of about 8 points. These results also suggest that in many contexts adding deep learning estimates to existing predictions based on gradient boosting offers limited additional improvement in accuracy.

- b. Household or sub-area models are usually preferable to area-level models when sub-area data are available.

The pros and cons of different models for small area estimation in different contexts has been a subject of contention for many years and there is not yet a consensus between different statisticians and practitioners. For the purposes of this discussion, we assume that recent census data are unavailable, necessitating the use of geospatial data. In most cases, geospatial data are available in the form of zonal statistics at the “sub-area level”, where the sub-area is a geographic area such as a grid or village. A zonal statistic, for example, could be the average night-time luminosity in the village or grid. Linking survey and geospatial data at the level of the enumeration area or village is quite common in practice. The Demographic and Health Surveys publicly release jittered geocoordinates for each EA in most cases, facilitating this type of linking. Meanwhile, the target area is typically a more aggregate administrative unit, such as a district or subdistrict. Finally, we define the regional level as a level above the target area for which the survey is considered to be representative.

Many analysts use Bayesian modeling for small area estimation. We focus here, however, on empirical best predictor models (Jiang and Lahiri, 2006, Molina and Rao, 2010), rather than purely Bayesian models, for three reasons. First, when they have been compared, EBP models give similar results to hierarchical Bayesian models (Guadarrama et al, 2016). Second, national statistics offices may be more comfortable with empirical Bayesian than Bayesian methods, partly due to discomfort with assuming a prior distribution. Finally, multiple well-documented and user-friendly software packages employ EBP methods, such as the EMDI and SAE packages in R, and the SAE package in Stata (Kreutzmann et al, 2019, Molina and Marhuenda, 2015, Nguyen et al, 2018).

Here, I focus on EBP models because they incorporate a conditional random effect that conditions on the sample, which is effectively used as a prior estimate. This distinguishes EBP models from two other popular alternatives: M-quantile (Chambers and Tzavidis, 2006) and ELL (Elbers, Lanjouw, and Lanjouw, 2003). Including a conditional random effect is particularly important when the auxiliary data are linked to the survey at the sub-area or area-level (Masaki et al, 2022). In this case, the sample contains more information relative to the auxiliary data than when using a typical household census, because the auxiliary data is the same for all households within a sub-area. This mechanically introduces correlation across households in a village, increasing the variance of the area effect. This in turn increases the weight given to the sample relative to the prediction in the empirical best predictor model when using aggregate predictors, as opposed to household-level predictors.

Within the set of EBP models, three main classes of model can be used to generate area-level poverty estimates using existing publicly available software packages.

The first type of EBP model for poverty estimation is a household-level model, as follows: (2) G(Yrasi) = β1Xras + β2Xra + β3Ir + ηra + εrasi , where G(Yrasi) is a transformed measure of household economic welfare of household i, typically measured as capita income or consumption. Household i lives in subarea s, target area a, and region r.

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