# **8 Conclusions**

Since the turn of the 21st century, the World Bank has been obtaining small area estimates of poverty and inequality indicators using the ELL approach. One of the reasons for the method’s popularity was the existence of software that made applying the method to real data relatively easy. This began with an implementation in SAS by Demombynes (2002), which was followed by PovMap implemented by Zhao (2006), and finally a Stata version (“sae” package by Nguyen et al., 2018). Along those lines, the research effected in this paper also represents a considerable update to the “sae” package in Stata.<sup>36</sup> Countries often set out to obtain small area estimates because more precise poverty estimates at a more granular level allow for improved allocation of resources, see Elbers et al. (2007). This research comes just in time for the 2020 round of population census and should provide an improved tool for the operationalization of the SDGs at a sub-national level.

An important aspect of the small area estimation procedures is how parameter estimates from an assumed population model are applied to census data to obtain the small area estimates. As noted in this document, the traditional ELL procedure is aligned to the approach used in multiple imputation, where the main aim is not prediction. Under multiple imputation, the method that yields the lowest MSE yields invalid statistical inference (Van Buuren, 2018). On the other hand, the goal of small area estimation is to improve precision.

This paper presents a substantial revision to the traditional methods by ELL (2002, 2003) and the updates by Van der Weide (2014) for small area estimation.<sup>37</sup> Our results show substantial gains of the proposed Census EB method with respect to the previous methods in all the considered scenarios (varying area population sizes and sampling fractions, model prediction power and distributional assumptions) and also of the considered parametric bootstrap MSE estimators. Thus, the updated methodology provides a considerable improvement in the quality of the SAE estimates obtained under the World Bank’s agenda. We show that, for a single population, the original ELL method tends to align with the national poverty estimates and does not capture the area heterogeneity, although its performance improves when averaging across populations. Nevertheless, caution should be taken when doing out of sample prediction even under EB methods, since in that case estimates are very similar to the traditional ELL ones and can thus deviate considerably from the truth. This is particularly relevant in cases where the explanatory power of the chosen correlates is low.

An additional finding of this research is the considerable bias of the CB-EB update by Van der Weide (2014) and as implemented by Nguyen et al. (2018) to the World Bank’s toolkit. The revised Census EB method is aligned with MR’s (2010) method, which shows a level of bias that is several orders of magnitude smaller than the previous CB-EB method. Furthermore, the MSE for the Census EB method is also considerably smaller. This research and its accompanying software implementation represent a massive improvement to the World Bank’s current toolkit and overall poverty mapping agenda.

This note serves as a background piece for a guidance note on small area estimation for the World Bank. The simulations executed here are done under a controlled scenario, and thus a natural question is how the findings would differ under a real-world application. Now that the initial limitations of the methods have been identified, the revisions can be put to the test on real-world data.

> 36An update to Nguyen et al. (2018) is in progress, but all Stata codes and commands used in this document are available at https://github.com/pcorralrodas/SAE-Stata-Package

> 37The revision is also accompanied by an update to the 2018 Stata “sae” package by Nguyen et al. (2018)

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