We evaluate the performance of these methods using unit-level census data across seven developing countries in Africa and Asia: Burkina Faso, Madagascar, Malawi, Mozambique, Sri Lanka, Tanzania, and Vietnam. These countries were selected due to the availability of georeferenced census data. In Malawi and Tanzania we are able to extend the evaluation to include a headcount poverty measure in addition to the asset index, while in the other five countries we evaluate prediction of an asset index, similar to Chi et al. (2022) and Masaki et al. (2022).

The first main method we evaluate is empirical best predictions based on a nested error linear model, which we refer to as EBP. This estimation method comes from a long history of small area estimation in statistics. (Battese et al., 1988; Jiang and Lahiri, 2006; Molina and Rao, 2010). We also evaluate three newer machine learning methods: Cubist regression models (Quinlan et al., 1992; Wang and Witten, 1997), extreme gradient boosting (Chen and Guestrin, 2016) – more commonly known as XGBoost – and boosted regression forests, or BRF (Friedberg et al., 2020; Tibshirani et al., 2018). As a robustness check, we also evaluate another traditional method commonly used in small area estimation, the ELL method (Elbers et al., 2003).<sup>2</sup> These methods differ in their level of parsimony and transparency on the one hand, and their predictive accuracy on the other, and a key goal of this exercise is to better understand the terms of this trade-off in the context of welfare prediction. In each case, we specify models at the sub-area level, which in these contexts refers to highly disaggregated administrative areas akin to groups of villages. We then aggregate predictions to obtain estimates at the target area for each country.

For predictors, we use satellite-derived geospatial indicators that are available across much of the globe, meaning that the methods and data evaluated here are widely applicable in cases where geolocated survey data are available. We use shapefiles from the seven countries to pull geospatial data from multiple sources, which is then combined with samples drawn from the unit-level census data. In each country, we simulate 100 two-stage samples – first randomly selecting enumeration areas and then randomly selecting households based on survey designs of actual household surveys in each country – and compare the overall performance across simulations, ensuring that the results are derived from one hundred possible samples rather than a single sample. Under these conditions, XGBoost and Cubist regression tend to outperform EBP and BRF in terms of accuracy, as measured both by Pearson correlations and Mean Squared Deviation. This can be seen clearly in the first two rows of Table 1.

> A key contribution of the paper is the evaluation of a two-stage residual block bootstrap to estimate uncertainty

> 2See Das and Haslett (2019) for a comparative analysis of several poverty mapping methods including the ELL method, EBP, and M-quantile. Pratesi and Spagnolo (2023) offer a recent overview of small area estimation methods for measuring poverty. Another potential SAE method is ESPREE (Isidro et al., 2016). However, we know of no readily available software packages that implement either M-quantile or ESPREE.

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