# **1 Introduction**

The eradication of poverty was the first Millennium Development Goals (MDGs) established by the United Nations in 2000 and continues as Sustainable Development Goals (SDG) 1.1.1, but governments can only properly target poverty if they know where it is. Traditionally, for a given country, the best source for information on the living standards of its population are household surveys. These surveys are a powerful tool towards defining and addressing the needs of people. These surveys, however, usually offer reliable information only at highly aggregated levels of the population. In other words, _direct_ survey estimates tend to be adequate for very large populations but inadequate for smaller populations.

Small area estimation (SAE) is a branch of statistics focused on improving the reliability of estimates and the associated measures of uncertainty for populations where samples cannot produce sufficiently reliable estimates (Rao and Molina, 2015). Small areas can be any population subgroup and are not necessarily tied to geographical areas. According to Ghosh and Rao (1994), the use of small area statistics increased towards the end of the 20th century due to improved computing power and the advent of theoretically sound statistical methods. The main principle behind small area statistical methods is to use modeling to “borrow strength” from auxiliary data sources (e.g. census or administrative data) to produce more efficient estimators than direct survey data alone. Model-based techniques for small area estimation commonly fall within two groups: i) area based models; for examples see Fay and Herriot (1979) and Torabi and Rao (2014); ii) unit-level models; for examples see Molina and Rao (2010) and Elbers, Lanjouw and Lanjouw (2003). The focus of this paper is to conduct model and design-based evaluation of different unit-level SAE methods. Model-based methods assume a data generating process for the population that follows the model’s assumptions, and the target parameters are assumed to be random (Tzavidis et al., 2018). In this paper, model-based evaluation is done considering two-stage sampling strategies and thus assumes a model that includes variation at the domain level as well as at the cluster level, where clusters are the primary sampling units, nested within domains (see Marhuenda et al., 2017). Design-based simulation entails applying the chosen methods under realistic conditions (Tzavidis et al., 2018). Here, a design-based evaluation of several estimators is performed using the 2015 Mexican Intra Censal Survey, which is used here as a census, and from which we draw repeated samples. The estimation methods considered are those of Elbers, Lanjouw and Lanjouw (2003 - ELL henceforth), the empirical best predictor of Molina and Rao (2010 - MR henceforth),<sup>1</sup> the twofold nested error extension of MR (2010) presented by Marhuenda et al. (2017), and finally an adaptation, presented by Nguyen (2012), that combines unit and area level information, and which has been proposed as an alternative when the available census data is too outdated to be considered for use.

The paper’s contribution is twofold: i) it presents a thorough evaluation of the considered methods as well as their pros and cons, and ii) it employs the sampling strategies most often encountered

> 1In reality, we apply the Census EB variant introduced by Guadarrama, Molina and Rao (2016)

2