_Table 13: Robustness check results for alternative methods for household level model_

||Sri Lanka|||||Tanzania|||||
|---|---|---|---|---|---|---|---|---|---|---|
||Mean<br>poverty|Mean<br>MSE|Mean<br>CV|Corr|CR|Mean<br>poverty|Mean<br>MSE|Mean<br>CV|Corr|CR|
|Baseline EMDI Estimates|3.7|4.6|32.0|87.6|84.3|18.6|11.1|17.5|87.6|74.8|
|Stata SAE with<br>traditional bootstrap|3.7|10.9*|43.6|85.5|95.5|19.7|44.6*|33.4|88.3|93.1|
|With no Empirical Best|3.7|17.5*|62.4|83.6|99.1|19.8|55.9*|38.0|89.2|95.6|
|Stata SAE with<br>parametric bootstrap|3.6|6.8|38.4|85.6|85.8|21.4|10.0|15.6|85.0|64.2|
|No heteroscedasticity<br>correction|3.8|5.5|33.9|88.0|84.9|22.4|10.7|16.0|84.4|66.7|
|EMDI estimates with:|||||||||||
|No simulation weights|3.7|4.8|31.9|87.5|82.8|18.3|11.8|17.8|87.4|73.0|
|Box-Cox transformation|3.5|4.7|31.2|87.4|81.9|15.8|13.1|18.7|87.5|76.1|
|Stepwise (p=0.01)<br>model selection|3.7|4.7|27.9|83.0|80.7|18.8|9.8|16.4|86.5|69.8|
|Swappedpovertyrates|19.6|18.4|17.4|94.8|84.9|2.8|1.6|32.9|86.1|69.8|

_Notes: Rows represent different variants of household-level model as listed in Table 12. Columns represent mean poverty rates, average mean squared error times 10,000, mean coefficient of variation, correlation with actual census value (Corr), and coverage rate (CR). All means are unweighted across 331 subdistricts in Sri Lanka and 159 Districts in Tanzania. All results except for mean poverty reflect benchmarking to survey estimates for 25 districts in Sri Lanka and 25 regions in Tanzania. Asterisks indicate mean estimated variance instead of mean squared error._ value threshold of 1 percent. The resulting models are overfit. This leads to less accurate predictions than the Lasso-selected model in both countries and slightly reduces mean squared error in Tanzania, leading to a moderate fall in coverage rates in both countries. Finally, we report the results of the EMDI estimators when the poverty rates of the two countries are swapped. Not surprisingly, the performance of the model improves in Sri Lanka when the poverty rate is set to 20 percent, as the remote sensing indicators better predict poverty rates when they are larger. When setting the poverty rate to 4 percent in Tanzania, the EMDI estimator tends to underestimate poverty, with a mean predicted poverty rate of 2.8 percent. However, the correlation between the estimates and the true census poverty rate remains strong at 86.1 percent, and the benchmarked coverage rate of 70 percent is respectable.

Overall, of the many robustness checks considered so far, there are only two main cases where the results are particularly sensitive to the choice of method. The first is the use of the traditional rather than parametric bootstrap, which leads to a much higher estimated variance, coefficient of variation, and coverage rate of the estimates. The traditional bootstrap is not recommended when using Empirical Best models on theoretical grounds, since the estimate is conditioned on the sample (Diallo and Rao, 2018). The other case where the results change dramatically is the omission of the empirical best option, which roughly quadruples the MSEs and doubles the CVs compared to the baseline estimates, 32