Economic Evolution and Demographic Change: Formal Models in Social Sciences

423 Pages·1992·9.891 MB·English

by  Tönu Puu (auth.), Günter Haag, Ulrich Mueller, Klaus G. Troitzsch (eds.)

Lecture Notes in Economics
and Mathematical Systems 395
Founding Editors:
M. Beckmann
H. P. Ktinzi
Editorial Board:
H. Albach, M. Beckmann, P. Dhrymes, G. Feichtinger, W. Hildenbrand
W. Krelle, H. P. Ktinzi, K. Ritter, U. Schittko, R. Selten
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Fachbereich Wirtschaftswissenschaften
FernuniversiHit Hagen
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lnstitut ftir Mathematische Wirtschaftsforschung (IMW)
U ni versitat Bielefeld
Universitatsstr. 25, W-4800 Bielefeld I, FRG
G. Haag U. Mueller K. G. Troitzsch (Eds.)
Economic Evolution and
Demographic Change
Formal Models in Social Sciences
Springer-Verlag
Berlin Heidelberg New York
London Paris Tokyo
Hong Kong Barcelona
Budapest
Editors
Gi.inter Haag
II. Institut f. Theoretische Physik
Universitat Stuttgart
W-7000 Stuttgart, FRG
Ulrich Mueller
Zentrum fi.ir Umfragen, Methoden und Analysen (ZUMA)
B2, I, W-6800 Mannheim, FRG
Klaus G. Troitzsch
Institut flir Sozialwissenschaftliche Informatik
Universitat Koblenz-Landau
Rheinau 3-4, W-5400 Koblenz, FRG
ISBN 978-3-540-56172-9 ISBN 978-3-642-48808-5 (eBook)
DOl 10.1007/978-3-642-48808-5
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© Springer-Verlag Berlin Heidelberg 1992
Typesetting: Camera ready by author/editor
42/3140-543210 -Printed on acid-free paper
To the memory of
Dr. rer. nat. Uta Haag
Preface
In recent years there has been a growing interest in the complex relations between
economic evolution and demographic change. The emergence of a unified European
market and the fall of the Iron Curtain are only two recent issues where the economical
developments cannot be understood without the demographic ones, and vice versa.
Our capability of building satisfactory models which incorporate economic and de
mographic variables alike, still is seriously hampered by the lack of adequate modeling
concepts and the lack of data. It can safely be questioned whether the dominant
paradigm of neoclassical economics, the stable general competitive equilibrium, which
would only have to be enriched along the established lines by a few demographic vari
ables can provide the adequate theoretical basis.
The same can be said about the dominant paradigm in demography, the Stable
Population Model. One of the many deficiencies shared by both of these two still
predominant but increasingly obsolete paradigms is the complete neglect of the spatial
dimension of sociality, the non-randomness of any spatial distribution of people and
their activities.
The contributions in this volume spring from the very ambition to collect innova
tive formal models in social sciences and to open up new pathways in model building
efforts. Many of the contributions herein have come from an international group of sci
entists who have undertaken basic research about dynamic processes such as economic
development, spatial adjustments and demographic change.
In view of the numerous links between mathematics, physics and social sciences one
might assume that a great manifold of quite different concepts exists and can be used
for modelling of socio-economic processes. However, it turns out that very universal
mathematical concepts exist which have recently been summarized and formulated in
the principles of synergetics, set up by H. Haken and which comprise mathematical
theories of stochastic processes and nonlinear dynamical systems.
Therefore, a growing number of economists have recently been inspired by the clear
parallels between economic evolution and demographic change with phenomena from
natural sciences such as selforganization, cyclical or even chaotic behaviour.
The book is the outgrowth of two conferences. The first of these meetings, "Interdis
ciplinary Colloquium on Forcasting for Systems with Chaotic Evolution", was organized
at the occasion of Wolfgang Weidlich's 60th birthday, April 1991, at the University of
Stuttgart by G. Haag and H. Grabert, the second, "Formal Models in Demography",
was arranged by G. Haag, U. Mueller and K.G. Troitzsch, December 1991 at the Center
VIII Preface
for Survey Research and Methodology (ZUMA), in Mannheim.
Of the many papers presented at these two meetings, a selection with a common
orientation towards evolution and adjustment processes in economy, demography, and
geography is published in this volume. The papers have in most cases been substantially
enlarged and revised for publication.
Therefore, it is natural to subdivide this volume into three parts, where Part I is
mainly related to demographic change, Part II to geographical development and Part III
is related to demographic change. The present volume aims at providing a new look
at this triangle in view of the classical background of discussions by introducing new
research ideas focussing in nonlinear dynamics and stochastic modelling.
Thus the main purpose of this book is to make a contribution to the interdisciplinary
work needed to integrate the efforts between these three research fields and to serve as
a res arch source in demonstrating the current state of art in dynamic modelling.
The book is addressed to social scientists in general, and those in particular with
a background in economics, geographics and demographics. It should be of interest
to mathematicians, physicists and systems analysts interested in model building and
applications of nonlinear dynamics.
Acknow ledgements
The first conference was supported by the "Volkswagen Stiftung", Hannover, which
over years also has funded the work of some of the contributors to this volume. The
second conference was supported by the "Fritz Thyssen Stiftung", Ki:iln.
We gratefully acknowledge this substantial support, without which none of the con
ferences could have taken place.
We gratefully acknowledge the excellent cooperation with W.A. Miiller of the
Springer Verlag, Heidelberg.
The manuscript has been edited and prepared for publication at the Institute for
Informatics and Social Science at the University of Koblenz. Sylvia Schuller and Ursula
Schwerin re-typed some of the papers, while Christian EiBing and Christoph Wick
prepared the whole manuscript. The editors are sincerely grateful for their perseverance
and unflagging attention to details.
Giinter Haag
Ulrich Mueller
Klaus G. Troitzsch
Table of Contents
Preface VII
I Formal Models in Economics 1
1 A chaotic process with slow feed back: The case of business cycles 3
by Tonu Puu
1.1 A first model .... 3
1.1.1 Investments. 3
1.1.2 Consumption 4
1.2 The cubic iterative map 5
1.2.1 Fixed points, cycles and chaos 5
1.2.2 Formal analysis of chaotic dynamics. 12
1.2.~ Symbolic dynamics . . . . 15
1.3 "Brownian random walk" 15
1.4 Digression on order and disorder. 18
1.5 The general model ... 19
1.5.1 Relaxation cycles .. 20
1.5.2 Other cycles . . . . . 26
1.5.3 The Slow Feed Back 26
1.6 Conclusion.......... 33
2 Nonlinear Interactions in the Economy 35
by Erik Mosekilde, Jesper S. Thomsen, and John Sterman
2.1 Introduction ....... . 35
2.2 The Long Wave Model . . 38
2.3 Mode-Locking and Chaos. 45
2.4 Conclusion ........ . 54
3 Fast and Slow Processes of Economic Evolution 62
by Ake E. Andersson
3.1 Introduction and Background ................ . 62
3.2 The Problems of Economic Development Theory . . . . . . . 63
3.3 Synergetic Development Economics - Some Basic Concepts 64
XII Table of Contents
3.4 The Arena ..... 65
3.5 Rules of the Game 66
3.6 Networks ..... . 66
3.7 Knowledge As Networks and Knowledge On Networks. 67
3.8 Communication and Creativity - some Historical Evidence 68
3.9 Creativity and Communications - Econometric Results 69
3.10 The Inverted Explanation ....... . 70
3.11 The Destruction of the Industrial Society 72
3.12 The New Economic Structure ..... . 73
4 A stochastic model of technological evolution 75
by W. Ebeling, M.A. Jimenez-Montano, E. Bruckner, and A. Scharnhorst
4.1 Introduction ................... . 75
4.2 A Substitution Model .............. . 78
4.3 Application of a general evolutionary model to technological change 82
4.4 Discussion . . . . . . . . . . . . . . 86
5 Evolution of Production Processes 96
by Klaus G. Troitzsch
5.1 Introduction .... 96
5.2 Basic Assumptions 97
5.3 Formalization ... 97
5.4 Chernenko's Results 99
5.5 An alternative macro model 100
5.6 Simulation results . . . . . . 101
5.7 Modeling evolution on the individual level 104
5.7.1 Simulation run with total extinction 105
5.7.2 Simulation run without extinction. 110
5.8 Conclusions . . . . . . . . . . . . . . . . . . 112
6 Innovation Diffusion through Schumpeterian Competition 115
by Michael Sonis
6.1 Introduction: From "Homo Economicus" to "Homo Socialis": Innovation
diffusion as a collective socio-ecological dynamic choice process. 115
6.2 Analytical basis of Schumpeterian Competition: Collective choice and
relative socio-spatial dynamics . . . . . . . . . . . . . . . . . . . . . .. 119
6.3 Explicit analytical presentation of the innovation diffusion dynamics:
Dynamic choice models. .......................... 122
6.4 Intervention of an active environment: Generation of innovation adoption
niches. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 123
6.5 Temporal innovation diffusion process. . . . . . . . . . . . . . . . . .. 125
6.5.1 Qualitative analysis of the Schumpeter competition cycles for
Clusters of competitive innovations . . . . . . . . . . . . . .. 128
6.5.2 Variational principle of meso-level collective choice behaviour. 134
6.6 Concluding Remark. . . . . . . . . . . . . . . . . . . . . . . . . . .. 137
Table of Contents XIII
7 Nonlinear Threshold Dynamics: Further Examples for Chaos in Social
Sciences 141
by Gustav Feichtinger
7.1 Introduction................................. 141
7.2 A Short Course into Chaos. . . . . . . . . . . . . . . . . . . . . . . .. 142
7.3 How Addictive Behaviour and Threshold Adjustment May Imply Chaos 143
7.4 How Asymmetric Investment Behaviour of Two Competing Firms Gen-
erates Chaos. . . . . 146
7.5 Concluding Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . .. 153
II Formal Models in Geography 155
8 Geography, Physics and Synergetics 157
by Denise Pumain
8.1 Introduction . . . . . . . . . . . . . 157
8.2 Models of geographical interactions 158
8.2.1 Polarization and gravitation 158
8.2.2 Reformulations of the gravity model . 160
8.2.3 The entropy maximizing approach. 162
8.2.4 About men and particles ...... 163
.....
8.3 Models of geographical structures 163
8.3.1 The relativity of geographical space 164
8.3.2 Fractality of geographical space 164
.....
8.3.3 Space-time convergence 166
8.3.4 The example of urban hierarchies '. 169
8.3.5 Processes and geographical forms 171
8.4 Conclusion . . . . . . . . . . . . . . . . . 173
9 Chaotic Behaviour in Spatial Systems and Forecasting 176
by Gunter Haag
9.1 Introduction ....................... . 176
9.2 An Example for Chaotic Evolution: Migratory Systems 178
9.2.1 A Numerical Simulation 181
9.3 Estimation of Trend Parameters . . . . . . . . . 185
9.4 The Estimation Procedure . . . . . . . . . . . . 185
9.5 Forecasting for Systems with Chaotic Evolution 186
9.5.1 Step I: Confidence Limits on Model Parameters by Monte Carlo
Estimation. . . . . . . . . . . . . . . . . . . . . . . . . . 187
9.5.2 Step II: Monte Carlo Simulation of Systems Trajectories .... 187
10 Model Identification for Estimating Missing Values in Space-Time
Data Series: Monthly Inflation in the US Urban System, 1977-1990 192
by Daniel A. Griffith
10.1 Introduction 192
10.2 Background . . 193