Estimating regional income indicators under transformations and access to limited population auxiliary information

Spatially disaggregated income indicators are typically estimated by using model‐based methods that assume access to auxiliary information from population micro‐data. In many countries like Germany and the UK population micro‐data are not publicly available. In this work we propose small area methodology when only aggregate population‐level auxiliary information is available. We use data‐driven transformations of the response to satisfy the parametric assumptions of the used models. In the absence of population micro‐data, appropriate bias‐corrections for small area prediction are needed. Under the approach we propose in this paper, aggregate statistics (means and covariances) and kernel density estimation are used to resolve the issue of not having access to population micro‐data. We further explore the estimation of the mean squared error using the parametric bootstrap. Extensive model‐based and design‐based simulations are used to compare the proposed method to alternative methods. Finally, the proposed methodology is applied to the 2011 Socio‐Economic Panel and aggregate census information from the same year to estimate the average income for 96 regional planning regions in Germany.