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Decomposing the Composition Effect: The Role of Covariates in Determining Between-Group Differences in Economic Outcomes

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  • Christoph Rothe

Abstract

In this article, we study the structure of the composition effect, which is the part of the observed between-group difference in the distribution of some economic outcome that can be explained by differences in the distribution of covariates. Using results from copula theory, we derive a new representation that contains three types of components: (i) the "direct contribution" of each covariate due to between-group differences in the respective marginal distributions, (ii) several "two-way" and "higher-order interaction effects" due to the interplay between two or more marginal distributions, and (iii) a "dependence effect" accounting for between-group differences in dependence patterns among the covariates. We show how these components can be estimated in practice, and use our method to study the evolution of the wage distribution in the United States between 1985 and 2005. We obtain some new and interesting empirical findings. For example, our estimates suggest that the dependence effect alone can explain about one-fifth of the increase in wage inequality over that period (as measured by the difference between the 90% and the 10% quantile).

Suggested Citation

  • Christoph Rothe, 2015. "Decomposing the Composition Effect: The Role of Covariates in Determining Between-Group Differences in Economic Outcomes," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 33(3), pages 323-337, July.
    • Handle: RePEc:taf:jnlbes:v:33:y:2015:i:3:p:323-337
    DOI: 10.1080/07350015.2014.948959
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    References listed on IDEAS

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    1. Trivedi, Pravin K. & Zimmer, David M., 2007. "Copula Modeling: An Introduction for Practitioners," Foundations and Trends(R) in Econometrics, now publishers, vol. 1(1), pages 1-111, April.
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    Cited by:

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    2. Trinh Thi, Huong & Simioni, Michel & Thomas-Agnan, Christine, 2018. "Assessing the nonlinearity of the calorie-income relationship: An estimation strategy – With new insights on nutritional transition in Vietnam," World Development, Elsevier, vol. 110(C), pages 192-204.
    3. Luis Ayala & Javier Martín‐Román & Juan Vicente, 2024. "What contributes to rising inequality in large cities?," Journal of Regional Science, Wiley Blackwell, vol. 64(5), pages 1760-1810, November.
    4. Hafifa Siddiq & Najmeh Maharlouei & Babak Najand & Arash Rahmani & Hossein Zare, 2023. "Immigration Status, Educational Level, and Perceived Discrimination in Europe," IJERPH, MDPI, vol. 20(3), pages 1-14, January.
    5. Awaworyi Churchill, Sefa & Munyanyi, Musharavati Ephraim & Prakash, Kushneel & Smyth, Russell, 2020. "Locus of control and the gender gap in mental health," Journal of Economic Behavior & Organization, Elsevier, vol. 178(C), pages 740-758.
    6. Georg Keilbar & Sonja Greven, 2026. "Counterfactual Density Effects and the German East--West Income Gap," Papers 2603.28470, arXiv.org, revised Apr 2026.
    7. Jeremiah Richey & Alicia Rosburg, 2020. "Decomposing joint distributions via reweighting functions: an application to intergenerational economic mobility," Econometric Reviews, Taylor & Francis Journals, vol. 39(6), pages 541-558, July.
    8. Trinh Thi, Huong & Simioni, Michel & Thomas-Agnan, Christine, 2018. "Decomposition of changes in the consumption of macronutrients in Vietnam between 2004 and 2014," Economics & Human Biology, Elsevier, vol. 31(C), pages 259-275.
    9. Qin, Yu & Zhu, Hongjia & Zhu, Rong, 2016. "Changes in the distribution of land prices in urban China during 2007–2012," Regional Science and Urban Economics, Elsevier, vol. 57(C), pages 77-90.
    10. David Gallusser & Matthias Krapf, 2019. "Joint Income-Wealth Inequality: An Application Using Administrative Tax Data," CESifo Working Paper Series 7876, CESifo.
    11. Lidia Panico & Maxime Tô, 2023. "A distributional decomposition of birthweight differences by maternal education: A comparison of France and the UK," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 21(3), pages 591-617, September.
    12. Rothe, Christoph & Wied, Dominik, 2020. "Estimating derivatives of function-valued parameters in a class of moment condition models," Journal of Econometrics, Elsevier, vol. 217(1), pages 1-19.

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