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

EXAMPLE 11.4
The
Goldfeld–Quandt
Test
To illustrate the Goldfeld–Quandt test, we present in Table 11.3 data on consumption
expenditure in relation to income for a cross section of 30 families. Suppose we postulate
that consumption expenditure is linearly related to income but that heteroscedasticity is
present in the data. We further postulate that the nature of heteroscedasticity is as given in
Eq. (11.5.10). The necessary reordering of the data for the application of the test is also
presented in Table 11.3.
Dropping the middle 4 observations, the OLS regressions based on the first 13 and the
last 13 observations and their associated residual sums of squares are as shown next (stan-
dard errors in the parentheses).
(
Continued
)
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384
Part Two
Relaxing the Assumptions of the Classical Model
Regression based on the first 13 observations:
ˆ
Y
i
=
3.4094
+
0.6968
X
i
(8.7049) (0.0744) 
r
2
=
0.8887
RSS
1
= 
377.17
df
= 
11
Regression based on the last 13 observations:
ˆ
Y
i
= −
28.0272
+ 
0.7941
X
i
(30.6421)
(0.1319)
r
2
= 
0.7681
RSS
2
= 
1536.8
df
= 
11
From these results we obtain
λ
=
RSS
2
/
df
RSS
1
/
df
=
1536
.
8
/
11
377
.
17
/
11
λ
=
4
.
07
The critical 
F
value for 11 numerator and 11 denominator df at the 5 percent level is 2.82.
Since the estimated 
F
(
=
λ
) value exceeds the critical value, we may conclude that there
is heteroscedasticity in the error variance. However, if the level of significance is fixed at
1 percent, we may not reject the assumption of homoscedasticity. (Why?) Note that the 
p
value of the observed 
λ
is 0.014.