Online Appendix for "Neighborhood Sanitation and Infant Mortality" by Michael Geruso and Dean Spears A.1 Sample Sizes Needed to Experimentally Identify Infant Mortality Externalities

In footnote 1 in the introduction, we noted that the number of neighborhood clusters required to detect even economically large infant mortality effects of open defecation (OD) via a field experiment is large, both because of the plausible effect size relative to the variance in mortality and because measuring local externalities necessarily implies randomization at the level of the locality, not the individual. We also noted that it can be difficult to generate a first stage effect on latrine use via experimental interventions. In this section, we illustrate these issues. We begin with a standard power calculation to determine the number of localities (clusters) required to detect an external effect of OD on IMR. Assume we wish to detect a minimum effect size of 3.5 infant deaths per thousand, which is 5% of mean IMR and a little larger than our OLS estimate of 2.7 to 2.9 deaths averted per 10 percentage point reduction in local open defecation. The calculation results in 8,622 clusters, based on a simple two-sided test. With the NFHS data, we can alternatively perform a more detailed calculation for the required sample size and cluster count via Monte Carlo simulation. Unlike the standard power calculation, this method naturally incorporates any heterogeneity in infant mortality that is present across clusters. For the simulation, we again assume that the true effect of a 10 percentage point reduction in local OD is equal to 5 percent of mean infant mortality, or 3.5 deaths per thousand. To implement the Monte Carlo simulation, we iterate over the following procedure, varying the number of sample clusters (Nc) included. We use PSUs from the NFHS data described in Section 2 as our clusters.