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Decomposing the Composition Effect

  • Rothe, Christoph


    (Columbia University)

This paper proposes a decomposition of the composition effect, i.e. 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. Our decomposition contains three types of components: (i) the "direct contributions" 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 covariates' marginal distributions, and (iii) a "dependence effect" accounting for between-group differences in dependence patterns among the covariates. Our methods can be used to decompose differences in arbitrary distributional features, like quantiles or inequality measures, and allows for general nonlinear relationships between the outcome and the covariates. It can easily be implemented in practice using standard econometric techniques. An application to wage data from the US illustrates the empirical relevance of the decomposition’s components.

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Paper provided by Institute for the Study of Labor (IZA) in its series IZA Discussion Papers with number 6397.

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Length: 31 pages
Date of creation: Feb 2012
Date of revision:
Publication status: published in: Journal of Business and Economic Statistics
Handle: RePEc:iza:izadps:dp6397
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  1. Victor Chernozhukov & Ivan Fernandez-Val & Blaise Melly, 2012. "Inference on counterfactual distributions," CeMMAP working papers CWP05/12, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  2. Vaart,A. W. van der, 2000. "Asymptotic Statistics," Cambridge Books, Cambridge University Press, number 9780521784504.
  3. 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.
  4. repec:sae:ecolab:v:16:y:2006:i:2:p:1-2 is not listed on IDEAS
  5. Nicole Fortin & Thomas Lemieux & Sergio Firpo, 2010. "Decomposition Methods in Economics," NBER Working Papers 16045, National Bureau of Economic Research, Inc.
  6. Joseph G. Altonji & Prashant Bharadwaj & Fabian Lange, 2012. "Changes in the Characteristics of American Youth: Implications for Adult Outcomes," Journal of Labor Economics, University of Chicago Press, vol. 30(4), pages 783 - 828.
  7. repec:oup:restud:v:67:y:2000:i:4:p:609-33 is not listed on IDEAS
  8. Rothe, Christoph & Wied, Dominik, 2012. "Misspecification Testing in a Class of Conditional Distributional Models," IZA Discussion Papers 6364, Institute for the Study of Labor (IZA).
  9. Nikolay Nenovsky & S. Statev, 2006. "Introduction," Post-Print halshs-00260898, HAL.
  10. Rothe, Christoph, 2010. "Identification of unconditional partial effects in nonseparable models," Economics Letters, Elsevier, vol. 109(3), pages 171-174, December.
  11. Melly, Blaise, 2005. "Decomposition of differences in distribution using quantile regression," Labour Economics, Elsevier, vol. 12(4), pages 577-590, August.
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