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Decomposing wage discrimination in Germany and Austria with counterfactual densities


Using income and other individual data from EU-SILC for Germany and Austria, we analyze wage discrimination for three break-ups: gender, sector of employment, and country of origin. Using the method of Machado and Mata (J Appl Econom 20(4):445–465, 2005) the discrimination over the whole range of the wage distribution is estimated. Significance of results is checked via confidence interval estimates along the lines of Melly (Estimation of counterfactual distributions using quantile regression. Working Paper, SIAW, University of St. Gallen, 2006). The economies of Germany and Austria appear structurally very similar and are highly interconnected. One would, therefore, expect to find similar levels and structures of wage discrimination. Our findings deviate from this conjecture significantly.

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  1. see

  2. A major rational for this sample restriction is the removal of self-selection bias. But, as our results on self-selection in the “Appendix” will show, filtering along the gender dimension is most likely insufficient for that purpose.

  3. In the econometric literature dealing with decomposition this discriminatory part is called structural effect, whereas the part associated with different characteristics is known as composition effect. We will keep using the terms “discrimination” and “explained differences” instead.

  4. A more thorough discussion of the shortcomings of the OB-decomposition is found e.g. in Fortin et al. (2011).

  5. Similar ideas are found in Gosling et al. (2000), Albrecht et al. (2003) and Melly (2005a). Testing with these approaches only yielded marginally different results relative to those of MM and are not reported here.

  6. Results using RIF-regressions with reweighting were not found qualitatively different from the MM-results. These results are available from the authors upon request.

  7. We found that the number of bootstrap samples S required to get stable results should be a multiple of the total number of observations. For the application we have chosen S = 40000 which is roughly four times the n 1 + n 2 number of observations in the case of Germany and eight times in the case of Austria. With this number of bootstraps the differences between the MM approach and Melly (2005b) are negligible for practical purposes.

  8. Formulated as a programming problem, quantile regression coefficients β(τ) for quantile τ are estimated as solution to min β(τ) (1/n)∑ i ρ τ [w − x i β(τ)] with ρ τ (u) = τ u for u ≥ 0 and \(\rho_\tau(u)=(\tau\!-\!1)u\) for u < 0. We use the R-package quantreg by Roger Koenker for that purpose (see Koenker 2012).

  9. Step 2 (b), by the probability integral transformation principle, simulates random sampling from the (estimated) conditional distributions of w ki conditional on X k , for k = 1,2. Or, put differently: The w ki consistently estimate the corresponding quantiles of the conditional distribution, see Koenker and Bassett (1978). Repeating these quantile estimates for S random draws of characteristics from the original distributions then amounts to integrating out these characteristics from the corresponding conditional distributions.

  10. For more details see Machado and Mata (2005). A formal proof of consistency and asymptotic normality of the derived difference measures is contained in Albrecht et al. (2009).

  11. Numerous non-basic counterfactual distributions can be imagined and found in the literature (see Cahuc and Zylberberg 2004 pp. 280–282 for a short discussion). For example, one based on fictitious non-discriminatory market remuneration coefficients β m for both groups. Such non-basic counterfactuals are not considered here.

  12. Melly provides a corresponding R-source code on

  13. Relevant approaches are found e.g. in Buchinsky (1998), Albrecht et al. (2004), Neuman and Oaxaca (2004a) or Ivanov (2008).

  14. This latter criterion may potentially introduce another type of sample selection bias, as it ignores different likelihoods of longer unemployment spells for each subgroup considered. See Sect. 3.5.

  15. Unfortunately, the understanding of these education levels has been different in Germany and Austria. This explains the implausible, massive differences in the proportions of these three levels between the two countries (see Tables 2 and 4 in the “Appendix”). This prohibits comparing the estimated standard quantile regression coefficients for these variables between countries. To our knowledge, statistical offices are aware of the corresponding shortcomings and currently work on improved definitions and comparable coding.

  16. Using “age”, “age2” and “experience” instead of “age”, “experience” and “experience2” lead to a worse fit and was formally rejected by corresponding tests.

  17. This is a fairly standard result and easy to interpret: Negative values for the bottom percentiles arise naturally, if the lowest incomes are associated with manual labor, which deteriorates in quality with age. Positive values for higher incomes simply reflect widespread seniority pay.

  18. Synonymously we will speak of overall wage differences or raw discrimination.

  19. Fournier and Koske (2012) report a difference of 25 % at the median (Fig. 7) where we find 20 %. One reason for this difference might be that we classify all persons born abroad as immigrants, while Fournier and Koske count only those born outside the EU. Furthermore, their underlying regression specification is not quite clear. The basic data set instead is the very same as used here.

  20. These results are unweighted and, thus, are not strictly comparable to the OLS results from above. But, as the comparison of total wage gaps reported in Tables 7 and 11 shows, the differences are quantitatively negligible.


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Grandner, T., Gstach, D. Decomposing wage discrimination in Germany and Austria with counterfactual densities. Empirica 42, 49–76 (2015).

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  • Wage discrimination
  • Decomposition
  • Quantile regression