_Table 10: Measures of uncertainty when mean squared errors are rescaled to achieve 95 percent coverage rate_

||Sri Lan<br>|kan sub<br>|districts<br>|Tanzan<br>|ian distr<br>|icts<br>|
|---|---|---|---|---|---|---|
||Scale<br>factor|Mean<br>MSE|Mean<br>CV|Scale<br>factor|Mean<br>MSE|Mean<br>CV|
|Horvitz-Thompson direct estimate with<br>rescaled MSE|N/A|N/A|N/A|2.5|460.3|108.3|
|Fay-Herriot model with rescaled MSE|2.46|20.4|75.3|1.44|51.5|41.1|
|Household-level model with rescaled MSE|2.37|10.3|47.9|3.61|40.2|33.2|

_Notes: Scale factor refers to a constant scaling factor that was multiplied by the estimated mean squared error to inflate the MSEs to achieve 95 percent coverage rates. Mean MSE is multiplied by 10,000._ second and third columns give the post-adjustment average MSE and CV.<sup>30</sup> In Sri Lanka, the household level model is substantially more efficient than the Fay-Herriot model when the mean squared errors are rescaled, as the average mean squared error is 45 percent lower. The difference between the FayHerriot and the household level model results is smaller in Tanzania, because the Fay-Herriot model performs better. The household level model remains moderately more efficient after the rescaling, however, as the average mean squared error and average CV are each about 20 percent lower.

Finally, table 11 compares the precision of the unit level model with the direct survey estimates for super-areas, which are districts in Sri Lanka and regions in Tanzania. The super-areas are levels for which the household survey is considered representative and survey-based monetary poverty rates are routinely published. In Sri Lanka, where there are 331 target areas, the mean squared errors for the subdistrict estimates are about sixty percent larger than the direct survey estimates for districts. In Tanzania, meanwhile, there are only 159 areas and the same number as super-areas as Sri Lanka. In this case, the average mean squared error of the small area district estimates is slightly lower than the direct estimates for regions, while the mean CV is modestly higher. This type of comparisons is useful to inform decisions by national statistics offices of whether small area estimates are sufficiently precise to publish.

_Table 11: Precision of household level EB model compared with direct estimates for super-areas_

||Sri La|nka|Tan|zania|
|---|---|---|---|---|
||Mean MSE|Mean CV|Mean MSE|Mean CV|
|Super-area estimates from direct sample<br>estimate(Horvitz-Thompson approximation)|1.4|16.8|11.4|15.8|
|Area estimates from Household EB model|4.6|32.0|11.1|17.5|

_Notes: Top row shows the unweighted mean squared error (MSE) times 10,000 and coefficient of variation (CV) for nonmonetary poverty estimates calculated from the national household budget survey across 25 Districts in Sri Lanka and 25 Regions in Tanzania. Bottom row shows the unweighted MSE times 10,000 and mean CV for non-monetary poverty estimates that incorporating geospatial data across 331 subdistricts in Sri Lanka and 159 Districts in Tanzania, benchmarked to survey estimates for 25 districts in Sri Lanka and 25 regions in Tanzania._ 30 In Sri Lanka, it is not possible to rescale the direct estimates to achieve 95 percent coverage because the arealevel poverty and variance estimates are zero for more than 5 percent of the sub-districts.

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