It is impossible to develop a general rule about the relative accuracy of different models, because their relative accuracy depends on the nature of the data. This is especially true when comparing across different sources of auxiliary data. For example, census data aggregated to the target area level may be preferable to geospatial data available at the sub-area level because it is more predictive of welfare, but current geospatial data may be preferable to old census data even if the latter is available at the household level.

Nonetheless, when considering a single source of auxiliary data, the household and sub-area models enjoy the important advantage of using auxiliary data at a more disaggregated level. The use of more spatially disaggregated data can lead to more accurate estimates of non-linear functions such as headcount poverty rates, though these gains in accuracy may be negligible in some contexts. An additional benefit from using more spatially disaggregated estimates is the additional precision gained by exploiting the additional variation across sub-areas within areas. Whether the benefit comes in the form of increased accuracy, precision, or both, when considering a single source of auxiliary data it is generally preferable to use a household or sub-area model rather than an area-level model when possible.

Although the general principal of using the most spatially disaggregated auxiliary data possible seems straightforward, there is not yet full consensus on this point in the literature. For example, Corral et al. (2021) argue that, when considering model-based bias, household models with aggregate variables suffer from omitted variable bias, and therefore recommend using an area-level model rather than a household-level model when the auxiliary data consist solely of sub-area or area-level means. Newhouse et al. (2022), however, show that this source of omitted variable bias is equally present in area-level and household models that use auxiliary data drawn from the population, such as census or administrative data. Furthermore, this source of model-based bias disappears when considering design-model bias, taking the expected value of the predictions prior to drawing the sample. Omitted variable bias is therefore not a relevant concern when selecting between different types of models.

Corral et al. (2022) nonetheless recommend the use of an area-level model rather than a householdlevel model when the predictors are available at the sub-area level, largely on the basis of results from a particular model-based simulation. This model-based simulation takes a simple random sample of households from all PSUs in the population. When the model-based simulation is altered to use a more realistic two-stage sample design in which a subset of PSUs are selected, the household model with subarea means generates more accurate predictions than the area-level model.<sup>3</sup> Using a two-stage sample effectively increases sampling error in the direct estimates, which in turn increases the benefit of using more geographically disaggregated auxiliary data to fill in the geographic gaps of the sample. Using a one-stage sample, on the other hand, makes the direct survey estimates more accurate, which favors area-level models in this case. This partly illustrates why it is important to be careful before inferring general results from particular model-based simulations (Tzavidis et al, 2018).

Relative to the area-level model, the household model benefits from using auxiliary data at the sub-area level. The greater variation of more spatially disaggregated data is particularly important when using algorithmic variable selection methods such as LASSO or stepwise regression to select models, which is increasingly common among practitioners. The availability of sub-area variation also becomes more

> 3 Code is available upon request from the author.

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