This document compares different methods for measuring the gender wage gap using data from the Polish Labor Force Survey in 2012. It introduces 7 methods that will be analyzed: Oaxaca-Blinder decomposition, Juhn-Murphy-Pierce, DiNardo-Fortin-Lemieux, Machado-Mata, Nopo, and Firpo-Fortin-Lemieux. The analysis will compare the gender wage gaps estimated using each method across 14 different model specifications, from a basic model to ones including additional controls like industry, occupation, education, and all available variables. The goal is to provide guidance for practitioners on how the choice of method and model specification can impact measures of the gender wage gap.

1. Gender wage gap: methods and differences
La brecha salarial de genero en Polonia
Un analisis comparativo de los metodos disponibles
(trabajo in colaboracion con Karolina Goraus y Joanna Tyrowicz)
Lucas Augusto van der Velde
Candidato Doctoral
Asistente de investigacion en GRAPE
Facultad de Ciencias Economicas
Universidad de Varsovia
November 5, 2013

2. Gender wage gap: methods and differences
Table of contents
1 Introduction
2 Available Methods
3 Data
4 Results
5 Conclusions

3. Gender wage gap: methods and differences
Introduction
Introduction
Motivation
Proliferation of methods and lack of comparability
W&W metanalysis showed that the selection of the method
has consequences for the gap

4. Gender wage gap: methods and differences
Introduction
Introduction
Motivation
Proliferation of methods and lack of comparability
W&W metanalysis showed that the selection of the method
has consequences for the gap
Our work

5. Gender wage gap: methods and differences
Introduction
Introduction
Motivation
Proliferation of methods and lack of comparability
W&W metanalysis showed that the selection of the method
has consequences for the gap
Our work
Goal: Provide a guide for the practitioner

6. Gender wage gap: methods and differences
Introduction
Introduction
Motivation
Proliferation of methods and lack of comparability
W&W metanalysis showed that the selection of the method
has consequences for the gap
Our work
Goal: Provide a guide for the practitioner
How: Compare the gender wage gap in different methods (7)
and specifications (14)

7. Gender wage gap: methods and differences
Introduction
Introduction
Motivation
Proliferation of methods and lack of comparability
W&W metanalysis showed that the selection of the method
has consequences for the gap
Our work
Goal: Provide a guide for the practitioner
How: Compare the gender wage gap in different methods (7)
and specifications (14)
Data: Polish LFS 2012

8. Gender wage gap: methods and differences
Introduction
What is the gap
Types of gap
Raw gap
Adjusted gap

9. Gender wage gap: methods and differences
Introduction
What is the gap
Types of gap
Raw gap
Adjusted gap
Assumptions
Uncounfoundedness
Common Support

10. Gender wage gap: methods and differences
Available Methods

11. Gender wage gap: methods and differences
Available Methods
Methods under analysis
Linear Regressions
Oaxaca-Blinder decomposition
Juhn, Murphy and Pierce
DiNardo, Fortin and Lemieux
Machado Mata
Nopo
Firpo, Fortin and Lemieux (RIF)

12. Gender wage gap: methods and differences
Available Methods
Presentation of the methods
Oaxaca (1973) and Blinder (1973)
Juhn, Murphy and Pierce (1993)
DiNardo, Fortin and Lemieux(1996)

13. Gender wage gap: methods and differences
Available Methods
Presentation of the methods
Oaxaca (1973) and Blinder (1973)
OLS based, estimates at the mean
Juhn, Murphy and Pierce (1993)
DiNardo, Fortin and Lemieux(1996)

14. Gender wage gap: methods and differences
Available Methods
Presentation of the methods
Oaxaca (1973) and Blinder (1973)
OLS based, estimates at the mean
¯
¯
ˆ ¯
ˆ ¯
Y M − Y F = βM X M − βF X F
Juhn, Murphy and Pierce (1993)
DiNardo, Fortin and Lemieux(1996)

15. Gender wage gap: methods and differences
Available Methods
Presentation of the methods
Oaxaca (1973) and Blinder (1973)
OLS based, estimates at the mean
ˆ ¯
¯
ˆ
ˆ ¯
ˆ
ˆ
¯
Y M − Y F = β ∗ (X M − X F ) + (β ∗ − β F )(X F ) + (β ∗ − β M )(X M )
Juhn, Murphy and Pierce (1993)
DiNardo, Fortin and Lemieux(1996)

16. Gender wage gap: methods and differences
Available Methods
Presentation of the methods
Oaxaca (1973) and Blinder (1973)
Juhn, Murphy and Pierce (1993)
OLS based approach with a solution for the quantiles
Based on very strong assumtpions
DiNardo, Fortin and Lemieux(1996)

17. Gender wage gap: methods and differences
Available Methods
Presentation of the methods
Oaxaca (1973) and Blinder (1973)
Juhn, Murphy and Pierce (1993)
DiNardo, Fortin and Lemieux(1996)
Distributional approach
Reweights the entire distribution of wages, which requires only
one logit (or probit) model

18. Gender wage gap: methods and differences
Available Methods
Presentation of the methods
Machado Mata(2005)
Nopo(2008)
Firpo, Fortin and Lemieux(2009)

19. Gender wage gap: methods and differences
Available Methods
Presentation of the methods
Machado Mata(2005)
Quantile regression approach
Computationally intensive
Nopo(2008)
Firpo, Fortin and Lemieux(2009)

20. Gender wage gap: methods and differences
Available Methods
Presentation of the methods
Machado Mata(2005)
Nopo(2008)
Non-parametric decomposition
Firpo, Fortin and Lemieux(2009)

21. Gender wage gap: methods and differences
Available Methods
Presentation of the methods
Machado Mata(2005)
Nopo(2008)
Non-parametric decomposition
∆ = ∆0 + ∆F + ∆M + ∆F
Firpo, Fortin and Lemieux(2009)

22. Gender wage gap: methods and differences
Available Methods
Presentation of the methods
Machado Mata(2005)
Nopo(2008)
Firpo, Fortin and Lemieux(2009)

23. Gender wage gap: methods and differences
Available Methods
Presentation of the methods
Machado Mata(2005)
Nopo(2008)
Firpo, Fortin and Lemieux(2009)
Based on the Recentered Influence Functions (RIF)

24. Gender wage gap: methods and differences
Available Methods
Presentation of the methods
Machado Mata(2005)
Nopo(2008)
Firpo, Fortin and Lemieux(2009)
Based on the Recentered Influence Functions (RIF)
Flexible approach that can be combined with other methods,
such as OB and the DFL

25. Gender wage gap: methods and differences
Available Methods
Summary
Selection Bias
OB
OK
JMP
OK
DFL
MM
OK
Nopo
OK
RIF

26. Gender wage gap: methods and differences
Available Methods
Summary
Selection Bias
Dimensionality Curse
OB
OK
OK
JMP
OK
OK
DFL
OK
MM
OK
OK
Nopo
OK
RIF
OK

27. Gender wage gap: methods and differences
Available Methods
Summary
Selection Bias
Dimensionality Curse
Detailed decomposition
OB
OK
OK
OK
JMP
OK
OK
OK
DFL
OK
MM
OK
OK
Nopo
OK
RIF
OK
OK

28. Gender wage gap: methods and differences
Available Methods
Summary
Selection Bias
Dimensionality Curse
Detailed decomposition
Distributional analysis
OB
OK
OK
OK
JMP
OK
OK
OK
OK
DFL
OK
MM
OK
OK
OK
OK
Nopo
OK
RIF
OK
OK
OK

29. Gender wage gap: methods and differences
Available Methods
Summary
Selection Bias
Dimensionality Curse
Detailed decomposition
Distributional analysis
Common Support
OB
OK
OK
OK
JMP
OK
OK
OK
OK
DFL
OK
MM
OK
OK
OK
Nopo
OK
OK
RIF
OK
OK
OK
OK

30. Gender wage gap: methods and differences
Available Methods
Summary
Selection Bias
Dimensionality Curse
Detailed decomposition
Distributional analysis
Common Support
Functional Form
OB
OK
OK
OK
JMP
OK
OK
OK
OK
DFL
OK
MM
OK
OK
OK
OK
OK
Nopo
OK
RIF
OK
OK
OK
OK
OK

31. Gender wage gap: methods and differences
Available Methods
Summary
Selection Bias
Dimensionality Curse
Detailed decomposition
Distributional analysis
Common Support
Functional Form
Compare across time
OB
OK
OK
OK
JMP
OK
OK
OK
OK
OK
DFL
OK
MM
OK
OK
OK
OK
OK
OK
Nopo
OK
RIF
OK
OK
OK
OK
OK
OK

32. Gender wage gap: methods and differences
Available Methods
How does the gap relate to...
The reference wages: The wage gap is larger when
expressed as a percentage of the wage of the unfavoured
group

33. Gender wage gap: methods and differences
Available Methods
How does the gap relate to...
The selection bias: the gap increases if the women
experience more selection than male

34. Gender wage gap: methods and differences
Available Methods
How does the gap relate to...
The addition of new variables: increases the value of the
gap when the differences within are larger than between

35. Gender wage gap: methods and differences
Available Methods
How does the gap relate to...
The different quantiles: varies if the differences are
larger for some groups (i.e. the better educated)

36. Gender wage gap: methods and differences
Available Methods
How does the gap relate to...
The common support: increases when the non-matched
women are better endowed than men

37. Gender wage gap: methods and differences
Data
Sample: Polish LFS 2012
Hourly wage
Age (years)
Experience (years)
Secondary education(%)
Tertiary Education(%)
Married (%)
Kids less than 5 (%)
Rural (%)
Cities (%)
Mazowieckie (%)
Obs
Male
11,91
40,64
19,15
0,75
0,16
0,69
0,21
0,44
0,29
0,1
18534
Female
11
41,29
17,89
0,62
0,33
0,68
0,17
0,36
0,35
0,11
17479
M-F
0,91
-0,65
1,26
0,13
-0,17
0,01
0,04
0,08
-0,06
-0,01
Impact
Inv. U
Inv. U
+
+
+
+
+
+
C-support
0,12
0,04
0,07
0,2
0,28
0,02
0,08
0,11
0,08
0,01

38. Gender wage gap: methods and differences
Data
Meet the sample: Beyond the mean
Total wages

39. Gender wage gap: methods and differences
Data
Meet the sample: Beyond the mean
Total wages
Hourly wages

40. Gender wage gap: methods and differences
Results
Different specifications
Basic: Age, Experience, Education, Married, kids, rural,
cities, Mazowieckie
Industry: ”Basic” + industry dummies (Agriculture,
Manufacture, Construction, services)
Industry plus: ”Industry” + Firm size & Ownership type
Occupations: ”Basic” + 9 occupational dummies (ISCO-1
codes)
Tenure: ”Basic” + tenure
Education: ”Basic” + 9 educational fields dummies
All

41. Gender wage gap: methods and differences
Results
Size of the gap
For the whole sample
Heckman
Raw
Basic
0,16
OB.
0,09
0,17
JMP*
0,13
0,18
MM*
0,13
0,16
RIF*
0,08
0,14
Nopo
Obs
33928
33928

42. Gender wage gap: methods and differences
Results
Size of the gap
For the whole sample
Heckman
Raw
Basic
Indus
0,16
0,17
OB.
0,09
0,17
0,16
JMP*
0,13
0,18
0,18
MM*
0,13
0,16
0,14
RIF*
0,08
0,14
0,13
Nopo
Obs
33928
33928
33574

43. Gender wage gap: methods and differences
Results
Size of the gap
For the whole sample
Heckman
Raw
Basic
Indus
Educ
0,16
0,17
0,19
OB.
0,09
0,17
0,16
0,22
JMP*
0,13
0,18
0,18
0,20
MM*
0,13
0,16
0,14
0,15
RIF*
0,08
0,14
0,13
0,17
Nopo
Obs
33928
33928
33574
33928

44. Gender wage gap: methods and differences
Results
Size of the gap
For the whole sample
Heckman
Raw
Basic
Indus
Educ
All
0,16
0,17
0,19
0,16
OB.
0,09
0,17
0,16
0,22
0,18
JMP*
0,13
0,18
0,18
0,20
0,18
MM*
0,13
0,16
0,14
0,15
* Results at the median
RIF*
0,08
0,14
0,13
0,17
0,14
Nopo
Obs
33928
33928
33574
33928
33567

45. Gender wage gap: methods and differences
Results
Size of the gap
Inside the common support
(In red when larger than in the total sample)
Heckman
OB.
JMP*
MM *
RIF*
Nopo
No of obs

46. Gender wage gap: methods and differences
Results
Size of the gap
Inside the common support
(In red when larger than in the total sample)
Heckman
Raw
OB.
0,09
JMP*
0,13
MM *
0,13
RIF*
0,09
Nopo
0,08
No of obs
33928

47. Gender wage gap: methods and differences
Results
Size of the gap
Inside the common support
(In red when larger than in the total sample)
Heckman
Raw
Basic
0,16
OB.
0,09
0,17
JMP*
0,13
0,19
MM *
0,13
0,16
RIF*
0,09
0,15
Nopo
0,08
0,17
No of obs
33928
34223

48. Gender wage gap: methods and differences
Results
Size of the gap
Inside the common support
(In red when larger than in the total sample)
Heckman
Raw
Basic
Indus
0,16
0,18
OB.
0,09
0,17
0,19
JMP*
0,13
0,19
0,20
MM *
0,13
0,16
0,17
RIF*
0,09
0,15
0,18
Nopo
0,08
0,17
0,17
No of obs
33928
34223
29202

49. Gender wage gap: methods and differences
Results
Size of the gap
Inside the common support
(In red when larger than in the total sample)
Heckman
Raw
Basic
Indus
Educ
0,16
0,18
0,19
OB.
0,09
0,17
0,19
0,22
JMP*
0,13
0,19
0,20
0,19
MM *
0,13
0,16
0,17
0,16
RIF*
0,09
0,15
0,18
0,20
Nopo
0,08
0,17
0,17
0,18
No of obs
33928
34223
29202
32237

50. Gender wage gap: methods and differences
Results
Size of the gap
Inside the common support
(In red when larger than in the total sample)
Heckman
Raw
Basic
Indus
Educ
All
0,16
0,18
0,19
0,16
OB.
0,09
0,17
0,19
0,22
0,17
JMP*
0,13
0,19
0,20
0,19
0,19
MM *
0,13
0,16
0,17
0,16
0,18
RIF*
0,09
0,15
0,18
0,20
0,20
Nopo
0,08
0,17
0,17
0,18
0,16
No of obs
33928
34223
29202
32237
3056

51. Gender wage gap: methods and differences
Results
Size of the gap
Inside the common support
(In red when larger than in the total sample)
Heckman
Raw
Basic
Indus
Educ
All
0,16
0,18
0,19
0,16
OB.
0,09
0,17
0,19
0,22
0,17
JMP*
0,13
0,19
0,20
0,19
0,19
MM *
0,13
0,16
0,17
0,16
0,18
RIF*
0,09
0,15
0,18
0,20
0,20
* Results at the median
Nopo
0,08
0,17
0,17
0,18
0,16
No of obs
33928
34223
29202
32237
3056

52. Gender wage gap: methods and differences
Results
Comparison of the methods
Mean
Range/Mean
Mean
Range/Mean
Heckman OB. JMP
Total Sample
0,17
0,18 0,18
0,20
0,36 0,17
Common Support
0,17
0,19 0,19
0,19
0,27 0,11
MM
RIF
0,15
0,26
0,13
0,69
0,17
0,12
0,17
0,66
Nopo
0,17
0,13

53. Gender wage gap: methods and differences
Results
Comparison of the methods
Mean
Range/Mean
Mean
Range/Mean
Heckman OB. JMP
Total Sample
0,17
0,18 0,18
0,20
0,36 0,17
Common Support
0,17
0,19 0,19
0,19
0,27 0,11
MM
RIF
0,15
0,26
0,13
0,69
0,17
0,12
0,17
0,66
Nopo
0,17
0,13
Estimations on the common support are larger and
experience smaller dispersion!

54. Gender wage gap: methods and differences
Conclusions
Conclusions
1
The results indicated that the adjusted gap is 20% of female
gap - two times the size of the raw gap.
2
The results were consistent across methods and specifications

55. Gender wage gap: methods and differences
Conclusions
Conclusions
1
The results indicated that the adjusted gap is 20% of female
gap - two times the size of the raw gap.
2
The results were consistent across methods and specifications
The calculation of the bias in the common support produced
slighlty higher results with a smaller dispersion.
The OLS produced slightly lower results
Nopo estimations are the less sensitive to the changes of
specification.
The quantile regressions showed larger variation between them.
More sensitive to the common support

56. Gender wage gap: methods and differences
Conclusions
Questions or suggestions?

57. Gender wage gap: methods and differences
Conclusions
Questions or suggestions?
Gracias por su atencion

58. Gender wage gap: methods and differences
Conclusions
References
Blinder, A. (1973): ”Wage Discrimination: Reduced Form and Structural
Estimates”, Journal of Human Resources, 8, 436-455.
DiNardo, J. , N. Fortn, and T. Lemieux, 1996 Labor market institutions and the
distribution of wages, 1973-1992: a Semi-parametric approach Econometrica,
Vol. 64, No.5, 1001 -1044.
Firpo, S., Fortn, N., and Lemieux, T. 2009 Unconditional Quantile regressions,
Econometrica, Vol. 77, No. 3, 953-973
Fortn, N., T. Lemieux and S. Firpo, 2010 Decomposition methods in Economics
NBER Working paper 16045
Juhn, C., K. M. Murphy, and B. Pierce (1993): ”Wage Inequality and the Rise
in Returns to Skill”, Journal of Political Economy”, 101, 410-442.
Machado, J. A. F., and J. Mata (2005): ”Counterfactual Decomposition of
Changes in Wage Distributions using Quantile Regression”, Journal of Applied
Econometrics, 20, 445-465.
Nopo, H(2008) Matching as a Tool to Decompose Wage Gaps, The review of
Economics and Statistics, May 2008, vol. 90, No. 2, Pages 290 299.
Weichselbaumer, D. and R. Winter-Ebmer (2003) ”A Meta-Analysis of the
International Gender Wage Gap,” IZA Discussion Papers 906