1. December 2006 ON THE MEASUREMENT OF ILLEGAL WAGE DISCRIMINATION Juan Prieto, Juan G. Rodríguez and Rafael Salas

2. Overview lMotivation lDiscrimination: classical view lA new appoach: endogenous allocation to groups lApplication to Germany and the UK lDiscussion

3. 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):

4. 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.

5. 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)…

6. Discrimination: latent class view (2) The log likelihood function: Where f(·) is the standard normal density function

7. 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: P ij By maximaizing the log likelihood function. Then we update ex post probabilities by using the Bayes rule and we obtain:

8. 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)

9. Example: let i = Hillary Clinton [HC] Pick X HC the human capital characteristics of HC:

10. Example: i= Hillary Clinton [HC] (2) The HC gap is: which is “normaly” positive since: Oaxaca-Blinder assume

11. Applications European households panel data: Germany 1994-2001: Model 1 and 2 (extended) UK 1994-2001: Model 1 and 2 (extended) Tables

12. 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

13. Table 1: definitions NameDefinition 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 POTEXPpotential experience (present age-age when started work) POTEXP2square of potential experience TENUREyears of experience at the current firm TENURE2square of tenure

14. Table 2: summary statistics GERMANYUNITED KINGDOM MeanStd. Dev.MeanStd. Dev. Male’s Ln(W/H)2.01900.48202.04680.4920 EDUC10.24080.42760.50070.5000 EDUC20.58590.49260.14200.3490 TENURE8.79766.72625.18925.1043 POTEXP20.628611.393718.678512.8569 N observations N individuals 22880 4621 15721 3590 Women’s Ln(W/H)1.75360.47071.86670.4704 EDUC10.21110.40810.43140.4953 EDUC20.59360.49120.14250.3496 TENURE7.26376.10564.64914.4976 POTEXP19.873111.227719.427313.0059 N observations N individuals 17369 3932 15200 3614

15. Table 3: Two models: class 1 GERMANYUNITED KINGDOM Model 1Model 2Model 1Model 2 Estimated coefficient Standard error Estimated coefficient Standard error Estimated coefficient Standard error Estimated coefficient Standard error 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  0.281860.000270.252170.000270.298300.000800.279100.00074

16. Table 4: Two models: class 2 GERMANYUNITED KINGDOM Model 1Model 2Model 1Model 2 Estimated coefficient Standard error Estimated coefficient Standard error Estimated coefficient Standard error Estimated coefficient Standard error 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  0.383220.000750.406980.000680.301890.000810.285500.00078

17. Table 5: prior probabilities GERMANYUNITED KINGDOM Model 1Model 2Model 1Model 2 Estimated coefficient Standard error Estimated coefficient Standard error Estimated coefficient Standard error Estimated coefficient Standard error 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 -12242.58 30921 7204 -9850.344 30921 7204 -7495.486

18. Results Germany unambiguously more discrimination than in the UK GERMANYUNITED KINGDOM Model 1Model 2Model 1Model 2 LC Wage Gap11.0669.9786.4397.480 OB Wage Gap24.42323.11718.15117.035 Total Wage Gap26.54218.009

19. Results

22. Conclusions lA new appoach: endogenous allocation to groups lApplication to Germany and the UK shows positive discrimination bias of Oaxaca-Blinder model lPositive gender discrimination in both countries

23. July 2006 ON THE MEASUREMENT OF ILLEGAL WAGE DISCRIMINATION: THE MICHAEL JORDAN PARADOX Juan Prieto, Juan G. Rodríguez and Rafael Salas