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

h
test
to test
serial correlation in such models. But this test is not as powerful, in a statistical sense, as
the 
Breusch–Godfrey test
to be discussed shortly, so there is no need to use the 
h
test.
However, because of its historical importance, it is discussed in Exercise 12.36.
Also, if the error term 
u
t
are not NIID, the routinely used 
d
test may not be reliable.
26
In
this respect the 
runs test
discussed earlier has an advantage in that it does not make any
(probability) distributional assumption about the error term. However, if the sample is large
(technically infinite), we can use the Durbin–Watson 
d
, for it can be shown that
27
√
n
1
−
1
2
d
≈
N
(0, 1)
(12.6.12)
25
For details, see Thomas B. Fomby, R. Carter Hill, and Stanley R. Johnson, 
Advanced Econometric
Methods,
Springer Verlag, New York, 1984, pp. 225–228.
26
For an advanced discussion, see Ron C. Mittelhammer, George G. Judge, and Douglas J. Miller,
Econometric Foundations,
Cambridge University Press, New York, 2000, p. 550.
27
See James Davidson, 
Econometric Theory,
Blackwell Publishers, New York, 2000, p. 161.
guj75772_ch12.qxd 14/08/2008 10:40 AM Page 437

---

That is, in large samples the 
d
statistic as transformed in Eq. (12.6.12) follows the standard
normal distribution. Incidentally, in view of the relationship between 
d
and 
ˆ
ρ
, the estimated
first-order autocorrelation coefficient, shown in Eq. (12.6.10), it follows that 
√
n
ˆ
ρ
≈
N
(0, 1)