Transformations Through Space and Time

Transformations Through Space and Time

NATO ASI Series Advanced Science Institutes Series A Series presenting the results of activities sponsored by the NA TO Science Committee, which aims at the dissemination of advanced scientific and technological knowledge, with a view to strengthening links between scientific communities. The Series is published by an international board of publishers in conjunction with the NATO Scientific Affairs Division A Life Sciences Plenum Publishing Corporation B Physics London and New York C Mathematical and D. Reidel Publishing Company Physical Sciences Dordrecht and Boston D Behavioural and Martinus Nijhoff Publishers Social Sciences Dordrecht/Boston/Lancaster E Applied Sciences F Computer and Springer-Verlag Systems Sciences Berlin/Heidelberg/New York G Ecological Sciences Series D: Behavioural and Social Sciences - No. 29

Transformations Through Space and Time An Analysis iqf Nonlinear Structures, Bifurcation Points and Autoregressive D e p e n d e n c i e ~ s edited by Daniel A. Griffith Department of Geography State University of New York at Buffalo Buffalo, New York USA Robert P. Haining Department of Geography University of Sheffield Sheffield England 1986 Martinus Ni,jhoff Publishers Dordrecht / Boston / Lancaster Published in cooperation with NATO Scientific Affairs Division

Proceedings of the NATO Advanced Study Institute on "Transformations Through Space and Time", Hanstholm, Denmark, August 3-14, 1985 Library of Congress Cataloging in Publication Data ISBN-13: 978-94-010-8472-7 e-isbn-13: 978-94-009-4430-5 001: 10.1007/978-94-009-4430-5 Distributors for the United States and Canada: Kluwer Academic Publishers, 190 Old Derby Street, Hingham, MA 02043, USA Distributors for the UK and Ireland: Kluwer Academic Publishers, MTP Press Ltd, Falcon House, Queen Square, Lancaster LA 1 1 RN, UK Distributors for all other countries: Kluwer Academic Publishers Group, Distribution Center, P.O. Box 322, 3300 AH Dordrecht, The Netherlands 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, photocopying, recording, or otherwise, without the prior written permission of the publishers, Martinus Nijhoff Publishers, P.O. Box 163, 3300 AD Dordrecht, The Netherlands Copyright 1986 by Martinus Nijhoff Publishers, Dordrecht Softcover reprint of the hardcover 1 st edition 1986

v PREFACE In recent years there has been a growing concern for the development of both efficient and effective ways to handle space-time problems. Such developments should be theoretically as well as empirically oriented. Regardless of which of these two arenas one enters. the impression is quickly gained that contemporary wo,rk on dynamic and evolutionary models has not proved to be as illuminating and rewarding as first anticipated. Historically speaking. the single. most important lesson this avenue of research has provided. is that linear models are woefully inadequate when dominant non-linear trends and relationships prevail. and that independent activities and actions are all but non-existent in the real-world. Meanwhile. one prominent imp 1 ication stemming from this 1 iterature is that the easiest modelling tasks are those of specifying good dynamic space-time models. Somewhat more problematic are the statistical questions of model specification. parameter estimation. and model validation. whereas even more problematic is the operationalization of evolutionary conceptual models. A timely next step in spatial analysis would seem to be a return to basics. with a pronounced focus both on specific problems (and data) and on the mechanisms that transform phenomena through space and/or time'. It appears that these transformation mechanisms must embrace both non-linear and autoregressive formalisms. Given. also. the variety of geographic forms. they must allow for bifurcation points to emerge. too. A better understanding of the transformation mechanisms will help dynamic and evolutionary spatial modeling. This last class of models is especially in need of enlargement. and accompanying its expansion should be clearer insights into the complexity of geographical organization. Because coming to grips with this issue requires a firm grasp of dynamic and evolutionary spatial modelling problems. it seemed appropriate to provide a forum for intensive interaction among scholars of spatial analysis. A NATO Advanced Studies Institute was held in July of 1980 at the Chateau de Bonas. in Bonas. France. to address critical issues associated with dynamic spatial modelling research. The successful and fruitful cooperation of European and North American scientists at this first Institute provided an impetus for organizing another one that focused on evolving geographical structures. This second NATO Institute was held in July of 1982 at <i Cappuccini>. in San Miniato. Italy. to address fundamental questions in the formulation and calibration of evolutionary geographical models. Again. and in turn. the successful and fruitful cooperation of European and North American scholars at this second Institute furnished the motivation for organizing a third one that would focus on transformations through space and time. One important consensus reached in these two previous Institutes maintains that space and time domains are inseparable. and that for many important classes of events the simultaneous treatment of space and time is an important criterion for

VI an acceptable model. Another conclusion has been that although numerous dynamic spatial models have been formulated, far more attention needs to be paid to the development of evolutionary spatial models, which are substantially fewer in number. This third Institute, the basis for this volume, held at the Hotel Hanstholm, Denmark, drew upon the scholarship and findings of these preceding two Institutes in order to take yet another step in the examination of space-time processes, patterns and structures. This third Institute had as its general objective the achievement of a more informed and deeper understanding of space-time processes and patterns for socio-economic phenomena, and how these patterns may be more accurately described and predicted. Hence it was far less ambitious in terms of the goals that were set for it. Its four specific aims were: (1) to acquire a more comprehensive understanding of space-time phenomena; (2) to identify and describe important real-world space-time processes; (3) to exchange ideas and perspectives, in a mul tidisciplinary forum, that are held by quantitative geographers, spatial economists, regional scientists, planners and statisticians from different NATO countries, concerning the mechanisms that transform phenomena over space and through time,: and, (4) to advance the understanding of space-time transformations, especially as they pertain to spatial structure, spatial interaction and urban dynamics. Accordingly, the Institute focused on theories and empirically based mathematical models of space-time transformations. International exchanges of ideas are both a valuable and a productive means of reviewing the stateof-the-art as well as stimulating fresh ideas that lead to a sound and lasting contribution to knowledge. In pursuit of this goal the lectures were organized around the following four principal themes: (a) transformations of geographical structures, (b) transformations of urban systems, (c) transformations involving interaction over space, and (d) transformations involving autoregressive dependencies. The mathematical formalisms behind all four themes are non-linear equations, bifurcation points, and autoregressive dependencies. Each of the expositions included in this volume touches upon all three of these principal notions, regardless of which of the four generic categories a paper falls into. Non-linear systems of equations are conspicuous in the models used to explore migration, predator-prey relations, quadratic programming problems, and other features affiliated with the transforming of geographical structures, in the retail models of transformations involving interaction over space, in the mode 1 s of government fisca 1 pol icy, urban

VII systems evolution, and entropy maximization that are concerned with transformations of urban systems, and in the autoregressive models, especially the time-series ARIMA ones. Bifurcation points are alluded to quite often, and are explicitly discussed within the context of urban systems. Autoregressive dependencies particularly are inspected in papers treating spatial autocorrelation mechanisms. All in all, these three principal formalisms are frequently developed and applied in this volume. We are indebted to the Scientific Affairs Division of the North Atlantic Treaty Organization, the National Science Foundation, and the State University of New York for providing funding of the Institute, to Drs. Robert Bennett, Bruno Dejon, Ross MacKinnon and Giovanni Rabino for serving as advisors to the Institute, and to Drs. Johannes Broecker, Ross MacKinnon, Gordon Mulligan, Keith Ord, Daniel Wartenberg, Anthony Williams and Michael Woldenberg for acting as referees during the editing of this volume. Special appreciation goes to Mr. Kjeld Olsen and his staff, of the Hotel Hanstholm, for their hospitality during the Institute, and for providing an inviting and relaxing physical environment, to the Geography Department of the State University of New York at Buffalo for providing word-processing facilities for the typesetting of this volume, and to Diane Griffith for the typing of much of this volume and her efforts in helping to put together both the Institute and this volume. Buffalo, New York February 19, 1986 Daniel A. Griffith and Robert P. Haining

IX TABLE OF CON'l'BNTS PREFACE INTRODUCTION SECTION 1. TRANSFORMATIONS OF GEOGRAPHICAL STRUCTURES Computable Space-time Equilibrium Models by W. Macmillan Trade as Spatial Interaction and Central Places by L. Curry Income Diffusion and Regional Economics by R. Haining Transportation Flows Within Central Place Systems by M. Sonis Stochastic Migration Theory and Migratory Phase Transitions by W. Weidlich and G. Haag Page V 1 7 10 27 59 81 104 SECTION 2. TRANSFORMATIONS OF URBAN SYSTEMS 118 Dynamic Central Place Theory: An Appraisal and Future Prospects by J. Huff. et. al. 121 Non-linear Representation of the Profit Impacts of Local Government Tax and Expenditure Decisions by R. Benne tt 152 Comprehensive Dynamic Urban Models: Integrating Macro- and Microapproaches by M. Birkin and M. Clarke 165 New Developments of a Dynamic Urban Retail Model With Reference to Consumers' Mobility and Costs for Developers by S. Lombardo 192 SECTION 3. TRANSFORMATIONS INVOLVING INTERACTIONS OVER SPACE 209 Disequilibrium in the Canadian Regional System: Preliminary Evidence. 1961-1983 by P. Kanaroglou and Y. Papageorgiou 212

x Modelling an Economy in Space and Time: The Direct Equilibrium Approach With Attraction-regulated Dynamics by B. Dej on 234 Towards a Behavioral Model of a Spatial Labor Market by C. Amrhein and R. MacKinnon Modeling Discontinuous Change in the Spatial Pattern of Retail Outlets: A Methodology by A. Fotheringham and D. Knudsen 247 273 SECI'ION 4. TRANSFORMATIONS INVOLVING AUTOREGRESSIVE DEPENDENCIES 293 Problems in the Estimation of the Spatial Autocorrelation Function Arising From the Form of the Weights Matrix by G. Arbia 295 EPILOGUE INDEX Model Identification for Estimating Missing Values in Space-time Data Series: Monthly Inflation in the U. S. Urban System. 1977-1985 by D. Griffith INSTITUTE PARTICIPANTS 309 320 322 325