# **1 Introduction**

It has been almost two decades since the publication of Elbers, Lanjouw and Lanjouw’s (2003 - ELL henceforth) seminal paper on small area estimation (SAE). The methodology proposed by these authors has been the de facto methodology used by the World Bank to obtain small area estimates of poverty and inequality indicators and perhaps constitutes the most applied SAE method across the globe. The World Bank, in an effort to make the implementation of the method as simple as possible, created a free software package with a simple point and click interface that could be easily used by any practitioner. The PovMap software (Zhao, 2006) is of great value to World Bank staff and to many statistical agencies, and its ease of use has allowed the ELL approach to be adopted worldwide. It has also permitted the World Bank to provide training and spread this knowledge to many statistical agencies.

After the work from Van der Weide (2014), several important modifications and additions were made to the PovMap software, and thus to the toolkit used by the World Bank. The first change was to add a new method for estimating the variances of the model errors, called Henderson’s Method III (H3 - Henderson, 1953), which does not require normality because it is based on the method of moments. The second improvement involved adjusting the original Generalized Least Squares estimators of the regression parameters considered in Elbers, Lanjouw and Lanjouw (2003) by including the survey weights following Huang and Hidiroglou (2003). Another important modification involved the addition of Empirical Best/Bayes (EB) prediction assuming normality. The modifications came about due to advances in the SAE literature (Molina and Rao, 2010 - MR) and criticism of the ELL methodology (Haslett et al., 2010 and MR, 2010). The final important change was to consider a different bootstrap approach for obtaining the EB estimators and their corresponding error measures.<sup>1</sup> To make the application of the World Bank’s method friendlier to more advanced practitioners and to those who seek more flexibility, a World Bank team produced a Stata version of PovMap (Nguyen et al., 2018) which is available under the name “sae”. The development of the tool has made running multiple simulations and tests of the software much more straightforward. Since the creation of the “sae” Stata suite of commands, the World Bank has shifted towards training statistical agencies using this approach, which can facilitate replicability. Additionally, the code in the Stata package is open, so that curious practitioners can see in detail how methods have been implemented.

Small area estimation is a broad branch of statistics that focuses on improving estimates’ precision when household surveys are not large enough to achieve a desired level of precision. Within small area estimation methods, model-based techniques “borrow strength” from a larger data set or auxiliary data across areas through models linking the areas (regression-type techniques), which yield indirect estimators (MR, 2010). Most of the model-based techniques fall into two groups, methods based on unit-level models and those based on area-level ones. The former are commonly used when data on units (e.g. households) are available; when only area-level data are available (e.g. area means), the latter are used, see Fay and Herriot (1979).

In the context of poverty, methods based on unit-level models typically rely on estimating the distribution of the household’s welfare given a set of auxiliary variables or correlates. The model parameters are then used to simulate multiple welfare vectors from the fitted distribution for every single household in the census which commonly lacks a welfare measure for poverty measurement (Elbers et al., 2007). Using the simulated census vectors, it is possible to obtain poverty rates or any other welfare indicator, for every area (including the non-sampled ones). Perhaps the two most popular approaches for unit-level small area estimation of poverty indicators are the traditional ELL (2003) method used by the World

> 1The bootstrap is not discussed in Van der Weide’s paper.

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