Exogeneity in Error Correction Models

200 Pages·1993·5.505 MB·English

by  Dr. Jean-Pierre Urbain (auth.)

Lecture Notes in Economics
and Mathematical Systems 398
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Jean-Pierre Urbain
Exogeneity in Error
Correction Models
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Author
Dr. Jean-Pierre Urbain
University of Limburg
Department of Quantitative Economics
P.O. Box 616
NL-6200 MD Maastricht, The Netherlands
ISBN-13: 978-3-540-56639-7 e-ISBN-13: 978-3-642-95706-2
DOl: 10.1007/978-3-642-95706-2
Library of Congress Cataloging-in-Publication Data.
Urbain, Jean-Pierre.
Exogeneity in error correction models/Jean-Pierre Urbain. p. cm. - Lecture notes in
economics and mathematical systems; 398)
Includes bibliographical references and index.
ISBN-13: 978-3-540-56639-7
I. Error analysis (Mathematics) 2. Economics-Statistical methods. I. Title. II. Series.
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Acknowledgements
The material contained in this monograph results of research realised
when I was working at the University of Liege. On looking back at the pro
cess of writing this monograph, I realise that many people have contributed
to its realisation.
First of all, I want to express my great indebtedness to Herman K. van
Dijk, for having guided my work over the recent years. His constant support,
both morally and intellectually, has been a major motivation for me to pursue
this research. He has always been willing to read, comment and discuss
the topics on which I have been working. Without his encouragments and
suggestions, this work would certainly never have been conducted.
Over the recent years, I have also benefited from numerous discussions
with Jim Lindsey. He has always been an astute and friendly critic who
helped me clarify the arguments at various points. His careful readings of
different versions of the manuscript, and more generally of my work, has
led to substantial improvement and clarification in the material contained
in this book. Luc Bauwens and Franz Palm contributed many important
comments and suggestions for which I am extremely grateful. I also would
like to express my gratitude to Yvan Langaskens for his support.
Several parts of this monograph have benefited from (oral or written)
comments from Phillip Hans Franses, David Hendry, Soren Johansen and
Mark Steel. In particular, I would like to thank Peter Boswijk for many
stimulating discussions and for collaboration in work on exogeneity tests.
Thanks are also due to Albert Corhay, Bernard Delhausse, Axel Lutgens
and Sergio Perelman for discussions, suggestions and encouragements.
Financial support of the Faculty of Economics and Business Adminis
tration of the University of Limburg (Post-doctoral fellowship 1992-93) is
gratefully aknowledged.
VI
Finally, I want to acknowledge the support and help of my parents,
friends and especially of my wife and my two daughters.
These acknowledgements would not be complete if I did not thank all
those whose music has accompanied me in my late hours of work.
This monograph is dedicated to Marina, Emilie and CeIine who had to
live through the pressure during the realisation of this work. I want to thank
them for their love.
Contents
List of Figures ix
List of Tables xi
1 Introduction and Summary 1
2 Cointegrated Systems 7
2.1 Some Historical Background to the Modelling of Economic
Time Series . . . . . . . . . . . . . . . . 9
2.2 futegration and Cointegration . . . . . . . . 17
2.3 The Modelling of Cointegrated Systems . . 24
2.4 Cointegration and Conditional Sub-systems 34
2.5 Error Correction Models 38
2.6 Conclusions........ 40
3 Weak Exogeneity in ECMs 43
3.1 Weak Exogeneity . . . . . 44
3.1.1 Definition and example 45
3.1.2 Empirical motivations . 50
3.2 Reduced Form Error Correction Models 51
3.2.1 The error correction system in reduced form. 51
3.2.2 Single equation error correction model in reduced form
and weak exogeneity . . . . . . . . . . . . . . . 53
3.3 ECMs in Structural Form . . . . . . . . . . . . . . . . . . .. 61
3.3.1 The error correction system in structural form .... 61
3.3.2 Single equation error correction model in structural
form and weak exogeneity . . . . . . . . . . . . . . .. 62
3.4 fuference on Weak Exogeneity in ECMs . . . . . . . . . . .. 65
3.4.1 Are orthogonality tests useful in single equation ECMs 65
VIII CONTENTS
3.4.2 Testing for the presence of cointegrating vectors in the
marginal models .. . . . . . . . . . . . . . . 67
3.5 Empirical lllustration .................... 68
3.5.1 Belgium consumption function: Steel (1987) . . . . 68
3.5.2 Aggregate import demand function: Urbain (1988) 72
3.5.3 The UK demand for money: Lubrano et al. (1986),
Steel and Richard (1991) 73
3.6 Conclusions......... 81
4 Testing for Weak Exogeneity 83
4.1 Introduction............................ 83
4.2 Exogeneity and the Incomplete SEM . . . . . . . . . . . . .. 85
4.3 The Behaviour of Orthogonality Tests in the Presence of (Co)-
Integrated Variables . . . . . . . . . . . . . . . . . . . . . .. 90
4.3.1 Testing for weak exogeneity within a limited informa-
tion framework . . . . . . . . . . . . . . . . . . . . 91
4.3.2 Small sample behaviour: some simulation evidence .. 93
4.3.3 Asymptotic distribution . . . . . . . . . . . . . . . . . 101
4.4 Testing for Weak Exogeneity in ECMs where the Short Run
Dynamic Parameters are Parameters of Interest . 107
4.5 Conclusions........................ 111
5 Empirical Analysis: The Case of Aggregate Imports 113
5.1 Background........................ 113
5.1.1 The imperfect substitutes model for aggregate trade
flows ............................ 114
5.1.2 Econometric issues in trade modelling ........ . 116
5.2 System versus Partial Approach to the Modelling of Belgium
Aggregate Imports ....................... . 123
5.2.1 Univariate analysis ................... . 124
5.2.2 Multivariate cointegration and simultaneous equation
models .......................... . 137
5.2.3 Partial modelling of aggregate imports: a structural
ECM. 149
5.3 Conclusions 160
6 Conclusions 161
Bibliography 165
A uthor Index 185
Subject Index 188
List of Figures
2.1 Stationary process .... . 20
2.2 1(1) process ........ . 20
2.3 near-l(l) process ..... . 21
2.4 Independent 1(1) processes 23
2.5 Bivariate cointegrated series 23
3.1 Real disposable income and M3 (in logs) . . . . . . . . . . 75
3.2 Deflator of the real disposable income and short term interest
rates (in logs) ..................... 75
3.3 Deflator of the real disposable income (in first diff.) 76
3.4 Short run interest rates (in first diff.) ..... 76
3.5 M3 (in first diff.) ................ 77
3.6 Real personal disposable income (in first diff.) 77
5.1 Import and domestic prices (in level) ..... . 125
5.2 Import prices (in first diff.) ... . . . . . . 125
5.3 Domestic prices (in first diff.) . . 126
5.4 Import volume (in level) ..... 126
5.5 Import volume (in first diff.) .. 127
5.6 Real income (in level) ..... . 127
5.7 Real income (in first diff.) . . . . . . . . . . 128
5.8 Sequential ADF tests: import volume .. 135
5.9 Sequential ADF tests: real income .... 136
5.10 Sequential ADF tests: domestic prices 136
5.11 Sequential ADF tests: import prices .. . 137
5.12 Restricted cointegrating vector ..... . 143
5.13 1-step Chow tests (PVAR): import volume equation 145
5.14 1-step Chow tests (PVAR): real income equation .. 146
.....
5.15 1-step Chow tests (PVAR): domestic prices equation 146
x
LIST OF FIGURES
5.16 I-step Chow tests (PVAR): import prices equation . 147
5.17 N-step ahead Chow tests: structural ECM . . . 158
5.18 N-step backward Chow tests: structural ECM . 159
5.19 I-step Chow tests: structural ECM . . . . . . . 159
List of Tables
3.1 Auxiliary regression for Lliai .... . . . . . . . . . . 70
3.2 Exogeneity tests by variable addition . . . . . . . . . . 71
=
3.3 Money demand in the UK: MLE approach with n 3 79
=
3.4 Money demand in the UK: MLE approach with n 5 80
4.1 Representation of incomplete SEMs . 88
4.2 Instruments used in the simulations 96
4.3 Empirical size of orthogonality tests 98
=
4.4 Empirical power of orthogonality tests, p 0.25 99
=
4.5 Empirical power of orthogonality tests , p 0.50 100
5.1 Testing for seasonal unit roots. . . . . . . . . . 130
5.2 Testing for unit roots at the zero frequency .. 132
5.3 Testing for breaking trend: the 1973 oil shock . 134
5.4 Lag length selection and Johansen's cointegration tests. 139
5.5 Multivariate cointegration analysis . . . . 141
5.6 Hypothesis tests on cointegrating matrix. 142
5.7 Statistics on the error processes . . 144
5.8 FIML estimation of the final SEM 148
5.9 Wald tests for Cointegration. . . . 151
5.10 Cointegrating vector estimates .. 152
5.11 Structural ECM and weak exogeneity 155
5.12 Weak exogeneity tests . . . 156
5.13 ECM for aggregate imports . . . . . . 157