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

(8.7.9)
Note:
By convention we put the larger of the two estimated variances in the numerator. (See
Appendix A 
for the details of the 
F
and other probability distributions.)
Computing this 
F
in an application and comparing it with the critical 
F
value with the
appropriate df, one can decide to reject or not reject the null hypothesis that the variances
in the two subpopulations are the same. If the null hypothesis is not rejected, then one can
use the Chow test.
Returning to our savings–income regression, we obtain the following result:
F
=
833
.
7683
178
.
5032
=
4
.
6701
(8.7.10)
Under the null hypothesis of equality of variances in the two subpopulations, this 
F
value
follows the 
F
distribution with 12 and 10 df, in the numerator and denominator, respec-
tively. (
Note:
We have put the larger of the two estimated variances in the numerator.) From
the 
F
tables in 
Appendix D
, we see that the 5 and 1 percent critical 
F
values for 12 and
16
For a detailed discussion, see William H. Greene, 
Econometric Analysis, 
4th ed., Prentice Hall,
Englewood Cliffs, NJ, 2000, pp. 293–297.
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Chapter 8
Multiple Regression Analysis: The Problem of Inference
259
10 df are 2.91 and 4.71, respectively. The computed 
F
value is significant at the 5 percent
level and is almost significant at the 1 percent level. Thus, our conclusion would be that the
two subpopulation variances are not the same and, therefore, strictly speaking we should
not use the Chow test.
Our purpose here has been to demonstrate the mechanics of the Chow test, which is used
popularly in applied work. If the error variances in the two subpopulations are het-
eroscedastic, the Chow test can be modified. But the procedure is beyond the scope of this
book.
17
Another point we made earlier was that the Chow test is sensitive to the choice of the
time at which the regression parameters might have changed. In our example, we assumed
that the change probably took place in the recession year of 1982. If we had assumed it to
be 1981, when Ronald Reagan began his presidency, we might have found the computed 
F
value to be different. As a matter of fact, in Exercise 8.34 the reader is asked to check this out.
If we do not want to choose the point at which the break in the underlying relationship
might have occurred, we could choose alternative methods, such as the