context of estimated crop acreage.<sup>4</sup> Existing studies that validate small area estimates of non-monetary poverty generated from mobile phone or geospatial data have, by and large, focused on extrapolation, or the use of big data to predict welfare in countries that are not surveyed. This differs from small area estimation, in which the objective is to predict poverty within the area covered by the sample, at a more granular level. To do this efficiently, it is crucial to use the survey data not only to train the prediction model, but also as a direct input into the estimates.

This study therefore makes three main contributions. First, it applies the prevailing framework for small area estimation to combine household survey data with geographically comprehensive geospatial indicators in an efficient way. Second, it evaluates the extent to which incorporating geospatial variables at the subarea level improves the precision of small-area poverty estimates. Finally, it assesses which of the commonly used SAE models – unit-level models (Elbers, Lanjouw, and Lanjouw 2003. Molina and Rao, 2010), and the Fay-Herriot area-level model (Fay and Herriot, 1979) – are best suited for combining survey and geospatial data to produce efficient and accurate estimates of both area-level poverty rates and the uncertainty associated with them.

We test these models in the context or generating small area estimates of non-monetary poverty in two developing countries, Sri Lanka and Tanzania. These countries were selected due to the availability of both census and survey data with subarea-level identifiers and matching polygon shapefiles close to the village level. The welfare prediction model uses survey data to estimate the value of a household welfare index as a function of subarea characteristics, and therefore differs from standard small area estimation models that predict welfare using household characteristics. The resulting estimates provide a large efficiency gain compared with direct survey estimates.

We mainly consider Empirical Best Predictor (EBP) models, which have a long history in small area estimation and can accommodate subarea-level auxiliary data to produce estimates of poverty rates and their mean squared error for target areas. EBP models differ from the “ELL method” (Elbers, Lanjouw, and Lanjouw 2003), that has traditionally been used for poverty mapping by the World Bank because they incorporate additional information from the survey by conditioning the area effect on survey residuals.<sup>5</sup> This can lead to substantial efficiency gains when the variation in welfare or poverty contributed by the sample is large, relative to the variation contributed by the auxiliary data. On the other hand, a drawback of EBP models is the required assumption that the stochastic error terms in the model follow a normal distribution. While this normality assumption can be tested by examining the residuals from the prediction model, violating the assumption will introduce bias into the estimates.

In the traditional case when the auxiliary data are household-level data from a census, the sample is a small fraction of the size of the census and EBP models typically lead to minor efficiency gains.<sup>6</sup> In these cases, it is not obvious that EBP models are preferred to simulations based on standard random effect models that do not condition the area effect on the sample but allow for departures from normality. When the auxiliary data are only available at the subarea level, however, the effective size and statistical power of the auxiliary data are much less than that of a full household census. The share of variation contributed by the sample therefore becomes larger, and as shown in results presented below, EBP

> 4 Battese, Harter, and Fuller (1988), Erciulescu et al (2019).

> 5 For example, the methods described in Elbers Lanjouw and Lanjouw (2003) and Tarozzi and Deaton (2009) are not EBP models.

> 6 Haslett (2016).

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