A specific example of a Oaxaca decomposition (from Mike Shannon):
- Say that wages (W) depend upon only education (ED), experience (EXP) and
whether the worker is unionized (UNION)
- assume that the relationship between these characteristics is linear.
- subscript "m" means male, "f" female
The wage equations for men and women are then:
Wm = am + bm EDm + cmEXPm + fm UNIONm
Wf = af + bf EDf + cfEXPf + ff UNIONf
where:
Edm, EXPm, UNIONm
measures years of education, experience
and share unionized for men
bm, cm, fm
the amount by which an extra year of
education, experience or being
unionized raises male wages.
(subscript f: versions for women)
- Regression analysis is used to obtain estimates of the coefficients a, b, c, f for
men and women separately.
e.g., choosing a, b, c, f involves choosing the line that best fits
sample data on wage rates, experience, education and union status.
- Estimated regression goes through sample means.
So if W, ED, EXP and UNION are the sample averages these equations
hold exactly:
Wm = am + bm EDm + cmEXPm + fm UNIONm
Wf = af + bf EDf + cfEXPf + ff UNIONf
- The gap in average wages is (think of ED, EXP and UNION as
values for men and women):
average
Wm-Wf = am + bm EDm + cmEXPm + fm UNIONm (af + bf EDf + cfEXPf + ff UNIONf)
add and subtract:
bm EDf , cmEXPf , fm UNIONf
Wm-Wf = bm (EDm-EDf) + cm (EXPm-EXPf) + fm (UNIONm-UNIONf)
+ (am-af) + ( bm-bf) EDf + (cm-cf) EXPf +
(fm-ff) UNIONf
- first three terms: are the part of the wage gap due to differences in
average characteristics between men and women
(EXPLAINED)
- If men and women had the same levels of education, experience
and unionization these terms would be 0.
- If education, experience and unionization all raise wages (b, c,
f>0):
- and if men better educated, have more experience and
higher rates of unionization then a positive share of
the gap is explained.
- the last four terms are the discriminatory part of the wage gap.
(DISCRIMINATION / UNEXPLAINED)
- Due to differences by sex in how characteristics are "treated"
when wages are determined in the labour market.
- if a, b, c and f are the same for men and women these terms are
zero: the gap then is entirely due to differences in
characteristics.
For our example, using 1994 data for 16-64 year old paid-workers:
Estimated wage equations:
Men:
Wm = -1.34 + .078 EDm + .27 EXPm + 3.76 UNIONm
Women:
Wf = -1.80 + .70 EDf + .21 EXPf + 4.62 UNIONf
Sample averages:
Wage
Yrs. Education (ED)
Yrs. Experience (EXP)
Proportion UNION
Men
Women
$14.74
14.15
13.86
0.32
$11.69
14.56
9.32
0.28
(Gap: $3.05 )
Decomposition:
Wm-Wf = bm (EDm-EDf) + cm (EXPm-EXPf) + fm (UNIONm-UNIONf)
+ (am-af) + ( bm-bf) EDf + (cm-cf) EXPf + (fm-ff) UNIONf
= + .078 x(14.15-14.56) + .27 x(13.86-9.32) + 3.76 x (.32-.28)
(-1.34+1.80) + (.78-.70) 14.56 + (.27-.21) 9.32 + (3.76-4.62) .28
3.05
=
1.07
+
1.99
Total gap =Explained + Unexplained /Residual
This means that (1.07/3.05)=35% of the gender gap is explained by differences
in education, experience and unionization rates between women and men.
Thus (1.99/3.05)=65% of the gender gap is unexplained. Would we have used a
more complete set of explanatory variables, we could claim that this part of the
gap is due to discrimination.