ON THE PITFALLS OF UNTESTED COMMON‐FACTOR RESTRICTIONS: THE CASE OF THE INVERTED FISHER HYPOTHESIS
| Date | 01 May 1988 |
| Author | Kevin D. Hoover |
| DOI | http://doi.org/10.1111/j.1468-0084.1988.mp50002002.x |
| Published date | 01 May 1988 |
OXFORD BULLETIN OF ECONOMICS AND STATISTICS, 50,2(1988)
0305-9049 S3.00
ON THE PITFALLS OF UNTESTED COMMON-
FACTOR RESTRICTIONS: THE CASE OF THE
IN VERl ED FISHER HYPOTHESIS
Kevin D. Hoovert
A common approach to single-equation time-series modelling is to start with
a static regression suggested by some economic theory; to estimate it using
ordinary least squares; and, if the Durbin-Watson statistic is sufficiently below
two, suggesting serial correlation in the residuals, to re-estimate it using a
Cochrane-Orcutt transformation. Then, if the Durbin-Watson statistic looks
respectable, one proceeds to hypothesis testing on the basis of the estimated
standard errors of the coefficients of the (transformed) static regression. The
Cochrane-Orcutt transformation imposes a common-factor restriction on the
estimated regression. Although it is well-known that such restrictions may not
be justified, the ease with which they are imposed in common econometric
computer packages and the fact that many econometrics texts present the
Cochrane-Orcutt transformation and its generalizations as a panacea for
serial correlation means that unwarranted common-factor restrictions are
routinely and wrongly imposed. It is too rarely appreciated that unwarranted
common-factor restrictions may lead an investigator to draw false statistical
inferences - sometimes the opposite of what the data in fact support.
In this paper, we shall review the theory of common factors. We shall then
illustrate a case of a wrongly-imposed common-factor restriction using
Carmichael and Stebbing's (1983) paper in support of the inverted Fisher
hypothesis. Finally, we shall use the same data to illustrate a constructive
alternative to blithely imposing common-factor restrictions.
I. THE COCHRANE-ORCUTT TRANSFORMATION AND COMMON-FACTOR
RESTRICTIONS
A simple two-variable static regression model may take the form
y=a0+a1x+e1, (1)
On estimating such a regression, an investigator may discover that the esti-
mates of r are serially-correlated. Econometrics textbooks tell him that serial
t I am grateful to Jeffrey Carmichael for supplying me with his data set for use in this paper. I
also thank him and David Hendry for comments on earlier drafts. Wen Hai and Jennifer Ballard
provided able research assistance.
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