Small area estimation of poverty using the ELL/PovMap method, and its alternatives

This section provides a brief overview of small area estimation and the Elbers et al. (2003) ELL method. We consider a target variable, denoted by Y, for which we seek estimates for a number of small subpopulations. These subpopulations usually correspond to small geographical areas, but can instead represent different subgroups that may be collocated (in which case the technique is sometimes called small domain estimation). In the original ELL method for poverty measures, Y is log-transformed per capita expenditure. For extensions to the under-nourishment measures, log kilocalorie intake per person or per adult equivalent is used instead. For stunting, underweight and wasting in children, Y is standardized height-for-age, weightfor-age, and weight-for-height respectively. Provided there are at least some sample data available for each small subpopulation, direct estimates of Y for these subpopulations can be derived from the sample survey data, for which Y has been measured directly on the final-stage sampled units (e.g. households or eligible children). Because sample sizes within even the sampled subpopulations are typically very small, these direct estimates are however generally not reliable. The core idea of small area estimation is that auxiliary information, denoted X, which is available from the survey and may also be available from other sources such as a census even for unsampled parts of the population, can be used to improve the estimates, giving lower standard errors than are possible using only direct estimates. In the ELL method, but not in those small area methods covered in Rao (2003), X represents additional variables that have been measured for the whole population, either by a census or via a GIS database. (For the Rao 2003 methods X is generally available only on the sampled units but, unlike ELL, the range of statistical models can be nonlinear.) For ELL, a linear regression-type relationship between Y and X namely: