# **1 Introduction**

Poverty maps provide granular estimates of poverty at the sub-national level in order to deepen the understanding of poverty in a given country, better inform the targeting of resources, and support the design of interventions tailored to local needs (Bedi et al. 2007; Elbers et al. 2007). Household surveys provide estimates that are sufficiently reliable for large areas in a given country but often lack the desired precision and coverage to be able to properly inform targeting interventions at a granular geographic level. Thus, it is necessary to rely on small area estimation.

Small area estimation is a branch of statistics focused on obtaining estimates of higher quality than those obtained directly from the household survey. These small area estimation techniques often combine data from household surveys and auxiliary information from censuses, registers, or others to produce estimates of higher quality than what is possible from survey data alone for areas or groups with small sample sizes. Since there is no such thing as a free lunch, to achieve these gains in quality it is necessary to rely on model assumptions which must be thoroughly checked.

The literature on small area estimation is rich and several variations on this basic procedure have been proposed. Unit-level models conduct estimation and prediction at the household level, assuming a linear relationship between the welfare measure and covariates (Hentschel et al., 1998; Elbers et al., 2003; Molina and Rao, 2010). Unit-level models are not well-suited to situations where the survey and census data correspond to different years, which is often the case in developing countries where censuses are conducted infrequently. Area-level models represent a feasible alternative that similarly relies on linear functional forms, but conduct estimation and prediction using only aggregate data for the geographical entities of interest (Fay and Herriot, 1979; Torabi and Rao, 2014). Unit-context models represent another alternative and are characterized by an estimation stage wherein household-level measures are modeled exclusively as a linear function of area-level characteristics (Nguyen, 2012; Lange et al., 2018; Masaki et al., 2020).<sup>1</sup> Recent developments in poverty mapping have focused on the application of machine learning to remotely-sensed data, largely in response to the issue of out-of-date census information. These approaches also use survey-derived welfare measures but are distinguished by a first stage where a machine-learning model is fit to remotely-sensed covariates (e.g., data derived from satellite imagery or call detail records) rather than census-based covariates. For example, Chi et al. (2022) matched data from several remotely-sensed data sources to survey-based measures of “village” wealth for 56 countries, and then fit a prediction model using gradient boosting machines.<sup>2</sup> They then applied the model to the populated surface of all 135 low- and middle-income countries to develop granular poverty maps for each country. Similar approaches have been used for individual countries, including Rwanda (Blumenstock et al., 2015), Senegal (Pokhriyal and Jacques, 2017),

> 1Despite their desirable features, the gains in precision offered by area-level models is often quite limited (see Molina and Morales (2009)).

> 2Their remotely-sensed data includes high-resolution satellite imagery, mobile phone data, topographic maps, and connectivity data from Facebook.

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