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On the Sensitivity of Wage Gap Decompositions

Journal of Labor Research volume 41, pages 1–33 (2020)Cite this article

Abstract

This paper investigates the sensitivity of average wage gap decompositions to methods resting on different assumptions regarding endogeneity of observed characteristics, sample selection into employment, and estimators’ functional form. Applying five distinct decomposition techniques to estimate the gender wage gap in the U.S. using data from the National Longitudinal Survey of Youth 1979, we find that the magnitudes of the wage gap components are generally not stable across methods. Furthermore, the definition of the observed characteristics matters: merely including their current values (as frequently seen in wage decompositions) entails smaller explained and larger unexplained components than when including both their current values and histories in the analysis. Given the sensitivity of our results, we advise caution when using wage decompositions for policy recommendations.

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Notes

  1. See also the method of Machado (2017), which permits arbitrary unobserved heterogeneity in the selection process.

  2. Olivetti and Petrongolo (2008) also estimate the Manski bounds (Manski 1989) on the distribution of wages, using the actual and the imputed wage distributions. Bičakova (2014) derives bounds on gender unemployment gaps.

  3. As an alternative use of panel data, Lemieux (1998) combines fixed effect estimation with decomposition methods and allows for heterogeneity of the return to fixed effects across groups. However, this strategy depends on individuals switching groups, which is rarely the case for gender.

  4. The methods discussed in this paper may also be used for investigating causal mechanisms in other empirical contexts. Examples include the analysis of the health effect of education operating via specific health behaviors as in Brunello et al. (2016), the assessment of the cognitive and non-cognitive mechanisms through which childcare affects outcomes later in life as in Heckman et al. (2013) and Keele et al. (2015), or the investigation of the causal mechanisms through which job seeker counselling affects employment as in Huber et al. (2017).

  5. See for instance Rubin (1974) for an introduction to the potential outcome framework.

  6. However, analogous results to Eqs. 2 and 3 cannot be applied to quantile decompositions, because the law of iterated expectations does not apply, see Fortin et al. (2011).

  7. The NLSY79 data consist of three independent probability samples: a cross-sectional sample (6,111 subjects, or 48%) representing the non-institutionalized civilian youth; a supplemental sample (42%) oversampling civilian Hispanic, black, and economically disadvantaged nonblack/non-Hispanic young people; and a military sample (10%) comprised of youth serving in the military as of September 30, 1978 (Bureau of Labor Statistics 2001).

  8. Specifically, we excluded 502 persons who reported to have worked 1,000 hours or more in the previous calendar year, but whose average hourly wages in the previous calendar year were either missing or equal to zero. We also dropped 54 working individuals with average hourly wages of less than $1 in the previous calendar year. Furthermore, 608 observations with missing values in observed characteristics (see Table 3 for the full list of characteristics) and 186 observations with missing values in the instruments for selection – the number of young children and the employment status of the respondent’s mother back when the respondent was 14 years old – were excluded.

  9. The included higher-order terms are marriage history squared and cubed, tenure squared and cubed, and years in current occupation squared and cubed. The interaction terms are between binary indicators for region in 1998 and urban residency, first job before 1975, first job in 1976-79, industry indicators, and employment in 1998; between education indicators and occupation indicators, years in current occupation, and the employment indicator 1998; and between tenure and the urban indicator, occupation indicators, years in current occupation, and the full-time employment indicator in 1998.

  10. Among the methods considered, the differences in the estimates of the total wage gap are statistically significant at the 10% level between Oaxaca-Blinder and IPW IV, IPW without and with controlling for W, IPW without W and IPW MAR, IPW without W and IPW IV, IPW with W and IPW MAR, IPW with W and IPW IV, and IPW MAR and IPW IV.

  11. The regression-based Oaxaca-Blinder estimator does not rely on common support, see the discussion in Section “Identification”, and therefore does not require trimming observations with extreme propensity score values.

  12. Table 7 in Appendix additionally provides the number and the share of trimmed observations for each propensity score.

  13. Huber and Solovyeva (2018) provide a simulation study in which the finite sample behavior of IPW with W, IPW MAR, and IPW IV is investigated. The findings suggest that ignoring or not appropriately controlling for sample selection can entail substantial biases, see Tables 1 and 2 therein.

  14. We note that when defining the female (rather than male) wages as reference (implying that G = 1 for women rather than men), the explained component increases and the unexplained component decreases substantially for IPW MAR. For the other decomposition methods, results are more homogeneous across reference group definitions.

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Authors and Affiliations

  1. Department of Economics, University of Fribourg, Fribourg, Switzerland

    Martin Huber

  2. NORC at the University of Chicago, Chicago, IL, USA

    Anna Solovyeva

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Appendix

Appendix

Fig. 5
figure 5

Distribution of the estimated \(\Pr (G=1|X)\) by treatment states in seleted population

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Fig. 6
figure 6

Distribution of the estimated \(\Pr (G=1|W)\) by treatment states in seleted population

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Fig. 7
figure 7

Distribution of the estimated \(\Pr (G=1|X, W)\) by treatment states in seleted population

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Fig. 8
figure 8

Distribution of the estimated \(\Pr (G=1|W)\) by treatment states in total population

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Fig. 9
figure 9

Distribution of the estimated \(\Pr (G=1|X, W)\) by treatment states in total population

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Fig. 10
figure 10

Distribution of the estimated \(\Pr (S=1|G, X, W)\) by selection states

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Fig. 11
figure 11

Distribution of the estimated \(p(Q)=\Pr (S=1|G, X, W, Z)\) by selection states

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Fig. 12
figure 12

Distribution of the estimated \(\Pr (G=1|W, p(Q))\) by treatment states in total population

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Fig. 13
figure 13

Distribution of the estimated \(\Pr (G=1|X, W, p(Q))\) by treatment states in total population

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Table 3 Summary statistics and mean differences by gender
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Table 4 Summary of the estimated treatment propensity scores in selected population
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Table 5 Summary of the estimated treatment propensity scores in total population
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Table 6 Summary of the estimated selection propensity scores in total population
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Table 7 Number of trimmed observations for each propensity score
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Table 8 Robustness check: No trimming
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Table 9 Robustness check: S defined as working at least 1700 hours in the previous year
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Table 10 Robustness check: S defined as working positive hours in the previous year
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Table 11 Robustness check: no interactions in X
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Table 12 Mother worked at 14 as an additional IV, full set of X
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Huber, M., Solovyeva, A. On the Sensitivity of Wage Gap Decompositions. J Labor Res 41, 1–33 (2020). https://doi.org/10.1007/s12122-020-09302-7

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Keywords

  • Wage decomposition
  • Gender wage gap
  • Causal mechanisms
  • Mediation

JEL Classification

  • C14
  • C21
  • J31
  • J71