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
-------------+-----------------------------Model | 1.69561118 2 .847805588
Residual | 2.99911484 46 .065198149
-------------+-----------------------------Total | 4.69472601 48 .097806792
Number of obs = 49
F( 2, 46) = 13.00
Prob > F = 0.0000
R-squared = 0.3612
Adj R-squared = 0.3334
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
------------------------------------------------------------------------------
1
Adding Gender Dummy to the Basic Linear Model
reg lnwage exper educ gender
reg lnwage exper educ gender
Source
SS
df
Model
Residual
2.15709294
2.53763307
3 .71903098
45 .056391846
Total
4.69472601
48 .097806792
lnwage
exper
educ
gender
_cons
Coef. Std. Err.
MS
t
P>t
.0192786 .0058033 3.32 0.002
.0600155 .0150724 3.98 0.000
.2297216 .069301 3.31 0.002
6.789133 .1238352 54.82 0.000
Number of obs= 49
F( 3, 45)
= 12.75
Prob > F
= 0.0000
R-squared
= 0.4595
Adj R-squared= 0.4234
Root MSE
= .23747
[95% Conf.
Interval]
.00759
.0296581
.0901424
6.539716
.0309671
.0903729
.3693009
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=
F( 5, 43)
=
Prob > F
=
R-squared
=
Adj R-squared =
Root MSE
=
Model
2.39836316 5 .479672632
Residual 2.29636285 43 .053403787
Total
lnwage
4.69472601
48 .097806792
Coef. Std. Err.
exper .0268629
educ .0098199
gender -.1054502
gened .064992
genexp -.0083474
_cons 7.038487
t
P>t
.0097107 2.77
.0287639 0.34
.2527238 -0.4
.0337371 1.93
.0120494 -0.69
.1954133 36.02
[95% Conf.
0.008
0.734
0.679
0.061
0.492
0.000
49
8.98
0.0000
0.5109
0.4540
.23109
Interval]
.007279
-.048188
-.6151164
-.0030454
-.0326474
6.644399
.0464465
.0678279
.404216
.1330293
.0159526
7.432576
2
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=
F( 10, 38) =
Prob > F
=
R-squared
=
Adj R-squared =
Root MSE
=
Model 3.69282737 10 .369282737
Residual1.00189865 38 .026365754
Total 4.69472601
lnwage Coef.
age
-.0013289
exper .0048438
educ .0066917
gender -.0377357
gened .0181287
genexp .0176315
clerical -.5142417
maint -.5633304
crafts -.3567004
race .1055984
_cons 7.624819
48 .097806792
Std. Err.
t
.0027404 -0.48
.0087836 0.55
.0226602 0.30
.2030467 -0.19
.0265796 0.68
.0099173 1.78
.0884251 -5.82
.1073432 -5.25
.0901508 -3.96
.062659 1.69
.1815666 41.99
49
14.01
0.0000
0.7866
0.7304
.16238
P>t
[95% Conf.
Interval]
0.631
0.585
0.769
0.854
0.499
0.083
0.000
0.000
0.000
0.100
0.000
-.0068766
-.0129377
-.0391814
-.4487822
-.0356789
-.002445
-.6932489
-.7806354
-.5392012
-.0212482
7.257257
.0042188
.0226253
.0525647
.3733107
.0719363
.0377079
-.3352344
-.3460254
-.1741996
.232445
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
-------------+-----------------------------Model | 3.65760234 6 .609600391
Residual | 1.03712367 42 .024693421
-------------+-----------------------------Total | 4.69472601 48 .097806792
Number of obs = 49
F( 6, 42) = 24.69
Prob > F = 0.0000
R-squared = 0.7791
Adj R-squared = 0.7475
Root MSE
= .15714
3
-----------------------------------------------------------------------------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
-------------+-----------------------------Model | 3.98540838 13 .306569875
Residual | .709317637 35 .020266218
-------------+-----------------------------Total | 4.69472601 48 .097806792
Number of obs = 49
F( 13, 35) = 15.13
Prob > F = 0.0000
R-squared = 0.8489
Adj R-squared = 0.7928
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
4
( 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
-------------+-----------------------------Model | 3.96311104 11 .360282822
Residual | .731614976 37 .019773378
-------------+-----------------------------Total | 4.69472601 48 .097806792
Number of obs = 49
F( 11, 37) = 18.22
Prob > F = 0.0000
R-squared = 0.8442
Adj R-squared = 0.7978
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.
5
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.
6