2
A model with one dummy and one continuous covariate
X
:
0
YM
X
u
αδ
β
=+
+ +
Example
:
M
=1 if male, and 0 otherwise;
X
=years of schooling;
Y
=wage.
•
Note that a dummy for male and a dummy for female provide the same
information. In particular, they sum to 1, i.e., they are perfectly collinear,
so can’t include both.
Similarly,
If
M
= 0, then
()
.
EY
X
αβ
If
M
= 1, then
0
() (
)
.
X
αδ β
+
So
0
δ
is the mean wage difference between male and female holding years of
schooling constant (given the same education level).
The graph for the estimated wage equations consists of two parallel lines
, where
α
is the intercept for the base group (
M
=0), i.e., females, and
0
+
is the
intercept for the group (
M
=1), i.e., males.
Figure
: the estimated wage equation (assuming
0
> 0 )
Program evaluation
: Often times, economists are interested in evaluating the
impact of some public policy, intervention, or program. Can include a dummy
indicating, for example, whether or not an individual participates in a job training
program, or receives unemployment insurance; or whether or not a kid enrolls in
Head Start. After controlling for all the relevant covariates that determine outcome,
the coefficient of the dummy gives the impact of interest, i.e., the impact of the job
training program, unemployment insurance, or Head Start.