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Decomposing the Composition Effect

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  • Rothe, Christoph

    () (University of Mannheim)

Abstract

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.

Suggested Citation

  • Rothe, Christoph, 2012. "Decomposing the Composition Effect," IZA Discussion Papers 6397, Institute for the Study of Labor (IZA).
  • Handle: RePEc:iza:izadps:dp6397
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    References listed on IDEAS

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    1. Victor Chernozhukov & Iván Fernández‐Val & Blaise Melly, 2013. "Inference on Counterfactual Distributions," Econometrica, Econometric Society, vol. 81(6), pages 2205-2268, November.
    2. Christoph Rothe & Dominik Wied, 2013. "Misspecification Testing in a Class of Conditional Distributional Models," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 108(501), pages 314-324, March.
    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. Fortin, Nicole & Lemieux, Thomas & Firpo, Sergio, 2011. "Decomposition Methods in Economics," Handbook of Labor Economics, Elsevier.
    5. Nikolay Nenovsky & S. Statev, 2006. "Introduction," Post-Print halshs-00260898, HAL.
    6. Stephen G. Donald & David A. Green & Harry J. Paarsch, 2000. "Differences in Wage Distributions Between Canada and the United States: An Application of a Flexible Estimator of Distribution Functions in the Presence of Covariates," Review of Economic Studies, Oxford University Press, vol. 67(4), pages 609-633.
    7. Vaart,A. W. van der, 2000. "Asymptotic Statistics," Cambridge Books, Cambridge University Press, number 9780521784504, March.
    8. 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.
    9. Rothe, Christoph, 2010. "Identification of unconditional partial effects in nonseparable models," Economics Letters, Elsevier, vol. 109(3), pages 171-174, December.
    10. repec:sae:ecolab:v:16:y:2006:i:2:p:1-2 is not listed on IDEAS
    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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    Cited by:

    1. Ghosh, Pallab Kumar, 2014. "The contribution of human capital variables to changes in the wage distribution function," Labour Economics, Elsevier, vol. 28(C), pages 58-69.
    2. Jan Eeckhout & Roberto Pinheiro & Kurt Schmidheiny, 2014. "Spatial Sorting," Journal of Political Economy, University of Chicago Press, vol. 122(3), pages 554-620.
    3. Domenico Depalo & Raffaela Giordano & Evangelia Papapetrou, 2015. "Public–private wage differentials in euro-area countries: evidence from quantile decomposition analysis," Empirical Economics, Springer, vol. 49(3), pages 985-1015, November.
    4. Boris Kaiser, 2016. "Decomposing differences in arithmetic means: a doubly robust estimation approach," Empirical Economics, Springer, vol. 50(3), pages 873-899, May.
    5. Thomschke, Lorenz, 2015. "Changes in the distribution of rental prices in Berlin," Regional Science and Urban Economics, Elsevier, vol. 51(C), pages 88-100.

    More about this item

    Keywords

    decomposition methods; counterfactual distribution;

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C18 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Methodolical Issues: General
    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models
    • J31 - Labor and Demographic Economics - - Wages, Compensation, and Labor Costs - - - Wage Level and Structure; Wage Differentials

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