Separation in Cointegrated Systems and Persistent‐Transitory Decompositions
| DOI | http://doi.org/10.1111/1468-0084.00077 |
| Date | 01 November 1997 |
| Author | Clive W. J. Granger,Niels Haldrup |
| Published date | 01 November 1997 |
OXFORD BULLETIN OF ECONOMICS AND STATISTICS, 59, 4 (1997)
0305-9049
SEPARATION IN COINTEGRATED SYSTEMS
AND PERSISTENT-TRANSITORY
DECOMPOSITIONS
Clive W. J. Granger and Niels Haldrup
I. INTRODUCTION
It is a frequent empirical finding in macroeconomics that several cointe-
gration relations may exist amongst economic variables but in the particu-
lar way that the single relations appear to have no variables in common.
It is also sometimes found in such systems that the error correction terms
or other stationary variables from one set of variables may have import-
ant explanatory power for variables in another set. For example Konishi
et al. (1993) considered three types of variables of US data: real, financial
and interest rate variables. They found that cointegration existed between
variables in each subset but not across the variables such that the
different sectors did not share a common stochastic trend. On the other
hand, it was also found that the error correction terms of the interest rate
relation and the sector of financial aggregates had predictive power with
respect to the real variables of the system. As argued by Konishi et al.
(1993) the situation sketched above may extend the usual ‘partial equili-
brium’ cointegration set-up to a more ‘general equilibrium’ setting
although in a limited sense.
The notion of separation initially developed by Konishi and Granger
(1992) and Konishi (1993) provides a useful way of describing formally
the aboved possibility: Consider two groups of I(1)-variables, X1tand X2t
of dimension p1and p2, respectively. X1and X2are assumed to have no
variables in common and in each sub-system there is cointegration with
the cointegration ranks being r1sp1and r2sp2. Hence it follows that the
dimensions of the associated common stochastic trends of each system
are p1µr1and p2µr2. Denote the two sets of I(1) stochastic trends W1t
*The first author acknowledges support from NSF grant SBR 93-08295. The research was
undertaken while the second author was visiting the UCSD during fall, 1995. We would like
to thank Namwon Hyung, the Editor and an anonymous referee for helpful comments.
449
© Blackwell Publishers Ltd, 1997. Published by Blackwell Publishers, 108 Cowley Road, Oxford
OX4 1JF, UK & 350 Main Street, Malden, MA 02148, USA.
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