So far, EBP is the only type of linear model we have evaluated. A popular alternative method was developed in Elbers et al. (2003) and is widely known as ELL. A key difference between EBP and ELL is that ELL does not condition the estimated random effect on the sample data. Partly because of that, ELL does not assume that the error terms are distributed normally. Appendix Table A3 compares Pearson and Spearman correlations for EBP and ELL. In all cases except assets in Tanzania, EBP outperforms ELL. On average, the benefit from using EBP rather than ELL is moderate, in terms of correlation with the true estimates, equal to 2.8 percentage points for assets and one percentage point for poverty. In two cases, Burkina Faso and Vietnam, the differences are larger, at 9.2 and 6.3 percentage points, respectively. Overall, in these contexts, EBP tends to generate more accurate estimates than ELL.

Accuracy of the prediction, however, is not the only measure of concern. It is also important to accurately estimate measures of uncertainty, since these are often used to determine whether the estimates are sufficiently reliable to publish publicly. Machine learning methods have been consistently shown to generate accurate point estimates, but are less amenable to estimating uncertainty. Table 6 presents two key statistics related to uncertainty, with the uncertainty measures calculated using a weighted two-stage residual block bootstrap, as described in section 2.7. The first statistic is the coverage rate, which shows how often the true value (from the census) lies within the estimated confidence intervals for a given prediction. We calculate coverage rates for 95% confidence intervals, meaning that if the point and uncertainty estimates are accurate, the coverage rate should be approximately 0.95. The second statistic is the total width of the confidence interval, which is an indicator of the extent to which estimated uncertainty varies across estimation methods.

Coverage rates for the four estimators vary quite a bit depending on the context and the method. On average, BRF is associated with the highest coverage rates, averaging 88.4 percent for assets and 88.8 percent for poverty. This is partly because BRF is less accurate than the other ML methods on average, leading to wider confidence intervals due to the use of a residual bootstrap. For assets, XGBoost has the second-highest coverage rates at 87.2 percent, followed by Cubist at 84.7 percent. For poverty, the ranking is the same, as XGBoost has a colverage rate of 85 percent with Cubist following at 82.3 percent. Coverage rates vary by context, however. Uncertainty estimates when predicting assets in Tanzania, for example, appear to be systematically underestimated for all estimators, especially for EBP at 39.1 percent. Figure A2 in the Appendix shows that part of the reason for this may be a systematic underestimation of poverty across the entire distribution, leading to decent correlation but poor coverage rates. We also note that the Tanzania census is from 2012, while some of the geospatial features such as land classification are from 2019. As such, we hesitate to put too much weight on the results from Tanzania. The coverage rate for Sri Lanka is also low for EBP (68.4 percent). We encourage further research to better understand why coverage rates are 22