 Functional ecological inferenceChristian Bontemps, Jean-Pierre Florens and Nour Meddahi Journal of Econometrics, 2025, vol. 248, issue C 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) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:econom:v:248:y:2025:i:c:s0304407624002690 DOI: 10.1016/j.jeconom.2024.105918 Access Statistics for this article Journal of Econometrics is currently edited by T. Amemiya, A. R. Gallant, J. F. Geweke, C. Hsiao and P. M. Robinson More articles in Journal of Econometrics from Elsevier |
Is your work missing from RePEc? Here is how to contribute.
Questions or problems? Check the EconPapers FAQ or send mail to .
EconPapers is hosted by the
School of Business at Örebro University.