informative sampling design. Implementing this methodology with the data from the focus countries is a useful area for future research. The EBP works by repeatedly simulating synthetic populations l r under model (1) using the expected value of what is unobserved given what is observed in the sample. Under the assumed rrh YY linear mixed model, this expectation has a closed form. Having fit model (1), the expected log household per capita consumption for each household in the population is computed as follows: l r r 1 r 2 3 r , (ll) (ll) (ll) rrh rr rr rr rr rrh where is the random effect predicted with the sample data, YY = XX ββ̂ + XX ββ̂ + DD ββ̂ + νν̂ + vv + εε is generated from , (ll= 1, . . , LL) (1 − (ll) )) , r rr is drawn from ) and is the area-specific shrinkage factor that depends on the rr vv2 νν̂ vv NN(0, σσ� (ll) estimated variance components and the area sample sizes (Molina and Rao, 2010). For each rr rrh εε<sup>2</sup> rr γγ� εε NN(0, σσ� γγ� simulated synthetic population, the target area-specific parameter, the headcount poverty rate, is computed using the simulated values of the welfare variable (per capita consumption) and the official national poverty lines for each country. This procedure is repeated L=100 times and the final estimated poverty rates for each area correspond to the average across the 100 simulations.

In this paper we implement a version of the EBP that calculates the expected value of headcount poverty given the estimated model parameters, for each population unit (which in this case is a grid). Under the assumed linear mixed model, this expectation has a closed form. Having fit model (1), the expected poverty rate for each grid is computed as follows: (1), the expected poverty rate for each grid is computed as follows: l r <u>r</u> 1 r 2 3 r = Φ � rr rr� , ll(ZZ) −XX ββ̂ −XX ββ̂ −DD ββ̂ −νν̂ rr where Φ is the standard normal cumulative distribution function, Z is the poverty line, and PP<sup>�</sup> σσ�vv<sup>2</sup> (1 −γγ�rr) + σσ�εε<sup>2</sup> 1 , 2 , 3 , , , and are estimated model parameters, and is the area-specific shrinkage factor ββ̂ ββ̂ that depends on the estimated variance components and the effective area sample size. The vv<sup>2</sup> εε<sup>2</sup> rr rr ββ̂ estimated target-area headcount poverty rate, σσ� σσ� νν̂ r , is computed by taking a weighted average of γγ� the grid-level poverty estimates in each area, with the grid population estimates from WorldPop playing the role of aggregation weights. Estimation is implemented using a modified version of PP<sup>�</sup> the povmap package (Edochie et al., 2024) in R to implement the estimation.<sup>7</sup> The Povmap package is a modified version of the EMDI package (Kreutzmann et al., 2019) that allows for aggregation weights when aggregating across population units (grids in this case). The two versions of implementing the EBP lead to the same estimates for a large number of Monte-Carlo iterations . To verify this, we compare poverty headcount and MSE estimates obtained using the traditional method with Monte-Carlo replications with those obtained by calculating the expected value approach for one focus country, and report the results in Appendix D. Estimates ll of the mean squared error (MSE) of the small area estimates are calculated using parametric LL= 100 bootstrap under model (1) (Gonzalez-Manteiga et al., 2007) as implemented in the Povmap package. MSE estimation adjusts for the fact that the population data we use contain only one observation per grid, while the actual population contains multiple households per grid. An empirical best predictor under the two-fold version of the nested error regression model is also available ( <mark>Marhuenda</mark> et al, 2017). The two-fold version of the EBP was used to produce official

> 7 The code is available on the development branch of the package at: https://github.com/SSA-Statistical-TeamProjects/povmap.