PRACTITIONERS CORNER: Maximum Likelihood Estimation of Cointegration Vectors: An Example of The Johansen Procedure‡
| Published date | 01 May 1989 |
| Date | 01 May 1989 |
| DOI | http://doi.org/10.1111/j.1468-0084.1989.mp51002006.x |
OXFORD BULLETIN OF ECONOMICS AND STATISTICS, 51,2(1989)
0305-9049 $3.00
PRACTITIONERS CORNER
Maximum Likelihood Estimation of Cointegration
Vectors: An Example of The Johansen Procedure
S. G. Hall
INTRODUCTION
The concept of cointegration has attracted increasing attention over recent
years, the key paper of Engle and Granger (1987) providing a spur to a great
deal of research in a number of directions. One strand of this research
involves the estimation and testing of cointegrating vectors within an OLS
framework. A two-step estimator may be constructed, by first estimating a
static regression, then taking the residuals from this equation and including
them in a full dynamic model. Engle and Granger show that this estimator is
consistent and that the convergence properties of the parameter estimates are
superior to standard OLS. This procedure involves normalizing the
cointegrating vector on one of the variables which makes the assumption that
the corresponding element of the cointegrating vector is non-zero. Doubts
have been raised about the usefulness of this procedure in the light of a
considerable degree of small sample bias which may occur in the parameter
estimates (e.g. Banerjee et al. (1986)). Despite this difficulty, a number of
applications of the two step estimator have been performed, including Hall
(1986), Jenkinson(1986)and Drobney and Hall(1987).
In practical applications there are a number of disadvantages to the two-
step procedure which are perhaps more important than the small sample bias.
In particular two problems are largely unresolved; first the assumption is
made that the cointegrating vector is unique, this may not, however, be the
case and the two-step procedure provides no framework for addressing this
question. Second, the test procedures do not have well defined limiting
distributions and as a result testing for cointegration is not a straightforward
procedure.
A recent paper by Johansen (1988) suggests a maximum likelihood estima-
tion procedure which offers solutions for both of these problems. It provides
I would like to thank D F. Hendry and S. Johansen for helpful comments on an earlier draft
of this paper, any remaining errors are of course my own responsibility. The views expressed in
this paper do not necessarily represent those of the Bank of England
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