PRACTITIONERS CORNER*: Testing for Structural Change at more than one Switch Point: Inadequate Degrees of Freedom and Dummy Variables
| Author | Haluk Erlat |
| DOI | http://doi.org/10.1111/j.1468-0084.1985.mp47003008.x |
| Date | 01 August 1985 |
| Published date | 01 August 1985 |
OXFORD BULLETIN OF ECONOMICS AND STATISTICS, 47,3 (1985)
0305-9049 $3.00
PRACTITIONERS CORNER*
Testing for Structural Change at more than one Switch
Point: Inadequate Degrees of Freedom and Dummy
Variables
Haluk Erlat
I. INTRODUCTION
This expository paper deals with testing for structural change in the
linear regression model, when the regression coefficients change more
than once (at known points) over the sample observations and when
some of the resultant subsamples contain insufficient observations to
estimate the regression relationship. This problem has been dealt with,
very elegantly, by Dufour (1982), who points out that the usual
approach based on predictive testing is not appropriate for this prob-
lem. This would seem to rule out a dummy variable formulation of the
problem, which gave very convenient results in the usual two sample
situation (Erlat, 1978; Dufour, 1980).
This convenience stemmed from the fact that the estimated coeffi-
cients of the dummy variables, when one is testing for structural change
in all the coefficients, gave the prediction errors in the subsample with
insufficient observations and their standard errors provided us with the
standard errors of prediction.1 In the case at hand, the problem rests in
choosing the subsample with adequate observations to generate the
predictions; this choice is arbitrary. Nevertheless, if one does have prior
information which could lead one to make such a choice, then a
dummy variable formulation would come in very handy. It is the aim of
this paper to show that the results in Erlat (1978) and Dufour (1980)
extend directly to the present situation. It may also be viewed as a
generalization of the results in Gujarati (1970).
A dummy variable formulation of the predictive Chow (1960) test in
the two subsample case was provided by Valentine (197 1) for the full
* The purpose of Practitioner's Corner is to publish brief methodological notes of interest
to applied economists. The Editors welcome submissions of this sort.
'For a similar use of dummy variables see Salkever (1976), Erlat (1979), Fuller (1980) and
Pagan and Nicholls (1984). The main difference between these studies and the ones cited in the
main text, is that the former do not require the actual values of the dependent variable be
known for the prediction period while the latter do require these values. The main objective of
the studies cited above is to obtain prediction standard errors in a simple, straightforward
fashion.
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