# **3. Small area estimation methodology**

In this section we present a summary of the small area methodologies we use to estimate headcount poverty rates at the level of the target area in the five countries of interest. We use a version of the Empirical Best Predictor (EBP) (Battese et al., 1988; Jiang and Lahiri, 2006; Molina and Rao, 2010; Tzavidis et al., 2018) under the unit context nested error regression model with households as the unit of analysis and covariates defined by zonal statistics of geospatial variables at grid cell level (centroid of enumeration areas within target areas). Our methodology is similar to the one used by Masaki et al. (2022), which uses small area estimation to estimate non-monetary poverty indicators in Tanzania and Sri Lanka with geospatial covariates, and Newhouse et al. (2022), which applies similar techniques with geospatial covariates to estimate monetary poverty in Mexico. Van der Weide et al. (2022) also examines the performance of poverty estimates with geospatial covariates in Malawi but using a spatial error model with subarea-level estimates of poverty rates as the outcome, and geospatial zonal statistics as covariates.

As mentioned in previous sections, when the census and survey data are collected from around the same time, using household-level census covariates is generally preferred, because the census tends to contain richer auxiliary information than geospatial data. When census data are sufficiently old, however, using cluster-level covariate aggregates taken from the old census can generate more accurate estimates than using old census household-level covariates (Lange et al., 2021). None of these variations of covariate use, however, reflect any changes in the distribution of the census covariates since the last census. Because, except for Burkina Faso, the census data in the focus countries of this paper are not up to date, we explore the use of more current geospatial data as covariates instead of old census data.

We opt for a household-level model of welfare over a grid cell-level model of poverty rates because it utilizes more detailed information about the distribution of the welfare variable, and it is easier to interpret. In addition, defining the grid cell-level poverty rate as the outcome to be estimated, as in the case of an area-level model, requires accounting for the corresponding sampling variability, which may be challenging at such a small level of aggregation. We also prefer a household-level model to an area-level model because the former allows for the use of auxiliary data at the grid cell level rather than at the target area level, which can improve the accuracy and precision of the estimates, as demonstrated in Masaki et al. (2022) and Newhouse et al. (2022).

We model the household log per capita consumption as a linear function of a subset of geospatial covariates selected through Lasso. The procedure is described in detail in Appendix B. The model equation takes the form: l r r 1 r 2 3 r , (1), where l r represents the log per capita consumption of household YY rrh = XX rrββ + XX ββ + DDrrββ + ννrr + εε rrh _h_ , for which the centroid of their survey enumeration area falls in grid _g_ within target area _a_ and region _r_ . This rrh YY value of consumption has been spatially deflated using estimated local prices. r represents the vector of grid cell geospatial zonal statistics, and r represents the vector of unweighted rr XX averages of the geospatial variables 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 rr r is a household-specific error term with r ) . Survey weights are incorporated DD rr rr vv<sup>2</sup> νν νν ~ NN(0, σσ into model estimation following Guadarrama et al. (2018), as described in Skarke et al. (2021). rrh rrh εε<sup>2</sup> εε εε ~ NN(0, σσ A recent paper by Cho et al. (2024) presents optimal predictors for general parameters under an