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9.5
The Dummy Variable Alternative to the Chow Test
9
In Section 8.7 we discussed the Chow test to examine the structural stability of a regression
model. The example we discussed there related to the relationship between savings and in-
come in the United States over the period 1970–1995. We divided the sample period into
two, 1970–1981 and 1982–1995, and showed on the basis of the Chow test that there was a
difference in the regression of savings on income between the two periods.
However, we could not tell whether the difference in the two regressions was because of
differences in the intercept terms or the slope coefficients or both. Very often this knowl-
edge itself is very useful.
Referring to Eqs. (8.7.1) and (8.7.2), we see that there are four possibilities, which we
illustrate in Figure 9.3.
1. Both the intercept and the slope coefficients are the same in the two regressions. This, the
case of
coincident regressions,
is shown in Figure 9.3
a
.
2. Only the intercepts in the two regressions are different but the slopes are the same. This
is the case of 
parallel regressions,
which is shown in Figure 9.3
b
.
3. The intercepts in the two regressions are the same, but the slopes are different. This is
the situation of 
concurrent regressions
(Figure 9.3
c
).
4. Both the intercepts and slopes in the two regressions are different. This is the case of 
dis-
similar regressions,
which is shown in Figure 9.3
d
.
The multistep Chow test procedure discussed in Section 8.7, as noted earlier, tells us only
if two (or more) regressions are different without telling us what the source of the difference is.
28,695
1
Wes
t
2.34
2.34
2.34
South
Northeast and
North Central
1
1
Y
X
25,741
25,583
FIGURE 9.2
Public school
teacher’s salary (
Y
)
in relation to per
pupil expenditure on
education (
X
).
9
The material in this section draws on the author’s articles, “Use of Dummy Variables in Testing for
Equality between Sets of Coefficients in Two Linear Regressions: A Note,” and “Use of Dummy
Variables . . . A Generalization,” both published in the 
American Statistician,
vol. 24, nos. 1 and 5,
1970, pp. 50–52 and 18–21.
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