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Neglected heterogeneity, Simpson’s paradox, and the anatomy of least squares


Winkelmann, Rainer (2024). Neglected heterogeneity, Simpson’s paradox, and the anatomy of least squares. Journal of Econometric Methods, 13(1):131-144.

Abstract

When a sample combines data from two or more groups, multivariate regression yields a matrix-weighted average of the group-specific coefficient vectors. However, it is possible that the weighted average of a specific coefficient falls outside the range of the group-specific coefficients, and it may even have a different sign compared to both group-level coefficients, a manifestation of Simpson’s paradox. The result of the combined regression is then prone to misinterpretation. The purpose of this paper is to raise awareness of this problem and to state conditions under which such non-convex weighting or sign reversal can arise, for a model with two regressors and two groups. Two illustrative examples, an investment equation estimated with panel data, and a cross-sectional earnings equation for men and women, highlight the relevance of these findings for applied work.

Abstract

When a sample combines data from two or more groups, multivariate regression yields a matrix-weighted average of the group-specific coefficient vectors. However, it is possible that the weighted average of a specific coefficient falls outside the range of the group-specific coefficients, and it may even have a different sign compared to both group-level coefficients, a manifestation of Simpson’s paradox. The result of the combined regression is then prone to misinterpretation. The purpose of this paper is to raise awareness of this problem and to state conditions under which such non-convex weighting or sign reversal can arise, for a model with two regressors and two groups. Two illustrative examples, an investment equation estimated with panel data, and a cross-sectional earnings equation for men and women, highlight the relevance of these findings for applied work.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:03 Faculty of Economics > Department of Economics
Dewey Decimal Classification:330 Economics
Scopus Subject Areas:Physical Sciences > Statistics and Probability
Social Sciences & Humanities > Economics and Econometrics
Physical Sciences > Applied Mathematics
Uncontrolled Keywords:Applied mathematics, economics and econometrics, statistics and probability, average treatment effect, covariance-weighting, heterogeneity spillover, non-convex average
Scope:Discipline-based scholarship (basic research)
Language:English
Date:24 April 2024
Deposited On:08 Feb 2024 07:41
Last Modified:29 Jun 2024 03:43
Publisher:De Gruyter
ISSN:2156-6674
OA Status:Hybrid
Free access at:Publisher DOI. An embargo period may apply.
Publisher DOI:https://doi.org/10.1515/jem-2023-0028
Related URLs:https://www.zora.uzh.ch/id/eprint/229123
Other Identification Number:merlin-id:24387
  • Content: Published Version
  • Language: English
  • Licence: Creative Commons: Attribution 4.0 International (CC BY 4.0)