characteristics. Once we obtain a sample of children who are matched (defined as the matched sample), we re-estimate the logistic regression on the matched sample. As mentioned earlier, in the context of this study, we consider children exposed to unimproved sanitation above the median value to be in the treated group while observations below the median value are included in the comparison group.<sup>20</sup> We also largely favor estimating regressions on the matched sample as opposed to simply estimating raw differences in the outcome value due to the double robustness discussed earlier.<sup>21</sup> Figure 2 presents the Propensity Score Balance between Treatment and Comparison Groups Prior to Matching. Figures 3 and 4 illustrate the propensity score balances before and after the matching specifications respectively. After matching, the estimated propensity scores in both the treatment and comparison group strongly align with each other. Similarly, as shown in Figure 4, the covariate balances across the different propensity score matching specifications have improved or narrowed.

Table 9 shows the results from our logistic regressions on the matched samples. Column (3) presents the regression results estimated on the coarsened exact matched sample,<sup>22</sup> and the results are very similar to those estimated from the nearest neighbor matched sample. For all age groups, it is estimated that unimproved sanitation exposure during the children’s early years decreases the likelihood of school enrollment by 7 percentage points, 8 percentage points for children between 6 and 7 years and around 4 percentage points for children between 8 and 9 years.

Columns (4) to (7) present the regression results on various propensity score matched samples. Similar but marginally stronger results are evident. Column (4) presents the regression results estimated on a caliper matched sample with three nearest neighbors. Unimproved sanitation decreases the likelihood of school enrollment by 8 percentage points for all children, about 8 percentage points for children between 6 and 7 years, and 4 percentage points for children between 8 and 9 years. The results were very similar when specified for the five nearest neighbors, as shown in column (5), suggesting that there is little concern for biases due to matching quality or number of matches while increasing the sample of

> 20 Again, the median unimproved sanitation ratio is found to be 34.5 percent; 3,517 children (55 percent) under the median value are categorized as the comparison group while 2,882 children (45 percent) above the median value are included in the treatment group.

> 21 In addition, these regressions allow for the estimation of the effects of unimproved sanitation in its current configuration as a continuous variable rather than a dichotomous variable. We use the dichotomous version of the variable for the matching process while retaining its continuous form for the subsequent regression analyses on the matched samples. This will also enable comparison with the earlier estimated results.

> 22 We specify covariates that are identified to be key correlates of school enrollment found in the earlier logistic regressions and then estimate the effect of unimproved sanitation on school enrollment controlling for the other covariates using a logistic regression (Blackwell et al., 2009). The resulting logistic regression will be able to control for the remaining imbalance resulting from the matching process. The variables included for the coarsened exact matching process are dummy indicators for urban households, households in the top 60 percentile of the wealth distribution, mother’s education, child’s sex and age, improved sanitation, as well as the Division. We matched the children within each DHS year, using the Stata user-written program _cem_ introduced in Blackwell et al. (2009) to execute the matching. Of the 6,399 children, 2,519 treatment children are matched to 3,175 children in the comparison group.

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