Introductory Econometrics ECON0701 (2009)
102
8.
Multiple regression analysis with qualitative explanatory
variables
•
extends the multiple regression model to situations in which the
regression parameters are di
f
erent for some of the observations
in a sample
•
dummy variables are a powerful tool for capturing
qualitative
characteristics
of individuals, such as gender, race, and geo
graph
icreg
iono
fres
idence
•
the introduction of dummy variables allows us to construct mod
els in which some or all model parameters change for some of
the observations in the sample
8.1.
Intercept dummy variables
•
example: a model of car speed
•
to incorporate the hypothesis that the model may di
f
er with
respect to di
f
erent types of cars, we develop a way to incorporate
such nonquantitative, or qualitative, factors into the model
•
one way to capture qualitative characteristics within economic
models is to use
dummy variables
(also called
binary
or
di
chotomous
variables):
y
i
=
β
0
+
β
1
x
i
+
θ
D
i
+
ε
i
(8.1)
where
y
i
= speed of car in miles per hour;
x
i
= age of car in
years;
D
i
=1
if red car,
D
i
=0
otherwise
•
in the above model,
D
i
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103
•
for red cars:
D
i
=1
in (8.1)
y
i
=(
β
0
+
θ
)+
β
1
x
i
+
ε
i
•
for other cars:
D
i
=0
in (8.1)
y
i
=
β
0
+
β
1
x
i
+
ε
i
•
a hypothesis: red cars travel faster (
H
0
:
θ
=0
versus
H
1
:
θ
>
0
)
•
adding the dummy variable
D
to the regression model in the
above way creates a
parallel shift
(or intercept shift) in the rela
tionship by the amount
θ
•
a dummy variable like
D
that is incorporated into a regression
model to capture a shift in the intercept as the result of some
qualitative factor is called an intercept dummy variable
•
provided that
ε
i
in (8.1) satis
f
es the assumptions of the regres
sion model, it is possible to estimate the model parameters via
OLS method as usual; the properties of the OLS estimator are
not a
f
ected by the fact that one of the explanatory variables
consists of zeros and ones
•
e.g.
y
=income,
x
1
= education level,
x
2
= experience,
MALE
=
0
for female (for the
f
rst 61 observations),
MALE
=1
for male
(for the last 32 observations)
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 Spring '09
 Paul
 Regression Analysis, Yi, Introductory Econometrics ECON0701

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