ERROR CORRECTION, PARTIAL ADJUSTMENT AND ALL THAT: AN EXPOSITORY NOTE*
| DOI | http://doi.org/10.1111/j.1468-0084.1985.mp47002002.x |
| Date | 01 May 1985 |
| Published date | 01 May 1985 |
OXFORD BULLETIN OF ECONOMICS AND STATISTICS, 47, 2(1985)
0305-9049 $3.00
ERROR CORRECTION, PARTIAL
ADJUSTMENT AND ALL THAT: AN
EXPOSITORY NOTE*
Stephen Nickell
I. INTRODUCTION
It can hardly have escaped notice that since the publication of Davidson
et al. (1978), the error correction model has become a very popular
specification for dynamic equations in economics. This popularity is
unquestionably deserved for, as David Hendry has noted on a variety
of occasions (see, for example, Hendry and Richard, 1983) it has a
number of advantages both in terms of its value in generating estimated
equations with desirable statistical properties and in terms of the ease
with which such equations may be interpreted.
In this note I consider the circumstances in which error correcting
behaviour represents the optimal response of economic agents in a
dynamic environment. In the process I shall touch on a number of
related issues particularly those concerned with optimal behaviour in a
growing environment (see, for example, Salmon, 1982; Currie, 1981).
However, I shall begin with the analysis of a general dynamic optimisa-
tion problem.
II. A DYNAMIC OPTIMIZATION PROBLEM
It is now commonplace in the study of dynamic models of behaviour to
assume that agents optimize with respect to a quadratic loss function.1
This has the double advantage of generating a linear decision rule while
simultaneously allowing first period certainty equivalence results to be
applied. All future random variables can thus be replaced by their
expectations. A simple example of this kind of problem involves an
agent at time t facing a sequence of expected optimal values, x_ ,x1,
* This note is based upon a working paper of the same title (Centre for Labour Economics,
WP no. 255) which was originally written in May 1980 for use by my graduate students.
Demand for this paper has subsequently grown to such an extent that the secretaries at the
Centre axe growing rather tired of photocopying it. It therefore seems sensible to make it some-
what more easily accessible. My thanks are due to David Hendry and John Knight for helpful
comments on an earlier draft.
'This trend was initiated by Holt et al. (1961) and continued by Tinsley (1971), Sims
(1974), Sargent (1978) and more recently by authors too numerous to mention.
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