Dummy Variable Approach for Wage Determination Process
Data 7-2
Is there “gender discrimination” against female salaries?
wage= dependent variable
Quantitative Variables:
educ= years of education beyond eight grade
exper= number of years at the company
age= age of the employee
Qualitative Variables:
Gender=1 for male, 0 for female
Race= 1 for white and 0 for non-white
Clerical= 1 for clerical workers and 0 for others
Maint= 1 for maintenance workers and 0 for others
Crafts= 1 for craftsmen, 0 for others
Basic Model (with only quantitative variables) after eliminating the insignificant ones
. reg lnwage exper educsq
Source | SS df MS Number of obs = 49
------+------F( 2, 46) = 13.00
Model | 1.69561118 2 .847805588 Prob > F = 0.0000
Residual | 2.99911484 46 .065198149 R-squared = 0.3612
------+------Adj R-squared = 0.3334
Total | 4.69472601 48 .097806792 Root MSE = .25534
------
lnwage | Coef. Std. Err. t P>|t| [95% Conf. Interval]
------+------
exper | .0236809 .0061404 3.86 0.000 .011321 .0360408
educsq | .0050225 .001171 4.29 0.000 .0026654 .0073796
_cons | 7.023367 .0924574 75.96 0.000 6.83726 7.209474
------
Adding Gender Dummy to the Basic Linear Model
reg lnwage exper educ gender
reg lnwage exper educ gender
Source SS df MS Number of obs = 49
F( 3, 45) = 12.75
Model 2.15709294 3 .71903098 Prob > F = 0.0000
Residual 2.53763307 45 .056391846 R-squared = 0.4595
Adj R-squared= 0.4234
Total 4.69472601 48 .097806792 Root MSE = .23747
lnwage Coef. Std. Err. t P>t [95% Conf. Interval]
exper .0192786 .0058033 3.32 0.002 .00759 .0309671
educ .0600155 .0150724 3.98 0.000 .0296581 .0903729
gender .2297216 .069301 3.31 0.002 .0901424 .3693009
_cons 6.789133 .1238352 54.82 0.000 6.539716 7.03855
Adding GenEd and GenExp Interactive Dummies to the Basic Linear Model
reg lnwage exper educ gender gened genexp
Source SS df MS Number of obs = 49
F( 5, 43) = 8.98
Model 2.39836316 5 .479672632 Prob > F = 0.0000
Residual 2.29636285 43 .053403787 R-squared = 0.5109
Adj R-squared = 0.4540
Total 4.69472601 48 .097806792 Root MSE = .23109
lnwage Coef. Std. Err. t P>t [95% Conf. Interval]
exper .0268629 .0097107 2.77 0.008 .007279 .0464465
educ .0098199 .0287639 0.34 0.734 -.048188 .0678279
gender -.1054502 .2527238 -0.4 0.679 -.6151164 .404216
gened .064992 .0337371 1.93 0.061 -.0030454 .1330293
genexp -.0083474 .0120494 -0.69 0.492 -.0326474 .0159526
_cons 7.038487 .1954133 36.02 0.000 6.644399 7.432576
Adding Race and Other Dummies and Interactive Dummies to the Basic Linear Model
reg lnwage age exper educ gender gened genexp clerical maint crafts race
Source SS df MS Number of obs = 49
F( 10, 38) = 14.01
Model 3.69282737 10 .369282737 Prob > F = 0.0000
Residual1.00189865 38 .026365754 R-squared = 0.7866
Adj R-squared = 0.7304
Total 4.69472601 48 .097806792 Root MSE = .16238
lnwage Coef. Std. Err. t P>t [95% Conf. Interval]
age -.0013289 .0027404 -0.48 0.631 -.0068766 .0042188
exper .0048438 .0087836 0.55 0.585 -.0129377 .0226253
educ .0066917 .0226602 0.30 0.769 -.0391814 .0525647
gender -.0377357 .2030467 -0.19 0.854 -.4487822 .3733107
gened .0181287 .0265796 0.68 0.499 -.0356789 .0719363
genexp .0176315 .0099173 1.78 0.083 -.002445 .0377079
clerical -.5142417 .0884251 -5.82 0.000 -.6932489 -.3352344
maint -.5633304 .1073432 -5.25 0.000 -.7806354 -.3460254
crafts -.3567004 .0901508 -3.96 0.000 -.5392012 -.1741996
race .1055984 .062659 1.69 0.100 -.0212482 .232445
_cons 7.624819 .1815666 41.99 0.000 7.257257 7.992382
. test educ gender
( 1) educ = 0
( 2) gender = 0
F( 2, 38) = 0.15
Prob > F = 0.8615
reg lnwage gened genexp clerical maint crafts race
Source | SS df MS Number of obs = 49
------+------F( 6, 42) = 24.69
Model | 3.65760234 6 .609600391 Prob > F = 0.0000
Residual | 1.03712367 42 .024693421 R-squared = 0.7791
------+------Adj R-squared = 0.7475
Total | 4.69472601 48 .097806792 Root MSE = .15714
------
lnwage | Coef. Std. Err. t P>|t| [95% Conf. Interval]
------+------
gened | .013453 .0075845 1.77 0.083 -.0018532 .0287591
genexp | .0199126 .0045951 4.33 0.000 .0106393 .029186
clerical | -.5351982 .0738917 -7.24 0.000 -.6843177 -.3860787
maint | -.6144296 .0875577 -7.02 0.000 -.7911281 -.4377311
crafts | -.3819542 .077238 -4.95 0.000 -.5378267 -.2260816
race | .1077367 .0545172 1.98 0.055 -.0022835 .2177568
_cons | 7.660213 .0687767 111.38 0.000 7.521416 7.79901
reg lnwage exper educ gened agecraft agemaint edcler edcraft edmaint expcraf
> t agesq maint race educsq
Source | SS df MS Number of obs = 49
------+------F( 13, 35) = 15.13
Model | 3.98540838 13 .306569875 Prob > F = 0.0000
Residual | .709317637 35 .020266218 R-squared = 0.8489
------+------ Adj R-squared = 0.7928
Total | 4.69472601 48 .097806792 Root MSE = .14236
------
lnwage | Coef. Std. Err. t P>|t| [95% Conf. Interval]
------+------
exper | .0137896 .0050352 2.74 0.010 .0035675 .0240116
educ | .2113221 .0661564 3.19 0.003 .0770174 .3456267
gened | .0300098 .0100945 2.97 0.005 .0095169 .0505026
agecraft | .0072451 .0039235 1.85 0.073 -.00072 .0152103
agemaint | .0102473 .0052486 1.95 0.059 -.0004079 .0209025
edcler | -.065343 .0096492 -6.77 0.000 -.084932 -.045754
edcraft | -.1013973 .02062 -4.92 0.000 -.1432582 -.0595364
edmaint | -.1104274 .0608454 -1.81 0.078 -.23395 .0130953
expcraft | .0129875 .0093965 1.38 0.176 -.0060885 .0320635
agesq | -.0000689 .0000312 -2.21 0.034 -.0001322 -5.62e-06
maint | -.2492969 .3247454 -0.77 0.448 -.9085651 .4099713
race | .0429904 .0569947 0.75 0.456 -.0727151 .1586958
educsq | -.0110515 .0046948 -2.35 0.024 -.0205825 -.0015205
_cons | 6.770712 .1980037 34.19 0.000 6.368744 7.172681
------
test race maint
( 1) race = 0
( 2) maint = 0
F( 2, 35) = 0.55
Prob > F = 0.5818
Drop maint and race!
FINAL MODEL
reg lnwage exper educ gened agecraft agemaint edcler edcraft edmaint expcraft
> agesq educsq
Source | SS df MS Number of obs = 49
------+------F( 11, 37) = 18.22
Model | 3.96311104 11 .360282822 Prob > F = 0.0000
Residual | .731614976 37 .019773378 R-squared = 0.8442
------+------Adj R-squared = 0.7978
Total | 4.69472601 48 .097806792 Root MSE = .14062
------
lnwage | Coef. Std. Err. t P>|t| [95% Conf. Interval]
------+------
exper | .0135265 .0049286 2.74 0.009 .0035401 .0235128
educ | .2361181 .0605299 3.90 0.000 .1134729 .3587632
gened | .0310887 .0098963 3.14 0.003 .0110369 .0511405
agecraft | .0078834 .0038282 2.06 0.047 .0001267 .0156401
agemaint | .0082571 .0043899 1.88 0.068 -.0006377 .0171519
edcler | -.0635395 .0093327 -6.81 0.000 -.0824493 -.0446298
edcraft | -.1078185 .0190925 -5.65 0.000 -.1465036 -.0691333
edmaint | -.1449785 .0438091 -3.31 0.002 -.2337442 -.0562128
expcraft | .014498 .008992 1.61 0.115 -.0037216 .0327175
agesq | -.0000632 .0000302 -2.09 0.043 -.0001244 -2.00e-06
educsq | -.0124626 .0044185 -2.82 0.008 -.0214152 -.0035099
_cons | 6.687347 .1790647 37.35 0.000 6.324528 7.050167
------
Note that educsq has a negative sign, i.e. the marginal effect of schooling diminishes with additional schooling. This is indicative of “diminishing returns to education.” With female and male employees who are similar in other characteristics, a male employee earns an average of 3% more than a female employee for each extra year of education (note: gened has a coefficient of 0.031). edcler, edcraft and edmaint have all negative signs such that as compared to the professional group (control group), one year extra year of schooling means 6.35% less in wages for clerical, 10.78% less in wages for craftmen and 14.5% less in wages for maintenance workers.
Experience: It has a positive effect on wages but no diminishing returns or other interactions.
Age: This has a significant diminishing returns as is evident from the negative sign of agesq.
Gender: The differential effect of gender depends on education, as gender alone is not even included in the model (intercept gender dummy is insignificant). The positive sign of gened implies that a significant gender differential exists when it comes to the marginal effect of education. One year of extra schooling adds more to the salaries of males than females with equivalent level of education. Hence, well-educated women have disproportionately lower average salaries than men with similar educational background.
Race: Race is not even in the model, and hence, no significant wage differentials along racial lines. But this cannot be generalized to the entire US job market.
Type of Job: Based on the final output, crafts etc. do not appear as intercept dummies but there exists significant interaction of the type of job performed and education as well as age. Age has a significant positive effect in raising the salaries of crafts and maintenance workers as compared to the professionals (control group). Age and experience go hand in hand in these types of jobs, and we may be capturing this effect for these groups of workers.
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