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

Hypothesis: 
α
4
=
0
Hypothesis: 
β
4
=
0
Do Not Reject
Reject
Do not reject
Accept both C and D
Accept D, reject C
Reject
Accept C, reject D
Reject both C and D
As this table shows, we will not be able to get a clear answer if the 
J
testing procedure leads
to the acceptance or rejection of both models. In case both models are rejected, neither
model helps us to explain the behavior of 
Y
. Similarly, if both models are accepted, as
Kmenta notes, “the data are apparently not rich enough to discriminate between the two
hypotheses [models].”
37
36
R. Davidson and J. G. MacKinnon, “Several Tests for Model Specification in the Presence of Alterna-
tive Hypotheses,” 
Econometrica,
vol. 49, 1981, pp. 781–793.
37
Jan Kmenta, op. cit., p. 597.
guj75772_ch13.qxd 29/08/2008 07:10 PM Page 490

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Chapter 13
Econometric Modeling: Model Specification and Diagnostic Testing
491
Another problem with the 
J
test is that when we use the 
t
statistic to test the significance
of the estimated 
Y
variable in models (13.8.5) and (13.8.6), the 
t
statistic has the standard
normal distribution only asymptotically, that is, in large samples. Therefore, the 
J
test may
not be very powerful (in the statistical sense) in small samples because it tends to reject the
true hypothesis or model more frequently than it ought to.
EXAMPLE 13.4
Personal
Consumption
Expenditure and
Disposable
Personal Income
To illustrate the 
J
test, consider the data given in Table 13.3. This table gives data on per
capita personal consumption expenditure (PPCE) and per capita disposable personal
income (PDPI), both measured in current (2008) dollars for the United States for the
period 1970–2005. Consider the following rival models:
Model A:
PPCE
t
=
α
1
+
α
2
PDPI
t
+
α
3
PDPI
t
−
1
+
u
t
(13.8.7)
Model B:
PPCE
t
=
β
1
+
β
2
PDPI
t
+
β
3
PCPE
t
−
1
+
u
t
(13.8.8)
Model A states that PPCE depends on PDPI in the current and previous time period;
this model is an example of what is known as the