III (Henderson 1953).<sup>18</sup> The _wiv_ for each household is simulated _M_ times using Monte Carlo simulation where each simulated welfare _m_ follows: where _μ_<sup>_∗_</sup> _im_<sup>and</sup><sup>_ξ_</sup> _ivm_<sup>_∗_are drawn from their assumed distributions.19Here,</sup><sup>_μ∗_</sup> _im_<sup>is generated as</sup><sup>_μ∗_</sup> _im_<sup>_∼_</sup> ̄ ˆ ˆ ˆ _N_ (ˆ _μi,_ ˆ _σμ_<sup>2(1</sup><sup>_−κ_ˆ</sup><sup>_i_)) for sampled municipalities,where</sup><sup>_μ_ˆ</sup><sup>_i_=</sup><sup>_κ_ˆ</sup> � _wi − xivδ_<sup>ˆ</sup> � and _κi_ = _σμ_<sup>2</sup><sup>_/_</sup> � _σμ_<sup>2+ ˆ</sup><sup>_σ_</sup> _ξ_<sup>2</sup><sup>_/ni_</sup> �, _ni_ is the sample size for municipality _i_ . For municipalities that are not part of the sample, then _μ_<sup>_∗_</sup> _im_ is generated as _μ_<sup>_∗_</sup> _im_<sup>_∼N_(0</sup><sup>_,_ˆ</sup><sup>_σ_</sup> _μ_<sup>2) whichcorrespondsto the methodused in ELLfor all municipalities</sup> regardless of whether or not they are in the sample. Thus, EB makes more use of the survey data for predictions corresponding to sampled areas. Note that EB methods only ensure that the area level means of the dependent variable are Empirical Best Linear Unbiased Predictors (EBLUP); it does not guarantee the same for poverty which is a non-linear parameter. Hence, the importance of replicating the welfare distribution.

One major aspect of concern for small area estimation is the estimation of noise. A statistical agency in a given country may seek to undertake a small area estimation application because the quality of the estimates derived from survey data may not be sufficiently precise or estimates may not even be possible since the area was not sampled. Hence, a big concern surrounding small area estimation is the estimation of MSEs for each area’s estimate. Estimates of noise are obtained via bootstrap replications where the model’s assumptions are exploited in order to obtain an estimated MSE (González-Manteiga et al., 2008).<sup>20</sup> This aspect is one of the biggest differences between poverty maps based on small area estimation and those based on machine learning. Statistical agencies across the globe will assess an estimate’s noise before deciding to publish it or not, thus the importance of such estimates.

The key assumption of the unit-level model is that the distribution of the explanatory variables is similar between the survey used for estimation and the census used for prediction. This assumption is generally violated if the census is outdated – which is often the case in developing countries – and in this event the application of the unit-level model will lead to similarly outdated poverty maps (Lange et al., 2018). Importantly, machine-learning approaches to poverty mapping are commonly motivated by the fact that censuses are outdated and are thus viewed as a way to produce timely poverty maps in a data-constrained environment. Stated differently, given the differing data requirements between the unit-level model and the machine-learning approach, the two methods are not generally considered to be direct competitors. The unit-level model nevertheless serves as a useful performance benchmark, as it is often viewed as the “gold standard” of poverty mapping.

Unlike unit-level models, unit-context models were specifically developed to be used in off-census

> 18Henderson’s method III is coupled with GLS to obtain the regression coefficients.

> 19See Corral et al. (2021b) for a more detailed description.

> 20For a much more detailed discussion on the estimation of noise refer to Rao and Molina (2015) and for a discussion focused on ELL and EB estimates refer to Corral et al. (2021b) and Corral et al. (2022).

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