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Decomposing Differences in Arithmetic Means: A Doubly-Robust Estimation Approach

  • Boris Kaiser

When decomposing differences in average economic outcome between two groups of individuals, it is common practice to base the analysis on logarithms if the dependent variable is nonnegative. This paper argues that this approach raises a number of undesired statistical and conceptual issues because decomposition terms have the interpretation of approximate percentage differences in geometric means. Instead, we suggest that the analysis should be based on the arithmetic means of the original dependent variable. We present a flexible parametric decomposition framework that can be used for all types of continuous (or count) nonnegative dependent variables. In particular, we derive a propensity-score-weighted estimator for the aggregate decomposition that is "doubly robust", that is, consistent under two separate sets of assumptions. A comparative Monte Carlo study illustrates that the proposed estimator performs well in a many situations. An application to the union wage gap in the United States finds that the importance of the unexplained union wage premium is much smaller than suggested by the standard log-wage decomposition.

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Paper provided by Universitaet Bern, Departement Volkswirtschaft in its series Diskussionsschriften with number dp1308.

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Date of creation: Oct 2013
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Handle: RePEc:ube:dpvwib:dp1308
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  1. Terza, Joseph V., 1998. "Estimating count data models with endogenous switching: Sample selection and endogenous treatment effects," Journal of Econometrics, Elsevier, vol. 84(1), pages 129-154, May.
  2. Richard K. Crump & V. Joseph Hotz & Guido W. Imbens & Oscar A. Mitnik, 2004. "Dealing with Limited Overlap in Estimation of Average Treatment Effects," Working Papers 0716, University of Miami, Department of Economics, revised 12 Jun 2007.
  3. Jacob A. Mincer, 1974. "Age and Experience Profiles of Earnings," NBER Chapters, in: Schooling, Experience, and Earnings, pages 64-82 National Bureau of Economic Research, Inc.
  4. Ben Jann, 2008. "The Blinder–Oaxaca decomposition for linear regression models," Stata Journal, StataCorp LP, vol. 8(4), pages 453-479, December.
  5. Ronald Oaxaca, 1971. "Male-Female Wage Differentials in Urban Labor Markets," Working Papers 396, Princeton University, Department of Economics, Industrial Relations Section..
  6. David Neumark, 1988. "Employers' Discriminatory Behavior and the Estimation of Wage Discrimination," Journal of Human Resources, University of Wisconsin Press, vol. 23(3), pages 279-295.
  7. José Mata & José A. F. Machado, 2005. "Counterfactual decomposition of changes in wage distributions using quantile regression," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 20(4), pages 445-465.
  8. Willard G. Manning & John Mullahy, 1999. "Estimating Log Models: To Transform or Not to Transform?," NBER Technical Working Papers 0246, National Bureau of Economic Research, Inc.
  9. Słoczyński, Tymon, 2012. "New Evidence on Linear Regression and Treatment Effect Heterogeneity," MPRA Paper 39524, University Library of Munich, Germany.
  10. Darity, William Jr & Guilkey, David & Winfrey, William, 1995. "Ethnicity, race, and earnings," Economics Letters, Elsevier, vol. 47(3-4), pages 401-408, March.
  11. Yun, Myeong-Su, 2004. "Decomposing differences in the first moment," Economics Letters, Elsevier, vol. 82(2), pages 275-280, February.
  12. John M. Krieg & Paul Storer, 2006. "How Much Do Students Matter? Applying The Oaxaca Decomposition To Explain Determinants Of Adequate Yearly Progress," Contemporary Economic Policy, Western Economic Association International, vol. 24(4), pages 563-581, October.
  13. Ian A. Munn & Anwar Hussain, 2010. "Factors Determining Differences in Local Hunting Lease Rates: Insights from Blinder-Oaxaca Decomposition," Land Economics, University of Wisconsin Press, vol. 86(1), pages 66-78.
  14. Steffen Mueller, 2012. "Works Councils and Establishment Productivity," Industrial and Labor Relations Review, ILR Review, Cornell University, ILR School, vol. 65(4), pages 880-898, October.
  15. Rothe, Christoph, 2012. "Decomposing the Composition Effect," IZA Discussion Papers 6397, Institute for the Study of Labor (IZA).
  16. Boris Kaiser, 2013. "Detailed Decompositions in Generalized Linear Models," Diskussionsschriften dp1309, Universitaet Bern, Departement Volkswirtschaft.
  17. Jacob A. Mincer, 1974. "Schooling, Experience, and Earnings," NBER Books, National Bureau of Economic Research, Inc, number minc74-1, December.
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