An information theoretic approach to ecological inference in presence of spatial heterogeneity and dependence
This paper introduces Information Theoretic â€“ based methods for estimating a target variable in a set of small geographical areas, by exploring spatially heterogeneous relationships at the disaggregate level. Controlling for spatial effects means introducing models whereby the assumption is that values in adjacent geographic locations are linked to each other by means of some form of underlying spatial relationship. This method offers a flexible framework for modeling the underlying variation in sub-group indicators, by addressing the spatial dependency problem. A basic ecological inference problem, which allows for spatial heterogeneity and dependence, is presented with the aim of first estimating the model at the aggregate level, and then of employing the estimated coefficients to obtain the sub-group level indicators. The Information Theoretic-based formulations could be a useful means of including spatial and inter-temporal features in analyses of micro-level behavior, and of providing an effective, flexible way of reconciling micro and macro data. An unique optimum solution may be obtained even if there are more parameters to be estimated than available moment conditions and the problem is ill-posed. Additional non-sample information from theory and/or empirical evidence can be introduced in the form of known probabilities by means of the cross-entropy formalism. Consistent estimates in small samples can be computed in the presence of incomplete micro-level data as well as in the presence of problems of collinearity and endogeneity in the individual local models, without imposing strong distributional assumptions. Keywords: Generalized Cross Entropy Estimation, Ecological Inference, Spatial Heterogeneity
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- Golan, Amos, 2007. "Information and entropy econometrics - volume overview and synthesis," Journal of Econometrics, Elsevier, vol. 138(2), pages 379-387, June.
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- Johnston, Ron & Pattie, Charles, 2000. "Ecological Inference and Entropy-Maximizing: An Alternative Estimation Procedure for Split-Ticket Voting," Political Analysis, Cambridge University Press, vol. 8(04), pages 333-345, July.
- Ludo Peeters & Coro Chasco, 2006. "Ecological inference and spatial heterogeneity: an entropy-based distributionally weighted regression approach," Papers in Regional Science, Wiley Blackwell, vol. 85(2), pages 257-276, June.
- Golan, Amos & Judge, George G. & Miller, Douglas, 1996. "Maximum Entropy Econometrics," Staff General Research Papers Archive 1488, Iowa State University, Department of Economics.
- Rosa Bernardini Papalia, 2010. "Data disaggregation procedures within a maximum entropy framework," Journal of Applied Statistics, Taylor & Francis Journals, vol. 37(11), pages 1947-1959.
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