# **1 Introduction**

Household surveys that are designed for national or sub-national (i.e. regions or states) level parameter estimates often lack a sufficiently large sample size to generate accurate direct estimates for smaller domains or sub-populations.<sup>1</sup> Any area for which the sample is not sufficiently large to produce an estimate of adequate precision is referred to as a small area. Consequently small area methods attempt to address low representativeness of surveys within areas, or the lack of data for specific areas/sub-populations. This is accomplished by incorporating information from supplementary sources. In the methodology presented by Elbers, Lanjouw, and Lanjouw (2003) the desired estimate is produced by a model done using survey data which is then linked to outside information such as a population census, administrative records, and/or geospatial information obtained through remote sensing. As Rao and Molina (2015) state, the availability of these auxiliary data as well as a valid model are essential for obtaining successful small area estimates (SAE).

In the case of poverty measures, which are nonlinear functions, small area estimation methods coupled with Monte Carlo simulations are a useful statistical technique for monitoring poverty along with its spatial distribution and evolution.<sup>2</sup> Poverty estimates are often produced by statistical agencies, and commonly are the product of a household survey. Household surveys usually are the main source of welfare (expenditure or income) used to produce poverty estimates, yet most are only reliable up to a certain geographical level. Therefore, a commonly adopted solution has been to borrow strength from a national census, administrative records, and/or geospatial information which allows for representativeness for small areas. Nevertheless, these outside data sources often lack detailed expenditure or income information required for producing estimates of poverty. Small area methods attempt to exploit each data’s attributes to obtain estimators that can be used at dis-aggregated levels.

Poverty at lower geographical levels can be used to identify areas that are in need of attention, or that may be lagging behind the rest of the country. For example, the Government of Ecuador after an earthquake that occurred on April 16, 2016 relied on small area estimates of poverty to decide where help was needed most. The small area estimates of poverty for Ecuador, which were released not long before the earthquake, proved to be an invaluable resource for the rebuilding effort in the country.

One of the most common small area methods used for poverty estimates is the one proposed by Elbers, Lanjouw, and Lanjouw (2003, henceforth ELL).<sup>3</sup> This methodology has been widely adopted by the World Bank and has been applied in numerous poverty maps<sup>4</sup> conducted by the institution. In its efforts to make the implementation of the ELL methodology as straightforward as possible, the World Bank created a software package that could be easily used by anyone. The software, PovMap (Zhao, 2006),<sup>5</sup> has proven to be an invaluable resource for the World Bank as well as for many statistical agencies, line ministries, and other international organizations seeking to create their own small area estimates of poverty. The software is freely available and has a graphical user interface which simplifies its use. Nevertheless, more advanced

> 1For example districts, municipalities, migrant populations, or populations with disabilities.

> 2Poverty is a nonlinear function of welfare, consequently small area estimation methods of linear characteristics are invalid (Molina and Rao, 2010). A proposed solution to this problem is to use Monte Carlo simulation to obtain multiple vectors of the measure of interest (Elbers, Lanjouw, and Lanjouw, 2003).

> 3For a detailed discussion of different applications of small area poverty estimates by the World Bank, readers should refer to Bedi et al. (2007), for other applications readers should refer to Rao and Moline (2015).

> 4Poverty map is the common name within the World Bank for the methodology where the obtained estimates are mapped for illustrative purposes.

> 5downloadable from: http://iresearch.worldbank.org/PovMap/PovMap2/setup.zip

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