1
Lecture 5 Regression with dummy variables
Dummy Variables
A dummy variable is a variable that equals either 1 or 0, representing two
groups/categories.
Examples
: male (= 1 if are male, 0 otherwise), urban (= 1 if in urban area, 0
otherwise), etc.
Dummy variables are also called binary variables, for obvious reasons.
A Dummy
Independent Variable
A simple model with one dummy (
d
) independent variable:
0
Y
d
u
α
δ
=
+
+
If
d
= 0, then
Y=
, and hence
(
)
u
E Y
α
α
+
=
,
If
d
= 1, then
0
0
(
)
, and hence
(
)
Y
u
E Y
α
δ
α
δ
=
+
+
=
+
.
The case of
d
= 0 is the base group, and
α
is the intercept for the base group;
0
δ
is
the
mean difference
in the outcome between the represented group (
d
=1) and the
base group.
•
Testing the significance of
0
δ
tells whether the mean
Y’s
are significantly
different between the two groups.
Example
: In a study of wage differences between male and female workers
of similar age and education, the following equation is estimated using OLS:
=
+
+ ,
W
F
u
α
β
where
W
is wage in dollars and
F
is a dummy that equals 1 if a worker is
female and 0 if male, and
u
is an error term. In the data, the average wage for
male
W
f
, and for male is
W
m
.
(i) How would you interpret the intercept
and slope
α
β
(ii) Based on your interpretation,
ˆ
ˆ
? and
?
α
β
=
=
•
When there is an intercept in the model, the coefficient of a dummy variable
always represents the mean difference between the dummy represented
group and the based group.

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