TESTING PARAMETER CONSTANCY AND SUPER EXOGENEITY IN ECONOMETRIC EQUATIONS
| DOI | http://doi.org/10.1111/j.1468-0084.1996.mp58004008.x |
| Date | 01 November 1996 |
| Author | Timo Teräsvirta,Eilev S. Jansen |
| Published date | 01 November 1996 |
OXFORD BULLETIN OF ECONOMICS AND STATISTICS, 58,4(1996)
0305-9049
TESTING PARAMETER CONSTANCY AND
SUPER EXOGENEITY IN ECONOMETRIC
EQUATIONS
Eilev S. Jansen and Timo Teräsvirta*
I. INTRODUCTION
The concept of super exogeneily is closely related to that of autonomy. An
economic relationship is autonomous, if it is structurally invariant under
changes in the institutions of society, policy rules or the expectations
processes of economic agents, cf. Favero and Hendry (1992). As defined
by Engle, Hendry and Richard (1983), super exogeneity entails that the
parameters of a conditional model are invariant to changes in the distri-
bution of weakly exogenous conditioning variables. This is a testable
hypothesis in the sense that any assertion concerning super exogeneity is
refutable for the set of changes in the exogenous process that have
occurred in the observation period. For a lucid discussion of different
concepts of exogeneity see Hendry (1995, chapter 5).
Engle and Hendry (1993) focus on the case where a linear conditional
model exhibits parameter constancy under the null, while under the alter-
native shifts in the process generating the independent variables induce
shifts in the parameters of the conditional model. They point out that
super exogeneity is a combination of weak exogeneity and invariance.
Weak exogeneity is investigated by testing the presence of the estimate
* The research of the second author was supported in part by the Swedish Research
Council for Humanities and Social Sciences. In addition to the conference in Florence,
versions of and material from this paper have been presented at the ERNSI Econometric
Workshop on Dynamic Models in Economics and Finance, Oegstgeest, May 1995, the Econo-
metric Society World Congress, Tokyo, August 1995, and in seminars at Humboldt-Universi-
tät zu Berlin, Universität München, International Institute of Economic Studies, Stockholm,
Stockholm School of Economics, University of Trondheim and Norges Bank. Comments
from participants at these occasions, as well as those from an anonymous referee of this
journal, are gratefully acknowledged. Discussions with øyvind Eitrheim, Rob Engle, Neil
Ericsson, and David Hendry have been very helpful. The responsibility for any errors and
shortcomings in the paper remains ours.
735
© Blackwell Publishers 1996. Published by Blackwcll Publishers, 108 Cowley Road, Oxford 0X4 IJF,
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736 BULLETIN
for the marginal model (or reduced form) residual in the conditional
model, whereas invariance is not rejected [rejectedj if the factors explain-
ing the regime shifts in the marginal model do not enter [enterl the
conditional model. Their test of super exogeneity is based on the idea of
approximating nonconstant coefficients (which imply lack of invariance)
with linear combinations of moments of the conditioning variables.
These tests of super exogeneity have been adopted in a number of
empirical applications. Engle and Hendry (1993) have an empirical
example on money demand, and the same procedures have also been
used in Hendry and Ericsson (1991) and Favero and Hendry (1992).
Other studies first establish weak exogeneity of the conditioning variables
in the linear system framework, and test invariance by methods inspired
by Engle and Hendry (1993) thereafter. This is the procedure summa-
rized in Ericsson (1992, pp. 263-64). Ericsson, Campos and Tran (1990),
Ahumada (1992), Bârdsen (1992), Brodin and Nymoen (1992), and
Nymoen (1992) all assume that parameter instability in the marginal
model is captured by intervention dummies and test for the presence of
these variables in the conditional equation. For a practically complete list
of references see Ericsson and Irons (1995).
The present paper is closely related to Engle and Hendry (1993) in that
we consider testing parameter constancy and super exogeneity within a
single equation conditional model. The idea is to extend their analysis by
taking advantage of the nonlinear smooth transition regression (STR)
model: see Granger and Teräsvirta (1993) for a discussion. This approach
offers the following advantages. First, an alternative to parameter
constancy may be parametrized as an STR. Nonlinear components in the
STR model may then be interpreted as indicators of regime shifts and
used in testing invariance. Second, an alternative to parameter constancy
in the possibly partially nonlinear conditional model may also be para-
metrized as an STR model and the test of invariance itself may be based
on such a parameterization. Engle and Hendry (1993) show how the
hypotheses of weak exogeneity and of (a form of) invariance can be
embedded into the conditional model. The use of the STR model as the
alternative offers a reformulation of this idea such that joint testing of
both weak exogeneity and (a form of) invariance is possible.
The plan of the paper is as follows. In Section II we consider our
conditional stochastic model and remind the reader of the concepts of
weak exogeneity, constancy and invariance needed to discuss super exoge-
neity. In Section III the issue is how to test parameter constancy in a
single equation conditional model which may be either linear or partially
nonlinear. The tests for weak exogeneity and invariance are presented in
Section IV, whereas Section V contains some extensions. The tests are
applied to data in Section VI, in which we reconsider a Norwegian
consumption function, which is a slightly modified version of that in
Brodin and Nymoen (1992). Section VII offers a few final remarks.
© Blackwcll Publishers 1996.
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