December 2006

1
December 2006

• ON THE MEASUREMENT OF ILLEGAL WAGE DISCRIMINATION
  
• Juan Prieto, Juan G. Rodríguez and Rafael Salas

2
Overview

• Motivation
• Discrimination classical view
• A new appoach endogenous allocation to groups
• Application to Germany and the UK
• Discussion

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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)

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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.

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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)

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Discrimination latent class view (2)

• The log likelihood function
• Where f() is the standard normal density
  function

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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

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Discrimination latent class view (4)

• The women wage discriminatory gap (w.r.t men) for
  iwomen
• which is more general than Oaxaca-Blinder,
• for iwomen (and 1 is the high wage class)

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Example let i Hillary Clinton HC

• Pick XHC the human capital characteristics of HC

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Example i Hillary Clinton HC (2)

• The HC gap is
• which is normaly positive since
• Oaxaca-Blinder assume

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Applications

• European households panel data
• Germany 1994-2001
• Model 1 and 2 (extended)
• UK 1994-2001
• Model 1 and 2 (extended)
• Tables

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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

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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
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Table 2 summary statistics
GERMANY GERMANY UNITED KINGDOM UNITED KINGDOM
Mean Std. Dev. Mean Std. Dev.
Males Males Males Males Males
Ln(W/H) 2.0190 0.4820 2.0468 0.4920
EDUC1 0.2408 0.4276 0.5007 0.5000
EDUC2 0.5859 0.4926 0.1420 0.3490
TENURE 8.7976 6.7262 5.1892 5.1043
POTEXP 20.6286 11.3937 18.6785 12.8569
N observations N individuals 22880 4621 22880 4621 15721 3590 15721 3590
Womens Womens Womens Womens Womens
Ln(W/H) 1.7536 0.4707 1.8667 0.4704
EDUC1 0.2111 0.4081 0.4314 0.4953
EDUC2 0.5936 0.4912 0.1425 0.3496
TENURE 7.2637 6.1056 4.6491 4.4976
POTEXP 19.8731 11.2277 19.4273 13.0059
N observations N individuals 17369 3932 17369 3932 15200 3614 15200 3614
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Table 3 Two models class 1
GERMANY GERMANY GERMANY GERMANY UNITED KINGDOM UNITED KINGDOM UNITED KINGDOM UNITED KINGDOM
Model 1 Model 1 Model 2 Model 2 Model 1 Model 1 Model 2 Model 2
Estimated coefficient Standard error Estimated coefficient Standard error Estimated coefficient Standard error Estimated coefficient Standard error
Wage equation for latent class 1 Wage equation for latent class 1 Wage equation for latent class 1 Wage equation for latent class 1 Wage equation for latent class 1 Wage equation for latent class 1 Wage equation for latent class 1 Wage equation for latent class 1 Wage equation for latent class 1
CONSTANT EDUC1 EDUC2 TENURE TENURE2 POTEXP POTEXP2 NTUNEMP OCCUP1 OCCUP2 OCCUP3 OCCUP4 OCCUP5 OCCUP6 OCCUP7 INDUST1 INDUST2 SIZE1 SIZE2 PUBSEC 1.53436 0.40728 0.10063 0.01950 -0.00018 0.02860 -0.00058 -- -- -- -- -- -- -- -- -- -- -- -- -- 0.00887 0.00329 0.00307 0.00078 0.00003 0.00041 0.00001 -- -- -- -- -- -- -- -- -- -- -- -- -- 1.71124 0.21244 0.05567 0.01862 -0.00025 0.02057 -0.00043 -0.08049 0.29187 0.30455 0.07989 0.01309 -0.07327 -0.04999 0.00430 -0.13777 0.06661 -0.15416 -0.10998 0.02252 0.00864 0.00343 0.00293 0.00073 0.00003 0.00041 0.00001 0.00190 0.00558 0.00369 0.00329 0.00389 0.00403 0.01924 0.00342 0.01315 0.00272 0.00320 0.00259 0.00273 1.57134 0.28463 0.14508 0.00952 -0.00045 0.03106 -0.00061 -- -- -- -- -- -- -- -- -- -- -- -- -- 0.01087 0.00373 0.00595 0.00130 0.00007 0.00050 0.00001 -- -- -- -- -- -- -- -- -- -- -- -- -- 1.53622 0.15649 0.07861 0.01336 -0.00054 0.02716 -0.00053 -0.05138 0.38995 0.36742 0.26355 0.05976 0.00545 -0.08239 0.08178 -0.11065 -0.01561 -0.10922 -0.08249 0.00919 0.01152 0.00437 0.00653 0.00132 0.00007 0.00054 0.00001 0.00221 0.00626 0.00672 0.00663 0.00781 0.00776 0.02560 0.00782 0.04391 0.00457 0.00439 0.00495 0.00431
? 0.28186 0.00027 0.25217 0.00027 0.29830 0.00080 0.27910 0.00074
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Table 4 Two models class 2
GERMANY GERMANY GERMANY GERMANY UNITED KINGDOM UNITED KINGDOM UNITED KINGDOM UNITED KINGDOM
Model 1 Model 1 Model 2 Model 2 Model 1 Model 1 Model 2 Model 2
Estimated coefficient Standard error Estimated coefficient Standard error Estimated coefficient Standard error Estimated coefficient Standard error
Wage equation for latent class 2 Wage equation for latent class 2 Wage equation for latent class 2 Wage equation for latent class 2 Wage equation for latent class 2 Wage equation for latent class 2 Wage equation for latent class 2 Wage equation for latent class 2 Wage equation for latent class 2
CONSTANT EDUC1 EDUC2 TENURE TENURE2 POTEXP POTEXP2 NTUNEMP OCCUP1 OCCUP2 OCCUP3 OCCUP4 OCCUP5 OCCUP6 OCCUP7 INDUST1 INDUST2 SIZE1 SIZE2 PUBSEC 0.76528 0.43196 0.23043 0.03765 -0.00093 0.03530 -0.00072 -- -- -- -- -- -- -- -- -- -- -- -- -- 0.01309 0.00664 0.00573 0.00143 0.00006 0.00066 0.00002 -- -- -- -- -- -- -- -- -- -- -- -- -- 0.95117 0.30612 0.21406 0.03253 -0.00095 0.03564 -0.00074 -0.07579 0.20181 0.23862 0.09888 0.08893 -0.06714 -0.05791 -0.00014 -0.09146 0.05874 -0.21300 -0.11006 0.07702 0.01628 0.00822 0.00688 0.00163 0.00007 0.00074 0.00002 0.00551 0.01341 0.01065 0.00763 0.00880 0.00852 0.02458 0.00821 0.02065 0.00610 0.00774 0.00743 0.00588 1.10080 0.18208 0.14438 0.02017 -0.00074 0.02784 -0.00058 -- -- -- -- -- -- -- -- -- -- -- -- -- 0.00906 0.00356 0.00559 0.00119 0.00006 0.00045 0.00001 -- -- -- -- -- -- -- -- -- -- -- -- -- 1.11306 0.12332 0.10577 0.01460 -0.00059 0.02455 -0.00051 -0.03403 0.25592 0.32309 0.22567 0.12257 -0.03722 -0.06800 0.07378 0.03741 0.07352 -0.11113 -0.05187 0.11999 0.01080 0.00396 0.00602 0.00122 0.00006 0.00045 0.00001 0.00268 0.00591 0.00674 0.00642 0.00568 0.00602 0.01991 0.00741 0.02504 0.00469 0.00434 0.00516 0.00419
? 0.38322 0.00075 0.40698 0.00068 0.30189 0.00081 0.28550 0.00078
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Table 5 prior probabilities
GERMANY GERMANY GERMANY GERMANY UNITED KINGDOM UNITED KINGDOM UNITED KINGDOM UNITED KINGDOM
Model 1 Model 1 Model 2 Model 2 Model 1 Model 1 Model 2 Model 2
Estimated coefficient Standard error Estimated coefficient Standard error Estimated coefficient Standard error Estimated coefficient Standard error
Estimated prior probabilities Estimated prior probabilities Estimated prior probabilities Estimated prior probabilities Estimated prior probabilities Estimated prior probabilities Estimated prior probabilities Estimated prior probabilities Estimated prior probabilities
CONSTANT WOMAN 0.80300 -1.29953 0.03655 0.05330 0.89352 -1.27903 0.03725 0.05450 0.04640 -0.89363 0.04072 0.05871 0.20405 -1.16482 0.04451 0.06412
N observations N individuals Log-likelihood 40249 8553 -14477.92 40249 8553 -14477.92 40249 8553 -12242.58 40249 8553 -12242.58 30921 7204 -9850.344 30921 7204 -9850.344 30921 7204 -7495.486 30921 7204 -7495.486
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Results

• Germany unambiguously more discrimination than in
  the UK

GERMANY GERMANY UNITED KINGDOM 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 26.542 18.009 18.009
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Results
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Results
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Results
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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

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July 2006

• ON THE MEASUREMENT OF ILLEGAL WAGE
  DISCRIMINATION THE MICHAEL JORDAN PARADOX
• Juan Prieto, Juan G. Rodríguez and Rafael Salas