2019.<sup>6</sup> The survey collected information on household and dwelling characteristics, educational attainment, asset ownership, and access to services. It forms the basis for constructing a household consumption aggregate and estimating the country's official poverty rate. The survey is representative at the regional (14 regions) and the national level. It contains information on 7,156 households (66,120 individuals) distributed across rural (55 percent) and urban areas (45 percent).

For the population census, the analysis relies on the 2013 Population and Housing Census.<sup>7</sup> The census questionnaire includes information on household characteristics and living conditions, but does not cover household expenditures, which are necessary for the calculation of poverty. Appendix A, table A.1 compares the variables available in the census and the household survey. The comparison is critical because a fundamental assumption of small area estimation is that the survey used to model welfare is representative of the entire population. Consequently, the objective is to ensure that the data in both the survey and census bear a close resemblance. The next subsections explain vulnerability estimation in the context of small area estimation techniques. The paper then describes how this compares with the Günther and Harttgen (2009) method, which relies solely on survey data.

# Estimation of vulnerability: Adding vulnerability to the poverty map

The first step is to estimate a function of the household income-generating function in the survey data. The regression uses a multilevel model because this allows the decomposition of the unexplained variance of the dependent variable—expenditure per capita in the case here—into a household (idiosyncratic) and a community (covariate) component. To illustrate the estimation formally, suppose represents households, while represents communes; and every household h is nested h= 1, . . . ; II withing a community . Equation 1 summarizes the model for the log of household per capita expenditure cc= 1, . . . ; CC l ) as a function of covariates , which vary by household h in community .<sup>8</sup> cc cch cch (yy xx cc

> 6 EHCVM (Enquête Harmonisée sur le Conditions de Vie des Ménages 2018–2019, Harmonized Survey on Household Living Standards 2018–2019), Living Standards Measurement Study, World Bank, Washington, DC, https://microdata.worldbank.org/index.php/catalog/4292.

> 7 RGPHAE 2013 (2013 Recensement Général de la Population et de l'Habitat, de l'Agriculture et de l'Elevage; Population and Housing Census, 2013) (dashboard), National Agency of Statistics and Demography, Dakar, Senegal, https://www.ansd.sn/enquete-et-etude/recensement-general-de-la-population-et-de-lhabitat-de-lagriculture-etde-lelevage.

> 8 Even though it is popular, the logarithmic transformation is not always ideal, especially for small values of welfare where it can produce left skewed distributions. The analysis implemented a data-driven approach to transformations by Box-Cox tests and a log-shift transformation, with the objective of selecting one that reduces departures from normality (see Corral Rodas et al. 2022). Simulation studies show that data-driven transformations may reduce bias and noise caused by departures from normality (see Corral Rodas et al. 2022; Tzavidis et al. 2018).

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