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December 2006
ON THE MEASUREMENT OF ILLEGAL WAGE
DISCRIMINATION
Juan Prieto, Juan G. Rodríguez and Rafael Salas
Overview
Motivation Discrimination: classical view A new appoach: endogenous allocation to groups Application to Germany and the UK Discussion
Discrimination: classical view
• Oaxaca-Blinder (1973) gender discrimination:
• Two wage equations for men (m), women (w):
• The women wage discriminatory gap (w.r.t men):
fifi XDCfm
'' ˆˆ
mimimi XLnWm
'ˆ
fififi XLnWf
'ˆ
Discrimination: classical view (2)
• Oaxaca-Blinder (1973) gender discrimination:
• The average women wage discriminatory gap (w. r. to men):
• Quantiles analysis can improve estimates locally:
• Newell and Reilly, 2001 • Albrecht, Björklund and Vroman, 2003• Gardeazábal and Ugidos, 2005.
fififi
fifi
XXN
DCN fmfm
'''' ˆˆˆˆ11
Discrimination: latent class view
• Latent class models for gender discrimination:
• Two wage equations for two different structures type/class 1 and type/class 2:
• Plus a vector of probabilities of individual i belonging to groups 1,2.
• This is estimated simultaneous and endogenously by maximum likelihood estimators that allocates individuals to groups according to their human capital characteristics, observed wages and sex, and trying to reduce internal errors of the two wage equations (by maximizing the log likelihood function)…
niiPiP ,...,1,)2(,)1(
iii XLnW 1'
1 1
iii XLnW 2'
2 2
Discrimination: latent class view (2)
• The log likelihood function:
• Where f(·) is the standard normal density function
n
i j ijj
ijiij P
XLnWfL
1
2
1
'
log
Discrimination: latent class view (3)
• The vector of probabilities of individual i belonging to
groups 1,2 are estimated as follows: • First, we estimate a priori probabilities of i belonging to j:
Pij • By maximaizing the log likelihood function.
• Then we update ex post probabilities by using the Bayes rule and we obtain:
niiPiP ,...,1,)2(,)1(
ni
PXLnW
f
PXLnW
f
iP
j ijj
ijiij
iii
i
,...,1ˆ
ˆ
)1(2
1
'
11
'1
1
Discrimination: latent class view (4)
• The women wage discriminatory gap (w.r.t men) for i=women :
• which is more general than Oaxaca-Blinder, for i=women (and 1 is the high wage class)
)ˆ()2()2()ˆ()1()1( ''
21 icf
icf
i XiPiPXiPiPDC
icf
i XiPiPDC ''
21
ˆˆ)1()1(
...,1)2(,1)1( exampleAniPiPcf
Example: let i = Hillary Clinton [HC]
• Pick XHC the human capital characteristics of HC:
90.0)1(
95.0)1(
HCP
HCPcf
35000ˆ)2(ˆ
,300000ˆ)1(ˆ
'
'
2
1
HC
HC
XHCW
XHCW
sexondependnotdoesIt
HCHC WactualandXandsexondependsIt '
1̂
)ˆ()2()2()ˆ()1()1( ''
21 HCcf
HCcf
HC XHCPHCPXHCPHCPDC
Example: i= Hillary Clinton [HC] (2)
• The HC gap is:
which is “normaly” positive since:
Oaxaca-Blinder assume
HCHC XX '2
'1
ˆˆ
)1()1( HCPHCPcf
HCcf
HC XHCPHCPDC ''
21
ˆˆ)1()1(
0)1(1)1( HCPHCPcf
Applications
• European households panel data:
• Germany 1994-2001: • Model 1 and 2 (extended)
• UK 1994-2001: • Model 1 and 2 (extended)
• Tables
Discrimination orderings
• Distributional appoach:
• Jenkins 1994: • discrimination curves from discrimination gaps
in a decreasing order
• del Río et al. 2006: • discrimination curves from discrimination gaps
in an increasing order, eliminating negative gaps
Table 1: definitions
Name Definition
Ln(W/H) natural logarithm of the hourly real wage
EDUC1 =1 if the individual has university studies; =0 otherwise
EDUC2 =1 if the individual has secondary school studies; =0 otherwise
POTEXP potential experience (present age-age when started work)
POTEXP2 square of potential experience
TENURE years of experience at the current firm
TENURE2 square of tenure
Table 5: prior probabilities
GERMANY UNITED KINGDOM
Model 1 Model 2 Model 1 Model 2
Estimated coefficient
Standard error
Estimated coefficient
Standard error
Estimated coefficient
Standard error
Estimated coefficient
Standard error
Estimated prior probabilities
CONSTANTWOMAN
0.80300-1.29953
0.036550.05330
0.89352-1.27903
0.037250.05450
0.04640-0.89363
0.040720.05871
0.20405-1.16482
0.044510.06412
N observationsN individualsLog-likelihood
402498553
-14477.92
402498553
-12242.58
309217204
-9850.344
309217204
-7495.486
Results
• Germany unambiguously more discrimination than in the UK
GERMANY UNITED KINGDOM
Model 1 Model 2 Model 1 Model 2
LC Wage Gap 11.066 9.978 6.439 7.480
OB Wage Gap 24.423 23.117 18.151 17.035
Total Wage Gap 26.542 18.009
Results
Results
Results
Conclusions
A new appoach: endogenous allocation to groups Application to Germany and the UK shows
positive discrimination bias of Oaxaca-Blinder model
Positive gender discrimination in both countries
July 2006
ON THE MEASUREMENT OF ILLEGAL WAGE
DISCRIMINATION: THE MICHAEL JORDAN PARADOX
Juan Prieto, Juan G. Rodríguez and Rafael Salas
