Agent-Based Computer Simulation of Dichotomous Economic Growth

163 Pages·2000·6.139 MB·English

by  Roger A. McCain (auth.)

AGENT-BASED COMPUTER SIMULATION OF
DICHOTOMOUS ECONOMIC GROWTH
Advances in Computational Economics
VOLUME 13
SERIES EDITORS
Hans Amman, University ofA msterdam, Amsterdam, The Netherlands
Anna Nagumey, University ofM assachusetts at Amherst, USA
EDITORIAL BOARD
Anantha K. Duraiappah, European University Institute
John Geweke, University ofM innesota
Manfred GiIli, University ofG eneva
Kenneth L. Judd, Stanford University
David Kendrick, University of Texas at Austin
Daniel McFadden, University of California at Berkeley
Ellen McGrattan, Duke University
Reinhard Neck, University ofK lagenjurt
Adrian R. Pagan, Australian National University
John Rust, University ofW isconsin
Berc Rustem, University ofL ondon
Hal R. Varian, University ofM ichigan
The titles published in this series are listed at the end oft his volume.
Agent-Based Computer
Simulation of Dichotomous
Economic Growth
by
Roger A. McCain
Drexel University, Philadelphia, PA, USA
Springer Science+Business Media, LLC
Library of Congress Cataloging-in-Publication Data
McCain, Roger A.
Agent-based computer simulation of dichotomous economic growthiby Roger A. McCain.
p.cm.--(Advances in computational economics; v.l3)
Includes bibliographical references and index.
ISBN 978-1-4613-7085-7 ISBN 978-1-4615-4613-9 (eBook)
DOI 10.1007/978-1-4615-4613-9
I. Economic development--Mathematical models. 2. Econometric models--Computer
simulation. I. Title. II. Series.
HD75.5 .M39 1999
338.9'001 '13--dc21 99-047346
Copyright © 2000 Springer Science+Business Media New York
Originally published by Kluwer Academic Publishers, New York in 2000
Softcover reprint of the hardcover 1st edition 2000
All rights reserved. No part of this publication may be reproduced, stored in a retrieval
system or transmitted in any form or by any means, mechanical, photo-copying, recording,
or otherwise, without the prior written permission of the publisher,
Springer Science+Business Media, LLC.
Printed on acid-free paper.
This book is dedicated to the memory of Mary Gharst McCain, who
wanted me to be a lawyer.
CONTENTS
ACKNOWLEDGMENT
ix
1 INTRODUCfION 1
2 DICHOTOMIZATION WITHOUT STEADY GROWTH:
BASELINE SIMULATIONS 5
Figures for Chapter 2 22
3 STEADY ECONOMIC GROWTH: THE COBB-DOUGLAS
CASE WITH "ENGINEERING-SCHOOL" HUMAN CAPITAL 31
Figures for Chapter 3 38
4 SIMULATIONS OF STEADY ECONOMIC GROWTH WITH
A COBB-DOUGLAS PRODUCfION FUNCfION 39
Figures for Chapter 4 46
5 GROWTH WITH NON-UNITARY ELASTICITIES OF
SUBSmUTION 55
Figures for Chapter 5 63
6 LEARNING-BY -DOING AND THE PUZZLES OF
ECONOMIC GROWTH: SURVEY AND INTERPRETATION 71
Figure for Chapter 6 92
7 LEARNING BY OOING AND DICHOTOMOUS DEVELOPMENT 93
Figures for Chapter 7 102
8 SIMULATIONS WITH IRREGULAR NEIGHBORHOODS 111
Figures for Chapter 8 117
9 BOOLEAN TRADE NETWORKS 123
Figures for Chapter 9 127
10 BACKWASH AND SPREAD: TRADE NETWORKS IN
A SPACE OF AGENTS WHO LEARN BY OOING 131
Figures for Chapter 10 136
11 CONCLUDING SUMMARY 141
REFERENCES 145
APPENDIX: PROGRAM CODE 149
INDEX 161
ACKNOWLEDGMENT
This book has benefited from the examples, discussion and feedback provided by
scholars attending the annual Conferences on Computation in Economics and
Finance, sponsored by the Society for Computational Economics, Geneva, 1996,
Palo Alto, 1997, and Cambridge, 1998. Particular thanks are due to the participants
in the interest group on Agent-Based Computational Economics. The assistance,
encouragement, suggestions, and collaboration of my wife, Katherine W. McCain,
have also been invaluable.
1
INTRODUCTION
This book reports a project in agent-based computer simulation of pro
cesses of economic growth in a population of boundedly rational, learning agents.
The agents learn by trial and error, but also and very importantly by imitation. The
learning process is simulated by genetic algorithms (Rawlins, Holland and Miller,
Arifovic, Dawid, McCain, 1994) and the agents are placed in the grid of a cellular
automaton or Boolean network (Albin 1977, Albin 1998, White and Engelen,
Bruun) in order to allow for effects of space. Thus, the study brings together a num
ber of theoretical and technical developments, only some of which will be familiar
to a particular reader in some cases. In this first chapter, then, I review some issues
in economic growth and outline the objectives of the study. In the second chapter,
the simulation techniques will be introduced and illustrated with baseline simula
tions of boundedly rational learning processes that do not involve the complications
of dealing with long-run economic growth. The third chapter will sketch the con
sensus modem theory of economic growth which will be the starting point for fur
ther study. In the fourth chapter, a family of steady growth models are simulated,
bringing the simulation, growth and learning aspects of the study together. In sub
sequent chapters, variants on the growth model are explored in a similar way. The
ninth chapter introduces trade, with a spacial trading model that is combined with
the growth model in the tenth chapter.
EXPLANATION BY COMPARATIVE COMPUTER SIMULATION
In a certain sense (Young 1998) a simulation outcome "explains" the
result, by constructing a process which gives rise to the result. The word "explain"
has been placed in quotations because the verb "to explain" has a constellation of
related meanings (Nozick), and a specific meaning is understood. The meaning is
logical sufficiency: if a compact set of assumptions can be shown to be sufficient to
produce a certain result (or to produce it relatively frequently) the assumptions are
said to "explain" the result. Of course, the explanation is even stronger if necessity
as well as sufficiency can be established, if the relation of assumptions to result is
nonobvious, if this relationship is established with relative rigor and reliability, is
supported by empirical evidence, and so on. And there may be still other meanings
that we might attach to "explanation" in other circumstances.
The strategy of explanation adopted here is computer simulation.
Simulations can be used to establish constructive sufficiency. Suppose we begin
with a model of an economic process in which certain assumptions are made and
certain consequences asserted. A simulation of the model is run, and the conse
quences are indeed observed. The assumptions can be said to be sufficient to produce
the consequences, since the simulation is a constructed example in which the
assumptions do produce the consequences. This may be helpful in complex models
in which analytic results could be difficult to obtain, and in which the consequences
depend in part on random or pseudorandom processes, and may be a source of other
insights about the relationship of the assumptions to the consequences. However,
computer simulation brings with it further potentialities. In practice, any
simulation model will contain assumptions other than the ones we want to test. By
2
varying those side assumptions, we can determine how robust our sufficiency result
is --whether, in fact, a larger set of assumptions is required to produce the result, or
it can be attributed more narrowly to the assumptions under test. If it were possible
to vary all other assumptions exhaustively, this could establish necessity as well as
sufficiency. In practice this will not usually be possible, but necessity can be more
or less closely approximated, improving the power of the explanation at every step.
That method, comparative computer simulation, is the method used in this book.
Thus, the study is an exercise in comparative simulation. That is, the
same family of growth models will be simulated under different assumptions about
the nature of the learning process and details of the production and growth processes.
The purpose of this procedure is to establish a relationship between the assumptions
and the simulation results. If, for example, a change of assumptions about learning
produces a parallel change in simulation results in a wide range of growth models
based on different assumptions about the production and growth processes, then we
may more confidently assert that the simulation results are a consequence of the
learning assumptions rather than a consequence of the details of the growth model or
of the producti ve process.
Agent-based computer simulation also lends itself to the study of economic
activity with bounded rationality. (Simon 1955, 1978; Arthur) The neoclassical
assumption of absolute rationality may enable the economist to obtain analytic
results on necessary and sufficient conditions, uniqueness and efficiency and so on.
But empirical studies contradict the assumption of absolute rationality) In an
agent-based computer simulation, however, we may specify the processes agents
use, and by which they learn, and the information available to them, in ways
consistent with bounded rationality. Sufficiency and other results may then be
shown to be robust to particular forms of bounded rationality; and by means of
comparative simulation, the range of application to boundedly rational choice
processes may be to some extent delineated. In this book we are particularly
concerned with bounded rationality and imitative learning, and the assumption of
imitative learning is a key explanatory principle on which we will rely.
PUZZLES OF ECONOMIC GROWTH
The major objective of this book is to explain a fundamental characteristic
of modem economic growth: dichotomization.
Recent work in "endogenous growth theory" has been aimed in part at
explaining the following judgments of fact: 2
1) There is little evidence that dense populations are associated with lower per capita
incomes, as the law of diminishing returns in the presence of fixed land resources
might lead us to expect.
2) There is no clear tendency for economic growth to slow or stop with diminishing
returns to capital investment}
3) There is no apparent tendency for the marginal productivity of capital to decline
as capital is accumulated or to be higher in less developed than in more developed
countries.
4) There is no tendency for all countries to converge to a similar level of productiv
ity.4
3
5) Just the contrary: growth tends to be highly dichotomized, with the world divided
between more and less developed countries and regions, convergence of national pro
ductivity levels only within "convergence clubs," and many countries are divided
between more and less developed regions. 5 Dichotomous development is one of the
most obvious and important aspects of modem economic growth, and is the funda
mental fact for the study of less developed countries. Dichotomous growth is a
complicated phenomenon distinguishable from either convergence or divergence in
economic growth. Instead, dichotomous growth is a combination of convergence
within regions and divergence among regions. The division of the world into more
and less developed countries is the most obvious instance of dichotomous develop
ment. The "dualistic" division within countries, separating leading from lagging
regions in economic development, is another instance, characteristic of all major
less developed countries and also of many more developed countries. The emergence
of "convergence clubs" (Quah) is yet another instance of dichotomous development.
Thus, dichotomous development merits attention in theories of economic growth.
6) When trained individuals migrate from poorer to richer countries, the productivity
of their human capital approximates that in the destination country rather than the
origin country; but this is not so of those who stay at home.6
These are "puzzles" from the point of view of neoclassical Solow-Swan
theory of economic growth. The "new growth theory," is designed to solve the puz
zles. In the "new growth theory," some of these judgments are reconciled as conse
quences of the accumulation of human capital or, more generally, knowledge capital
(including investments in research, development, and design). This explanation goes
very roughly as follows: knowledge capital is partly a public good, so that
externalities and increasing returns can lead to endogenous autonomous growth con
sistently with some of the propositions above.7 However, it is difficult to accom
modate them all, and a further puzzle arises from the "new growth theory." If human
capital accumulation produces externalities and the nation is the unit of analysis.
then larger nations would be expected to grow faster than smaller nations. But there
is no evidence that this is so. This will be our seventh puzzle:
7) Whatever externalities there may be in human capital formation, there is no evi
dent tendency for larger nations to grow faster than smaller nations.
Thus, the book will return again and again to this key question: to what
extent can the simulations "explain" the puzzles of economic growth, and particu
larly the key puzzle of dichotomization, by constructing growth and learning pro
cesses that produce the puzzling results? And just what assumptions of the simula
tions are most predictably associated with the puzzling results?