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

excluded variable
specification bias. Often the inclusion of such vari-
ables removes the correlation pattern observed among the residuals. For example, suppose
we have the following demand model:
Y
t
=
β
1
+
β
2
X
2
t
+
β
3
X
3
t
+
β
4
X
4
t
+
u
t
(12.1.2)
where 
Y
=
quantity of beef demanded, 
X
2
=
price of beef, 
X
3
=
consumer income, 
X
4
=
price of pork, and 
t
=
time.
4
However, for some reason we run the following regression:
Y
t
=
β
1
+
β
2
X
2
t
+
β
3
X
3
t
+
v
t
(12.1.3)
Now if Eq. (12.1.2) is the “correct’’ model or the “truth’’ or true relation, running
Eq. (12.1.3) is tantamount to letting 
v
t
=
β
4
X
4
t
+
u
t
. And to the extent the price of pork
affects the consumption of beef, the error or disturbance term 
v
will reflect a systematic
414
Part Two
Relaxing the Assumptions of the Classical Model
3
Gerhard Tintner, 
Econometrics
, John Wiley & Sons, New York, 1965.
4
As a matter of convention, we shall use the subscript 
t
to denote time series data and the usual sub-
script 
i
for cross-sectional data.
guj75772_ch12.qxd 14/08/2008 10:40 AM Page 414

---

Chapter 12
Autocorrelation: What Happens If the Error Terms Are Correlated?
415
0
Time
0
Time
0
Time
0
Time
u,u
0
Time
(
a
)
(
b
)
(
c
)
(
d
)
(
e
)
u,u
u,u
u,u
u,u
×
×
×
×
×
× ×
× ×
×
×
×
×
×
×
×
×
×
×
×
×
×
×
×
×
×
×
×
×
×
×
×
× × × ×
×
×
×
×
×
× ×
×
× × ×
×
×
× × ×
×
××
× ×
× × ×
× ×
×
×
× ×
× ×
×
×
FIGURE 12.1
Patterns of
autocorrelation and
nonautocorrelation.
pattern, thus creating (false) autocorrelation. A simple test of this would be to run both
Eqs. (12.1.2) and (12.1.3) and see whether autocorrelation, if any, observed in model (12.1.3)
disappears when model (12.1.2) is run.
5
The actual mechanics of detecting autocorrelation
will be discussed in Section 12.6 where we will show that a plot of the residuals from
regressions (12.1.2) and (12.1.3) will often shed considerable light on serial correlation.
5
If it is found that the real problem is one of specification bias, not autocorrelation, then as will be
shown in Chapter 13, the OLS estimators of the parameters in Eq. (12.1.3) may be biased as well as
inconsistent.
guj75772_ch12.qxd 14/08/2008 10:40 AM Page 415

---

416