small area estimates of poverty rates in Burkina Faso using the latest census in the country. These estimates are used as part of the sensitivity analysis in Section 4.

An alternative approach to small area estimation with geospatial covariates is modeling directly the poverty rates using an area-level model (Fay and Herriot, 1979). In this case, both the direct estimates of poverty rates, denoted by , and the geospatial covariates, denoted by r , are aggregated at the target area level. The FH model consists of two stages: the sampling model<sup>rr</sup> rr<sup>d</sup> and the linking model. The combination of both stages results in an area-level linear mixed pp̂ XX model denoted by = r 1 2 ,<sup>rr</sup> where r represents the vector of unweighted averages of the geospatial variables selected for rr<sup>d</sup> rr rr rr pp̂ XX ββ + DD ββ + νν + εε the model at the target area level. represents a set of regional dummy variables, is a random effect specified at the target area level with XX ) and is the sampling error 2 rr 2 rr with ) . The sampling variance DD is estimated under the sampling design and is νν rr vv<sup>2</sup> rr νν ~ NN(0, σσ εε assumed to be known. The variance component of the random effect is estimated by maximum rr εεaa εεaa εε ~ NN(0, σσ σσ likelihood methods (e.g., the adjusted maximum-likelihood of Li and Lahiri, 2010) to guarantee positive variance estimates. The MSE of the estimator under the FH model can be obtained by analytic solutions (e.g. Prasad and Rao, 1990) or by bootstrap techniques (Gonzalez-Manteiga et al., 2007). In this paper the FH model is estimated using the Fayherriot Command in Stata (Halbmeier et al, 2019) with no transformation. The routine works similarly to the way the FH model is estimated in the EMDI and Povmap packages (Harmening et al., 2023) in R. Transformed versions of the FH models, using for example the arcsin transformation, are also available and can be considered when modeling proportions. Transformed FH models can be also estimated by using the EMDI and Povmap R packages.

# **3.1 Model selection and assessment**

The geospatial data listed in Table A1 were used to construct averages of zonal statistics both at the grid cell level and the target area level which are used as covariates in model (1). In addition, we include dummy variables at the region level. For model selection we use Lasso to select a set of predictor variables while avoiding overfitting. Estimation of the Lasso penalty parameter is implemented by minimizing the Bayesian Information Criterion (Zhang et al., 2010). The regional dummies are unpenalized and therefore are guaranteed to be selected in the model. Details are provided in Appendix B.

Broadly, the signs and patterns of the coefficients of the unit context model reflect a positive association between population and building density, and a negative association between welfare and remoteness, as proxied by agricultural production and a high prevalence of grassland and shrubland. Fitting model (1) in the five countries under consideration leads to R<sup>2</sup> values ranging from 0.19 in Chad to 0.32 in Niger. This range is consistent with similar applications in other contexts. In similar household-level models with aggregation of geospatial covariates at similar spatial scales, the R<sup>2</sup> was 0.30 in Tanzania and 0.27 in Sri Lanka when predicting per capita consumption, and 0.13 in Mexico when predicting per capita income. Geospatial variables do not vary within grids-cells and therefore can only explain variation in welfare across enumeration areas. However, the R<sup>2</sup> is not necessarily the most accurate measure of the benefit of incorporating auxiliary data, as small area estimates based on models with weaker predictors can also be of acceptable quality. Overall, the R<sup>2</sup> values in the focus countries indicate that the geospatial variables measured at grid cell level (enumeration areas) are moderately predictive of