Spatial Disaggregation of Social Indicators: An Info-Metrics Approach
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Spatial Disaggregation of Social Indicators: An Info‑Metrics Approach Esteban Fernandez‑Vazquez1,2 · Alberto Diaz Dapena1,3 · Fernando Rubiera‑Morollon1,2 · Ana Viñuela1,2 Accepted: 25 July 2020 © The Author(s) 2020
Abstract In this paper we propose a methodology to obtain social indicators at a detailed spatial scale by combining the information contained in census and sample surveys. Similarly to previous proposals, the method proposed here estimates a model at the sample level to later project it to the census scale. The main novelties of the technique presented are that (i) the small-scale mapping produced is perfectly consistent with the aggregates -regional or national- observed in the sample, and (ii) it does not require imposing strong distributional assumptions. The methodology suggested here follows the basics presented on Golan (2018) by adapting a cross-moment constrained Generalized Maximum Entropy (GME) estimator to the spatial disaggregation problem. This procedure is compared with the equivalent methodology of Tarozzi and Deaton (2009) by means of numerical experiments, providing a comparatively better performance. Additionally, the practical implementation of the methodology proposed is illustrated by estimating poverty rates for small areas for the region of Andalusia (Spain). Keywords Small area estimation · Poverty mapping · Spatial disaggregation · Info-metrics andentropy
1 Introduction The use of social indicators at an appropriately disaggregated geographical scale is a relevant issue, not only for research but also for policy-making because efficient policy design sometimes requires information with a high degree of spatial disaggregation. Official data, however, are not widely produced with a high detail of spatial disaggregation and are generally only available at a national or -sometimes- regional level. If the geographical location of these individual agents is observable at a highly disaggregated spatial scale, the indicators for * Esteban Fernandez‑Vazquez [email protected] 1
REGIOlab: Regional Economics Laboratory at the University of Oviedo, Oviedo, Spain
2
Department of Applied Economics, University of Oviedo, Asturias, Spain
3
Department of Economics and Statistics, University of Leon, León, Spain
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the small areas could be calculated simply by summing or averaging the individual estimates. In most cases, however, researchers have to deal with databases that might allow for a precise spatial location of the individuals, such the microdata of a Population Census, but that do not normally contain information on economic variables related to distributional issues, such as household income. On the other hand, the surveys that contain data about these indicators— such as household surveys—do not normally provide detailed information on the geographical location of the individuals surveyed. Even when they do, the small sample sizes for the sub-regions of interest make the estimates directly obtained very unstable (see Marc
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