Dougherty: Introduction to Econometrics 3e
Study Guide
Chapter 7
Heteroscedasticity
Overview
This chapter begins with a general discussion of homoscedasticity and heteroscedasticity: the meanings of the
terms, the reasons why the distribution of a disturbance term may be subject to heteroscedasticity, and the
consequences of the problem for OLS estimators.
It continues by presenting several tests for heteroscedasticity
and methods of alleviating the problem.
It shows how apparent heteroscedasticty may be caused by model
misspecification.
It concludes with a description of the use of heteroscedasticityconsistent standard errors.
Learning outcomes
After working through the corresponding chapter in the text, studying the corresponding slideshows, and doing
the starred exercises in the text and the additional exercises in this guide, you should be able to:
explain the concepts of homoscedasticity and heteroscedasticity
•
•
•
•
•
•
•
•
describe how the problem of heteroscedasticity may arise
explain the consequences of heteroscedasticity for OLS estimators, their standard errors, and
t
and
F
tests
perform the Goldfeld–Quandt test for heteroscedasticity
perform the White test for heteroscedasticity
explain how the problem of heteroscedasticity may be alleviated
explain why a mathematical misspecification of the regression model may give rise to a problem of apparent
heteroscedasticity
explain the use of heteroscedasticityconsistent standard errors.
Additional exercises
A7.1
Is the disturbance term in your CES expenditure function heteroscedastic?
Sort the data by
EXPPC
, regress
CATPC
on
EXPPC
and
SIZE
, and perform a Goldfeld–Quandt test to
test for heteroscedasticity in the
EXPPC
dimension.
Repeat using
LGCATPC
as the dependent variable.
A7.2
The observations for the occupational schools (see Chapter 5 in the text) in the figure suggest that a
simple linear regression of cost on number of students, restricted to the subsample of these schools, would
be subject to heteroscedasticity.
Download the data set from the heteroscedastic data sets folder on the
website and use a Goldfeld–Quandt test to investigate whether this is the case.
If the relationship is
heteroscedastic, what could be done to alleviate the problem?
© Christopher Dougherty, 2007
The material in this book has been adapted and developed from material originally produced for the degrees and diplomas by distance
learning offered by the University of London External System (
www.londonexternal.ac.uk
)
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A7.3
A researcher hypothesizes that larger economies should be more selfsufficient than smaller ones and that
M
/
G
, the ratio of imports,
M
, to gross domestic product,
G
, should be negatively related to
G
:
u
G
G
M
+
+
=
2
1
ββ
with
β
2
< 0.
Using data for a sample of 42 countries, with
M
and
G
both measured in US$ billion, he fits
the regression (standard errors in parentheses):
^
G
M
= 0.37 – 0.000086
G
R
2
= 0.12
(1)
(0.03)
(0.000036)
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 Econometrics, Regression Analysis, Heteroscedasticity, Christopher Dougherty, London External

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