Theory of Markets: Trade and Space-time Patterns of Price Fluctuations A Study in Analytical Economics

418 Pages·1995·10.62 MB·English

by  Professor Bertrand M. Roehner (auth.)

Advances in Spatial and Network Economics
Managing Editor Editorial Board
David F. Batten Me E. Andersson
Martin J. Beckmann
Jacques Thisse
Robert E. Kuenne
Takashi Takayama
Titles in the Series
Martin J. Beckmann and Tonu PUll
Spatial Structures
Aisling J. Reynolds-Feighan
The Effects of Deregulation on U.S. Air
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Kiyoshi Kobayashi and Kazuhiro Yoshikawa (Eds.)
The Cosmo-Creative Society
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and Lars Westin (Eds.)
Patterns of a Network Economy
Bertrand M. Roehner
Theory of Markets
Trade and Space-time Patterns of Price Fluctuations
A Study in Analytical Economics
With 149 Figures
Springer-Verlag
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Professor Bertrand M. Roehner
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University Paris VII
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lSBN-13:978-3-642-79481-0 e-lSBN-13:978-3-642-79479-7
DOl: 10.1007/978-3-642-79479-7
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The earth is often in astronomical calculations considered as a point
and with substantially accurate results. But the precession of the
equinoxes becomes explicable only when account is taken of the
ellipsoidal bulge of the earth. So in the theory of value a market is
usually considered as a point in which only one price can obtain; but
for some purposes it is better to consider a market as an extended
region.
Harold HOTELLING
Stability in competition (Economic Journal 1929)
"Data! data! data!" he cried impatiently. "I can't make bricks
without clay."
Sir Arthur Conan DOYLE
The Adventure of the Copper Beeches.
I Preface
Book titles, because they are compromises between concision and precision,
provide but an approximate description of real content. For this book an al
ternative and more comprehensive title would be: An investigation of spatial
arbitrage as an introduction to the theory of commodity markets: trade and
space-time patterns of price fluctuations. In this title, both the specificities
and the limitations of our approach are emphasized. Firstly, our approach con
centrates on the basic mechanisms of spatial arbitrage, leaving aside a number
of accessory facets of international trade such as the impact of quotas or of ex
change rates. Secondly, for the sake of simplicity we restrict ourselves to single
commodity markets; the interrelationship of different goods on multi-commodity
markets are only occasionally mentioned. The previous restrictions, however
drastic they may at first appear delimit and define what can be considered as the
core of the process of trade and of spatial transactions. Having thus simplified
the object of our study, we are able to tackle the problem in a systematic way
and to model spatial differentials along with their relationships to the volume
of trade both in eqUilibrium and in non-equilibrium situations. As far as the
subtitle of the book is concerned, we shall postpone the discussion of what is
meant by the expression "analytical economics" until the concluding chapter.
The starting point of our inquiry was a simple yet basic problem in economic
history: a great number of price records have been collected and published
during the last fifty years; they constitute a set of time series characterized
both by good resolution in time and by rather long time spans of two or even
three centuries. Yet in spite of a number of attempts going back to Beveridge
(1921,1922), Labrousse (1932), Abel (1935) or Kendall (1953) the question of
their economic significance is still largely unanswered, especially as far as short
term price fluctuations are concerned. Is it possible to uncover the mechanisms
of market integration from an analysis of price series? What is the relationship
between the volume of trade and the level of transport rates? How are arbitrage
policies actually implemented? In which ways is the exchange pattern between
markets modified during price peak periods? In the process of analysing such
issues, some definite spatial price patterns showed up; this was all the more
surprising in view of the chaotic behaviour of short-term prices. Furthermore,
growing evidence gradually accumulated showing that the validity of those
patterns actually extends to modern commodity markets as well.
viii Preface
While investigating the aforementioned issues, we were led to address a number
of related econometric questions. What are the distinctive features of spatial
autoregressive pr9cesses? Could multiple price series adequately be described
within the framework of space-time autoregressive processes? What are the
characteristic properties of space-time propagation models?
What we believe to be one of the most interesting features of our empiri
cal findings is the stability of emerging price patterns; they may provide firm
points of reference in the ever changing economic world. The first chapters
will probably be more appealing to economists and economic historians, while
econometricians will rather focus on the last ones.
This book relates an inquiry which has been in progress for a number of years.
It is a real pleasure at this point to thank the many people who kindly pro
vided support and advice. I am indebted to Edmond Malinvaud whose initial
encouragements were at the starting point of this study. I am grateful to Guy
Laroque whose guidance was enlightening on several occasions. By their sug
gestions Luc Anselin, David Batten, Fran~ois Bourguignon, Hubert Jayet and
Alain Montfort gave me the opportunity of enlarging the scope of my work.
Many thanks to them. The American Cliometric Society and the European CJio
metric Society welcomed discussion of this work even at an early stage of its
development; I am grateful to many of its members for stimulating suggestions
and discussions, especially to Donald McCloskey, Larry Neal, Kevin O'Rourke,
Gunnar Persson, Pascal Saint Amour, Pierre Sicsic and Jeffrey Williamson.
While writing this book I had the opportunity of teaching statistical and spatial
geography and this has been a refreshing experience. Moreover my contacts in
the field of geographical analysis always have been a source of stimulation; I
am particularly pleased to express my gratitude to Gordon Clark, Peter Haggett,
Robert Haining, Denise Pumain and Therese Saint Julien.
Finally, I would like to express many thanks to my colleagues at the level of
my department and especially to Alain Bouquet, Fran~ois Delduc, Bernard Diu,
Giorgio Giavarini, Jean Kaplan, Jean Letessier and Galliano Valent.
The book is dedicated to my wife Brigitte and to my son Sylvain whose cheerful
encouragements and stimulating support have been invaluable.
Bertrand Roehner
Paris, January 1994
Contents
PART I PROLOGUE
Chapter 1 Introduction 1
1 Smith's "invisible hand" in commodity markets I
2 Spatial interaction in economic theory 2
3 Spatial interaction in geographical analysis 3
4 Regional market integration and famines 5
5 Organization of commodity markets 7
5.1 The twentieth century wheat market 7
5.2 Which prices? 7
5.3 Long term evolution of ocean freight rates 10
6 Spatial price differentials 15
6.1 Three examples of spatial price differentials 15
6.2 Evolution of spatial price differentials 20
7 The concept of market integration 22
8 Defining and delimiting the problems to be investigated 25
9 The methodology of our approach: parsimony as a condition of
testability 27
10 Empirical findings 28
10.1 Interdependence between markets 28
10.2 Price intercorrelations 29
10.3 Variations in trade with respect to transportation costs 29
lOA The evolution of market integration 31
10.5 The evolution of price volatility 33
11 Outline of the book 34
Chapter 2 Pricing models 37
1 Dynamic market models with exogenous price expectations 37
x Contents
1.1 Cobweb models without inventories 38
1 Conservative price anticipation 39
2 Extrapolative price anticipation 41
3 Adaptative price anticipation 41
4 The problem of mixed time scales 42
1.2 Cobweb models with inventories 43
1 A linear model 44
2 An example: the FAO cocoa price model 45
3 Comparison with empirical evidence 46
4 Nonlinear models 49
2 Rational expectations models 50
2.1 Origins of the concept of rational expectations 50
2.2 Rational expectations in commodity markets without
inventories 54
2.3 Rational expectation with inventories 57
2.4 More about expectional equations 58
3 Oligopoly theory and spatial competition 60
3.1 The monopoly optimum 60
1 The firm is able to sell all it wishes 60
2 The firm cannot sell all it wishes 60
3.2 The duopoly eqUilibrium 61
1 Coumot's model 61
2 Nash eqUilibrium 62
3 Spatial competition: two marketplaces 62
4 Spatial competition: several marketplaces 64
A Appendix A: Conditional expectation: a mathematical reminder 66
A.l Conditional expectation: two random variables 66
1 Definitions 66
2 Basic properties of conditional expectation 67
A.2 Conditional expectation: generalization to n random variables 68
B Appendix B: Consumption, closing stocks and prices of cocoa, sugar
and wheat 70
PART II Equilibrium models
Chapter 3 The stochastic Enke-Samuelson arbitrage model 73
1 Defining the stochastic Enke-Samuelson model 74
1.1 The spatial price equilibrium model 74
1 General presentation 74
2 The spatial price eqUilibrium model for two markets 75
Contents xi
3 Algebraic solution 77
4 Variational solution 78
1.2 Possible generalizations to more than two markets 79
1 The algebraic solution 79
2 The variational solution 79
1.3 The stochastic Enke-Samuelson model 80
1 The rationale of a stochastic model 80
2 Smoothing and linearization of the model 81
3 Consistency tests of the model 82
4 Predictions of the model 83
2 The stochastic Enke-Samuelson model for two markets 83
2.1 Basic equations 86
2.2 Solutions of the linear model 88
1 Uncorrelated local shocks (identical means) 88
2 Correlated local shocks (identical means) 90
3 Correlated local shocks (different means) 90
4 Linear versus nonlinear model 92
3 Chain of markets 92
3.1 Chain of markets: direct trade relations restricted to closest
neighbours 95
1 Solving the linear model 96
2 Proof 97
3 Price differentials as a function of distance 100
4 Linear versus nonlinear model 100
3.2 Chain of markets with an arbitrary exchange pattern 100
1 Equations and results 101
2 Roots of reciprocal equation 102
3 Covariance function 103
4 Variance 104
5 Trade 105
6 Discussion 105
4 Market networks 106
4.1 Solving the linear Enke-Samuelson model 106
1 Equations of the model 106
2 Solution by Fourier transformation 107
3 Integral representation of the covariance function 107
4 Asymptotic expressions of the price covariance function 109
5 Approximation formula 109
4.2 Process of market integration 110
4.3 Price differentials as a function of inter-market distance 112
A Appendix A: Covariance function of a network of markets 113