Table Of ContentThe Dynamics of Business Cycles
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Michael Reiter
The Dynamics
of Business Cycles
Stylized Facts, Economic Theory,
Econometric Methodology
and Applications
With 22 Figures
Physica-Verlag
A Springer-Verlag Company
Series Editors
We mer A. Muller
Peter Schuster
Author
Dr. Michael Reiter
SEMECON
University of Munich
SchackstraBe 41I
D-80539 Munchen, FRG
ISBN-13: 978-3-7908-0823-0 e-ISBN-13: 978-3-642-95919-6
DOl: 10.1007/978-3-642-95919-6
Die Deutsche Bibliothek -CIP-Einheitsaufnahme
Reiter, Michael:
The dynamics of business cycles: stylized facts. economic
theory, econometric methodology and applications I Michael
Reiter. -Heidelberg: Physica-Verl., 1995
(Contributions to economics)
ISBN-13: 978-3-7908-0823-0
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Preface
This study is a revised version of my doctoral dissertation at the Economics
Department of the University of Munich. I want to take the opportunity to
express my gratitude to some people who have helped me in my work. My
greatest thanks go to the supervisor of this dissertation, Professor Claude
Billinger. Bis ideas have formed the basis of my work. Be permanently sup
ported it with a host of ideas, criticism and encouragement. Furthermore, he
provided a stimulating research environment at SEMECON.
This study would not have been possible in this form without the help of
my present and former colleagues at SEMECON. I am indebted to Rudolf
Kohne-Volland, Monika Sebold-Bender and Ulrich Woitek for providing soft
ware and guidance for the data analysis. Discussions with them and with
Thilo Weser have helped me to take many hurdles, particularly in the early
stages of the project. My sincere thanks go to them all.
I had the opportunity to present a former version of my growth model at
a workshop of Professor Klaus Zimmermann. I want to thank all the parti
cipants for their helpful comments.
I also acknowledge critical and constructive comments from an anonymous
referee.
Table of Contents
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
Part I. Methodology
1. Importance of Stylized Facts. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
1.1 Limitations of statistical testing. . . . . . . . . . . . . . . . . . . . . . . . . . 9
1.2 Evaluating economic models. . . . . . . . . . . . . . . . . . . . . . . . . . . .. 11
2. Further Methodological Issues . . . . . . . . . . . . . . . . . . . . . . . . . . .. 13
2.1 Continuous versus discrete time models ................... 13
2.2 Models of cyclical growth versus models of fluctuations. . . . .. 14
2.3 Detrending the data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 15
2.4 Annual versus quarterly data ............................ 16
2.5 Applying models to more than one country ......... . . . . . .. 17
Part II. Business Cycle Stylized Facts
3. Stylized Facts: Method ................................... 21
3.1 Characterizing deviations from trend: spectral analysis. . . . .. 21
3.2 Spectral estimation: the maximum-entropy spectrum. . . . . . .. 24
3.3 Cross spectral analysis: interpretation and estimation ... . . .. 25
4. Stylized Facts: Results.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 27
4.1 Main aggregates of national accounts ..................... 27
4.2 Longer series of fixed investment ......................... 34
4.3 Private consumption. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 36
4.4 Nominal variables ...................................... 39
4.5 Relationship between real and nominal variables. . . . . . . . . . .. 44
Vlll Table of Contents
Part III. Business Cycle Models
5. SOA Models. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 53
5.1 The SOA of equipment investment. . . . . . . . . . . . . . . . . . . . . . .. 54
5.2 Recent research on inventories ........................... 57
5.3 The SOA of production and inventories ................... 58
5.4 Errors in measurement .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 60
5.5 Empirical results ....................................... 62
6. Consumption........ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 73
6.1 Two models of consumption. . . . . . . . . . . . . . . . . . . . . . . .. . . .. 73
6.2 Estimated consumption equations ........................ 76
6.3 Complete models. . . . . . . . . . . . . .. . . .. . . .. . . . . . . .. . . .. . . .. 80
6.4 Empirical results ....................................... 82
6.5 Appendix: computation of permanent income .............. 84
7. Prices and Wages ......................................... 97
7.1 Introduction........................................... 97
7.2 Price and consumption equations. . . . . . . .. . . . . . . . . . . . . . . .. 98
7.3 Complete model ........................................ 100
7.4 Empirical results ....................................... 100
7.5 Summary: explaining business cycle stylized facts ........... 107
Part IV. Cyclical Growth
8. Determinants of Growth .................................. 119
8.1 Growth, saving and productivity ......................... 119
8.2 Design of the model .................................... 122
9. A Real Model of Cyclical Growth ......................... 125
9.1 Formulation of the cyclical growth model .................. 125
9.2 Steady state ........................................... 133
9.3 Deviations from steady state and stability ................. 137
9.4 Time-varying productivity growth ........................ 139
9.5 Parameter restrictions and exogenous variables ............. 140
9.6 Empirical results ....................................... 140
9.7 Appendix I: Linearizations ............................... 147
9.8 Appendix II: Linearization error .......................... 152
Table of Contents ix
Part V. Continuous Time Econometrics
10. Estimating Continuous Time Models ..................... 159
10.1 Linear stochastic differential equations .................... 159
10.2 Estimation of a first order system ........................ 161
11. The Discrete Kalman Filter .............................. 163
11.1 The state space model .................................. 163
11.2 The Kalman filter: recursive formulas and ML-estimates ..... 164
11.3 Initialising the Kalman filter .................... ,. ........ 166
12. An Exact Gaussian Estimator for General Linear
Continuous Time Models ................................. 169
12.1 The exact discrete analogue .............................. 169
12.2 Evaluation of integrals .................................. 172
12.3 Efficient computation of the filter ......................... 175
12.4 Exogenous variables .................................... 177
12.5 Fixed-interval smoothing ................................ 179
13. Further Topics ............................................ 181
13.1 Asymptotic properties of the estimators ................... 181
13.2 Sensitivity analysis ..................................... 182
13.3 A Monte-Carlo study ................................... 182
13.4 Spectral densities of continuous time models ............... 185
13.5 Numerical maximization ................................. 186
13.6 Partial adjustment equations ............................. 187
Conclusions ................................................... 189
A. Abbreviations ............................................ 193
B. Data ...................................................... 195
References .................................................... 207
Introdu ction
The fundamental nature of economic fluctuations is a point of obvious im
portance, but also one of the least understood questions in economics. Under
dispute are not details, but the basic mechanisms underlying the business
cycle phenomenon. Are these fluctuations of a sufficiently regular period to
be called cycles, or rather irregular ups and downs? Are these movements the
outcome of an endogenous process, or simply caused by exogenous shocks,
such as import price increases, changes in foreign demand, switches of pol
icy? Are the unpleasant concomitants of business cycles, like unemployment,
a sign of coordination failures of a market economy, or, quite the reverse,
optimal responses of economic agents to exogenous shocks?
This study tries to contribute to a solution of at least some of these
questions, on a methodological as well as on a substantive level. The empirical
investigations start with a thorough determination of stylized facts, then a
series of structural economic models is formulated and estimated to explain
these stylized facts. Since the disputes are related not only to models, but also
to the methodology to be used, I will address many methodological questions
of business cycle analysis and present the tools that I regard as appropriate.
Before giving an overview of this volume, I want to set forth some method
ological points that distinguish the present work from most of the comparable
studies. The first, and I think innovative point is that data analysis and model
building and evaluation are closely integrated. The primary tool employed
here to uncover stylized facts is the cross-spectral analysis of time series. The
advantage of spectral analysis is that it contains the complete information
about the cyclical characteristics of linear time series, and it displays this
information in an easily interpretable way. After estimating the structural
models, the cross spectra that are implied by these models are compared to
those obtained by the data analysis. The underlying methodological postu
late is that it is more important for a model to explain stylized facts than
to pass some formal specification tests. This point is extensively discussed in
Chapter l.
As a further non-standard feature, the structural models presented are
formulated and estimated in continuous time. While this method is presently
used only by a minority of econometricians, mainly because of its mathemat-
2 Introduction
ical complexity, it offers, for the problems under consideration, important
advantages over the standard discrete time estimation methods.
As I have indicated above, my concern is to identify the principal mech
anisms of business cycles, not to discuss details. This implies a modeling
strategy different from those of most other authors. It is not my aim to
obtain models that are optimal in the sense of yielding the most precise fore
casts. Many of my equations could be improved in obvious ways so that they
would probably give better predictions. Instead, my strategy is to accept the
simplest equation that is compatible with economic theory and is able to
explain the stylized facts. I think that this is the first step in a modeling
strategy that will ultimately also yield better forecasts. An advantage of sim
ple models depicting fundamental relationships is that they can be expected
to hold equally well for all industrialized countries. It is therefore natural to
investigate data of several countries. As a first step in this direction, all the
models in this study are applied to the data of two countries, Germany and
USA. One of the most encouraging results is the wide range of similarities
between these two economies.
Many of the basic ideas shaping the present study are not new, but stand
in a meanwhile long tradition. The work is part of an ongoing project on
business cycles that is carried out at SEMECON, University of Munich. The
project originated in the early works of Hillinger (1963, 1966); its current state
is documented in Hillinger (1992c). The SEMECON research is characterized
by the following features: It uses a methodology coming from the natural
sciences, which incorporates the thorough determination of stylized facts.
The models used to explain these stylized facts are based on the second
order accelerator (SOA) of fixed investment and production (explained in
Chapter 5). The models are formulated and estimated in continuous time.
Compared to earlier publications of SEMECON, the main contributions of
the present study are the following:
1. Some aspects of the underlying methodological principles are more thor
oughly discussed. New tools to implement the methodological ideas are
used.
2. Stylized facts are determined for a wider set of variables, including prices
and wages.
3. The business cycle models are enlarged to endogenize additional real and
also nominal variables.
4. A model of cyclical growth that can explain dominant features of long
term growth is developed.
5. A more sophisticated method for estimating continuous time models, due
to Harvey and Stock (1985), is used. A method to incorporate exogenous
variables into this framework is developed.
The study is divided into five parts. The Part I discusses the general
methodological principles employed. The econonometric methodology is de
scribed in Part V. At a technical level, the models are formulated in continu-
