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Global and National Macroeconometric Modelling

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Global and National
Macroeconometric
Modelling: A Long-Run
Structural Approach
Anthony Garratt
Department of Economics, Birkbeck College, London
Kevin Lee
Department of Economics, University of Leicester
M. Hashem Pesaran
Faculty of Economics and Trinity College, Cambridge
Yongcheol Shin
Leeds University Business School
1

3
Great Clarendon Street, Oxford OX2 6DP
Oxford University Press is a department of the University of Oxford.
It furthers the University’s objective of excellence in research, scholarship,
and education by publishing worldwide in
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Oxford is a registered trade mark of Oxford University Press
in the UK and in certain other countries
Published in the United States
by Oxford University Press Inc., New York
© Anthony Garratt, Kevin Lee, M. Hashem Pesaran, and Yongcheol Shin, 2006
The moral rights of the authors have been asserted
Database right Oxford University Press (maker)
First published 2006
All rights reserved. No part of this publication may be reproduced,
stored in a retrieval system, or transmitted, in any form or by any means,
without the prior permission in writing of Oxford University Press,
or as expressly permitted by law, or under terms agreed with the appropriate
reprographics rights organization. Enquiries concerning reproduction
outside the scope of the above should be sent to the Rights Department,
Oxford University Press, at the address above
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and you must impose the same condition on any acquirer
British Library Cataloguing in Publication Data
Data available
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Data available
Typeset by Newgen Imaging Systems (P) Ltd., Chennai, India
Printed in Great Britain
on acid-free paper by
Biddles Ltd, King’s Lynn, Norfolk
ISBN 0–19–929685–5 978–0–19–929685–9
10 9 8 7 6 5 4 3 2 1

Preface
National and global macroeconometric modelling has had a long and ven-
erable history in the UK, with important implications for macroeconomic
policy in general and monetary policy in particular. It is an activity that
involves sustained research input of several investigators with a variety
of skills. The present work is not an exception and its completion has
required the enthusiasm and commitment of a large number of individu-
als and institutions. It was given initial impetus by funding from the UK’s
Economic and Social Research Council (Grant no. L116251016) and from
the Newton Trust of Trinity College, Cambridge (under Anil Seal), to whom
we are very grateful. They funded a project on ‘Structural Modelling of the
UK Economy within a VAR Framework using Quarterly and Monthly Data’,
conceived and originally housed in the Department of Applied Economics
(DAE) at the University of Cambridge in the mid-1990s. The authors all
worked at Cambridge at the time, along with Brian Henry and Martin
Weale who were also co-applicants on the project. Although the team dis-
persed over the years (Garratt to Leicester and then Birkbeck; Henry to LBS
and then Oxford; Lee to Leicester; Shin to Edinburgh and Leeds; and Weale
to the National Institute), we remain very grateful for the resources and
congenial atmosphere provided by co-researchers and colleagues during
our time working at and visiting the DAE.
The research associated with the project extended well beyond the orig-
inal intentions of the funded project, however, and has beneﬁted from
the help and expertise of many friends and colleagues. We are particu-
larly grateful to Richard Smith and Ron Smith, who have collaborated
with us and made essential contributions to various aspects of the work
in the book, and we have received invaluable comments from Manuel
Arrelano, Michael Binder, Carlo Favero, Paul Fisher, Clive Granger, David
Hendry, Cheng Hsiao, George Kapetanios, Adrian Pagan, Bahram Pesaran,
Til Schuermann, James Stock, Ken Wallis and Mike Wickens. The book
draws on material from a variety of our published journal articles also, and
we are particularly grateful to the constructive and enlightening comments
v

Preface
received from the editors and referees of Econometric Reviews (especially
regarding parts of the material of Chapter 6), Economic Journal (Chapters 4
and 9), Economics Letters (Chapter 6), Journal of the American Statistical Asso-
ciation (Chapters 7 and 11) and Journal of Econometrics (Chapter 6). And
the project has also been assisted greatly by the contributions of Yoga
Affandi, Mutita Akusuwan, Mahid Barakchian, James Mitchell, Dimitrios
Papaikonomou and Eduardo Salazar.
While we have been keen to disseminate various aspects of our work in
the form of publications in academic journals, it was always our intention
to write up the project in the form of a book describing the entire pro-
cess of model building, including the methodology tying the economics
and the econometric techniques together, descriptions of the data collec-
tion and analysis, and the use of the model in various decision-making
contexts. We hope that our description will increase transparency on the
process of model building. In the light of new economic and econometric
ideas, and with the advent of fast and readily available computing power,
macroeconometric model-building is an activity that can be widely pur-
sued for a better understanding of national and global economies and their
interlinkages. We hope this book serves to reduce the investment required
in the ﬁrst stages of the sustained effort required in building and using
macroeconometric models.
November 2005
vi

Contents
List of tables xii
List of figures xiii
1 Introduction 1
1.1 Historical background 3
1.2 Alternative modelling approaches 4
1.3 The long-run modelling approach 6
1.4 The organisation of the book 9
2 Macroeconometric modelling: Alternative approaches 13
2.1 Large-scale simultaneous equation models 13
2.2 Unrestricted and structural VARs 16
2.2.1 Unrestricted VARs 16
2.2.2 Structural VARs 18
2.3 Dynamic stochastic general equilibrium models 19
2.4 The structural cointegrating VAR approach 23
2.4.1 Comparisons with the alternative approaches 24
3 National and global structural macroeconometric modelling 33
3.1 Identification in a dynamic structural vector error
correction model 34
3.1.1 Identifying long-run relationships 36
3.1.2 Identifying short-run structural parameters
and shocks 37
3.1.3 A modelling strategy 39
3.2 Specifying the dynamic structure of a
macroeconomic model 41
3.2.1 Dynamics of DSGE models 41
3.2.2 Dynamics of adjustment cost models 46
3.2.3 Identification of short-run dynamics based on
‘tentative’ theory on contemporaneous relations 48
3.2.4 Measuring the effects of monetary policy 51
vii

Contents
3.2.5 Identification using ‘tentative’ theory on
long-run relations 54
3.3 National macroeconomic modelling in a global context 56
3.3.1 VARX models: VAR models with weakly
exogenous variables 57
3.3.2 Developing satellite or sectoral models 59
3.4 Global vector autoregressive (GVAR) models 62
4 An economic theory of the long run 67
4.1 Production technology and output determination 68
4.2 Arbitrage conditions 71
4.3 Accounting identities and stock-flow relations 74
4.4 Long-run solvency requirements 75
4.4.1 Liquidity (real money balances) 78
4.4.2 Imports and exports 78
4.5 Econometric formulation of the model 81
5 An economic theory of the short run 87
5.1 Modelling monetary policy 89
5.1.1 The monetary authority’s decision problem 89
5.1.2 The derivation of the base rate 92
5.1.3 The structural interest rate equation 96
5.2 Alternative model specifications 98
5.2.1 Forecast-inflation targeting 98
5.2.2 Choice of targets and their desired levels 99
6 Econometric methods: A review 105
6.1 Augmented VAR or VARX models 107
6.1.1 The structural VARX model 107
6.1.2 The reduced form VARX model 109
6.1.3 Impulse response analysis 110
6.2 Cointegrating VAR models 117
6.2.1 Treatment of the deterministic components 118
6.2.2 Trace and maximum eigenvalue tests of
cointegration 122
6.2.3 Identifying long-run relationships in a
cointegrating VAR 123
6.2.4 Estimation of the short-run parameters of the
conditional VEC model 128
6.2.5 Analysis of stability of the cointegrated system 129
6.2.6 Impulse response analysis in cointegrating VARs 132
viii

Contents
6.3 The cointegrated VAR model with I(1)
exogenous variables 135
6.4 Small sample properties of test statistics 140
6.5 Empirical distribution of impulse response functions and
persistence proﬁles 141
7 Probability forecasting: Concepts and analysis 145
7.1 Probability forecasting 145
7.1.1 Probability forecasts in a simple univariate AR(1)
model 147
7.2 Modelling forecast uncertainties 153
7.2.1 Future and parameter uncertainties 153
7.2.2 Model uncertainty: Combining probability forecasts 157
7.2.3 Bayesian model averaging 158
7.2.4 Pooling of forecasts 159
7.3 Computation of probability forecasts: Some practical
issues 161
7.3.1 Computation of probability forecasts using
analytic methods 163
7.3.2 Computation of probability forecasts based on
VAR models by stochastic simulation 164
7.3.3 Generating simulated errors 166
7.4 Estimation and forecasting with conditional models 168
8 The UK macroeconomy 171
8.1 Domestic and foreign output 173
8.2 Domestic and foreign prices 178
8.3 Exchange rates 187
8.4 Domestic and foreign interest rates 189
8.5 Real money balances relative to income 193
9 A long-run structural model of the UK 197
9.1 The different stages of estimation and testing 198
9.2 Unit root properties of the core variables 200
9.3 Testing and estimating of the long-run relations 204
9.3.1 Small sample properties of the tests of restrictions
on the cointegrating vectors 208
9.4 The vector error correction model 209
9.4.1 The long-run estimates 209
9.4.2 Error correction speciﬁcations 212
ix

Contents
9.4.3 Comparing the core model with benchmark
univariate models 218
9.5 An alternative model specification 221
10 Impulse response and trend/cycle properties of the UK model 225
10.1 Identification of monetary policy shocks 227
10.2 Estimates of impulse response functions 231
10.2.1 Effects of an oil price shock 232
10.2.2 Effects of a foreign output equation shock 236
10.2.3 Effects of a foreign interest rate equation shock 239
10.2.4 Effects of a monetary policy shock 242
10.3 Trend/cycle decomposition in cointegrating VARs 248
10.3.1 Relationship of GRW and BN decompositions 250
10.3.2 Computation of the GRW decomposition 252
10.3.3 An application to the UK model 254
10.4 Concluding remarks 260
11 Probability event forecasting with the UK model 263
11.1 An updated version of the core model 264
11.1.1 Estimation results and in-sample diagnostics 265
11.1.2 Model uncertainty 266
11.1.3 Evaluation and comparisons of probability
forecasts 269
11.2 Probability forecasts of inflation and output growth 274
11.2.1 Point and interval forecasts 275
11.2.2 Predictive distribution functions 278
11.2.3 Event probability forecasts 280
11.3 A postscript 286
11.4 Concluding remarks 286
12 Global modelling and other applications 289
12.1 Recent applications of the structural cointegrating VAR
approach 289
12.2 Regional interdependencies and credit risk modelling 292
12.3 A monthly version of the core model 297
12.4 Probability forecasting and measuring financial distress
in the UK 303
12.4.1 A satellite model of the UK financial sector 303
12.4.2 UK financial distress in the early 1990s and
early 2000s 305
12.5 Directions for future research 306
x

Contents
13 Concluding remarks 309
Appendices
A Derivation of the interest rate rule 315
A.1 The relationship between policy instruments and targets 316
A.2 Deriving the monetary authority’s reaction function 318
A.3 Inflation targeting and the base rate reaction function 319
A.4 Reaction functions and targeting future values of variables 320
B Invariance properties of the impulse responses with respect to
monetary policy shocks 323
C Data for the UK model 327
C.1 Definitions and sources of the core model variables 327
D Gauss programs and result files 333
D.1 General comments on the Gauss programs 334
D.2 Impulse response and persistence profile programs 334
D.3 Programs for computing probability forecasts 337
D.3.1 Programs for computing out-of-sample
probability event forecasts 338
D.3.2 Programs for computing in-sample probability
event forecast evaluation 339
D.4 Program for computing the decomposition of trends in
cointegrating VARs 342
Bibliography 343
Index 363
xi

List of tables
8.1 Historical unconditional probabilities for output growth (4-quarter
moving average).
178
8.2 Historical unconditional probabilities for inflation (4-quarter
moving average).
182
9.1a Augmented Dickey–Fuller unit root tests applied to variables in the
core model, 1965q1–1999q4.
201
9.1b Phillips and Perron unit root tests applied to variables in the core
model, 1965q1–1999q4.
202
9.2 Akaike and Schwarz Information Criteria for lag order selection. 204
9.3 Cointegration rank test statistics for the core model,

pt − p∗
t , et , rt , r∗
t , yt , y∗
t , ht − yt , p̃t , po
t

.
205
9.4 Reduced form error correction specification for the core model. 213
9.5 Model selection criteria for the core model and alternative time
series specifications.
220
11.1 Error correction specification for the over-identified model,
1985q1–2001q1.
267
11.2 Forecast evaluation of the benchmark model. 270
11.3 Diagnostic statistics for the evaluation of benchmark and average
model probability forecasts.
271
11.4a Point and interval forecasts of inflation and output growth (four
quarterly moving averages, per cent, per annum).
276
11.4b Point and interval forecasts of inflation and output growth (quarter
on quarter changes, per cent, per annum).
276
11.5a Probability forecasts of single events involving inflation. 283
11.5b Probability forecasts of events involving output growth and
inflation.
283
12.1 Reduced form error correction equations of the monthly model. 300
12.2 Probability forecasts involving credit–income disequilibria and low
growth 1990q2–1992q1 and 2001q2–2003q1
306
xii

List of ﬁgures
8.1a UK output, yt . 173
8.1b First difference of UK output, yt . 174
8.1c Foreign output, y∗
t . 174
8.1d First difference of foreign output, y∗
t . 175
8.1e UK and foreign output, yt and y∗
t . 176
8.1f Difference of UK and foreign output, yt − y∗
t . 176
8.2a UK producer prices, pt . 179
8.2b First difference of UK producer prices, pt . 179
8.2c UK retail prices, p̃t . 180
8.2d First difference of UK retail prices, p̃t . 180
8.2e Second difference of UK producer prices, 2pt . 182
8.2f Second difference of UK retail prices, 2p̃t . 183
8.3a Foreign producer prices, p∗
t . 184
8.3b First difference of foreign producer prices, p∗
t . 184
8.3c Relative prices, pt − p∗
t . 185
8.3d First difference of relative prices, (pt − p∗
t ). 185
8.4a Oil price, po
t . 186
8.4b First difference of the oil price, po
t . 186
8.5a Effective exchange rate, et . 187
8.5b First difference of the effective exchange rate, et . 188
8.6a UK interest rates, rt . 189
8.6b First difference of UK interest rates, rt . 190
8.6c Foreign interest rates, r∗
t . 190
8.6d First difference of foreign interest rates, r∗
t . 191
8.6e UK and foreign interest rates, rt and r∗
t . 191
8.6f Difference of UK and foreign interest rates, rt − r∗
t . 192
8.7a Money income ratio, ht − yt . 194
8.7b First difference of the money income ratio, (ht − yt ). 194
xiii

List of Figures
9.1 Asymptotic and empirical distribution generated by the simulated
annealing algorithm of the test of the long-run over-identifying
restrictions.
209
9.2a Actual and fitted values for the (pt − p∗
t ) reduced form ECM
equation.
214
9.2b Actual and fitted values for the et reduced form ECM equation. 214
9.2c Actual and fitted values for the rt reduced form ECM equation. 215
9.2d Actual and fitted values for the r∗
t reduced form ECM equation. 215
9.2e Actual and fitted values for the yt reduced form ECM equation. 216
9.2f Actual and fitted values for the y∗
t reduced form ECM equation. 216
9.2g Actual and fitted values for the (ht − yt ) reduced form ECM
equation.
217
9.2h Actual and fitted values for the (p̃t ) reduced form ECM equation. 217
10.1 Persistence profiles of the long-run relations of a positive unit shock
to the oil price.
234
10.2 Generalised impulse responses of a positive unit shock to the oil
price.
235
to the foreign output equation.
237
10.4 Generalised impulse responses of a positive unit shock to the
foreign output equation.
238
to the foreign interest rate equation.
240
10.6 Generalised impulse responses of a positive unit shock to the
foreign interest rate equation.
241
to monetary policy.
243
10.8 Generalised impulse responses of a positive unit shock to monetary
policy.
244
to the UK interest rate equation.
246
10.10 Generalised impulse responses of a positive unit shock to the UK
interest rate equation.
247
10.11 Actual UK output (yt ) and the GRW permanent component. 256
10.12 GRW transitory components of UK output and inflation: yt and pt . 256
10.13 GRW and BN transitory components of UK output: yt . 257
10.14 GRW transitory components of UK and foreign output: yt and y∗
t . 258
10.15 BN transitory components of UK and foreign output: yt and y∗
t . 258
10.16 Hodrick–Prescott transitory components of UK and foreign output:
yt and y∗
t .
259
xiv

List of Figures
10.17 GRW transitory components of UK and foreign interest rates: rt
and r∗
t .
260
10.18 Actual and the GRW permanent component of UK interest rates: rt . 260
11.1a Inflation (four-quarter moving average). 277
11.1b Output growth (four-quarter moving average). 278
11.2a Predictive distribution functions for inflation (benchmark model
with parameter uncertainty).
279
11.2b Predictive distribution functions for output growth (benchmark
model with parameter uncertainty).
279
11.3 Probability estimates of inflation falling within the target range
using the benchmark model.
281
11.4 Probability estimates of a recession using the benchmark model. 282
11.5 Probability estimates of meeting the inflation target without a
recession (future and parameter uncertainty).
284
11.6 Probability estimates of meeting the inflation target without a
recession (future uncertainty only).
285
12.1 Impulse response of a negative one standard error shock to US real
equity prices on real equity prices across regions.
296
12.2 Impulse response of a negative one standard error shock to US real
equity prices on real output across regions.
297
12.3 Monthly generalised impulse responses to a positive unit shock to
monetary policy.
301
12.4 Monthly generalised impulse responses to a positive unit shock to
the oil price.
302
xv

1
Introduction
Macroeconometric modelling is at the heart of decision-making by govern-
ments, industrial and ﬁnancial institutions. Models are used to organise
and describe our understanding of the workings of the national and global
economies, provide a common framework for communication, predict
future economic developments under alternative scenarios, and to evalu-
ate potential outcomes of policies and external events. This book aims to
contribute to this important literature by providing a detailed description
of the ‘long-run structural modelling approach’ applied to modelling of
national economies in a global context. The modelling approach builds on
recent developments in macroeconomic theory and in time series econo-
metrics, and provides a transparent framework for forecasting and policy
analysis. The book covers theoretical as well as practical considerations
involved in the model-building process, and gives an overview of the
econometric methods.
The modelling strategy is illustrated through a detailed application to
the UK economy. This application is intended to be of interest in its own
right, as well as providing a blueprint for long-run structural modelling
by potential users of the approach in other contexts. To this end, we also
provide the data and computer code employed in the UK modelling exer-
cise to illustrate the steps taken and to facilitate replication of the methods
and their application to other datasets. Hence, the book aims to provide
a description of the construction and use of the UK macroeconometric
model in sufﬁcient detail so that it will be of use to practitioners who
might wish to undertake a similar sort of exercise; users are persuaded
of the cohesion between the modelling activity and the end uses of the
model; and the policy analyses and forecasts that are presented are read-
ily interpretable and of direct use by decision-makers. We also describe
various extensions of the modelling exercise, including an explanation
1

Introduction
of how the modelling approach could be applied to develop a global
macroeconometric model, developed from scratch or accommodating the
UK model, and an explanation of how the UK model could be used to focus
on specific features of the national economy which might be of specific
interest to particular decision-makers.
In describing our modelling activities, we address directly the anxieties
of those who make use of macroeconomic models but who recognise also
the uncertainties and ambiguities involved in modelling and associated
forecasting. So, in explaining our strategy, we make an explicit distinction
between those elements of economic theory that we believe with some
degree of confidence (usually associated with the long-run properties of
the economy) and those elements for which economic theory is less clear-
cut (on the short-run dynamics arising out of the precise sequencing of
decisions, for example). We also compare our views on the working of the
macroeconomy with those of alternative modelling approaches, noting
the areas in which there is broad agreement and those in which there
is less consensus. We note too that, once we have estimated our model,
we can test formally the validity of hypotheses implied by our specific
economic theory. This discussion aims to place our modelling approach
in context, trying to reconcile it with the work of other macromodellers.
And it aims to reassure the reader that the modelling approach is securely
anchored to a firm and transparent theoretical base.
The distinction drawn between confidently held views and less confi-
dently held beliefs on the underlying economic theory also informs our
interpretation of the model and its dynamic properties. Hence, there are
some properties of the model which reflect the influence of the views
on the long-run relationships between variables implied by economic
theory. But other aspects of the dynamic properties of the model are
interpretable only if one has a particular view on the short-run processes
driving decision-making, and these views may be more contentious. By
explicitly drawing these distinctions, we are able to provide more reli-
able and informed predictions on the outcome of policies and on the
reactions of the macroeconomic variables of interest to external events
and to relate the model predictions directly to the underlying economic
theory.
Most importantly, when considering the use of models in forecasting,
we emphasise the needs of decision-makers and other end-users. For this
reason, we do not present our forecasts only in the form of point forecasts
with confidence intervals, as is usually the case, but provide tables and
graphs of ‘probability forecasts’. These measures refer to events considered
2

Historical Background
to be of interest to decision-makers (such as ‘recession’ or ‘low inflation’
at various forecast horizons, for example) and indicate the likelihood of
these events taking place according to the estimated model. The probabil-
ity forecasts convey the uncertainty surrounding the model’s forecasted
outcomes in a clear and transparent way.
1.1 Historical background
Macroeconometric modelling in the UK and elsewhere has undergone
a number of important changes over the past twenty or thirty years,
driven by developments in economic and econometric theory as well
as changing economic circumstances. One important impetus in this
process was Lucas’ (1976) critique of macroeconometric policy evalu-
ation, which resulted in widespread adoption of the rational expectations
methodology in macroeconomic models. It also provoked considerable
scepticism concerning the use of large-scale macroeconometric models
in policy analysis and initiated the emergence of a new generation of
econometric models explicitly based on dynamic intertemporal optimi-
sation decisions by firms and households. At the same time, Sims’ (1980)
critique raised serious doubts about the traditional, Cowles Commission
approach to identification of behavioural relations, which had been based
on what Sims termed ‘incredible’ restrictions on the short-run dynamics of
the model. This critique generated considerable interest in the use of vec-
tor autoregressive (VAR) models in macroeconometric analysis.1 A third
impetus for change in the way in which macroeconometric modelling has
been undertaken came from the increased attention paid to the treatment
of non-stationarity in macroeconomic variables. The classic study was that
by Nelson and Plosser (1982), who showed that the null hypothesis of a
unit root could not be rejected in a wide range of macroeconomic time
series in the US. This resurrected the spectre of spurious regression noted
originally by Yule (1926), Champernowne (1960), and more recently by
Granger and Newbold (1974). Subsequently, the work of Engle and Granger
(1987), Johansen (1991) and Phillips (1991) on cointegration showed pos-
sible ways of dealing with the spurious regression problem in the presence
of unit root variables, with important consequences for macroeconometric
modelling in particular.
1 Sims’ critique also extends to the identification of rational expectations models.
3

Introduction
1.2 Alternative modelling approaches
Different purposes require different models. A purely theoretical model
may be adequate for some purposes while, for other purposes, a purely stat-
istical description of the data may be adequate. However, in many cases,
we need to combine theoretical coherence with a good description of the
data. This synthesis has taken four main forms. First, there are large-scale
macroeconometric models such as the various vintages of HM Treasury’s
model of the UK economy and the Federal Reserve Board’s model of the US
economy. These models can contain hundreds of variables and equations
and are typically built on detailed sub-models of the various sectors of
the macroeconomy. The large-scale models have made many important
innovations over the years but, by their very nature and because of the
questions they are designed to address, they have evolved slowly. Hence,
they have essentially followed the tradition of the Cowles Commission,
making a distinction between exogenous and endogenous variables and
imposing restrictions, often on the short-run dynamic properties of the
model, in order to achieve identification. The parameters have been typ-
ically estimated by least squares or by instrumental variables methods,
and full information estimation of the model parameters has rarely been
attempted.
Secondly, following the methodology developed by Doan, Litterman
and Sims (1984), Litterman (1986), and Blanchard and Quah (1989),
there are unrestricted, Bayesian, and ‘structural’ vector autoregression
(VAR) specifications that are used extensively in the literature. VAR and
Bayesian VARs (BVAR) are primarily used for forecasting. The structural
VAR approach aims to provide the VAR framework with structural con-
tent through the imposition of restrictions on the covariance structure of
different types of shocks. The basis of the structural VAR analysis is the
distinction made between shocks with temporary (transient) effects from
those with permanent effects which are then related to economic theory in
a rather loose manner by viewing the two types of shocks as demand and
supply type shocks, for example. The approach does not attempt to model
the structure of the economy in the form of specific behavioural relation-
ships. Its application is also limited to relatively small models where the
distinction between the two types of shocks is sufficient to deliver identi-
fication. The particular application considered by Blanchard and Quah to
illustrate their approach, for example, is based on a bivariate VAR in real
output and the rate of unemployment.
4

Alternative Modelling Approaches
The third approach is closely associated with the Dynamic Stochastic
General Equilibrium (DSGE) methodology originally employed in the Real
Business Cycle literature. This approach developed following the seminal
work of Kydland and Prescott (1982) and Long and Plosser (1983), and pro-
vides an explicit intertemporal general equilibrium model of the economy
based on optimising decisions made by households and ﬁrms. Originally,
the emphasis of these models was on real factors (e.g. productivity shocks)
but more recently the ‘New Keynesian DSGE models’ have been developed
to allow for monetary policy rules, adjustment costs, heterogeneity, and
endogenous technological progress, for example, and also to accom-
modate nominal rigidities.2 In consequence, the differences between
the DSGE and the most recent incarnations of traditional macroecono-
metric models have become less pronounced. Also many of the DSGE
models can be approximated by restricted VAR models, which also renders
them more comparable with other modelling approaches.3
The fourth approach, and the one which we aim to promote in this book,
is the ‘structural cointegrating VAR’ approach. This approach is based on
the desire to develop a macroeconometric model that has transparent
theoretical foundations, providing insights on the behavioural relation-
ships that underlie the functioning of the macroeconomy. Implicit in the
modelling approach is the belief that economic theory is most inform-
ative about the long-run relationships, as compared to the short-run
restrictions that are more contentious. The approach allows testing of
the over-identifying restrictions on the long-run relations and provides
a statistically coherent framework for the analysis of the short run. At
the practical level, the approach is based on a log-linear VARX model,
where the familiar VAR model is augmented with weakly exogenous vari-
ables, such as oil prices, and country-speciﬁc foreign variables.4 On the
assumption that the individual macroeconomic series have a unit root,
each of the long-run relationships derived from theory is associated with
a cointegrating relationship between the variables, and the existence of
these cointegrating relationships imposes restrictions on a VAR model of
the variables. Hence, the approach provides an estimated structural model
of the macroeconomy, in which the only restrictions on the short-run
2 See Section 2.3 for details.
3 See, for example, Kim and Pagan (1995), and Christiano et al. (1998). New Keynesian
versions of the DSGE models have also been developed successfully by Smets and Wouters
(2003) and Christiano et al. (2005).
4 The econometrics of VARX models are described in detail in Chapter 6.
5

Introduction
dynamics of the model are those which are imposed through the decision
to limit attention to log-linear VARX models with a specified maximum
lag length.5 The work of King et al. (1991), Gali (1992), Mellander et al.
(1992) and Crowder et al. (1999) is in this vein, although our own work has
shown the flexibility of the approach, including the first attempts to use
the structural cointegrating VARX modelling approach to build national
and global macroeconometric models.6
It is worth noting at the outset that, while the approach that we advocate
emphasises the importance of long-run restrictions, it is entirely possi-
ble to investigate also the validity and implications of specific theories
on the short run while still following our modelling strategy. Of course,
this would require the imposition of further restrictions on the cointe-
grating VAR, but these additional short-run restrictions can be imposed
without reference to the restrictions imposed on the long run and have
no bearing on the influence of the long-run restrictions (or vice versa).
Indeed, there are many questions of interest that necessitate the use of
a macroeconometric model and which require the investigator to take a
view on the short-run behaviour of the macroeconomy; investigating the
effects of monetary policy, for example. This can be done and, indeed, we
shall devote some time in the book to the examination of monetary policy
using our estimated model for the UK.
1.3 The long-run modelling approach
The long-run structural modelling approach begins with an explicit state-
ment of a set of long-run relationships between the macroeconomic
variables of interest, derived from macroeconomic theory, including key
arbitrage and solvency conditions for example. These long-run relation-
ships are then embedded within an otherwise unrestricted VARX model,
augmented appropriately with country-specific foreign variables. The
VARX model is then estimated, using recently developed econometric
5 Hence, the approach cannot capture directly the possibility that some of the macroeco-
nomic relationships contain a moving average component or involve important asymmetries
in adjusting to shocks, for example. The impact of these influences on the dynamics of the
macroeconomy can only be approximated within the context of a non-linear dynamic model.
6 The work of these earlier papers is more limited in scope. The models of King et al. (1991),
Gali (1992) and Crowder et al. (1999) are closed economy models unsuitable for modelling a
small open economy such as the UK. The model of Mellander et al. (1992) attempts to capture
the open nature of the Swedish economy only by adding a terms of trade variable to the
consumption–investment–income model analysed by King et al. (1991).
6

The Long-run Modelling Approach
methods, to obtain an augmented cointegrating VAR model which incorp-
orates the structural long-run relationships. This direct procedure also
yields theory-consistent restrictions on the intercepts and/or the trend
coefficients in the VAR, which play an important role in testing for cointe-
gration and co-trending, as well as for testing restrictions on the long-run
relations.
The approach shares common features with many applications of coin-
tegration analysis. However, it is distinct because many applications of
cointegration analysis start with an unrestricted VAR and then (sometimes)
impose restrictions on the cointegrating relations, without a clear a priori
view of the economy’s structural relations. This latter more statistical
approach is likely to be applicable when there exists only one cointegrating
relationship among the variables in the VAR. When the number of coin-
tegrating relations are two or more, without a clear and comprehensive
theoretical understanding of the long-run relations of the macroecon-
omy, identification of the cointegrating relations and the appropriate
choice of intercepts/trends in the underlying VAR model will become a
very difficult, if not an impossible, undertaking. By beginning the analysis
with an explicit statement of the underlying macroeconomic theory, the
structural cointegrating VAR approach that we employ places the macro-
economic theory centre-stage in the development of the macroecono-
metric model.
The long-run structural approach has a number of other strengths in
undertaking national and global macroeconometric modelling too. Being
based on a cointegrating VAR with fully specified long-run properties, the
estimated model possesses a transparency which is frequently lost in larger
macromodels and our approach ensures that the resultant macromodel
has a long-run structural interpretation. Further, by clarifying the relation-
ship between economic theory and the short- and long-run restrictions of
our model, our approach makes clear the difficulties involved in inter-
preting the effects of shocks in general, and in the analysis of impulse
responses in particular. And our approach allows for a fairly general
dynamic specification, and avoids some of the difficulties involved in other
modelling approaches where a tight economic theory is used to impose
very rigid restrictions on the short-run dynamics at the expense of fit with
the data.7
The UK model that we present as the detailed illustration of our approach
focuses on five domestic variables whose developments are widely regarded
7 See, for example, Kim and Pagan’s (1995) discussion of some of the early DSGE models.
7

Introduction
as essential to a basic understanding of the behaviour of the UK macro-
economy; namely, output, prices, the nominal interest rate, the exchange
rate and real money balances. It also contains four foreign variables: for-
eign output, the foreign price level, the foreign interest rate, and oil prices.
The analysis gives a forum with which to illustrate further strengths of our
modelling approach, providing insights on the UK from at least three per-
spectives. First, the econometric methodology that has been developed
provides the means for testing formally the validity of restrictions implied
by specific long-run structural relations within a given macromodel. The
ability to test rigorously the validity of long-run restrictions implied by
economic theory within the context of a small and transparent, but reas-
onably comprehensive, model of the UK macroeconomy is an important
step towards an evaluation of the long-run underpinnings of alternative
macrotheories. As such we test and implement an approach standard in
theory but rare in practice. Second, our approach allows an investigation
of the short-run dynamic responses of the model to shocks, while ensur-
ing that the effects of the shocks on the long-run relations eventually
vanish. This provides an important insight into the dynamics of coin-
tegrating models where shocks have permanent effects on the levels of
individual variables in the model. The methods employed enable us to
undertake realistic policy evaluation exercises following one of two routes.
The first route imposes no restrictions on the short-run dynamics of the
model and investigates the model properties using ‘generalised impulse
response analysis’. This route avoids the strictures of Sims’ critique and pro-
vides insights on the macroeconomy’s dynamic responses which, unlike
the orthogonalised impulse responses, are invariant to the order of the
variables in the underlying VAR. The second route supplements the long-
run restrictions with additional restrictions based on theorising on the
short run. This route is susceptible to the criticisms of Sims and requires
strong assumptions to be made on issues which are not uncontentious.
But the route allows us to investigate the impact of very specific policy
innovations (e.g. monetary policy shocks) and other external events (e.g.
oil price innovations). And third, the relative simplicity of the cointegrat-
ing VAR model enables us to generate forecasts not just of the most likely
outcomes of our macroeconomic variables, but also to generate forecasts
of the likelihood of various events taking place and to investigate the
sources of uncertainty surrounding these forecast probabilities. Hence,
for example, we are able to evaluate the likelihood of the Bank of Eng-
land hitting its inflation target over the near or longer term, and whether
this is compatible with avoiding recession. Hence, our approach relates
8

The Organisation of the Book
the forecasts to the underlying properties of the macroeconomic model
and presents the forecasts in a way which is helpful to those agents for
whom the performance of the UK economy is an important influence on
decision-making.
1.4 The organisation of the book
The book can be considered to be in three parts. In the first part, con-
sisting of Chapters 2–7, we discuss the way in which economic theory
and econometric analysis can be brought together to construct a macro-
econometric model in which the long-run relationships are consistent
with economic theory and where the short-run dynamics have an interpre-
tation. The second part, consisting of Chapters 8–9, is devoted to the prac-
tical detail of estimating a long-run structural macroeconometric model,
illustrated by a detailed description of the estimation of a model of the
UK macroeconomy. And in the third part, consisting of Chapters 10–13,
we discuss the interpretation and use of long-run structural macroecono-
metric models, describing the uses of the illustrative UK model along with
extensions of the modelling activity to investigate global macroecono-
metric models and other specified issues in a national macroeconometric
context.
In more detail, Chapter 2 briefly describes some alternative approaches
to macroeconometric modelling, focusing primarily on their long-
run characteristics and the consensus that has developed surrounding
desirable long-run properties. Chapter 3 describes a framework for macro-
econometric modelling which draws out the links with economic the-
ory relating to the long run and with theory relating to the short
run. The chapter elaborates a modelling strategy that can be employed
to accommodate directly the theory of the long run and notes the
ways in which short-run theory can also be accommodated. It also
reviews the recent literature on modelling short-run dynamics, high-
lighting the difficulties in obtaining consensus on appropriate short-run
restrictions and commenting on the approaches taken in the literature
in examining policy shocks in general and monetary policy in partic-
ular. Chapter 4 describes a specific theoretical framework for macro-
economic modelling of a small open economy that can be embedded
within a macroeconometric model, noting the testable restrictions on
the long-run relations suggested by the theory. Complementing this,
Chapter 5 explores a set of identifying restrictions on the short-run
9

Introduction
dynamics that might be used to supplement the long-run restrictions if
the model is to be used to investigate the effect of economically mean-
ingful shocks. Chapter 6 then briefly reviews the econometric methods
needed for the empirical analysis of cointegrating VAR models, includ-
ing new material (on the conditions under which error correction models
are mean-reverting, for example) that are particularly useful in practical
macroeconometric modelling. Finally in this part, Chapter 7 provides
an introduction to the interpretation and estimation of probability fore-
casts which we consider to be a particularly useful method for presenting
forecasts.
The part of the book concerned with the practical construction of the
illustrative model of the UK economy begins with Chapter 8, which
provides an overview of the data. Chapter 9 describes the empirical
work underlying the construction of the UK model, discusses the results
obtained from testing its long-run properties, and compares the model
with benchmark univariate models of the variables. This description of
the modelling work not only provides one of the first examples of the use
of these cointegrating VAR techniques in an applied context, but it also
includes a discussion of bootstrap experiments designed to investigate the
small sample properties of the tests employed.
The final part of the book is concerned with the use of long-run structural
macroeconometric models. It begins with Chapter 10, which discusses
the dynamic properties of the estimated model. Chapter 11 is concerned
with forecasting and prediction based on the model. Here we elaborate
the notion of probability forecasting, which provides a useful means
of conveying the uncertainties surrounding forecasts obtained from the
model, and illustrate the usefulness of probability forecasts with refer-
ence to the Bank of England’s inflation targets and the UK’s growth
prospects. Chapter 12 describes some recent extensions of the model
and some other applications, including an introduction to the develop-
ment of a model of the global macroeconomy using the same modelling
approach.
Finally, in the appendices, we provide an account of the construction
and sources of the data plus instructions on how to replicate the results
presented in the empirical sections of the book. Much of the modelling
work described in the book can be undertaken using Pesaran and Pesaran’s
(1997) econometric package Microfit. But for those who prefer to work with
a programmable language, to adapt some of the procedures for example,
we provide in the appendices also a simple manual for the use of a set of
10

The Organisation of the Book
computer programs written in Gauss that can be used to replicate or extend
the analysis of the book too. The data and code are available through the
authors’ webpages. It is worth noting that the use of the programs, as
described in the manual, is relatively straightforward to follow, although
the user will need some familiarity with Gauss to implement them.
11

2
Macroeconometric modelling:
Alternative approaches
This chapter provides an overview of the main approaches to macro-
econometric modelling, focusing in particular on the implications of the
different approaches for modelling the long run. We discuss the ‘struc-
tural cointegrating VAR’ approach to macroeconometric modelling in
general terms and compare it to other approaches currently followed
in the literature; namely, the large-scale simultaneous equation macro-
econometric models, structural VARs, and the dynamic stochastic general
equilibrium (DSGE) models. The primary purpose of the review is to ascer-
tain the extent to which there is a consensus on the desired long-run
properties of a macroeconometric model and to compare the effective-
ness of the different approaches to macroeconomic modelling in their
attempts to test and incorporate these long-run properties into models in
practice.
2.1 Large-scale simultaneous equation models
Large-scale simultaneous equation macroeconometric models (SEMs) have
a long history and can be traced back to Tinbergen and Klein and the sub-
sequent developments at the Cowles Commission. Prominent examples
of large-scale models include the ﬁrst and second generation models
developed at the Federal Reserve Board (see, for example, Ando and
Modigliani, 1969, Brayton and Mauskopf, 1985, and Brayton and Tinsley,
1996), Fair’s (1994) model of the US economy, Murphy’s (1988, 1992)
model for Australia, and the various vintages of models constructed for
the UK at the London Business School (LBS), the National Institute of
13

Macroeconometric Modelling
Economic and Social Research (NIESR), HM Treasury (HMT), and the Bank
of England (BE).1
The relatively poor forecasting performance of the large-scale models in
the face of the stagflation of the 1970s, in conjunction with the advent of
rational expectations and the critiques of Lucas (1976) on policy evalu-
ation and Sims (1980) on identification, brought about a number of
important changes in the development and the use of large-scale SEMs
throughout the 1980s and subsequently. Important developments have
taken place in three major areas.2 First, in response to Sims’ criticism
of the use of ‘incredible’ identifying restrictions involving short-run
dynamics, and under the influence of developments in cointegration
analysis (e.g. Engle and Granger, 1987), a consensus has formed that
the important aspect of a structural model is its long-run relationships,
which must be identified without having to restrict the model’s short-run
dynamics. Second, in response to the criticism that large-scale models paid
insufficient attention to the micro-foundations of the underlying rela-
tionships and the properties of the macroeconomic system considered
as a whole, there is now a greater use made of economic theory in the
specification of large-scale models. And third, in response to the criticisms
of Lucas, considerable work has been undertaken to incorporate rational
expectations (RE), or strictly speaking model consistent expectations, into
large-scale macromodels.
Under the influence of these developments, more recent generations
of large-scale models have shared a number of important features. Almost
invariably, the models have comprised of three basic building blocks: equi-
librium conditions, expectations formation, and dynamic adjustments.
The equilibrium conditions have been typically derived from the steady
state properties of a Walrasian general equilibrium model, and there
seems to be clear evidence of a developing consensus on what consti-
tutes the appropriate general equilibrium model for characterising the
long-run relations built around utility maximising households and profit-
maximising firms facing appropriate budget and technology constraints.
1 Bodkin et al. (1991) provide a comprehensive survey of the history of macroeconometric
model building. The evolution and the development of macroeconometric modelling at the
Federal Reserve Board is reviewed by Brayton et al. (1997). For the UK these developments were
documented in a series of volumes produced by the ESRC Macroeconomic Modelling Bureau
(see, for example, Wallis et al. 1987). Further reviews of the modelling in the UK and elsewhere
can be found in Smith (1994), Wallis (1995) and Hall (1995).
2 A detailed discussion of these developments in the case of the UK practice can be found
in Hall (1995). Similar arguments have also been advanced by Brayton et al. (1997) in the case
of the US experience.
14

Large-scale Simultaneous Equation Models
This consensus side-steps the Sims critique by focusing on the long run
and remaining agnostic on short-run dynamics.
Despite the progress made, and the growing consensus on what con-
stitutes best practice in macroeconometric modelling, large-scale models
have continued to be viewed with some scepticism by some, particularly in
the area of policy analysis.3 The complexity of the interactions of different
parts of a large dynamic model means that the accumulated response of
the macroeconomy to a particular shock or change in a given exogenous
variable can be difficult to interpret, particularly as far as their effects on
the long-run relations are concerned.4 It is also difficult to identify and
correct for misspecification in large-scale models, as attempts to fix one
part of the model can have far reaching (and often unpredictable) con-
sequences for the properties of the overall model.5 Furthermore, as far as
estimation is concerned, full information methods are often not an option
given the size of the models. With these difficulties in mind, it has been
argued that it is simply not possible for large-scale models to follow a best
practice approach because of their size and complexity.
These difficulties are particularly apparent in the modelling exercises
undertaken to consider global interactions. One of the first attempts at
global linkages was Larry Klein’s Project Link adopted by the United
Nations which linked up traditional large-scale macroeconometric mod-
els developed originally for national economies. Other examples include
the IMF’s MULTIMOD multi-regional model (Laxton et al. (1998)) and
the National Institute’s Global Econometric Model (NiGEM) which estim-
ates/calibrates a common model structure across OECD countries, China
and a number of regional blocks and the IMF’s MULTIMOD. The
country/region-specific models in NiGEM are still large, each comprised
of 60–90 equations with 30 key behavioural relationships.6 These contri-
butions provide significant insights into the interlinkages that exist among
the major world economies and have proved invaluable in global forecast-
ing. However, there are important weaknesses in the models. For example,
3 See, for example, Whitley (1997).
4 Innovative methods for characterising and summarising SEM’s short-run and long-run
properties have been developed to address this problem, however, primarily through stoch-
astic simulation methods. See, for example, Wallis et al. (1987), Turner (1991) and Wallis and
Whitley (1987). Methods for the analysis of the long-run properties of large macroeconometric
models have also been developed by Murphy (1992), Fisher et al. (1992), and Wren-Lewis et al.
(1996).
5 See, for example, the empirical exercise of Fisher et al. (1992) relating to the current account
balance reaction to nominal exchange rate changes in the models developed by NIESR, LBS,
BE and HMT at that time.
6 For a recent detailed account, see Barrell et al. (2001).
15

as argued in Pesaran, Schuermann and Weiner (2004), these models do not
typically address the financial linkages that exist among the world’s major
economies. Moreover, they can be rather cumbersome to use in practice
and the interlinkages of the different relations in different country models
are often difficult to interpret.7
To summarise, while important progress has been made in the construc-
tion and use of large-scale SEMs, it is still often argued that these models are
subject to a number of limitations that arise primarily from their large and
complex structure. As Brayton et al. (1997) conclude: ‘Large-scale macro-
models are by their nature slow to evolve.’ Simultaneous estimation and
evaluation of such models is currently computationally prohibitive and,
given the available time series data, may not be even feasible. A full inte-
gration of theory and measurement has proved elusive to large-scale model
builders. Despite the imaginative attempts made over the past two decades,
it remains a formidable undertaking to construct a theory-consistent large-
scale macroeconometric model which has transparent long-run properties
and fits the data well.
2.2 Unrestricted and structural VARs
2.2.1 Unrestricted VARs
The unrestricted VAR approach introduced into macroeconometrics by
Sims (1980) stands at the other extreme to large-scale models. It focuses
on modelling a relatively small set of core macroeconomic variables using
a VAR specification with particular emphasis on the statistical fit of the
model to the data possibly at the expense of theoretical consistency, both
from a short-run and a long-run perspective. Sims’ objective was to invest-
igate the dynamic response of the system to shocks (through impulse
response functions) without having to rely on ‘incredible’ identifying
restrictions, or potentially controversial restrictions from economic the-
ory. This strategy eschews the need to impose long-run relationships on
the model’s variables, and relies exclusively on time series observations to
identify such relationships if they happen to exist.
According to the Wold decomposition theorem, all covariance station-
ary processes can be written as the sum of a deterministic (perfectly pre-
dictable) component and a stationary process possessing an infinite order
7 The global VAR model of Pesaran, Schuermann and Weiner (2004) adopts the structural
cointegrating VAR approach to developing a model to analyse global financial and real inter-
actions. As explained in Section 3.4 and illustrated in Section 12.2, this analysis provides the
modelling outcome with considerably more transparency.
16

Unrestricted and Structural VARs
moving average (MA) representation.8 Restricting attention to ‘invertible’
processes,9 one obtains a unique MA representation, also known as the
‘fundamental’ representation which fully characterises the sample auto-
correlation coefficients. Such a fundamental representation can be approx-
imated by a finite order vector autoregressive moving average (VARMA)
process. However, estimation of VARMA models poses important estima-
tion problems, particularly when the number of variables in the VARMA
model is relatively large. For this reason, Sims chooses to work with a finite
order VAR model which is much simpler to estimate, but involves further
approximations. To perform impulse response analysis, Sims’ approach
then requires the use of a Choleski decomposition of the variance covari-
ance matrix of the model’s innovations/shocks. This enables the MA
representation to be written in terms of orthogonalised innovations. It is
the responses of the macroeconomic variables to these orthogonalised
shocks that are described in Sims’ orthogonalised impulse responses.
This approach to modelling has been subject to a number of criticisms
(see, for example, Pagan, 1987), some of which are worth noting here.
First, the approach requires care in the initial stages in the choice of trans-
formation of the data to achieve stationarity. In particular, it is important
that economically meaningful, and statistically significant, relations are
not excluded from the analysis at this stage by the choice of transforma-
tion. For example, a VAR model in the first differences of I(1) variables is
mis-specified if there exists a cointegrating relationship between two or
more of the I(1) variables. Second, care is needed in the choice of vari-
ables to be included in the VAR analysis, and it is difficult to imagine
how this choice could be made without reference to some underlying eco-
nomic theory. And third, since the choice of the Choleski decomposition
is not unique, there are a number of alternative sets of orthogonalised
impulse responses which can be obtained from any estimated VAR model.
A particular choice of orthogonalisation might be suggested by economic
theory, and Sims’ original approach to choosing an orthogonalisation was
to impose a causal ordering on the variables in the VAR. However, such a
causal ordering can be difficult to justify in practice. In the absence of a
generally accepted casual ordering, the orthogonalised impulse responses
are difficult to interpret economically.
8 See, for example, pages 108–109 of Hamilton (1994).
9 Limiting attention to the fundamental Wold representation is not uncontentious. As
shown in Hansen and Sargent (1991), for example, the MA representation that underlies the
VAR model can be non-fundamental (in the sense that one or more of the roots of the MA
process fall inside the unit circle) and at the same time be economically meaningful.
17

Due to their flexibility and ease of use, VAR models are used extensively
in forecasting and as benchmarks for evaluation of large-scale and DSGE
models. In order to mitigate the curse of dimensionality and the large
number of parameters typically estimated in VAR models, Doan, Litterman
and Sims (1984) have also proposed Bayesian VARs (BVARs) which com-
bine unrestricted VARs with Bayesian, or what has come to be known
as ‘Minnesota’ priors. Other types of priors have also been considered in
the literature; DeJong et al. (1993), for example, combine a VAR(1) model
with prior probabilities on its parameters derived from a RBC model. This
approach represents a coherent attempt to take advantage of the empir-
ical simplicity of the VAR approach while at the same time making use
of economic theory and, as discussed later in this chapter, is an approach
which has been taken up recently in the context of Dynamic Stochastic
General Equilibrium modelling. See also Section 2.3 on the use of Bayesian
techniques in DSGE models.
2.2.2 Structural VARs
The structural VAR approach builds on Sims’ approach but attempts to
identify the impulse responses by imposing a priori restrictions on the
covariance matrix of the structural errors and/or on long-run impulse
responses themselves. This approach is developed by Bernanke (1986),
Blanchard and Watson (1986) and Sims (1986) who considered a priori
restrictions on contemporaneous effects of shocks, and subsequently by
Blanchard and Quah (1989), Clarida and Gali (1994) and Astley and Garratt
(1996) who use restrictions on the long-run impact of shocks to iden-
tify the impulse responses. In contrast to the unrestricted VAR approach,
structural VARs explicitly attempt to provide some economic rationale
behind the covariance restrictions used, and thus aim to avoid the use of
arbitrary or implicit identifying restrictions associated with orthogonalised
impulse responses. However, while the use of ‘theory based’ covariance
restrictions in small systems allow the impulse responses to be identified
under the structural VAR approach, such restrictions still do not enable
identification of the long-run relationships among the variables. Further-
more, even the covariance restrictions are not always easy to interpret or
motivate from an economic perspective, particularly in the case of VAR
models with three or more variables. So, as explained in detail in the fol-
lowing chapters, the number of exactly identifying covariance restrictions
required increases rapidly with the number of variables in the VAR. In
a system involving m variables and a set of m orthogonalised structural
18

DSGE Models
shocks, the required number of such restrictions is equal to m(m − 1)/2.
For example, in the case of the core model of the UK presented in this
book, which includes nine endogenous variables, the number of covari-
ance restrictions required to exactly identify the impulse responses will be
36, even if the covariance of the structural shocks is assumed to be diag-
onal. It is not clear how so many restrictions could be identified within
the structural VAR framework, let alone motivated from an appropriate
economic theory perspective.
There are also inherent difficulties with the interpretation that are given
to the impulse responses obtained under the structural VAR approach.
For example, in Blanchard and Quah (1989), a bivariate VAR model of
unemployment and output growth is investigated by first solving the two
variables in terms of two orthogonalised white-noise shocks, and then
estimating impulse responses under the identifying assumption that one
of the shocks has no long-run effects on output levels. They then refer to
this shock as the ‘demand shock’, and refer to the other shock as the ‘supply
shock’.10 However, while it might be an interesting exercise to consider the
effects on output and unemployment of the two different types of shock,
and while it might be possible to elaborate a model of the macroecon-
omy in which demand shocks have the property assumed by Blanchard
and Quah, there seems little rationale in referring to these innovations as
‘demand’ and ‘supply’ shocks in the context of the purely statistical model
used by these authors. The different types of shock considered in this ana-
lysis are defined with reference to their statistical properties (i.e. whether or
not they have a permanent effect on output levels) and not with reference
to a model of how consumers and producers behave in a macroeconomy.11
Also, in the context of VAR models with three or more variables, the pos-
sibility of more than one permanent or transitory shock poses a further
identification problem since many combinations of stationary shocks will
themselves be stationary. For further details see Section 3.2.5.
2.3 Dynamic stochastic general equilibrium models
Unrestricted VARs and the Structural VARs make minimal use of economic
theory, while the use of theory in large-scale models is typically modular,
10 Recall that since m = 2, only one covariance restriction is needed to identify the
impulse responses.
11 For a more detailed critical evaluation of the structural VAR approach see Levtchenkova
et al. (1998).
19

in the sense that the theory is used in a coherent manner only in specific
modules or parts of the model. In contrast, the DSGE models develop a
general equilibrium approach to modelling using stochastic intertemporal
optimisation techniques applied to decision problems of representative
households and firms.12
The DSGE model is expressed in terms of ‘deep’ structural parameters,
such as the parameters that enter the preferences, production technolo-
gies and the probability distributions of taste and technology shocks.
In practice, very simple forms are chosen for these functions (power
utility function and Cobb–Douglas production functions, for example).
Nevertheless, the resultant optimal decision rules are complicated func-
tions of the macroeconomic variables. These are generally approximated
around the deterministic steady-state values of the macroeconomic vari-
ables to provide a log-linear system of rational expectations (RE) equations
with backward and forward components. The RE solution of this system
is obtained assuming certain transversality conditions hold (thus ruling
out bubble effects), the DSGE model provides the correct characterisa-
tion of economy, the representative agent paradigm is acceptable, and that
the underlying processes remain stable into the infinite future. The latter
assumption is made implicitly (although rarely acknowledged) in order to
derive the expected present value of the discounted future variables that
enter the RE solution. Under these assumptions the RE solution can be
written as a VAR (or a VARX in the case of open economies) model subject
to cross-equation parametric restrictions.13
The proponents of the DSGE approach to macroeconomic modelling
argue that this approach takes macroeconomic theory seriously in a way
that the large-scale SEMs do not. In particular, it is argued that the use of a
general equilibrium framework ensures that the DSGE models display stock
equilibria, rather than the flow equilibria which are characteristic of the
traditional approach to macroeconometric models. The derivation of the
model’s relationships as solutions to intertemporal optimisation problems
of households and firms ensures that the model has an internal consist-
ency and a relationship with economic theory that is lost in traditional
large-scale models. However, we have already noted that the proponents
12 For a survey of early developments in the literature on DSGE models, see the contributions
in the volume edited by Cooley (1995), while discussion of the more recent ‘New Keynesian’
DSGE models is given in Smets and Wouters (2003) and Christiano et al. (2005).
13 A specific illustration of this procedure is given in Chapter 3 below. See also, for example,
Binder and Pesaran (1995), Kim and Pagan (1995), Wickens (1995), and Pesaran and Smith
(2005) in the case of open economy DSGE models within a global context.
20

DSGE Models
of large-scale models have made considerable progress in relating the
structure of their models to economic theory, particularly in relation to
the long-run properties of the model. Indeed, we noted that there has
developed a consensus on the appropriate theory for the characterisation
of the long run, based on Walrasian general equilibrium theory, which
has been adopted (at least in part) in many of the current generation of
large-scale models. In this respect, therefore, the differences in the theo-
retical underpinnings of the DSGE models and the large-scale models are
less polarised than is sometimes argued.
However, there are important differences between the two approaches
both in content and in emphasis. In particular, they differ significantly
in their treatment of short-run dynamics. The DSGE models not only pro-
vide the form of relationships between economic variables that exist in the
long run, but also provide an explicit statement of the dynamic evolution
of the macroeconomy in response to shocks. It is argued (for example, in
Plosser, 1989) that the foundations of typical Keynesian models are static
in nature, and that the dynamics are introduced arbitrarily through accel-
erator mechanisms for investment and inventory behaviour, or through
arbitrary nominal rigidities in wage and price setting, or through par-
tial adjustment mechanisms in various forms, for example. The lack of
cohesion in the derivation of the long-run and dynamic properties in
the large-scale models represents a fundamental shortcoming of the large-
scale SEMs, according to this argument, encouraging the view that the
long-run evolution of the macroeconomy can be considered indepen-
dently of short- and medium-term fluctuations. In contrast, there are no
dichotomies between the determinants of long-run growth and short-run
fluctuations in DGSE models (though the long run is often not modelled
explicitly in its entirety in DSGE models either and actual data are often
(arbitrarily) filtered before they are analysed).
In fact, one can distinguish two phases in the development of the DSGE
models which have separate implications for modelling macrodynamics.
In the first phase, one of the primary motivating ambitions behind the
DSGE models was to establish that the dynamic responses of the macro-
economy are consistent with a model in which there are no market failures,
the predicted outcomes are Pareto optimal, and intervention by a social
planner to force agents to change their actions will be welfare reducing.
The ‘real business cycle’ agenda that lay behind the first phase of the devel-
opment of the DSGE approach to modelling therefore played down the
potential role of monetary policy in generating economic fluctuations and
instead placed considerable emphasis on real shocks. Indeed, many of the
21

calibration exercises undertaken in the first phase of the DSGE literature
ignored the monetary sector altogether.
It was quickly recognised that this first phase of models required some
refinement if it was to provide a satisfactory understanding of economic
fluctuations. The first generation of DSGE models were therefore extended
to incorporate features such as adjustment costs (e.g. Kydland and Prescott,
1982, Christiano and Eichenbaum, 1992a, and Cogley and Nason, 1995);
signal extraction and learning (e.g. Kydland and Prescott, 1982, and Cooley
and Hansen, 1995); aggregation (e.g. Christiano, Eichenbaum and Mar-
shall, 1991 on temporal aggregation and Cooley et al. 1997 and Ríos-Rull,
1995 on cross-sectional aggregation); endogenous technological progress
(e.g. Stadler, 1990 and Hercowitz and Sampson, 1991) and information
heterogeneities (e.g. Kasa, 2000). However, it remained unclear whether a
model could be developed that would be capable of simultaneously deal-
ing with all of these factors in a satisfactory manner and, even if it could,
whether it would be any more transparent or easy to interpret than the
available stock of large-scale models. Moreover, by limiting attention to
particular sources of dynamics, the first-phase models following the DSGE
approach were likely to be too restrictive. In fact, as it turned out, when
the models were confronted with the data, in Litterman and Weiss (1985),
King et al. (1991), Christiano and Eichenbaum (1992b) or Kim and Pagan
(1995), for example, the evidence suggested that this was indeed the case.
The second phase in the development of DSGE models returned to
the simpler basic characteristics of the earliest DSGE models, emphasis-
ing the micro-foundations of macroeconomic fluctuations, but explicitly
incorporating nominal frictions and paying more attention to monetary
factors influencing business cycles. There were early attempts to incor-
porate money in DSGE models (see, for example, Cooley and Hansen,
1989, 1995), but there is now a considerable literature elaborating ‘New
Keynesian DSGE models’, which have price and wage rigidities at their
core and which are designed to consider the impact of monetary policy
(see Clarida et al. (1999) for a review). A simple New Keynesian DSGE model
consists of an ‘IS curve’ relating output to the expected real interest rate, a
Phillips curve relating inflation to expected inflation and output (measured
as deviations from its trend), and a policy rule relating the nominal inter-
est rate to output and inflation. The IS curve is motivated with reference
to optimising behaviour on the part of households, the Phillips curve is
based on profit-maximising pricing behaviour on the part of monopolisti-
cally competitive firms, and the policy rule is based on a policy-maker that
optimises an objective function describing welfare in terms of inflation
22

The Structural Cointegrating VAR Approach
and output.14 As in all DSGE models, the decisions made by households,
firms and the policy-maker are interrelated and intertemporal, generating
explicit dynamic structures. But this class of models also pays particular
attention to the rigidities that exist in price setting, frequently incorporat-
ing ‘Calvo (1983) contracts’, in which prices are reset only periodically and
with a fixed probability, to motivate both backward- and forward-looking
effects in the Phillips curve, for example. These modelling assumptions
have important implications for the dynamic properties of the DSGE
models, their ability to fit the data and their implications for monetary
policy analysis. Indeed, recent modelling exercises by Gali and Gertler
(1999), Clarida et al. (2000), Smets and Wouters (2003), Favero and Rov-
elli (2003), Del Negro and Schorfheide (2004), Del Negro et al. (2005)
and Christiano et al. (2005), among others, indicate that these second-
generation DSGE models are able to introduce more flexible dynamics,
often with the help of Bayesian estimation techniques, and can perform
relatively well in explaining various episodes of historical macroexperience
and in forecasting.
2.4 The structural cointegrating VAR approach
The structural cointegrating VAR modelling strategy is described in detail
in Section 3.1.3 of the next chapter. But, stated briefly, the strategy begins
with an explicit statement of the long-run relationships between the
variables of the model obtained from macroeconomic theory. These rela-
tionships will typically be based on stock-flow and accounting identities,
arbitrage (equilibrium) conditions, and long-run solvency requirements
that ensure stationary asset–income ratios. The long-run relationships are
approximated by log-linear equations, with disturbances that characterise
the deviations of the long-run relations from their realised, short-run
counterparts. These deviations are referred to as the ‘long-run structural
shocks’. Not all of the variables contained in the long-run relationships
suggested by economic theory are observable, however, and in writing the
long-run relationships in terms of observable variables, ‘long-run reduced
form shocks’ are derived as functions of the long-run structural shocks.
The long-run, or error correcting, relations are then embedded within
an otherwise unrestricted log-linear VAR model of a given order in the
14 For an open economy version of the New Keynesian DSGE model see, for example, Gali
and Monacelli (2005).
23

variables of interest to obtain a cointegrating VAR model which incorpo-
rates the structural long-run relationships as its steady-state solution. This
allows testing for the presence of the cointegrating relations and the over-
identifying restrictions implied by the long-run economic theory. In this
way, the cointegrating VAR model will embody the long-run theory restric-
tions in a transparent, and an empirically consistent, manner. The theory
also imposes restrictions on the intercepts and/or the trend coefficients in
the VAR, which play an important role in testing for cointegration as well
as co-trending, often ignored in other approaches to macroeconometric
modelling.15
2.4.1 Comparisons with the alternative approaches
COMPARISON WITH LARGE-SCALE SEMS
As the discussion above makes clear, the structural cointegrating VAR
approach to macroeconometric modelling begins by describing the rela-
tionships which define the long-run structure of the macroeconomy, and
embeds these long-run relationships within an otherwise unrestricted VAR
model of the macroeconomy. The number of variables chosen to include in
the core model is selected to ensure that the system can be estimated simul-
taneously, taking into account all of the potential feedbacks between the
variables captured by the short-run dynamics and suggested by the long-
run economic relationships. One of the primary strengths of this approach,
therefore, is that the model is developed and estimated in a way that
ensures that the long-run relations of the estimated model are data consist-
ent and theoretically coherent. Furthermore, this is accomplished without
compromising short-run empirical adequacy as an important criteria by
which models in the final analysis must be judged. The transparency of the
model’s long-run properties would also be important for impulse response
analysis and forecasting, particularly over the medium term.
Despite its advantages, the cointegrating VAR model is still highly
restrictive and, given the available time series data, it can deal with at most
8–10 variables simultaneously. This clearly precludes addressing many
important issues if we were to confine our analysis to a single cointegrating
VAR model. Macroeconometric models are used for many different pur-
poses by government, academic and corporate institutions, and no one
15 See Chapter 6 for a discussion of the relevant econometric issues involved in the analysis
of cointegrating VARs.
24

model will be appropriate for all of these uses (see Whitley, 1997). How-
ever, traditional macroeconometric models tend to become large often in
response to demands for more disaggregated analysis, and for addressing a
wider range of policy questions. For example, a central bank may require a
detailed model of the monetary sector, corporate institutions might require
forecasts and analysis disaggregated by the main industrial sectors (energy,
construction, agriculture, transportation, etc.), and government agencies
might be required to investigate the effects of a given policy on particu-
lar interest groups and/or markets. As will be discussed in more detail in
Chapter 3 below, our approach to meeting these model-specific require-
ments is through the development of appropriate satellite models. These
are constructed using similar econometric techniques to those employed
in the estimation of the core model, and are then linked up to the core
model, with the core variables (and the associated error correction terms
from the core model) influencing sectoral developments, but not vice versa
(see Pesaran and Ron Smith, 1997). The distinction between the core and
satellite models is made possible by allowing the error correction terms
of the core model to enter the relationships of the satellite models but
not vice versa. This enables consistent estimation of the satellite model
by treating the variables of the core model as weakly exogenous. Exam-
ples of satellite models include models of the labour market, households’
portfolio and expenditure decisions, foreign trade and fiscal policy.16
COMPARISON WITH UNRESTRICTED AND STRUCTURAL
VAR MODELLING
Unrestricted and restricted VAR modelling places great emphasis on char-
acterising the dynamic behaviour of variables and makes considerable use
of impulse response analysis as a means of illustrating the timing of the
reactions of various variables to different types of structural shock. The
identification of the structural shocks, using the reduced form shocks
obtained from the estimated VAR models, requires a well-defined eco-
nomic theory of the short run, concerned with the sequencing of decisions
and information available to different economic agents and with the
various rigidities arising in decision-making. This emphasis on identify-
ing the effects of specific economic shocks and the associated short-run
dynamics contrasts with that of the structural cointegrating VAR approach.
16 An illustration of how a satellite model of the household sector might be coupled with
the core macroeconomic model is described in Chapter 12.
25

The structural cointegrating VAR approach to modelling emphasises the
long-run relationships that exist between variables. This is based on the
view that economic theory is typically more informative on these long-run
relationships than it is on the short-run dynamics, noting that theory is fre-
quently silent on the sequencing of decisions, the structure of information
sets across agents, and the nature of rigidities that arise from transac-
tions costs. The structural cointegrating VAR approach describes explicitly
the nature of the ‘long-run structural errors’ that arise from a specific
economic theory and that characterise deviations from long-run relation-
ships. It also clarifies the links between these long-run structural errors
and the ‘long-run reduced form errors’ that can be related to the data
at hand.
If it is the case that economic theory is insufficiently well-defined
to provide credible identifying restrictions on the short-run behaviour
of economic agents, then a more general method of analysing impulse
responses is required; that is, one that allows an examination of the short-
run dynamic interrelations of the model without needing to identify the
nature of the shocks. The current literature on impulse response analysis
focuses on the effects of identified shocks are often difficult to accom-
plish in a satisfactory manner, particularly in the case of VAR models with
8–10 variables often encountered in the analysis of small open economies.
The source of the difficulty lies in the unobservable nature of the shocks
of interest such as monetary policy shocks, say, or demand and supply
shocks. An alternative, less ambitious approach is to consider the impulse
response functions associated with unit shifts in observable variables, such
as output, interest rates and inflation. Clearly, a unit shock to the inter-
est rate variable need not be the same as a monetary policy shock, since
many different internal and external factors could influence interest rates.
But the impulse response associated with a unit (one standard error) shift
in interest rates would be informative about the dynamic properties of
the model as well as being relevant to private sector decisions that are
concerned with the consequences of a rate rise rather than the precise rea-
sons behind its occurrence. The Generalised Impulse Response Function
(GIRF), introduced in Koop et al. (1996) and developed in Pesaran and
Shin (1998), provides such a method. Unlike the more familiar orthogo-
nalised IR functions, the GIRFs are invariant to the ordering of the variables
included in the VAR and provide an empirically coherent solution to the
analysis of impulse responses so long as the shocks under consideration
relate to observed variables. For example the GIRFs can be used to com-
pute the time profile of the effects of a shock to oil prices, output or
26

interest rate without any ambiguities. In many applications, such as the
analysis of market interactions or the sensitivity of market or credit risks to
changes in the market environment, the GIRFs are sufficient. The effects
of system-wide shocks on the variables of the VAR or on the cointegrating
relations can also be analysed using the persistence profile methodol-
ogy advanced in Pesaran and Shin (1996). This type of analysis is also
invariant to the ordering of the variables in the VAR and does not require
economic identification of the shocks. The identification problem arises
when it is further required to decompose the effects of the shocks to the
observed variables into unobserved theoretical concepts such as supply,
demand, or monetary policy shocks. In such cases, as we shall demonstrate
in Chapter 10, the GIRF approach need to be combined with additional
a priori restrictions from economic theory, preferably within a decision
context.17
It is worth emphasising that the structural cointegrating VAR approach
to modelling is not incompatible with the identification of economically
meaningful shocks to the macroeconomy and the application of more
standard impulse response analysis. Rather, this is a question of emphasis.
The structural cointegrating VAR approach implies that the structural rela-
tionships that are suggested by theory for the short run are less robust
and can be held with less confidence. But it is perfectly possible to elab-
orate an economic theory which motivates both short-run and long-run
restrictions and the structural cointegrating VAR approach would remain
valid (supplemented with the additional restrictions suggested on the short
run). These issues are discussed in detail in Chapter 3 below, which con-
centrates on the identification issues associated with short-run structures,
and in Chapter 5, where a specific model of short-run decision-making
is elaborated to illustrate the issues involved in showing how monetary
policy shocks can be identified without having to identify other types of
shocks that might also impinge on the macroeconomy.
COMPARISON WITH DSGE MODELLING
In DSGE modelling, the derivation of the long-run, steady-state relations of
the macromodel starts with the intertemporal optimisation problems faced
by households and firms and then solves for the long-run relations using
the Euler first-order conditions and the stock-flow constraints. Given the
invariably non-linear nature of the Euler equations and the linear forms
17 The econometric issues involved in GIR analysis are discussed in Chapter 6 and their
application to the core model of the UK economy is described in Chapter 10.
27

of the constraints, the resultant relations of the model economy are usu-
ally approximated by log-linear relations (the real business cycle literature
and the New Keynesian DSGE literature follow this methodology). The
long-run relations are then obtained by assuming that the model econ-
omy is stationary and ergodic in certain variables, such as growth rates,
capital per effective worker and asset–income ratios, and typically ignoring
expectational errors. The structural cointegrating VAR approach, on the
other hand, works directly with the arbitrage conditions which provide
intertemporal links between prices and asset returns in the economy as a
whole. The arbitrage conditions, however, must be appropriately modified
to allow for the risks associated with market uncertainties.
Clearly, the above two approaches are closely related and yield similar
results as far as the long-run relations are concerned. The main difference
between the two approaches lies in the empirical validation of the long-
run relations and their treatment of short-run dynamics. The strength of
the intertemporal optimisation approach lies in the explicit identification
of macroeconomic disturbances as shocks to tastes, to technology, to pol-
icy, and so on, rendered possible by the explicit statement on the form of
the short-run dynamics. However, this is achieved at the expense of often
strong assumptions concerning the form of the underlying utility and
cost functions, expectations formation process and the related assump-
tion that the DSGE model remains stable into the indefinite future, and
the process of technological change. In contrast, the cointegrating VAR
approach advanced in this work is silent on short-run dynamics, but is in
line with the DSGE model as far as the long-run relations are concerned.
Our approach also has the added advantage that particular long-run rela-
tions are considered only when adequately supported by the evidence. We
test the validity of the long-run relations rather simply imposing them on
a priori grounds.
Both the DSGE modelling approach and the structural cointegrating VAR
approach represent attempts to combine theory and evidence to obtain
models that will be useful for policy- and decision-makers. The differ-
ences in approach reflect modellers’ strength of conviction on different
aspects of the theory and evidence. So, the structural cointegrating VAR
approach assumes that we understand how the economy works in the
long run with some degree of confidence, and allows theory to inform this
aspect of modelling. But it is less sure on the short-run dynamics and so
turns to the evidence on these. In comparison, the DSGE approach empha-
sises more the use of theory in the modelling of both the short run and
long run.
28

We shall show, in Chapter 6, that the estimation of our structural
cointegrating VAR model is straightforward using estimation techniques
developed in Pesaran and Shin (2002) and Pesaran, Shin and Smith (2000).
The issue of combining theory and evidence is typically less straightfor-
ward in the larger DSGE models where the highly restricted VAR model
suggested by the theory cannot be readily reconciled with the data.
Kapetanios et al. (2005) discuss this issue, outlining the steps taken in the
construction of a ‘conceptual model’ (for example, a restricted VAR derived
from a variant of a DSGE model) and its translation into a ‘data adjusted
model’ which can better match the data in policy-oriented macroeco-
nomic modelling. One approach to making this translation is Ireland’s
(2004) method based on ‘tracking shocks’. Here, any observed macroeco-
nomic variable is assumed to differ from its corresponding latent variable
(as generated by the conceptual model) by a tracking shock. This shock,
in turn, is assumed to follow some known stochastic process. Forecasts
are provided as an average reconciliation of the data and the outcome
suggested by the conceptual model, with the split between theory and
evidence depending on the nature of the tracking errors in the sam-
ple.18 Alternatively, Del Negro and Schorfheide (2004) describe a Bayesian
method, along similar lines to that developed by DeJong et al. (1993), in
which a New Keynesian DSGE is used to provide priors for a VAR and
these are updated in the light of the data, where the investigator explic-
itly chooses the weight to be placed on the theory-based prior relative to
the evidence. The paper also shows how the posterior inference on the
VAR parameters can be translated into posterior inference for the DSGE
parameters so that theory and evidence is combined and summarised in
such a way as to retain its economic meaning. A third possible method,
advocated by Christiano et al. (2005), focuses on matching theoretical and
empirical impulse responses.
Kapetanios et al. (2005) make the important point that, no matter which
method is used to combine theory and evidence, the underlying concep-
tual model will need to accommodate cointegrating relations if the effects
of some shocks are persistent (so that some of the variables are I(1) vari-
ables and long-run relations exist between them in levels). This feature
will provide its own restrictions on the VAR derived from the conceptual
model so that, once the theory-based long-run relations are incorporated
18 Recent models in various central banks adopt a DSGE structure as their core theoretical
components, but also allow for non-core empirically based dynamics. See, for example, the
TOTEM model of the Bank of Canada as described in Cayen, Corbett and Perrier (2005) or
Adolfson et al.’s (2005) description of their model of the Swedish economy.
29

into the model, it can be written as a VECM (see also Giannone et al.
(2005)). They note that failing to impose these restrictions (if cointegra-
tion exists in the data) will cause difficulties when trying to match the
theory with data and will cause considerable problems in forecasting.19 A
related issue arises in many DSGE models in which analysis is carried out
using variables measured as deviations from some ad hoc trend estimate
(e.g. the Hodrick–Prescott filter). Of course, the choice of a misspecified
trend will generate bias in estimation so the choice of trend is much more
significant than many DSGE modellers are prepared to acknowledge. But
perhaps even more importantly, the use of this type of de-trending makes
it rather difficult to test hypotheses based on long-run theory. In con-
trast, our approach readily allows the long-run theory to be tested and the
equilibrium values to be explicitly identified.
The long-run structural and the DSGE approaches both represent
attempts to reconcile theory and data. The differences between the
approaches are based on differences in emphasis and practicalities rather
than principle. The methods taken in the DSGE models to reconcile the-
ory and data oblige the projected paths of the variable to converge to the
equilibrium value suggested by the theory of the core conceptual model.
This implicitly places emphasis on the long-run properties of the theory,
which are held with some confidence, exactly as in our approach. But
this is achieved in a more restricted way than in our long-run structural
approach (being based on a single weighting parameter in the Bayesian
method described above, for example) and the long-run relations sug-
gested by theory are typically not tested in the DSGE models. The short-run
restrictions suggested by the DSGE models (including those implied by
the forward-looking expectations involved20) can be accommodated, and
tested, within the cointegrating VAR framework used in the long-run
structural approach.
In short, many economists might accept the view that economic theory
is more likely to provide a coherent guide to the long-run characteristics
of the macroeconomy than its short-run dynamics, and the mainstream
macroeconometric and structural VAR models are based on a pragmatic
approach to capturing the dynamics. As we shall demonstrate in the
19 Christiano, Eichenbaum and Evans’s (2005) attempts to tie down model parameters
by matching impulse responses will suffer from this shortcoming, for example, since the
impulse responses are based on short-run dynamics and are not consistent with the presence of
long-run relations in levels.
20 See Section 3.2 for details on how the expectation effects are accommodated in the long-
run structural model.
30

following chapter, our own approach is to allow the dynamics to be ﬂexibly
estimated within a VAR or VARX framework, but to impose restrictions on
the system to ensure that the estimated relationships are theory-consistent
in the long run. Theory-inspired short-run restrictions can then be consid-
ered in the light of their empirical validity, and not adopted blindly since
they are implied by a particular macroeconomic theory.
31

3
National and global structural
macroeconometric modelling
The discussion of the previous chapter suggested that there is a degree
of consensus surrounding the desirable long-run properties of a macro-
economic model and that most recently developed models will be similar
in this regard whether they have been developed following the SEM,
VAR or DSGE approaches. There is far less agreement about the way in
which short-run dynamic adjustment should be tackled, however, and in
this chapter we broaden the discussion to consider this aspect of macro-
economic modelling too. To this end, in the following section, we present a
canonical dynamic structural model. This allows us to clarify the distinc-
tion between short-run and long-run effects and to illustrate the issues
involved in identifying these respective effects. Using the model, we can
also provide a general description of the modelling strategy involved in
constructing a ‘structural cointegrating macroeconomic model’ as applied
to the UK in the subsequent chapters of the book. We believe that this
strategy provides a coherent approach to dealing with both short-run and
long-run influences in a way that can reflect the strength of conviction
with which we believe the underlying economic theory.
The description of the canonical dynamic structural model also helps
explain how the identification of short-run dynamics relates to the
identification of economically meaningful shocks and the measurement
of their dynamic effects. These issues are important since they lie at the
heart of the discussion surrounding the identification of monetary policy
shocks and the measurement of their effects. In this chapter, we shall
review the attempts that have been made in the literature to impose struc-
ture on the short-run dynamics of macroeconomic models and to identify
the effects of different types of shock, and particularly monetary policy
shocks.
33

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can hold him on the dock.
Another thing, mused Gwynn. The Edmeston Agency may be
quite all right, but the man's name is Grätz.
He's been under scrutiny. He seems to be all right.
All the same—his name is all wrong. What was that chauffeur's
name?
Bush.
Busch?
He spells it without a c. I saw his signature on the Agency rolls.
Have you his history?
He's Canadian. I've sent for it.
You'll find that his father spelled his name with a c, remarked
Gwynn, gloomily. But Vane only laughed.
I'm off, he said. Stick around where I can get you on the
telephone if necessary. But I don't think it will be necessary.
I do, muttered Gwynn.

CHAPTER V
KAREN
The journey was the usual one through interminable London
streets alternately respectable and squalid; and straight ahead
through equally interminable suburbs with their endless terraces,
semi-detached and detached villas, and here and there a fine old
house behind neglected garden walls, making its last forlorn stand
against the all-destroying inroad of the London jungle.
There had been a heavy haze in London, but no fog. In the
country, however, beyond the last outstretched suburban tentacle of
the inky octopus the morning sun glimmered low through a golden
smother, promising a glimpse of blue sky.
To Guild, one heath has always resembled another, and now, as
they passed through the country at high speed, there seemed to him
very little difference between the several named points which
marked his progress toward Westheath. Hedges alternated with ivy-
covered walls on either side of a wide, fine road; trees were splendid
as usual, sheep fat, cattle sleek. Here and there a common or heath
glimmered bewitchingly where sunlight fell among the whins; birds
winged their way, waters glimmered, and the clean, singing August
wind of England blew steadily in his face strangely reviving within
him some ancient, forgotten, pre-natal wistfulness. Maybe it came
from his American mother's English mother.
Near two villages and once on the open highway policemen
leisurely signalled the chauffeur to stop, and came sauntering around
to the tonneau to question Guild as to his origin, his business, and
his destination; quiet, dignified, civil, respectable men they seemed

to be in their night cloaks and their always smart and business-like
helmets and uniforms.
All seemed satisfied, but all politely suggested that passports were
now becoming fashionable in England. And Guild thanked them
pleasantly and drove on.
Bush, he said to his chauffeur, this spy scare was ridiculed by
the newspapers, but it looks to me as though it were being taken
rather seriously after all.
It is, sir.
I understand that about thirty thousand German and Austrian
reservists have been arrested in England since war began?
I hear so, sir.
I suppose the country really is swarming with spies. The paper
yesterday said that there was still a great and serious leakage of
military information out of England. One paper, yesterday afternoon,
reported that a number of spies had already been shot in the Tower.
I have heard so, sir, said the chauffeur smilingly.
He was a blond, good-looking young fellow. Always his lips
seemed to rest in pleasant curves as though his reveries were
agreeable.
A few hideously modern detached villas were passed, then
hedges, walls, a wood, a modern bridge.
How near are we to Westheath now? asked Guild, leaning
forward in his seat.
We are there, sir. And the smiling chauffeur slowed the car to a
standstill at a cross-roads where furze and broom grew rankly over

the heath and a few rather tawdry villas appeared among the trees
beyond.
Guild looked at his watch. It was only a little after seven, an
unearthly hour for a call upon any young girl, not to mention one to
whom he was personally unknown.
A policeman still wearing his waterproof night cloak, came
leisurely across to learn what was wanted.
I am looking for the villa of Miss Girard—Miss Karen Girard,
explained Guild.
Hyacinth Villa, Number 169. Take the road to the right. It is the
only house.
Thank you.
The car moved forward, swung to the right. About a quarter of a
mile away stood a small, modern stucco dwelling behind its hedge of
privet. Beyond that there were woods again and dewy uplands
glimmering with furze and brake.
When they arrived they found the driveway closed by a gate.
Never mind; I'll walk to the house, said Guild.
The smiling chauffeur leaned back and opened the tonneau door;
Guild descended, looked at the iron gate between its ugly stucco
posts, peered through it up the drive with its parallel rows of recently
planted lime trees. Everything about the place was recent if not
brand new—ugly with the ugliness of well-to-do bad taste. Red
geraniums and yellow cannas had been planted in fearsome
juxtaposition, salvia flanked a red brick terrace—a most unholy
combination of colour. In the early morning the sun exposed the
place without mercy. It was lonesome and amazingly depressing.

Glancing up at the gate again he discovered a nickel-plated label
riveted to one of the stucco posts. On it was the name of the place,
Hyacinth Villa, and its number 169.
There was no lodge, no bell, but the wicket gate was not locked.
So Guild entered.
Shall I drive up to the house, sir? inquired the chauffeur.
No; wait out here.
There seemed to be no sign of life about the house when at last
he arrived in front of it—nobody apparently stirring at that hour. He
hesitated; he still wore the same knickerbockers and cap which he
had worn in Belgium. His sack, which was now in the car, contained
only fresh linen; and he began to wonder what his reception might
be in such a costume and at such an hour. He doubted that the
unconventionality of the daughter of a Prussian aristocrat might
extend far enough to accept him, his rather shabby clothes, and his
explanation of the visit.
It was all very well for this young girl to kick over the tradition, cut
home traces in the sacred cause of art, call herself Girard, and live in
an impossible villa for art's sake. Few well-born Fräuleins ever did
this sort of thing, but there had been instances. And anybody in
Germany will always add that they invariably went to the devil.
Guild rang. After he had waited long enough he rang again. After
that he resumed his ringing. Keeping his finger pressed on the
electric button and laying his ear to the door. The bell was doing its
duty inside the house; he could hear it.
Presently he heard a fumbling of chains and locks inside, the door
opened on a crack and a sleepy voice inquired: Is it you, Anna?
Guild hesitated: I wish to see Miss Girard. Is she at home?
Who are you? demanded the voice no longer sleepy.

My name is Guild. I am sorry to disturb Miss Girard at such an
hour, but I cannot help it. Is Miss Girard in?
Yes; I am Miss Girard.
Are you Miss Karen Girard?
Yes. Why do you wish to see me?
I can't tell you here. Are you dressed?
There was a pause, then she said: No.
Please dress as quickly as you can. Dress for travel.
What!
If you have a travelling dress put it on. You can pack your
luggage while I am talking to you. But dress as quickly as you can
and then return and let me in.
She said after a moment's silence: I certainly shall not do any of
those things until I know more about you and about your errand
here.
I have a message for you from General Baron Kurt von Reiter.
That is possible, she said quietly. What is the message?
I was to say to you that the question which you were to decide
on the first of November must be decided sooner.
I must have clearer proof that your message is genuine. I am
sorry to distrust you but I have been annoyed lately.
Very well, he said. Open the door a little more. Don't be afraid.
I merely wish you to look at a ring which I wear. I want you to draw
it from my finger and look at what is engraved inside.

There was another silence. Then the door crack slowly widened.
Please extend your hand, she said.
There was just enough of space for him to slip his hand between
door and frame and he did so. There came a light, soft touch on his
ring-finger. The ring slipped off.

There came a light, soft touch on his
ring-finger
When she spoke again her voice was altered: I shall dress
immediately, she said. I shall not keep you waiting long. You will

find the door open. Please come in when I have gone upstairs.
Thank you.
He could hear her light, flying feet on the stairs; he waited a little
longer, then opened the door.
The hallway was dark, and he left the door open, then entered the
room to the left which seemed to be a library, music-room and living-
room combined. Books, piano, easy chairs and sofas loomed in the
dim light of drawn curtains. An easel on which stood a water-colour
drawing occupied the end of the room, and beside it was a table on
which were porcelain dishes, tubes of colour and scattered badger
brushes.
It was evident that Miss Girard's talents were multiple, for he
noticed also a violin and music stand near the piano, and on the
violin score as well as on the score spread across the piano the same
hand had written Karen Girard.
He stood by the table, mechanically picking up, one after another,
the books lying there. Some of the books were printed in French,
some in German, in Italian, in Danish, in Swedish, in English. Miss
Girard's name was written in all of them. Miss Girard appeared to be
accomplished.
In the dim light Guild began to saunter around the room
encountering various evidences of Miss Girard's taste and mode of
living—one or two Braun photographs of Velasquez, Boucher, and
Gainsborough on the walls—certainly a catholicism of taste entirely
admirable;—one or two graceful bits of ancient Chinese art—blue
and gold marvels of Pekin enamel; a mille-fleur tapestry panel, a
bundle of golf clubs, a tennis bat, and a pair of spurs.
He thought for himself that when a girl goes in for all of these
accomplishments it is because the gods have been otherwise unkind,
and that she has to.

At the same time he remembered the voice he had heard through
the scarcely opened door—the lovely voice of a young English girl—
than which in all the world there is nothing half so lovely.
And it suddenly occurred to him that there had not been in it the
faintest kind or trace of a German accent—that only its childish and
sleepy sweetness had struck him first, and then its purity and its
youthful and cultivated charm.
Yes, truly, the gods had been kind to this young German girl of
nineteen, but it would be a little too much to ask of these same gods
that they endow her with figure and features commensurate with her
other charms and talents.
Then he suddenly remembered her profession, and that she was
studying still for the dramatic profession. And he knew that this
profession naturally required exterior charm of any woman who
desired to embrace it.
While these ideas and speculations were occupying his mind he
heard her on the stairs, and he turned and came forward as she
entered the room.
She was a slender, straight girl of medium height; and her face
was one of those fresh young faces which looked fragrant. And
instantly the thought occurred to him that she was the vivid, living
incarnation of her own voice, with her lilac-blue eyes and soft white
neck, and the full scarlet lips of one of those goddesses who was not
very austere.
She wore a loosely-belted jacket of tan-coloured covert-cloth, and
narrow skirts of the same, and a wide golden-brown hat, and tan
spats. The gods had been very, very kind to Miss Girard, for she even
adorned her clothes, and that phenomenon is not usual in Great
Britain or among German Fräuleins however accomplished and
however well born.

She said: I beg your pardon for detaining you so long on the
outside door-step. Since the war began my maid and I have been
annoyed by strangers telephoning and even coming here to ask silly
and impertinent questions. I suppose, she added, disdainfully, it is
because there is so much suspicion of foreigners in England.
I quite understand, he said. Being German, your neighbors
gossip.
She shrugged her indifference.
Shall we talk here? she asked gravely, resting one very white
hand on the back of a chair. You come from General Baron Kurt von
Reiter. The ring is a credential beyond dispute.
We can talk anywhere you wish, he said, but there is little time,
and somebody must pack a traveller's satchel for you. Have you a
maid?
She went to London yesterday evening. She was to have
returned on the eleven o'clock train last night. I can't understand it.
Are you alone in the house?
Yes. My cook sleeps out. She does not come until half-past nine.
My maid serves my breakfast.
You haven't had any, then?
No.
Can you fix something for yourself?
Yes, of course. Shall I do so now?
Yes. I'll go to the kitchen with you while you are doing it. There
are several things to say and the time is short.

She led the way; he opened the kitchen shutters and let in the
sunshine, then stood a moment watching her as she moved about
the place with graceful celerity, preparing cocoa over an alcohol
lamp, buttering a roll or two and fetching cup, plate, spoon and
marmalade.
Have you breakfasted? she asked, looking at him over her
shoulder.
Yes—it is very good of you——
There will be plenty of cocoa and rolls—if you care for them. The
rolls are yesterday's and not fresh.
She poured the cocoa in two cups and looked at him again in
grave invitation.
You are sure there is plenty? he asked, smilingly.
Plenty.
Then—I do seem to be rather hungry.
He drew a chair for her; she seated herself and ate with a
youthful appetite. He drank his cocoa, ate his rolls, and tried not to
look at her too often.
This is why I am here, he said. I saw General Baron von Reiter
four days ago under somewhat extraordinary circumstances.
He told me that since the war broke out he had not been able to
communicate directly with you or to get you out of England, and he
asked me to find you and bring you to his estate at Trois Fontaines in
Luxembourg.
To Quellenheim? she asked, surprised and disturbed. Is he
there?

No, he is with a field army, and he does not know where orders
from staff headquarters may send him.
Still, she said, hesitating, I should think that he might wish me
to go to Silesia——
Silesia is threatened by the Russian army.
Silesia! she repeated, incredulously. Cossacks in Silesia? She
sat, her cup of cocoa half raised to her lips, her surprised and
disconcerted eyes on his. Then she set the cup aside.
He wishes me to go to Quellenheim? With you?
Yes.
Why?
Travelling on the continent is precarious.
Her eyes rested on his; she said with a candour which he began
to understand was characteristic of her: He seems to have
confidence in you. I never heard him speak of you. You are
American?
Yes.
That is odd. He never cared for Americans.
Guild said: He could not send a German into England.
That is true. Nor an Englishman either. No Englishman would be
likely to do anything to oblige a German.
She rose: I don't understand why Anna, my maid, is still absent,
she added uneasily. My maid often goes to London, but never
before has she remained over night. I don't know why she remained.
She knew I was alone in the house.

She lifted her serious blue eyes to Guild, then gazed out of the
window, evidently perplexed to the point of apprehension.
I am worried, she said, very much worried. But that doesn't
help, does it?
What was her errand in London? asked Guild.
She has a brother there. I suppose it's all right or she would have
telephoned me.
He said: No doubt it is all right. And, may I ask you to hasten?
She rose: Where am I to go with you?
To London and then to the steamer.
Today?
Today is Wednesday. No other Holland Line boat sails for
Amsterdam before Sunday, and I have yet our passage to secure and
I must also go to the War Office for a few moments. You see we
have very little time.
But I can't pack my boxes then?
You will have to leave them.
You mean I may take only a satchel?
A suit-case and satchel if you wish. Leave a note for your maid
instructing her to send by express whatever else you wish sent after
you.
Is this haste necessary, Mr. Guild?
Yes, it is. I want to get out of England. I am not sure that I can
get out if we wait until Sunday.

Why not?
I may be detained. I may not be permitted to leave with you. All
foreigners are under more or less suspicion. I am rather sure that I
have been under surveillance already at the Berkeley Hotel.
They had moved out into the hall together while he was speaking,
and now, together, they went up the stairs.
If you don't mind, she said, my room is in disorder, but I'll have
to pack there and you will have to sit there if you wish to talk to me.
It was a white and chintz room in dainty disorder.
She went away and returned in a moment or two with a satchel
and suit-case. These she placed on the bed, opened, and then,
dragging out various drawers of chiffonier and chest, began to
transfer her apparel to the two bags.
I am extremely sorry, he said, to hurry you so inconveniently.
I don't mind, she replied, busy with her packing. You see I am
an actress and I have travelled with a company in the provinces.
That was an experience! She turned her pretty head and looked at
Guild. I had no maid then, except at the theatres where we played,
and I had to share her with three other girls. Really, Mr. Guild, it
taught me how to pack things rather rapidly.
Her white hands were flying as she folded and placed garment
after garment in the suit-case, serene, self-possessed, quite
undisturbed by his presence at the rather intimate display of her
apparel.
The garments were bewilderingly frail to him; she tucked and
packed them into place; a faint fresh scent seemed to freshen the
place.

He said: I don't think we are going to have any trouble about
leaving England. But, if any trouble does arise, would you have
sufficient confidence in me to do what I say?
She continued her packing for a few moments without replying,
then turned and looked at him.
And at the same moment the telephone on the table beside her
bed tinkled.
There is Anna now! she exclaimed with the emphasis of relief.
Will you pardon me? No, I don't mean you are to leave the room
——
She lifted the receiver: Yes, I am here.... Yes, this is Miss Girard.
Yes, Miss Karen Girard.... Mr. Louis Grätz? Oh, good morning!
At the name of the man with whom she was speaking Guild
turned around surprised. At the same instant the girl's face flushed
brightly as she sat listening to what the distant Mr. Grätz was saying
to her.
Guild watched her; perplexity, surprise, a deeper flush of
consternation, all were successively visible on her youthful face.
Yes, she said to Mr. Grätz. Yes, I will do whatever he wishes....
Yes, he is here—here in my room with me. We were talking while I
packed. Yes, I will do so. And, turning her head a little she said to
the young man behind her: The Edmeston Agency desires to speak
to you.
He rose and took the receiver from her hand and bent over beside
her listening.
Are you there? inquired a pleasant voice.
Yes.

I am Grätz of the Edmeston Agency. Get that young lady out of
the house at once. Do you understand?
Yes.
Her maid is in trouble. This agency may be in trouble at any
moment. She must not wait to pack. Get her into the car and take
her to the wharf and on board at once. Do you understand?
Yes.
Take her as your wife. Do you understand?
I understand what you say, he said, amazed.
That is sufficient. Do as I tell you if you want to leave England.
Very well. But I must first go to the War Office——
No!
I must!
No. It is useless; hopeless. It would have been the thing to do
yesterday. An explanation there would have given you credentials
and security. But not today. She could not hope to leave. Do you
understand?
No, but I hear you.
She could not expect permission to leave because her maid has
been arrested.
What!
Yes! The charge is most serious.
What is it?

Get into your car with the young lady and start at once. Don't go
to the steamship office in Fenchurch Street. Don't go to the War
Office. Go nowhere except to the wharf. Your passage has been
secured as Mr. and Mrs. Kervyn Guild of New York. The initials on the
baggage will be K. G. Your steamer tickets will be handed to you.
You will pay no attention to the man who hands them to you, no
attention to anybody. You will go aboard and go to your cabin until
the ship is out at sea. Do you understand?
Perfectly.
Good-bye.

CHAPTER VI
MR. AND MRS.
Guild hung up the receiver, stood a moment in thought then
turned around and looked gravely at the girl behind him. She gazed
back at him as though still a trifle breathless after some sudden
shock.
What did that man say to you over the wire? he asked in
pleasant, even tones.
He told me to trust you, and do what you told me to do. He said
Anna, my maid, had been arrested.
Who is he? asked Guild grimly.
Do you mean Mr. Grätz?
Yes; who is Mr. Grätz?
Don't you know him? she said, astonished.
I have never laid eyes on him. Your father recommended to me
the Edmeston Agency and mentioned the name of a Louis Grätz who
might be of use to me. That is all I know.
My—father—you say?
Certainly, General Baron von Reiter.
Oh!... Then it must be quite all right. Only—I don't understand
about my maid——
Did Mr. Grätz tell you she had been arrested?

Yes.
On a serious charge?
Yes.
Have you any idea what that charge may be? he asked, studying
her face.
I haven't any idea, she said; have you?
I don't know; perhaps I have. Is your maid German?
Yes.
You brought her with you from Germany?
Yes.
Where did you get her?
General von Reiter's housekeeper found her for me.
He hesitated, still looking steadily into those violet blue eyes of
hers which seemed to question him so candidly. No, there could be
no dishonesty there.
Miss Girard, he said, I find that I am going to be very much
more frank with you than there once seemed any occasion for being.
I am also going to say something to you that may possibly offend
you. But I can't help it. It is this: Have you, through your letters to or
from your father, imparted or received any military intelligence which
might be detrimental to Great Britain or to her allies?
Do you mean am I a sort of spy? she asked, flushing to the
roots of her hair.
In substance it amounts to that. And I shall have to ask you to
answer me. And I'll tell you why I ask. I didn't intend to tell you; my

personal and private affairs did not concern you. But they do now.
And these happen to be the facts in my case: I was taken prisoner in
Belgium by the cavalry forming the advance of your father's
command. It happened four days ago; I was sentenced to military
execution, led out for that purpose, reprieved by your father himself
on condition that I undertake to find you and conduct you safely to
Trois Fontaines near the Grand Duchy of Luxembourg.
If I am unsuccessful in the undertaking, I am pledged to go back
voluntarily and face a firing squad. If I am successful I am permitted
to go free, and so are my fellow-hostages. And the little town where
I was arrested is to be spared.
He passed one hand over his eyes, thoughtfully, then, looking at
her very seriously:
There seemed to be no reason why an honorable man might not
accept such terms. I accepted them. But—things have happened
here which I neither understand nor like. And I've got to say this to
you; if my taking you back to your father means any detriment to
England or to the cause England represents—in other words, if your
returning to him means the imparting to him of any military
information gathered here by you, then—I won't take you back;
that's all!
After a moment, half to herself, she said: He really thinks me a
spy. I knew it!
I don't think so. I am merely asking you! he retorted impatiently.
There is something dead wrong here. I was intending to go to the
War Office to tell them there very frankly about my predicament, and
to ask permission to take you back in order to save my fellow-
hostages, the village, and my own life; and now a man named Grätz
of whom I know nothing calls me on the telephone and warns me
not to go to the War Office but to get you out of England as soon as
I can do it.

What am I to think of this? What does this man Grätz mean
when he tells me that your maid has been arrested on a serious
charge and that the Edmeston Agency of a German automobile is in
danger?
The girl stood very still with one slender hand resting on her
satchel, her face pale and quietly serious, her brows bent slightly
inward as though she were trying to remember something or to solve
some unpleasant problem not yet plain to her.
One thing is clear, she said after a moment, lifting her candid
eyes to his; and that is, if you don't take me back certain friends of
yours will be executed and a village in which you seem interested will
be destroyed.
If taking you back means any harm to England, he said, I won't
take you.
And—your friends? What becomes of them?
My friends and the village must take the same chances that I
do.
What chances? Do you mean to go back without me?
I said I would, he replied drily.
You said that if you went back without me they'd execute you.
That's what I said. But there's no use in speculating on what is
likely to happen to me if I go back without you. If you don't mind I
think we had better start at once. We have had our warning from
this man Grätz.
He gave her a searching glance, hesitated, then apparently came
to an abrupt conclusion.

Miss Girard, he said coolly, your father once took a good look at
me and then made up his mind about me. And he was not mistaken;
I am what he believes me to be. Now, I also have seen you, and I've
made up my mind concerning you. And I don't expect to be
mistaken. So I say to you frankly I am an enemy to Germany—to
your country—and I will not knowingly aid her—not to save my own
skin or the skins of anybody else. Tell me then have you any military
knowledge which you intend to impart to your father?
No, she said.
Have you any suspicion that your maid has been involved in any
such risky business?
I have no knowledge of anything military at all. I don't believe
my maid has, either.
You can recall no incident which might lead you to believe that
your maid is engaged in that sort of affair?
The girl was silent. He repeated the question. She said: Anna has
complained of being followed. I have already told you that she and I
have been annoyed by impertinent telephone calls and by strange
men coming here. Do you suppose they were from Scotland Yard?
Possibly. Have you any suspicion why your maid has been
arrested? he persisted. She hesitated; her straight brows knitted
slightly again as though in a perplexed effort to remember and to
understand. Then she looked up at Guild out of troubled eyes and
shook her head:
I don't know—I don't know—whatever my suspicions may be
——
Suspicions!
My personal suspicions could scarcely concern you, Mr. Guild.

The snub was direct; he reddened.
Very well, he said. What you say gives me a decent chance for
life. He drew a quick breath of relief. I'm mighty glad, he said; I
have—have seen men die. It isn't—an—agreeable sight. I think we'd
better go.
In a moment.
She took her satchel and went into another room with it, closing
the intervening door. She was gone only a few seconds. When she
returned she had locked the satchel; he closed and strapped her
suit-case and took it in his hand. Together they descended the
stairway and started through the lower hall.
And what occurred there happened like lightning.
For, as he passed the door of the darkened living room, a man
jumped out behind him and threw one arm around his throat, and
another man stepped in front of him and snapped a pair of handcuffs
on his wrists.
It was not even a struggle; Guild was being held too tightly. The
girl shrank back against the wall, flattening herself against it, staring
dumbly at the proceeding as though stunned. She did not even cry
out when the man who had handcuffed Guild turned on her and
caught her by the elbow.
Come along quietly, miss, he began, when suddenly his voice
died out in a groan and he crumpled up on the floor as Bush, the
chauffeur, sprang from the passage-way behind him and struck him
with something short and heavy.
The man who had thrown his arm around Guild's throat from
behind, flung his handcuffed victim aside and whipped out a revolver,
but the chauffeur knocked it out of his fist and hit him in the face
two heavy, merciless blows, hurling him senseless across the stairs.

And all the while the blond young chauffeur was smiling his fixed and
murderous smile. And he was like a tiger now in every movement as
he knelt, rummaged in the fallen men's pockets, found the key to the
handcuffs, leaned over and unlocked them as Guild held out his
manacled hands.
The chauffeur hit him ... two heavy, merciless blows,
hurling him senseless across the stairs
Please watch them, sir, he said cheerfully. I must find a curtain
or something——
He ran into the living-room, ripped off a long blue curtain, tore it
into strips with his powerful blond hands, grinning cheerfully all the
while.

Best to tie them up, sir—this way—allow me, sir—this is the
better way—the surer——
Guild, working hard, he scarcely knew why, felt a touch on his
arm.
Are they dead? whispered Karen Girard unsteadily.
No—stunned.
Are they robbers?
The blond chauffeur looked up, laughed, then rolled a strip of
cloth into a ball for a gag.
I'm not entirely sure what they are, said Guild. I'll tell you what
I think when we're in the car.
The chauffeur completed his business, looked over the results of
his efforts critically, rose to his feet, still smiling.
Now, sir, if you please—and madam— And he possessed himself
of the luggage.
Take the door-key, if you please, sir. Lock it on the outside. Thank
you. This way, if you please, sir. I took it upon myself to bring the car
up to the kitchen entrance.
The car stood there; the bags were flung in; Karen Girard stepped
into the tonneau; Guild followed. At the same moment a woman
appeared, coming along the brick walk.
My maid of all work, exclaimed Karen. What shall I say to her?
Anything, madam, but send her home, whispered Bush.
The girl leaned from the car and called out: I have locked the
house and am going away for the day, Mrs. Bulger. Please come
tomorrow, as usual.

The woman thanked her, turned and went away again down the
brick walk. They watched her out of sight.
Now! said Guild to the chauffeur, drive to the Holland steamship
wharf at——
I know, sir, smiled the blond chauffeur.
Which reply troubled the young man exceedingly, for it was
evident to him now that, if not herself a spy, this young girl in his
charge was watched, surrounded and protected by German agents of
a sinister sort—agents known to her father, in evident communication
with him, and thoroughly informed of the fact that he wanted his
daughter to leave England at once and under the particular escort of
Guild.
Nor had Guild the slightest doubt that the two men who had
followed and handcuffed him were British Government agents, and
that if this young girl's maid had really been arrested for espionage,
and if the Edmeston people, too, were suspected, then suspicion had
been also directed toward Miss Girard and naturally also to him, who
was her visitor.
Guild's troubled gaze rested once more upon the young girl beside
him. At the same moment, as though he had spoken to her she
turned and looked at him out of eyes so honest, so fearless that he
had responded aloud before he realized it: It's all right. I know you
are not deceiving me.
No, she said, I am not. But could you tell me what all this
means—all this that has happened so swiftly, so terribly——
I have a pretty clear idea what it means.... It's just as well that
those detectives did not arrest me.... Tell me, did you ever before
see this chauffeur, Bush?
Never, Mr. Guild.

He nodded; he was slowly coming to a definite conclusion
concerning the episode but he kept his own counsel. She said in a
low, embarrassed voice: You think me cowardly. I know it. But I
really didn't know what to do.
She was very much in earnest, very intent on his expression, and
he did not dare smile.
What could you have done, Miss Girard? he asked, pleasantly.
I don't know. I—I felt as though we—you and I—were allies—and
that I ought to help you. But it all passed too quickly——
There was nothing you could have done for me, he smiled.
She said reflectively: I myself don't quite see how I could have
helped matters. But I didn't wish you to believe me afraid to help
you.
He looked into her wistful eyes smilingly: Somehow, he said, I
don't believe you are really very much afraid of anything.
A slight shudder passed over her. Violence is new to me. I am not
very experienced—not very old you know. And I never saw men
fight. And when—she lowered her voice—when that chauffeur
struck them so heavily—so dreadfully—I—I have never seen men
fight like that—strike each other in the face as though they—they
meant murder——
Don't think of it now, Miss Girard. You must keep your nerve. He
forced a laugh; you'll need all your composure, too, because I've
got something to tell you which you won't like. Shall I tell you now?
Yes, please.
Then—the man, Grätz, says that you must go aboard that
steamer as my wife.

The girl looked at him bewildered. Somebody, continued Guild,
has taken passage for us as Mr. and Mrs. Kervyn Guild. Grätz
warned me. My name is Kervyn. Yours is Karen. Our initials are alike.
If there is any suspicion directed toward us there are the initials on
your satchel and suit-case—and presumably on your clothing. Do you
understand?
Yes.
Do you mind?
I mind a little—yes. But I'll do what is necessary, she said,
confused.
I think it is necessary. This man Grätz who seems to know more
about my business than I do, tells me so. I believe he is right.
She raised her tragic eyes to his but said nothing.
He leaned nearer to her and spoke in a low voice:
I've been trying to reason it out, he said, and I'll tell you what
my conclusion is: A German automobile took me to the British lines
under a white flag. No doubt Government agents had been informed
by telegraph and they followed me as soon as I landed on English
soil.
At the Berkeley Hotel I felt very sure that I was being watched.
Now, it appears, that this maid of yours has been arrested, and, from
what I suspect in regard to the Edmeston Agency—the agency to
which your father directed me—I feel very certain that somehow
your maid has been involved in the espionage maintained here by
the German Government.
That chauffeur in front of us is from the Edmeston garage; you
see what he did to those two detectives! It's very plain to me now
that, innocent as you are, you never will be permitted to leave

England, even if they don't arrest you, unless you can get out today
with me.
And if you don't leave England it means for me something very
serious. It means that I shall have to keep my word and go back
alone.
I know, she nodded, looking up at him very earnestly.
He said without the slightest dramatic emphasis: It really does
mean my death, Miss Girard. I think, knowing your father, that there
could be no possible hope for me if I go back there without you....
And so, knowing that, I am naturally most anxious to clear out of
England while I can do so—get away from here with you—if I can
take you with a clear conscience. And—he looked at her, I feel that
I can do that because you have told me that you have gathered no
information for the enemies of England. And—he smiled—to look
into your face, Miss Girard, is to believe you.
Some of the pretty color faded from her cheeks; she said: You
asked me if I were a spy. I am not. You asked me if, knowingly, I
carry any military information which might aid the enemies of
England. And I answered you that, knowingly, I do not carry any
such information.
That is sufficient, he concluded, smilingly.
No, it is not sufficient, she said. I wish to say a little more. Let
me go to Trois Fontaines alone. I am accustomed to travel. There is
no need to involve you. As long as I arrive there what difference
does it make whether or not you accompany me?
I promised to accompany you.
You promised that I should arrive safely at Trois Fontaines. It
doesn't matter whether you accompany me. Please—please don't. I
had rather you did not go.

He said, gravely: I know how you must feel about travelling as
my wife——
It isn't that.
What is it then? he asked, surprised.
I don't wish you to take the risk of travelling with me.
What risk? The worst that could happen to you would be your
arrest and detention. If you are not a spy, you can not be proven
one.
Her blue eyes gazed absently out across the sunny landscape
through which they were speeding.
You are not a spy, he replied; what risk do you run—or I?
She said, still gazing into the sunlit distance: What is done to
spies—if they are caught?
It usually means death, Miss Girard.
I have— she swallowed, caught her breath, breathed deeply;
then—I have heard so.... It is possible that I might be suspected
and detained.... I had rather you did not attempt to go with me....
Because—I do not wish you to get into any difficulty—on my—
account.
Nothing serious could happen to either you or me through
anything that you have done.
I am not sure.
I am, he said. And added in a lower voice: It is very generous
of you—very kind.
Her own voice was lower still: Please don't go with me, Mr. Guild.
Let me go to the wharf alone. Let me take my chances alone. If

there is any difficulty they will arrest you, too. And if I—were
convicted——
You could not be. That is utterly impossible. Don't think of such
things, Miss Girard.
I must think of them. Will you tell me something? She turned
and looked at him curiously, almost wistfully.
I want to ask you something. You—you said to me that if you
thought me a spy, you would not help me to escape from England.
You said so, didn't you?
Yes.
You mean it, don't you?
I am afraid I do.
Why? You are not English. You are an American. America is
neutral. Why are you an enemy to Germany?
I can't tell you why, he said.
Are you an enemy to Germany?
Yes—a bitter one.
And if I were a spy, trying to escape from England—trying to
escape—death—you would refuse to help me?
She had turned entirely toward him on the seat beside him; her
child-like hands clasped on the robe over her knees, her child-like
face, pale, sweet, wistful, turned to his.
Would you abandon me? she asked.
The situation is impossible——

Yes, but tell me.
I don't care to think of such a——
Please answer me. Is your partisanship so bitter that you would
wash your hands of me—let me go to my death?—go to your own,
too, rather than help me?
Miss Girard, you are losing your composure——
No; I am perfectly composed. But I should like to know what you
would do under such circumstances with a girl nineteen years old
who stood in danger of death.
I can't tell you, he said, perplexed and impatient. I can't tell
now what I might do.
Would you denounce me?
No, of course not.
Would you feel—sorry?
Sorry! He looked at her; I should think I would!
Sorry enough for me to help me get away?
Yes.
Even if I carried military information to Germany?
He looked into her eyes searchingly for a moment. Yes, he said;
I'd do what I could for you to get you out of England.
Even if I had lied to you?
You couldn't lie to anybody.

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