Table Of ContentLecture Notes in Economics
and Mathematical Systems 385
Editorial Board:
H. Albach, M. Beckmann (Managing Editor)
P. Dhrymes, G. Fandel, G. Feichtinger, W. Hildenbrand
W. Krelle (Managing Editor)
H. P. Kunzi, K. Ritter, U. Schittko, P. Schonfeld, R. Selten, W. Trockel
Managing Editors:
Prof. Dr. M. Beckmann
Brown University
Providence, RI 02912, USA
Prof. Dr. W. Krelle
Institut fUr Gesellschafts-und Wirtschaftswissenschaften
der Universitat Bonn
Adenauerallee 24-42, W-5300 Bonn, FRG
Javier Gardeazabal Marta Regulez
The Monetary Model
of Exchange Rates
and Cointegration
Estimation, Testing and Prediction
Springer-Verlag
Berlin Heidelberg New York
London Paris Tokyo
Hong Kong Barcelona
Budapest
Authors
Dr. Javier Gardeazabal
Dr. Marta Regulez
Instituto de Economfa PUblica
Universidad del Pars Vasco
48940 Lejona-Vizcaya, Spain
ISBN-13: 978-3-540-55635-0
DOl: 10.10071978-3-642--48858-0
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A OSCAR
PREFACE
This monograph is the result of merging parts of the
authors's doctoral dissertations presented at The University of
Pennsylvania in the spring of 1991.
We would like to thank the members of our dissertation
committees, Francis X. Diebold, Roberto S. Mariano and Marc Nerlove for
their guidance and helpful comments. We received very good comments from
Albert Ando, Yin-Wong Cheung, William English, S0ren Johansen, W.
Krelle, Bruce Mizrach and seminar participants at the University of
Pennsylvania and the XV Simposio de Analisis Econ6mico in Barcelona. Our
thanks also to Werner A. MUller of Springer-Verlag for his help. Of
course, any remaining errors are ours.
We are indebted to Departamento de Trabajo del Gobierno Vasco
and the Department of Economics at the University of Pennsylvania for
financial support through our graduate studies. The research underlying
this work was partially supported by two Alfred P. Sloan Foundation
Fellowships.
We could not have written this monograph without the support
received from our families.
Sections wi thin chapters are numbered using roman numerals.
References to equations within the same chapter are of the form (11.7)
whereas if they correspond to different chapters are (2.1V.4).
TABLE OF CONTENTS
CHAPTER 1. Introduction 1
CHAPTER 2. The Monetary Model of Exchange Rate Determination.
I. Introduction. . . . 7
II. Monetary Models . . . 8
III. The Asset Market View 13
IV. Empirical Evidence 15
V. Treatment of Nonstationary Variables 16
CHAPTER 3. Long Run Exchange Rate Determination I.
I. Introduction . . . . . . . . . . . . . . . . 18
II. Some Preliminary Definitions and Engle and Granger Procedure. 21
III. Interpretation of Previous Results in terms of Cointegration 22
IV. Testing for Cointegration Using Engle and Granger Methodology. 25
V. Empirical Results 27
VI. Conclusions 31
APPENDIX A 33
CHAPTER 4. Long Run Exchange Rate Determination II.
I. Introduction .......... . 41
II. Description of The Time Series Model 43
III. The Data And Diagnostic Tests 45
111.1. Data Description ................ 45
111.2. Diagnostic Tests on the Assumptions of the VAR ....... 47
IV. Estimation And Testing For Cointegration . . . . . . . . . . 48
V. Tests of Several Hypotheses . . . . . . . . . . . . . . . . . 52
V.1. Testing for Known Co integrating Vectors . ... . . . . . . . . 52
V.1.1 Testing for Trivial Cointegrating Vectors ......... 54
V.1.2. Testing for Cointegration between Fundamentals ....... 56
V.2. Tests of the same Linear Restrictions on all Cointegrating
Vectors. . . . . . . . . . . . . . . . . . . . . . .. 57
V.2.1. Testing the Exclusion of a Variable from all
Cointegrating Vectors. . . . . . . . . . . . . . . . . . 58
V.2.2 Testing for the Restrictions of a Monetary Equation .... 59
VI. Conclusions 61
APPENDIX A 63
APPENDIX B 69
CHAPTER 5. Short Run Exchange Rate Determination.
I. Introduction . . . . . . . 73
II. Weak Exogeneity of the Exchange Rate 73
III. Testing for Weak Exogeneity . . . . 76
IV. The Asset Market View Derived from an Error Correction Model . 77
V. Conclusions 79
APPENDIX A .... 80
CHAPTER 6. Effect of Non-Normal Disturbances on Likelihood Ratio
Tests.
I. Introduction . . 81
II. The Data Generating Process 83
III. Hypotheses Tests . . . . . 85
111.1. Tests on the Number of Cointegrating Vectors 85
111.2. Tests of Linear Restrictions on the Cointegrating Vector 88
x
111.3. Tests of Restrictions on the Loadings Matrix ...... . 88
IV. The Simulation Exercise . . . . . . . . . . . . . . . . . . . 89
IV.1. Empirical Size of the Tests ................ 91
IV.2. Power of the Tests . . . . . . . . . . . . . . . . . . . . . 93
V. Conclusions . . . . . . . . 94
APPENDIX A: Size of the Tests . 96
APPENDIX B: Power of the Tests 102
CHAPTER 7. Estimation of the Time Series Model.
I. Introduction . . . . . . . . . . 105
II. Two Different Interpretations of the Time Series Model 106
III. Estimation of the Model ........... . 109
111.1. Unrestricted Model ..... . 109
111.2. Restricted Short Run Dynamics ... . 110
111.3. Restricted Long Run Dynamics .... . 112
111.4. Restricted Short and Long Run Dynamics 115
111.4.1. Gaussian Reduced Rank Maximum Likelihood Estimator 115
111.4.2. Two Step Procedure ................. . 117
CHAPTER 8. Prediction in Co integrated Systems.
I. Introduction . . . . . . . . . . . . . . . . . . . . . . .. 119
II. Properties of the True Forecasts from a Co integrated System 120
III. Estimated Forecasts from a Cointegrated System. . . . . . . 124
CHAPTER 9. Nominal Exchange Rate Prediction.
I. Introduction . . . . . 129
II. Review of Literature. 130
III. Forecasting Exercise 135
IV. Conclusions 140
Appendix A . . . . . . . 142
CHAPTER 10. A Simulation Exercise.
I. Introduction ....... . 150
II. The Data Generating Process 153
II I. Results 156
Appendix A . . . . . . . . . . . 161
CHAPTER 11. Conclusions 178
DATA APPENDIX 183
BIBLIOGRAPHY 185
Chapter 1. Introduction
These notes draw from the Theory of Cointegration and use it
in order to test the monetary model of exchange rate determination. The
analysis is empirical, that is, we take a theoretical model of exchange
rate determination and asses its empirical performance. We have also
addressed several issues concerning to the Theory of Cointegration.
The starting point is the monetary model. Its several versions
give rise to different equations of exchange rate determination. They
express the domestic currency value of a unit of foreign currency as a
linear combination of differentials between domestic and foreign
fundamentals. These fundamentals are money supplies, interest rates,
national incomes, etc.
These models have been tested in many occasions. The
impression one gets from these studies is that the monetary model does
not capture the short run dynamics of the exchange rate, specially when
assessed in terms of forecasting accuracy. Meese and Rogoff (1983)
compared the forecasting performance of the monetary models of exchange
rate determination with that of time series models, the forward rate and
the random walk. The naive random walk beats the other models. However,
even though those equations of exchange rate determination may be bad
indicators of how exchange rates are determined in the short run, they
could still describe long run equilibrium relationships between the
exchange rate and its fundamentals.
The concept of long run equilibrium relationship is borrowed
from the theory of co integration. In plain words, we say that various
nonstationary time series are co integrated when linear combinations of
2
them are stationary. Stationary deviations from those long run
relationships are allowed in the short run.
In the empirical tests of monetary models they look for a set
of regressors that explain a high percentage of exchange rate
variability and, at the same time, leave a white noise disturbance. In
addition, they usually omit any consideration to the nonstationarity of
several of the variables involved. The theory of cointegration takes
into account the nonstationarity and looks for a stationary, possibly
correlated over time, disturbance.
This monograph also focuses on the issue of optimal prediction
in partially nonstationary multivariate time series models. In
particular, we carry out an exchange rate prediction exercise.
The type of nonstationarity allowed for is somehow
restrictive. We assume that stationarity of a p-dimensional time series
can be obtained by taking first differences of all its components.
However, by doing so, we will generally introduce some unit roots in the
moving average representation of the differenced time series. This is so
because the number of unit roots, d, is smaller than its dimension. In
this sense the time series is partially nonstationary. The d unit roots
are shared by all the elements of the vector time series and we will say
that the p univariate time series have d common stochastic trends. The
difference between the dimension of the system and the number of common
trends, r = p - d, is the number of cointegrating vectors or stationary
linear combinations of the individual time series. The Theory of
Co integration treats these co integrating vectors as long run static
equilibrium relationships from which the p variables deviate temporarily
in the short run. In terms of exchange rate determination, the long run
relationships determine the long run value of the exchange rate.
3
The rest of the analysis is organized as follows:
Chapter 2 describes several versions of the monetary model.
All the discussion in this chapter is by now in the textbooks of
International Monetary Theory (see for instance Baillie and McMahon
(1990». However, we felt that a short discussion of the old monetary
models would not hurt and, furthermore, improve these notes by making
them self contained.
In chapters 3 to 5 and 9 we test the monetary model as a long
run approximation for mark, pound and yen, US dollar rates.
Chapter 3 introduces some definitions, and presents evidence
on the nonstationary character of the variables involved in the monetary
model. We use the unit root tests developed by Dickey and Fuller (1979),
Phillips (1987) and Phillips and Perron (1988) in order to determine
a given time series is stationary in levels, first differences
wheth~r
or trend stationary. We find that the variables that are considered as
fundamental determinants of the exchange rate have different kinds of
nonstationarity. That is, some are stationary in levels, some in first
differences and some others trend stationary.
We also analyze the stationarity of the difference between
domestic and foreign fundamentals. That is, we look for co integration
between pairs of fundamentals with a known co integrating vector using
Engle and Granger (1987) methodology. We find that, in general, foreign
and domestic fundamentals are not cointegrated, at least when we impose
a particular cointegrating vector.
We have reviewed several pieces of empirical evidence on the
long run character of the monetary equations of exchange rate
determination and its building blocks (purchasing power parity, money
demands) using the theory of cointegration. The existing evidence in the
