I am writing an undergraduate dissertation on UK gender pay gap using LFS data. I am having trouble interpreting the decomposition results of categorical variables since I have chosen to omit a base category to reference it from. I use the standard oaxaca with the males coefficients as the reference category. First oaxaca estimates 2 seperate OLS regressions for male and female wage equations, and then using a transformation alters them in the following way:
Male wage eq: Ym = XmBm +um
Female wage eq: Yf= XfBf +uf
Decomposition: Ym - Yf = (Xm - Xf)Bm + (Bm - Bf) Xf
In my regression Y is ln(hourlywage), X is the endowments, B the beta coefficients from the ols regression. M indicates that the subject is male and F that they are female. The first term is the explained portion due to differences between male and female endowments i.e. men being aged higher and therefore reflected in wages. The second part is the unexplained portion due to differences in coefficients or how employers value the workers differently.
The regression is performed on Stata 13.1 using Ben Jann's (2008) command, i have studied this paper extensively.
My command is as follows.
Code:
oaxaca lnhourlywage AGE AGE2 TENURE EDUCATION2-EDUCATION6 ETHGBEUL2-ETHGBEUL11 FDPCH19 dumMARRIED ForeignBorn dumLARGEFIRM dumPUBLIC dumPT nGOR9D2-nGOR9D12 SC10MMJ2-SC10MMJ9 INDS07M2-INDS07M21, by (SEX) weight(1) vce(robust)
overall
Code:
overall
group_1 2.621392 .0094686 276.85 0.000 2.602834 2.63995
group_2 2.41126 .0079192 304.48 0.000 2.395739 2.426782
difference .2101316 .0123437 17.02 0.000 .1859383 .2343249
explained .1324336 .0141093 9.39 0.000 .1047799 .1600873
unexplained .077698 .0142629 5.45 0.000 .0497432 .1056528
explained
AGE .0050777 .0118256 0.43 0.668 -.0181 .0282555
AGE2 -.0057998 .0103723 -0.56 0.576 -.0261291 .0145295
TENURE .0046142 .0012856 3.59 0.000 .0020944 .007134
EDUCATION2 .0026564 .0013117 2.03 0.043 .0000856 .0052273
EDUCATION3 -.0062741 .0022621 -2.77 0.006 -.0107079 -.0018404
EDUCATION4 .0097052 .0027188 3.57 0.000 .0043765 .0150339
EDUCATION5 -.003627 .0016846 -2.15 0.031 -.0069288 -.0003252
EDUCATION6 -.0085428 .0040202 -2.12 0.034 -.0164223 -.0006633
ETHGBEUL2 .0001289 .0002574 0.50 0.617 -.0003756 .0006334
ETHGBEUL3 -.0002747 .0005227 -0.53 0.599 -.0012992 .0007498
ETHGBEUL4 -.0008174 .0005127 -1.59 0.111 -.0018223 .0001876
ETHGBEUL5 -.0007007 .0006411 -1.09 0.274 -.0019572 .0005559
ETHGBEUL6 -.0000719 .0002336 -0.31 0.758 -.0005299 .000386
ETHGBEUL7 -.0003041 .0002951 -1.03 0.303 -.0008824 .0002742
ETHGBEUL8 .0000172 .0001927 0.09 0.929 -.0003604 .0003949
ETHGBEUL9 .0014672 .0008816 1.66 0.096 -.0002606 .0031951
ETHGBEUL10 -.0000808 .000672 -0.12 0.904 -.0013978 .0012362
ETHGBEUL11 .0005043 .0006998 0.72 0.471 -.0008672 .0018759
FDPCH19 -.000341 .0003802 -0.90 0.370 -.0010861 .0004042
dumMARRIED .0027049 .0010319 2.62 0.009 .0006823 .0047274
ForeignBorn .0008964 .0006809 1.32 0.188 -.0004381 .0022309
dumLARGEFIRM .0093653 .0019585 4.78 0.000 .0055266 .013204
dumPUBLIC .0036633 .0046232 0.79 0.428 -.005398 .0127246
dumPT .0219573 .0097025 2.26 0.024 .0029407 .0409739
nGOR9D2 -.0002087 .0003383 -0.62 0.537 -.0008718 .0004544
nGOR9D3 .000038 .0001399 0.27 0.786 -.0002363 .0003123
nGOR9D4 8.90e-06 .0001011 0.09 0.930 -.0001893 .0002071
nGOR9D5 .000421 .000448 0.94 0.347 -.000457 .001299
nGOR9D6 .0006032 .0006304 0.96 0.339 -.0006322 .0018387
nGOR9D7 .0003375 .0011976 0.28 0.778 -.0020097 .0026847
nGOR9D8 .0006368 .0008569 0.74 0.457 -.0010428 .0023164
nGOR9D9 -.0000971 .0002552 -0.38 0.704 -.0005972 .0004031
nGOR9D11 .0000947 .0002681 0.35 0.724 -.0004308 .0006201
nGOR9D12 -.0000849 .0005172 -0.16 0.870 -.0010985 .0009287
SC10MMJ2 -.0012014 .0009469 -1.27 0.204 -.0030573 .0006544
SC10MMJ3 -.0031096 .0012749 -2.44 0.015 -.0056084 -.0006109
SC10MMJ4 .0385581 .0049023 7.87 0.000 .0289498 .0481663
SC10MMJ5 -.0383838 .0045403 -8.45 0.000 -.0472825 -.029485
SC10MMJ6 .0516481 .0060227 8.58 0.000 .0398439 .0634523
SC10MMJ7 .0209449 .0031875 6.57 0.000 .0146975 .0271923
SC10MMJ8 -.031815 .0035123 -9.06 0.000 -.0386989 -.0249311
SC10MMJ9 -.0044424 .0027582 -1.61 0.107 -.0098484 .0009635
INDS07M2 .002221 .0008739 2.54 0.011 .0005082 .0039338
INDS07M3 .0275756 .0093634 2.95 0.003 .0092238 .0459274
INDS07M4 .0027406 .0009769 2.81 0.005 .000826 .0046553
INDS07M5 .0037671 .0013213 2.85 0.004 .0011775 .0063567
INDS07M6 .0177626 .0051666 3.44 0.001 .0076362 .0278889
INDS07M7 -.0005174 .0007723 -0.67 0.503 -.0020312 .0009963
INDS07M8 .015639 .0044324 3.53 0.000 .0069517 .0243263
INDS07M9 -.0009997 .0009588 -1.04 0.297 -.0028789 .0008795
INDS07M10 .0114097 .0030692 3.72 0.000 .0053942 .0174253
INDS07M11 .0076543 .0024591 3.11 0.002 .0028346 .012474
INDS07M12 .0002329 .0004162 0.56 0.576 -.0005828 .0010486
INDS07M13 .0054532 .0021438 2.54 0.011 .0012514 .0096549
INDS07M14 .001217 .0009685 1.26 0.209 -.0006812 .0031152
INDS07M15 -.002001 .0013888 -1.44 0.150 -.0047231 .0007211
INDS07M16 -.0134662 .0105766 -1.27 0.203 -.034196 .0072636
INDS07M17 -.0163777 .0142296 -1.15 0.250 -.0442672 .0115118
INDS07M18 -.0003783 .0004939 -0.77 0.444 -.0013464 .0005898
INDS07M19 .0000692 .0002542 0.27 0.786 -.0004291 .0005674
INDS07M21 .0005594 .0004978 1.12 0.261 -.0004162 .001535
unexplained
AGE .3944143 .2342884 1.68 0.092 -.0647825 .8536112
AGE2 -.1797622 .1290525 -1.39 0.164 -.4327004 .073176
TENURE -.0112057 .0106252 -1.05 0.292 -.0320308 .0096193
EDUCATION2 .0016734 .0032534 0.51 0.607 -.004703 .0080499
EDUCATION3 .0203164 .0110235 1.84 0.065 -.0012892 .0419221
EDUCATION4 .0185935 .0102016 1.82 0.068 -.0014013 .0385883
EDUCATION5 .0093388 .005847 1.60 0.110 -.0021211 .0207986
EDUCATION6 .0325869 .0187112 1.74 0.082 -.0040864 .0692601
ETHGBEUL2 -.0011213 .0007751 -1.45 0.148 -.0026403 .0003978
ETHGBEUL3 -.0071021 .0035068 -2.03 0.043 -.0139753 -.0002288
ETHGBEUL4 .001985 .0010814 1.84 0.066 -.0001344 .0041045
ETHGBEUL5 -.002007 .0014089 -1.42 0.154 -.0047685 .0007544
ETHGBEUL6 -9.44e-07 .0007947 -0.00 0.999 -.0015586 .0015567
ETHGBEUL7 -.0003573 .000293 -1.22 0.223 -.0009316 .0002171
ETHGBEUL8 -.0007657 .0004981 -1.54 0.124 -.0017419 .0002105
ETHGBEUL9 -.0035339 .0017266 -2.05 0.041 -.006918 -.0001498
ETHGBEUL10 -.0038603 .0017137 -2.25 0.024 -.0072191 -.0005014
ETHGBEUL11 -.0027829 .0014262 -1.95 0.051 -.0055782 .0000123
FDPCH19 -.0000574 .0090339 -0.01 0.995 -.0177635 .0176486
dumMARRIED .0367891 .0116264 3.16 0.002 .0140018 .0595763
ForeignBorn .0163412 .006664 2.45 0.014 .00328 .0294025
dumLARGEFIRM .0265318 .0057515 4.61 0.000 .015259 .0378046
dumPUBLIC -.0133706 .0114932 -1.16 0.245 -.035897 .0091557
dumPT -.0116705 .0138848 -0.84 0.401 -.0388842 .0155431
nGOR9D2 .003055 .0059856 0.51 0.610 -.0086766 .0147866
nGOR9D3 -.0044866 .0048935 -0.92 0.359 -.0140777 .0051044
nGOR9D4 -.0035009 .0042639 -0.82 0.412 -.0118581 .0048562
nGOR9D5 .0023759 .0038633 0.61 0.539 -.005196 .0099478
nGOR9D6 .0009906 .0053927 0.18 0.854 -.0095789 .0115601
nGOR9D7 -.0026652 .0055004 -0.48 0.628 -.0134459 .0081154
nGOR9D8 -.0011883 .0072098 -0.16 0.869 -.0153192 .0129426
nGOR9D9 .0000127 .0056967 0.00 0.998 -.0111526 .0111781
nGOR9D11 .0010843 .0044143 0.25 0.806 -.0075676 .0097363
nGOR9D12 .000713 .0033906 0.21 0.833 -.0059325 .0073585
SC10MMJ2 .0066436 .011267 0.59 0.555 -.0154394 .0287266
SC10MMJ3 .0079522 .0060274 1.32 0.187 -.0038613 .0197656
SC10MMJ4 .0011118 .008778 0.13 0.899 -.0160927 .0183162
SC10MMJ5 .0024493 .0008813 2.78 0.005 .000722 .0041766
SC10MMJ6 .0053725 .0088547 0.61 0.544 -.0119824 .0227273
SC10MMJ7 .0046947 .0061072 0.77 0.442 -.0072752 .0166645
SC10MMJ8 .0016438 .0009278 1.77 0.076 -.0001747 .0034623
SC10MMJ9 .0050696 .0047682 1.06 0.288 -.0042759 .0144151
INDS07M2 .0000547 .0001878 0.29 0.771 -.0003133 .0004227
INDS07M3 -.0007536 .0082814 -0.09 0.927 -.0169848 .0154776
INDS07M4 -.0002869 .0006815 -0.42 0.674 -.0016227 .0010489
INDS07M5 -.000028 .0004139 -0.07 0.946 -.0008393 .0007833
INDS07M6 -.0002444 .0033183 -0.07 0.941 -.0067481 .0062593
INDS07M7 -.0045209 .0233454 -0.19 0.846 -.050277 .0412352
INDS07M8 .0010744 .0034373 0.31 0.755 -.0056626 .0078114
INDS07M9 -.000082 .009397 -0.01 0.993 -.0184998 .0183359
INDS07M10 -.0013234 .0036651 -0.36 0.718 -.0085068 .00586
INDS07M11 .0009762 .0061018 0.16 0.873 -.010983 .0129355
INDS07M12 -.0001798 .0017793 -0.10 0.920 -.0036671 .0033075
INDS07M13 .0009825 .0089838 0.11 0.913 -.0166255 .0185905
INDS07M14 -.0010676 .0066975 -0.16 0.873 -.0141945 .0120593
INDS07M15 -.0042303 .0142962 -0.30 0.767 -.0322503 .0237896
INDS07M16 .0004553 .0320498 0.01 0.989 -.0623611 .0632717
INDS07M17 -.0100713 .0408718 -0.25 0.805 -.0901785 .0700359
INDS07M18 -.00205 .003774 -0.54 0.587 -.0094468 .0053468
INDS07M19 -.0039289 .0035324 -1.11 0.266 -.0108523 .0029945
INDS07M21 -.0003552 .000351 -1.01 0.311 -.0010432 .0003327
_cons -.2490229 .2102742 -1.18 0.236 -.6611528 .1631069
My dependent variable is lnhourlywage and thus the overall differential is 0.21 indicating that females earn 21% than males (logarithmic dependent variable enables us to interpret as relative changes in wage). The unexplained portion is the mean increase in female wages if we apply the male coefficients (betas) to womens endowments (X values), and the explained portion is the mean increase in womens wages if women had the same endowments as men. The unexplained portion is then attributed to discrimination in the labour market. (FEEL FREE TO CORRECT ME IF I AM WRONG).
My queries lie in:
Interpreting the explained portion, for example: If females had the same amount of tenure as men, the overall increase in females wages is 0.46%?
and for example in the unexplained portion: With regards to tenure the overall increase in females wages if we apply the male coefficients to the females endowments is -11.2%? (so an overall decrease)
With regards to categorical variables: 'the mean increase in womens wages if we applied the male coefficients to the female endowments of being a member of INDS07M11, over the omitted base category (INDS07M1), is 0.097%'
Main question is: Is it simple enough to say that the contribution to the unexplained is the sum of the vector of contributions for each categorical variable? For example can i sum INDS07M2 to INDS07M21 and this be the 'overall contribution of industry relative to the omitted base (Agriculture and Forestry here) to the unexplained wage gap?'
The decomposition of individual variables, how can i interpret the contribution of age to the explained/unexplained portions? Does the squared term need to be accounted for? (I am aware that during wage equation interpretation of square terms the formula for the unit change in y for a unit change in x is: B1 + B2X1 , does the same apply here?)
I can only apologise if i have displayed the table incorrectly as i am unsure how to present it (i am new). All help will be greatly appreciated. Thank you.
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