model would not be expected to perform well in a sample of only 24 districts, we only report average evaluation statistics for the two types of direct estimates and the household level unit level models.

Results for the household-level model are reported with and without benchmarking. As above, the benchmarked point estimates were rescaled to match the direct estimates for each of the three regions in the population, for each sample drawn in each simulation, and the mean squared error were multiplied by the square of the same scaling factor. The direct estimates are computed in each simulation by calculating the weighted share of sample households that are poor in each district, using the weights calculated in step 3 above. We again compare the direct estimates obtained using the Horvitz-Thompson approximation with results from standard enumeration area clustering, which give identical point estimates but differ in their estimated variances.

Table 17 displays the results, which confirm that the household model continues to perform well when using repeated samples from the three selected regions. The household model in these simulations demonstrate a moderate amount of bias, with a mean of 42.4 percent prior to benchmarking as compared with 46.5 percent in the population. This bias results from the distribution of the residuals deviating substantially from normality at the tails.<sup>42</sup> The estimates produced by the household level model, however, are far more precise than the HorvitzThompson direct estimates, with average mean squared errors that are about a quarter as large and average CVs about half the size. The household model estimates are only moderately more precise than the standard direct estimates, reflecting a high degree of correlation in household welfare across EAs within district. The standard direct estimates ignore this correlation and therefore greatly underestimate uncertainty, which are reflected in a coverage rate of 48.7 percent. In contrast, the coverage rate of the benchmarked estimates from the household model is 68 percent, which is moderately below the coverage rate for all of Tanzania using the HBS sample reported in Table 8 (74.8%). The coverage rate of the household model, despite being much more precisely estimated, is only modestly below the HorvitzThompson direct estimates. This is because the household model estimates are more accurate, as seen in the higher correlation and lower root mean squared error.

To sum up, when using repeated samples in three poor Tanzanian regions, incorporating remote sensing data in a household-level model dramatically improves precision compared to the Horvitz-Thompson direct estimates. Adding the remote sensing data reduces mean squared error by about 75 percent and CV by about half, which is more or less comparable to quadrupling the sample size. Because the small area estimates are much more accurate than the direct estimates, the increased precision comes at a modest cost in terms of coverage rate. Compared with the standard direct estimates assuming independence across enumeration areas, the small area estimates are not only slightly more precise, but also significantly boost accuracy and coverage. Overall, the main results derived for the full country based on budget survey the specific sample drawn for the budget survey are maintained when focusing on three Tanzanian regions and generating estimates of the area poverty rates and their mean squared errors using 250 different samples.

> 42 As shown in the bottom of Table 17, the kurtosis of the residuals is 2.5 for the area effect and 3.7 for the household errors.

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