Some applications include:
time series data
•
changes in government economic policy (regime changes)
•
seasonality
cross-section data.
A labour force survey may record
individual characteristics such as:
•
gender
(male / female)
•
educational achievement
(high school / university)
•
marital status
(married / single)

2
Econ 326 - Chapter 7
Example
A survey of professors at ABC University has data for:
i
y
annual salary for professor i
i
x
years of teaching experience for professor i
A research question is:
Is there a salary differential between male professors and female
professors ?
This differential is known as the ‘gender wage gap’.
Define the
dummy variable
:
=
female
if
male
if
0
1
D
i
for
i = 1, 2, . . . , N
This is the
‘gender dummy’
variable.
In general, a dummy variable is an artificial variable that assigns
arbitrary codes to different groups.
The use of 0-1 codes suggests that the name
binary variable
or
indicator variable
may be a more descriptive name than
dummy
variable
.
The term ‘dummy variable’ is widely used in econometrics work and
so is the term used here.

3
Econ 326 - Chapter 7
The gender dummy variable can be included in the salary
determination equation to get the linear regression equation:
i
i
2
i
i
e
x
D
y
+
β
+
δ
+
β
=
1
The equation has a differential intercept:
1
β
is the intercept for the female professor
δ
+
β
1
is the intercept for the male professor
δ
is the salary differential between male and female professors.
The use of dummy variables as explanatory variables does not affect
any of the statistical properties of the least squares (OLS) estimator.
Estimation and hypothesis testing can proceed as before.

4
Econ 326 - Chapter 7
The figure below shows that, with
δ
> 0,
the intercept dummy
variable gives different, but parallel, regression lines for male
professors and female professors.
The vertical distance between the two lines is the amount
δ
.
annual salary
years of teaching experience
female professor
male professor

5
Econ 326 - Chapter 7
The parameters
1
β
,
2
β
and
δ
can be estimated by the
least squares principle.
Is there a ‘gender wage gap’ ?
To test the claim that male professors earn more than female
professors with the identical teaching experience consider:
0
:
H
0
=
δ
against
0
:
H
1
>
δ
This is a one-tail test.
The test statistic is the t-statistic for a test of significance that is
reported as a standard part of least squares (OLS) estimation output.
If the coefficient on the gender dummy variable is positive then the
p-value for this one-tail test is obtained by dividing the p-value for a
two-tail test by 2.
For a significance level of 0.05, if the p-value is less than 0.05 then the
null hypothesis is rejected in favour of the alternative that male
professors have higher salaries than female professors.

6
Econ 326 - Chapter 7
Another way to proceed is to define the gender dummy variable as:
=
male
if
female
if
0
1
F
i
The dummy variable
F
can replace the dummy variable
D
in the
salary determination equation.

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