Functional ecological inference

Christian Bontemps, Jean-Pierre Florens and Nour Meddahi
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Christian Bontemps: TSE-R - Toulouse School of Economics - UT Capitole - Université Toulouse Capitole - UT - Université de Toulouse - EHESS - École des hautes études en sciences sociales - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement, ENAC - Ecole Nationale de l'Aviation Civile, CNRS - Centre National de la Recherche Scientifique
Jean-Pierre Florens: TSE-R - Toulouse School of Economics - UT Capitole - Université Toulouse Capitole - UT - Université de Toulouse - EHESS - École des hautes études en sciences sociales - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement, CNRS - Centre National de la Recherche Scientifique, EHESS - École des hautes études en sciences sociales
Nour Meddahi: TSE-R - Toulouse School of Economics - UT Capitole - Université Toulouse Capitole - UT - Université de Toulouse - EHESS - École des hautes études en sciences sociales - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement, CNRS - Centre National de la Recherche Scientifique, EHESS - École des hautes études en sciences sociales

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Abstract: In this paper, we consider the problem of ecological inference when one observes the conditional distributions of Y|W and Z|W from aggregate data and attempts to infer the conditional distribution of Y|Z without observing Y and Z in the same sample. First, we show that this problem can be transformed into a linear equation involving operators for which, under suitable regularity assumptions, least squares solutions are available. We then propose the use of the least squares solution with the minimum Hilbert–Schmidt norm, which, in our context, can be structurally interpreted as the solution with minimum dependence between Y and Z. Interestingly, in the case where the conditioning variable W is discrete and belongs to a finite set, such as the labels of units/groups/cities, the solution of this minimal dependence has a closed form. In the more general case, we use a regularization scheme and show the convergence of our proposed estimator. A numerical evaluation of our procedure is proposed.

Keywords: Ecological inference; Linear operator; Generalized inverse; Hilbert–Schmidt norm; Regularization (search for similar items in EconPapers)
Date: 2025-03
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Published in Journal of Econometrics, 2025, 248, pp.105918. ⟨10.1016/j.jeconom.2024.105918⟩

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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-05141883

DOI: 10.1016/j.jeconom.2024.105918

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