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

EXAMPLE 9.5
(
Continued
)
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Chapter 9
Dummy Variable Regression Models
291
There are several methods of deseasonalizing a time series, but we will consider only one
of these methods, namely, the 
method of dummy variables.
13
To illustrate how the dummy
variables can be used to deseasonalize economic time series, consider the data given in
Table 9.3. This table gives quarterly data for the years 1978–1995 on the sale of four major
appliances, dishwashers, garbage disposers, refrigerators, and washing machines, all data in
thousands of units. The table also gives data on durable goods expenditure in 1982 billions of
dollars.
To illustrate the dummy technique, we will consider only the sales of refrigerators over
the sample period. But first let us look at the data, which is shown in Figure 9.4. This fig-
ure suggests that perhaps there is a seasonal pattern in the data associated with the various
quarters. To see if this is the case, consider the following model:
Y
t
=
α
1
D
1
t
+
α
2
D
2
t
+
α
3
t
D
3
t
+
α
4
D
4
t
+
u
t
(9.7.1)
where 
Y
t
=
sales of refrigerators (in thousands) and the 
D
’s are the dummies, taking a value
of 1 in the relevant quarter and 0 otherwise. 
Note that to avoid the dummy variable trap, we
are assigning a dummy to each quarter of the year, but omitting the intercept term.
If there
is any seasonal effect in a given quarter, that will be indicated by a statistically significant 
t
value of the dummy coefficient for that quarter.
14
Notice that in Eq. (9.7.1) we are regressing 
Y
effectively on an intercept, except that we
allow for a different intercept in each season (i.e., quarter). As a result, the dummy coeffi-
cient of each quarter will give us the mean refrigerator sales in each quarter or season
(why?).