177 P. Christie, M. Shannon Economics of Education Review 20 2001 165–180
dummies. Similarly coefficients on Grades 5–8 and Grades 9–13 have quite different size coefficients across
specifications. In many Canadian surveys these categor- ies would be aggregated into a single “some secondary
education” grouping. The restrictions required to sim- plify our 19 category educational variable to a seven cat-
egory variable, similar to that found in the Labour Mar- ket Activity Survey LMAS, were tested and rejected
for both sexes and each year.
19
Tests of the joint signifi- cance of the field of study variables also suggest that
they contribute to explaining variation in earnings.
20
Apparently, the greater detail adds significantly to the ability of the regressions to explain variation in earnings.
5. Decomposition of the wage gap
The average log-earnings gap was 0.434 in 1985 for full-time, full-year workers. This had fallen to 0.387 by
1990. The first row of Table 9 reports the decomposition of the 1990 gender wage gap into explained and residual
components along the lines of Oaxaca 1973:
w
m
2 w
f
5 X
m
2X
f
b
m
1 X
f
b
m
2b
f
2 where X is a vector of average values of wage-determin-
ing characteristics, b is the vector of coefficients
obtained by regressing the log-wage on the variables in X
and, as before, m and f superscripts denote male and female respectively. The first term of the equation meas-
ures that part of the gap explained by gender differences in average characteristics. The second term is the
residual component which accounts for differences in unobservable characteristics and wage discrimination.
The first term in Eq. 2 is often interpreted as the size of the wage gap if there were no discrimination. Under
this interpretation Eq. 2 uses male wage coefficient estimates as the proxy for wage structure in the absence
of discrimination. This choice is somewhat arbitrary and the results are potentially sensitive to this choice. Cotton
1988 suggests that a weighted average of male and female wage coefficient estimates
b
c
may be a more reasonable
no-discrimination proxy.
21
Cotton’s decomposition gives:
w
m
2 w
f
5 X
m
2X
f
b
c
1 X
m
b
m
2 b
c
1X
f
b
c
2b
f
3
19
For 1990, with industry and occupation dummies the test statistics were F20, 69877
= 15.8 for women and F20,
108255 =
26.1 for men. The specifications used to test these attainment restrictions excluded field dummies.
20
The F-tests for the joint significance of the field variable coefficients gave F12, 69865
= 13.8 for women and F12,
108243 =
27.7 for men in 1990 with industry and occupation dummies present.
21
The weights are simply the male and female shares of the combined wage equation samples.
where the first term is the explained component, now evaluated using
b
c
rather than b
m
, the second term meas- ures the male residual or treatment advantage and the
last term the female residual or treatment disadvantage. Taken together the last two terms are the counterpart of
Oaxaca’s residual effect. Results of the Cotton decompo- sition are reported in Table 10.
We look first at the Oaxaca decomposition results. For 1985 with industryoccupation variables included, 0.155
of the log-earnings gap 36 can be explained by differ- ences between men and women in the average level of
earnings-determining characteristics and 0.279 is due to differences in payoffs to these characteristics for men
and women see the second part of Table 9. In 1990, 0.125 32 was explicable in terms of different average
characteristics and 0.261 due to different payoffs. The differences in component size between the two years
suggests
that relative
improvements in
earnings- determining characteristics accounted for about one half
of the fall in the measured gap. Further decomposition of the explained component reveals that gender differ-
ences in industry of employment are the largest contribu- tor to the explained portion of the gap in both years. This
is followed by occupation in 1985 and field of study in 1990. Differences in educational attainment by gender
had little effect on the explained component in either year, while differences in field of study accounted for
0.017 of the explained component in 1985 and 0.025 in 1990.
22
As Oaxaca and Ransom 1999 point out, a simi- lar decomposition of the residual component by charac-
teristic is sensitive to the choice of dummy variable ref- erence groups and therefore unreliable — consequently
it is not reported.
When industryoccupational dummies are left out of the specification the picture changes substantially. The
explained component falls by nearly half. Differences in the field of education become a more important determi-
nant of the size of the diminished explained component in both years. In both sets of results, the greater relative
importance of differences in field of study compared to differences in attainment is consistent with the results in
Section 3.
23
When the Cotton decomposition is used in place of
22
On a sample of university graduates Wannell 1990 also found that differences in field were more important in
explaining the wage gap than differences in levels.
23
Earnings equations were estimated and Oaxaca decompo- sitions were also performed on a subsample of university edu-
cated workers who worked full-time, full-year. For the 1991 Census sample, differences in field of study accounted for from
0.047 industry-occupation controls present to 0.069 no indus- try-occupation dummies of a total log-earnings gap of 0.277.
Differences in educational attainment for this group accounted for 0.012 of the gap both with and without industry-occu-
pation dummies.
178 P. Christie, M. Shannon Economics of Education Review 20 2001 165–180
Table 9 Oaxaca decomposition of the gender earnings gap, full-time year workers in 1990 and 1985
a
With industryoccupation Without industryoccupation
Gap Explained
Residual Gap
Explained Residual
1990 Results: Total
0.387 0.125
0.261 0.386
0.062 0.324
Due to: Educational attainment
20.003 20.007
Field of study 0.025
0.037 Location
20.004 20.004
Maritalfamily 0.013
0.015 Occupation
0.014 –
Industry 0.053
– Hours
0.019 0.012
Age 0.005
0.005 Other personal
0.004 0.005
1985 Results: Total
0.434 0.155
0.279 0.433
0.079 0.354
Due to: Educational attainment
20.004 20.008
Field of study 0.017
0.034 Location
20.004 20.004
Maritalfamily 0.024
0.028 Occupation
0.028 –
Industry 0.064
– Hours
0.015 0.012
Age 0.010
0.012 Other personal
0.005 0.007
a
Oaxaca decomposition: see Eq. 2.
the Oaxaca decomposition, the explained component is smaller in all years and specifications. However, in all
other respects the results are quite similar. The explained component is smaller when industry and occupational
dummies are left out, educational attainment remains an unimportant contributor to the explained component
while field of study contributes positively and is especially important in the absence of industry and occu-
pational dummies. The major new insight provided by the Cotton decomposition is its breakdown of the
residual into a male advantage and female disadvantage component. The latter term accounts for most of the
residual term in all years and specifications. Over time the fall in the combined residual term reflects a decline
in the female disadvantage term.
Projections of future and past log-wage levels, along the lines of those presented in Section 3, were made
based upon the earnings regression estimates. Under the assumption that in the future educational attainment and
field of study patterns of older workers converge to that of 25–34 year olds, the 1990 gap changes from 0.387 to
0.361 when industryoccupation dummies were present or 0.350 when the latter were absent. If, projecting back-
wards in time, the 55–64 year old patterns were to pre- vail for workers age 25 and older, the gap would be
0.386 with industryoccupation or would climb to 0.406 no industryoccupation. As in Section 3, these
changes are driven by the changes in educational attain- ment.
6. Comparison with previous studies