# **1 Introduction**

A poverty map is a spatial description of the distribution of poverty in a given country or region. While such a map is useful for policy makers and researchers when small geographic units (e.g., cities, towns, or villages) are discernable, estimates based on household surveys are typically not representative or associated with high uncertainty at such levels of disaggregation. On the other hand, most censuses do not contain information on consumption (or a surrogate such as income or expenditures) required to calculate poverty. To overcome these problems, Elbers et al. (2003), henceforth ELL, developed small area estimation poverty maps, a methodology that can be used to combine information from a detailed household survey with that from a comprehensive census. The general methodology usually consists of two steps, calibration of a statistical model based on survey data and application to the comprehensive census data. In the first step, a multiple linear regression analysis is used to estimate a model of household consumption based on survey data (which includes a consumption module). The explanatory variables in the model are restricted to the subset available in both the survey and the census.<sup>1</sup> In the second step, the estimated model parameters are applied to census data. The regression model predicts the conditional mean of consumption Since one is typically also interested in higher moments of the distribution, simulation methods are used to introduce a random disturbance term. The simulations provide estimates of consumption per capita for every household in the census.

Several criticisms have been raised with regard to the ELL estimator and extensions and alternatives have been discussed. Haslett et al. (2010) propose alternative regression techniques to estimate the survey regression in the first stage. Tarozzi and Deaton (2009) and Molina and Rao (2010) argue that unexplained variation between areas impairs the performance of the ELL estimator as ELL only account for variation between clusters which are nested into areas. While also applying a two-stage approach similar to ELL, Molina and Rao (2010) use area-specific random effects instead of cluster-specific random effects. Moreover, in their empirical Bayes approach they simulate out-of-sample consumption values for the census conditional on the consumption values from the survey. Thus, in contrast to ELL, their simulated census data explicitly includes observed sample information. Das and Chambers (2017) propose another correction for the ELL method which is robust to significant unexplained between-area variability. Their correction relies on the relationship between variance components estimators under the ELL model and a model which additionally contains an area-specific random effect. Marhuenda et al. (2017) discusses the direct application of such a model including cluster-specific and area-specific random effects for poverty mapping via extending the empirical Bayes method of Molina and Rao (2010). Comprehensive discussions on different small area estimation methods can be found in Guadarrama et al. (2016) and

> 1The ELL estimator requires relevant explanatory variables for the model predicting consumption to be measured in a comparable way both in the census and in the survey, including the same degree of potential measurement error. Differences in coding schemes or even the way the interview was conducted can prevent reasonable harmonization between census and survey variables. See also Tarozzi and Deaton (2009) for a brief discussion.

2