However, for in-sample areas the household level model is significantly more accurate, such that the household-level model is more accurate overall (results not shown). In Tanzania, the area-level model also generates slightly more accurate predictions than the household-level model, although the difference is negligible. Interestingly, in the one simulation comparison in Mexico, the two models perform essentially equally well in-sample but the household model is moderately more accurate outof-sample. Mexico also is different than the other cases in using a relatively small number of proprietary geospatial variables, which may also partly explain why estimates are far more accurate out-of-sample in Mexico than Burkina Faso. In addition, the simulation results reported for Mexico are based on arealevel aggregates instead of sub-area level aggregates, due to the lack of sub-area identifiers in the census data. This may explain why the household model and area-level model perform equally well in sampled areas in this context.

The comparisons reported in Table 3 are far from conclusive and should be interpreted with caution, since all except for one case are based on a single sample. In addition, the area-level models estimated here use direct survey estimates of variance as inputs into the model, obtained using the HorvitzThompson approximation of variance. As noted above, using smoothed variance estimates and accounting for spatial correlation should increase the accuracy of area-level models. Finally, the evaluation metrics are often themselves EBP estimates based on household census data, since official welfare measures are never observed in the census. Nonetheless, despite the limited evidence so far, the household level model appears to generate more accurate predictions than the area-level model in the majority of cases, sometimes by substantial margins. Additional evidence would be useful to get a better sense of the conditions under which household models or area-level models generate more accurate estimates.

As noted above, a key benefit of incorporating sub-area level auxiliary data in a household model framework is increased efficiency. In Burkina Faso, the mean estimated mean-squared error for sampled areas was half as small when estimating a household model with sub-area predictors (Edochie et al, forthcoming). A similar 45 percent reduction in mean MSE was observed for in-sample municipalities in Mexico when incorporating sub-area level predictors (Newhouse et al, 2022). While these are only two contexts, they suggest a large efficiency gain when using a household model with sub-area level predictors, relative to an area-level model.

Another option is the sub-area level model given in equation (2), in which the unit of analysis is the subarea and the dependent variable is sub-area-level poverty rates, in the spirit of Torabi and Rao (2014). Unfortunately, there is virtually no empirical evidence to our knowledge on the relative accuracy of estimates produced by a sub-area vs. a household model. In Mexico, when using a single household survey sample, the R<sup>2</sup> was equal to 0.70 relative to the evaluation benchmark, less than the 0.74 value for the household-level model. However, this only pertains to one context, and further research is needed to rigorously evaluate these different types of models.

Many of the same studies also compare coverage rates across the models, which are useful for evaluating the accuracy of uncertainty estimates. If estimates of uncertainty are unbiased, coverage rates should be approximately equal to 95 percent. Table 4 lists estimated coverage rates from selected studies. When estimating the household model, confidence intervals are calculated based on mean squared error, under the assumption that the point estimates are unbiased. For estimating coverage rates, generally the area-level model fares better than the household model, providing coverage rates of 18