Group Comparisons: Using “What If” Scenarios to
Decompose Differences Across Groups
—
Page 1
Group Comparisons:
Using “What If” Scenarios
to Decompose Differences Across Groups
We saw that the effects of education and job experience were smaller for blacks than for whites.
However, we also saw that blacks had lower levels of education and less job experience than
whites. Both of these contribute to the differences in income between whites and blacks. How
can we disentangle the relative importance of these differences?
One way to address this is via a
“
what if
”
question: Suppose that blacks had as much education
and job experience as whites, but the effects of education and job experience were the same for
blacks as they are now. What would the gap be between whites and blacks then? In other words,
if you control for compositional differences on the independent variables, how much difference
remains between whites and blacks on the dependent variable? To answer this we proceed as
follows.
1.
First, remember that in the real world (the real world we made up in this example,
anyway) the difference between the average black and white income is $11,250. Further, on
average whites also have more education and more job experience.
. use http://www.nd.edu/~rwilliam/stats2/statafiles/blwh.dta, clear
. tabstat income educ jobexp, by(black) columns(variables)
Summary statistics: mean
by categories of: black
black 
income
educ
jobexp
+
white 
30.04
13.9
14.1
black 
18.79
10.2
11.2
+
Total 
27.79
13.16
13.52

Remember too that the effects of education and job experience are greater for whites (for variety
I’ll use Stata’s
estimates
command to make side by side comparisons easier):
. quietly reg income educ jobexp if black
. estimates store blackmodel
. quietly reg income educ jobexp if !black
. estimates store whitemodel
. estimates table blackmodel whitemodel

Variable  blackmodel
whitemodel
+
educ 
1.6779491
1.8933377
jobexp 
.421975
.72225495
_cons  3.0512005
6.4611885

To find out how much difference there would be in our hypothetical world where blacks have the
same average levels of education and job experience as whites, while education and job
experience continue to have the same effect on blacks as they do now, we next do the following.
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Group Comparisons: Using “What If” Scenarios to
Decompose Differences Across Groups
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Page 2
2.
Regress income on education and job experience for blacks only.
. quietly reg income educ jobexp if black
3.
Use the
predict
command, but select whites only:
. predict whcompblcoef if !black
(option xb assumed; fitted values)
(100 missing values generated)
In other words, you estimate the regression using one group, blacks, but then compute the
predicted values using the other group, whites. In effect, what this does is give us predicted
values of income for a hypothetical group that has the same levels of education and job
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 Spring '11
 RichardWilliams
 Regression Analysis, Mean, Job Experience

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