The McGraw-Hill Series Economics essentials of economics brue, McConnell, and Flynn Essentials of Economics

FIGURE 11.3
Illustration of
heteroscedasticity.
3
I am indebted to Michael McAleer for pointing this out to me.
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Part Two
Relaxing the Assumptions of the Classical Model
As a concrete example, recall our study of advertising impressions retained (
Y
) in rela-
tion to advertising expenditure (
X
). (See Exercise 8.32.) If you regress 
Y
on 
X
only and ob-
serve the residuals from this regression, you will see one pattern, but if you regress 
Y
on 
X
and 
X
2
, you will see another pattern, which can be seen clearly from Figure 11.5. We have
already seen that 
X
2
belongs in the model. (See Exercise 8.32.)
6. Another source of heteroscedasticity is 
skewness
in the distribution of one or more
regressors included in the model. Examples are economic variables such as income,
wealth, and education. It is well known that the distribution of income and wealth in most
societies is uneven, with the bulk of the income and wealth being owned by a few at the top.
7. Other sources of heteroscedasticity: As David Hendry notes, heteroscedasticity can
also arise because of (1) incorrect data transformation (e.g., ratio or first difference transfor-
mations) and (2) incorrect functional form (e.g., linear versus log–linear models).
4
1
9
2
3
4
5
6
7
8
10
26
10
9
8
7
6
5
4
3
2
1
15
25
Stock prices (% change)
Consumer prices (% change)
Chile
FIGURE 11.4
The relationship
between stock prices
and consumer prices.
2
–40
4
6
8 10 12 14 16 18 20 22
–20
0
20
40
(
b
)
2
–60
–40
4
6
8 10
(
a
)
12 14 16 18 20 22
–20
0
20
40
60