and implemented in PK cannot be seen to “destroy” the PK results. Rather, more defensible symmetric trimming methods, as well as asymmetric trimming of more observations, reinforce the PK results.

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