and yields substantially less accurate estimates in Sri Lanka as measured by the correlation with the census. Otherwise, the results are largely robust to the range of robustness checks considered.

Next, we perform two additional robustness checks. The first of these examines the results of the household model using different benchmarking procedures. In particular, we examine two alternatives to the baseline estimates, in which both the point estimates and standard errors are benchmarked. The first alternative only benchmarks the point estimates, while the second performs no benchmarking. The results are shown in Table 14. In both countries, not benchmarking the standard errors slightly reduces the average mean squared error. Average CV is minimized in both countries by benchmarking only the point estimates. In Sri Lanka, benchmarking only the point estimates slightly reduces the CV while not benchmarking increases it because an additional district is included.<sup>34</sup> This leads to a modest fall in coverage in Sri Lanka, but a more significant reduction in Tanzania, where the coverage rate declines from 74.8 percent with benchmarking to 69.8 percent without. Benchmarking the mean squared errors, all else equal, overstates uncertainty in cases like these where mean poverty is underestimated. This partially mitigates the downward bias in the household model’s mean squared error estimates, which leads the benchmarking procedure to improve coverage. The benchmarked estimates are therefore preferred, although the results are qualitatively similar when either the point estimates are benchmarked, or when no benchmarking is carried out.

The final robustness check examines how the baseline household level model fares when random noise is added to the welfare aggregate. This better approximates a monetary welfare measure such as per capita consumption or income, which contain a greater portion of unexplained variance resulting from both transient welfare shocks and measurement error. We add two error term components to the existing measure of non-monetary welfare, to make an alternative noisier measure of “true welfare”. The first error component is an area effect, drawn form a normal distribution with mean zero and variance 0.5, and the second is a household specific error term with mean zero and variance 1. These variance values were chosen arbitrarily, with the aim of achieving a model R<sup>2</sup> of approximately 0.2, which is similar to the R<sup>2</sup> when regressing monetary welfare on similar geospatial indicators in Tanzania (Belghith et al, 2020). The poverty line is set according to the new, noisier, welfare measure, equal to the 4<sup>th</sup> percentile of the sample welfare in Sri Lanka, and the 20<sup>th</sup> percentile of the sample in Tanzania.

Table 15 displays the results when estimating area-level poverty using direct estimates, the Fay-Herriot model, and the household model with a noisier welfare aggregate. Household model diagnostics are displayed below the results. In the household model, the additional noise causes the marginal R<sup>2</sup> to fall to about 0.2 in both cases. This is substantially lower than the values reported when predicting the nonmonetary welfare index, which were 0.27 for Sri Lanka and 0.3 for Tanzania (Table 7). However, the conditional R<sup>2</sup> remains high, and even slightly above what is reported for the non-monetary welfare measure in Table 7. This reflects the additional variance in the area-specific component, which is captured by the mean of the sample residuals for each area and therefore incorporated into the small area predictions by the empirical best estimator.

> 34 The estimated poverty rate for Ratnapura district is zero in the HIES sample. The CV is therefore not defined for this district after benchmarking and excluded from the average.

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