Table Of ContentMACROECONOMIC
MODELLING
S. G. HALL
S. G. B.HENRY
Bank of England
London, U.K.
1988
NORTH-HOLLAND
AMSTERDAM · NEW YORK · OXFORD TOKYO
® ELSEVIER SCIENCE PUBLISHERS B.V., 1988
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LIBRARY OF CONGRESS
Library of Congress Catalog1ng-in-Publication Data
Hal 1, S. G.
Macroeconomic modelling / S.G. Hall, S.G.B. Henry.
p. cm. — (Contributions to economic analysis ; 172)
Bib 1iography: ρ.
ISBN (invalid) 0-444-70429-9 (U.S.)
1. Macroeconomics—Mathematical models. I. Henry, S. G. B.
II. Title. III. Series.
HB172.5.H355 1988
339' .0724—dc 19 88-5379
CIP
PRINTED IN THE NETHERLANDS
Introduction to the series
This series consists of a number of hitherto unpublished studies, which are
introduced by the editors in the belief that they represent fresh contributions to
economic science.
The term 'economic analysis' as used in the title of the series has been adopted
because it covers both the activities of the theoretical economist and the research
worker.
Although the analytical methods used by the various contributors are not the
same, they are nevertheless conditioned by the common origin of their studies,
namely theoretical problems encountered in practical research. Since for this
reason, business cycle research and national accounting, research work on behalf of
economic policy, and problems of planning are the main sources of the subjects
dealt with, they necessarily determine the manner of approach adopted by the
authors. Their methods tend to be 'practical' in the sense of not being too far
remote from application to actual economic conditions. In addition they are quanti-
tative.
It is the hope of the editors that the publication of these studies will help to
stimulate the exchange of scientific information and to reinforce international
cooperation in the field of economics.
The Editors
For Jacqueline and Vivienne
ix
PREFACE
This book arose out of research done by the authors in the period
between 1983 and 1987 whilst at the National Institute of Economic and
Social Research. A number of things combined to impart the basic thrust
of the research; partly the developments in formulating and estimating
Rational Expectations Models, and partly actual developments in the UK
economy itself. On the latter point, the sharp downturn in output, even
more rapid falls in employment, and the large overappreciation of
sterling, all posed new demands on empirical model builders. Many
existing empirical models simply failed to account for these rapid
changes in the aggregate economy since they did not have sufficiently
volatile properties. Thus the developments in the Rational Expectations
literature seen highly relevant to these phenomena, especially those
developments emphasising the real consequences of a combination of
inertia in certain markets coupled with fast moving - forward looking -
markets elsewhere. In many respects much of the research summarised in
this volume recounts the problems in embedding this type of dynamic
behaviour in a large scale macro economic model and our, possibly
imperfect, resolution of them. We should emphasise that in this
endeavour, we have not implanted many of the key behavioural features
of, say, the seminal Dornbusch model of exchange rate overshooting. Our
research has attempted to build on much of the spirit of this approach,
but also attempts to provide robust econometric models of dynamic
behaviour, aimed at outperforming alternative backward looking models,
as judged by statistical criteria. This leads us to emphasise inertia
in the real exchange rate, as well as the likely presence of forward
χ Preface
looking expectation formation among foreign exchange operators. We also
stress the potential for forward looking behaviourin goods markets, and
factor demands. Apart from the econometric issues which this work has
entailed (and which we survey in in the first half of the book), there
are quite considerable problems in implementing forward looking
behaviour in a large scale macroeconomic model, if the model is to be
used in a regular way for forecasting and policy simulation. The
developments undertaken in this part of our research are summarised in
the second half of the book. This shows, we hope, that though the
problems are computationally formidable, manageable solutions are
distinctly possible, which shed some light on how the British economy
has behaved over the last decade.
In our research endeavours over the last few years, our debts to
other researchers at the National Institute and elsewhere have been
numerous. Among our collègues we would like to single out particularly
Andrew Britton, Simon Wren-Lewis, Andreas Drobny, Keith Cuthbertson, and
Simon Brooks for their help. For collègues outside the National
Institute we would like to thank Andrew Harvey and Andrew Hughes-Hallett
for comments on earlier drafts of parts of the manuscript. We also
extend thanks to David Currie for general encouragement, and also in his
role as supervisor of Stephen Hall's thesis, which was the basis for
part of chapter 6.
In preparing the manuscript for the publishers, Patricia Facey made
valiant efforts with early drafts. Latterly, Gillian Clisham has dealt
with an increasingly difficult schedule of revisions and amendments with
great cheerfulness. To both we are extremely grateful.
xi
Lastly, the research reported here was part of a program of
econometric research financed by the Macromodelling Consortium of the
Economic and Social Research Council. We would like to express our
thanks for this support.
1
Chapter 1
DYNAMIC MODELLING AND RATIONAL EXPECTATIONS
1. Introduction
The link between dynamic modelling and expectation formation has
occupied much of the economics profession for well over a decade. The
clearest example of the linkage between the two lies in the 'deep
structural1 approach associated with the Rational Expectations
Hypothesis (REH). In this case the behaviour of agents is often
described as the optimal outcome of an explicit dynamic program subject
to costly adjustment. Then the hypothesis of rationally formed
expectations is embedded in this program. In principle, such a model
separates lags arising from the economic environment, and lags due to
expectation formation, hence avoiding the strictures of the 'Lucas
critique'. This approach is in contrast to models where these dynamics
are compounded, implying that model reduced form parameters will change
as e.g. policy stance and, hence, expectation formation, change. Policy
evaluation by simulation techniques could well be invalid in such
models.
These propositions are, of course, very familiar. What is
surprising perhaps is the limited degree to which empirical models have
attempted to implement this distinction, and the purpose of this chapter
is to explore some of the consequences of the conjuncture of lags and
expectations, and provide illustrations using models of both the labour
market and the foreign exchange market. As we suggest in later
sections, our reasoning is that these examples are ones where extremely
2 S.G. Hall and S.G.B Henry
variable behaviour is often manifest. While this property of
variability has been associated with exchange rates in the
'overshooting* literature for some time (starting with the seminal
article by Dornbusch (1976)), there is also a semblance of similar jumps
in employment. We consider some of these points briefly now.
An analysis of employment implying such sharp changes is relatively
straightforward (see Henry (1979) and Nickell (198*0). For the
continuous case, a simple version of the firm1s optimising problem is
that it seeks to maximise the discounted functional
r ( )t
J e ~ [p(t) R (L, t) - w(t) L(t) - c (L(t) + 6L(t))] dt (1)
where R(.) is the firm's real revenue function (dependent upon
employment (L)), ρ is output price, w is a given wage rate, and c(.) is
an adjustment cost function with the term in 6(t) representing
voluntary quitting. The Euler equation in this case is
p(t)R = w(t) + (r + 6) c» - (L(t) + 6L) c"(t) (2)
L
The general solution for an equation of this kind, together with its
associated transversality condition is given in section 2. It shows
that the path of employment depends upon a future weighted stream of
expected values of the forcing variables; prices and wages in this case.
But if, for illustrative purposes, these forcing variables are held
constant, a stationary problem ensues.
The interesting situation is, however, the non-stationary case
Ch. 1: Dynamic Modelling 3
where forcing variables are not constant. A special case of this is
where a single change occurs in the forcing variables. This may be
interpreted as a once-for-all change in expected future variables
at Τ let us say. When this happens the new equilibrium for the firm is
e.g. L* , produced by a fall in expected future prices, and given by a
new equilibrium trajectory. Assuming employment is initially at L*, the
subsequent movement of L(t) will be a change in employment which occurs
immediately, before the change in forcing variables, moving along that
unstable path guaranteed to place L(t) on the new saddlepath at t = T.
This is not an immediate jump to the new saddlepath however, as there
are costs of adjusting labour.
The dynamic analysis of the foreign exchange market has typically
used a related analytical framework to that given already for the case
of employment. We may devote a few moments to its salient features here
however, because it will be used later in our account of the foreign
exchange modelling reported in section MB, and because this next model
has additional features which may also be related to labour market
behaviour.
This analysis is usually couched in complete model terms, and takes
a general form for the first order matrix case (see Blanchard and Kahn
(1980) and Buiter (1982)).
X X.
t+1 = A t (3)
tPt+1_
