_Table 14: Robustness check for benchmarking_

||Sri Lanka<br>|<br>||||Tanzania<br>|<br>||||
|---|---|---|---|---|---|---|---|---|---|---|
|Benchmarking|Mean<br>poverty|Mean<br>MSE|Mean<br>CV|Corr|CR|Mean<br>poverty|Mean<br>MSE|Mean<br>CV|Corr|CR|
|Baseline estimates|3.7|4.6|32.0|87.6|84.3|18.6|11.1|17.5|87.6|74.8|
|Benchmark point<br>estimates only|3.7|4.2|29.9|87.6|79.5|18.6|9.7|16.9|87.6|71.1|
|No benchmarking|3.7|4.2|39.1|88.1|82.2|18.6|9.7|17.5|83.7|69.8|

_Notes: Columns represent mean poverty rates, mean squared error times 10,000, coefficient of variation, correlation with actual census value (Corr), and coverage rate (CR). Top row reports estimates when point estimates and MSEs are benchmarked to survey results for each super-area. Bottom row shows results without benchmarking._ The overall results, with a few exceptions, are similar to the main results for the non-monetary welfare measure reported in Tables 8 and 9. The household level model produces the most precise estimates, as judged by mean squared error. The MSE reduction achieved using the household-level model in Sri Lanka is smaller than the baseline results, reflecting the challenge of accurately predicting the bottom tail of the welfare distribution with a noisier welfare measure. The average CV rises greatly in Sri Lanka, due to large positive outliers, when using the noisier measure. These outliers are areas with very low predicted poverty rates, yet high mean squared error, due to the greater variability in the area effect in these simulations. This illustrates that average CV should be interpreted with caution in settings with low poverty rates and highly variable area effects. Nonetheless, even with a noisier welfare aggregate, the reduction in mean squared error Sri Lanka compared with the direct estimates is roughly equivalent to doubling the size of the sample. In Tanzania, where the poverty rate is much higher, the householdlevel model leads to a 78 percent reduction in the mean squared error, a factor comparable to that reported in Table 8. The analogous reduction in average CV is 30 percent, which is also comparable to roughly doubling the sample size.

Turning to accuracy and coverage, exploiting sub-area variation using the household model substantially improves accuracy, as measured by the correlation with the true noisier welfare measure. In Sri Lanka, the correlation is over 4 percentage points higher for the household level model than the Fay-Herriot model, while in Tanzania the comparable difference is over 10 percentage points. The correlation in absolute terms remains respectable in Sri Lanka (0.80) and high in Tanzania (0.84 percent) when using the noisier welfare measure. Finally, coverage rates for the household level model decline only modestly in Tanzania and increase significantly in Sri Lanka in comparison with the direct estimates. In Sri Lanka, the coverage rate reported in Table 15 for the noisy welfare measure is remarkably similar to the one for non-monetary poverty reported in Table 8 (84.9% vs. 83.7%). In Tanzania, the coverage rate is higher for the noisy welfare measure (78.0% vs. 73.6%). Accuracy and coverage are particularly important measures to consider because, unlike estimated precision, they are only observed when a “true” census population is available. Overall, the results presented in Table 15 indicate that the accuracy and coverage of the household level model remain high, in comparison with both the Fay-Herriot and direct estimates, when additional noise is introduced into the welfare measure.

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