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Population Dynamics in Space UNIVERSITY of UMEÅ1987 A Contribution to Population Dynamics in Space by Nikias Sarafoglou Umeå Economic Studies No. 179 UNIVERSITY OF UMEÅ1987 ISSN 0348-1018 UNIVERSITY OF UMEÂ Department of Economics S-901 87 UHEA A Contribution to Population Dynamics in Space by Nikias Sarafoglou m UNIVERSITY OF UMEA 3 Department of Economics Civilekonom Nikxas Sarafoglou, .institutionen för nationalekonomi för­ svarar fredagen den 11 mars 1988 kl 10.00 i Humanisthuset, hörsal E, Umeå universitet, en akademisk avhandling med titeln "A Contribution to Population Dynamics in Space" för vinnande av ekonomie doktorsexamen. ABSTRACT Sarafoglou, N., 1987. A Contribution to Population Dynamics in Space, Umeå Economic Studies, No. 179, 225 pages. Population models are very often used and considered useful in the policy-making process and for planning purposes. In this research I have tried to illuminate the problem of analysing population evolution in space by using three models which cover a wide spectrum of comple­ mentary methodologies: a The Hotell.ing-Puu model b A multiregional demographic model c A synergetic model Hotelling's work and Puu's later generalization have produced theoreti­ cal continuous models treating population growth and dispersal in a combined logistic growth and diffusion equation. The multiregional model is a discrete model based on the Markovian assumption which simulates the population evolution disaggregated by age and region. It is further assumed that this population is governed by a given pattern of growth and interregional mobility. The synergetic model is also a discrete model based on the Markovian assumption incorporating a probabilistic framework with causal structure. The quantitative description of the population dynamics is treated in terms of trend parameters, which are correlated in turn with demo-economic factors. Keywords: Population growth, population age structure, migration, labour market, housing market, production function, stochas­ tic differential equations, partial differential equations. Author's address: University of Umeå, Department of Economics, S-901 87 Umeå, Sweden. ISSN: 0348-1018 ISBN: 91-7174-320-0 Tryckort: Umeå Tryckår: 1987 Mailing address Telephone Post giro account S-901 87 UMEÅ, Sweden 090 - 16 50 00 1 5815-3 exvai aÿxeputtêvo trtoùs yoveis (um AâCapo Rax Hopla There is real outer world which exists independently of our act of knowing. The real outer world is not directly knowable. Planck's canons (1932) 1 Acknowledgements As you set out for Ithaka hope your road is a long one, full of adventure» full of discovery • • • • • p • Hope your road is a long one. May there be many summer mornings when, with what pleasure, what joy, you enter harbours you're seeing for the first time; may you stop at Phoenician trading stations to buy fine things, mother of pearl and coral, amber and ebony, sensual perfumes of every kind - as many sensual perfumes as you can; and may you visit many Egyptian cities to learn and go on learning from their scholars. Keep Ithaka always in your mind. Arriving there is what you're destined for. But don't hurry the journey at all. Better if it lasts for years, so you're old by the time you reach the island, wealthy with all you've gained on the way, not expecting Ithaka to make you rich. Ithaka gave you the marvellous journey. Without her you wouldn't have set out. She has nothing left to give you now K. Kavafis "Ithaka" I started writing this dissertation during my stay at the Inter­ national Institute for Applied Systems Analysis, Laxenburg, summer 1984, and I realized my "Ithaka" at the Department of Economics, Umeå University. I want to express my deep gratitude to my supervisor Professor Â.E, Andersson. Access to his wide spectrum of knowledge, his far-reaching ideas and his living international research network is a creative stimulus for any student of regional economics. He taught me that regional science is based on interaction of homo oeconomicus with other homines. I am also indebted to Professor T. Puu for his invaluable help with continuous models. He taught me that the analysis of homo oeconomicua needs spatial dimensions, despite mainstream spaceless economics. 11 I reserve a special expression of gratitude to my colleaque M.O. Olsson who has been a continuous and constructive source of help during all these years. I am beholden to Or. G. Haag, Professor W. Weidlich, Dr. M. Munz from Stuttgart University for their co-operation and hospitality in Stuttgart. I would also like to acknowledge the qntique and suggestions of Professor R. Ginsberg during my stay in Philadelphia. Deep appreciation goes to all who helped me with their insightful comments while this work was in preparation: Professor F. Snickars from the Royal Institute of Technology, Professor J.E. Lane, Professor D. Batten, Professor A. Karlqvist, Professor H. Wallin, Professor U. Zaknsson, Professor L. Ivarsson, Professor B. Johansson, Professor K.G. Löfgren, and Dr. S. Ersson from Umeå University. I am grateful to my colleaques K.G. Holmberg for computer assistance, and to B. Knström, L. Engström for their comments. I am obliged to Dr. N. Broadbent. for his linguistic contribution. Special thanks are due to the secreterial staff of the Department I.M. Nilsson, E. Cederblad, G. Renström, who word-processed the manuscript, to its final form. I qratefully acknowledge the financial support from the Faculty of Social Sciences of Umeå University, the Swedish Council for Planning and Coordination of Research (FRN), Ministry of Labor, and Gösta Skoglunds International Fond. My gratitude goes to my friend P. Sauramo from the Department of Economics of Helsinki University for his encouraging and useful comments. Last but not. least, I mention my appreciation to Asa for her stoicism and mental support these past, years. Umeå, December 1987 Nikias Sarafoglou I A CONTRIBUTION TO POPULATION DYNAMICS IN SPACE AND TIME TABLE OF CONTENTS page ACKNOWLEDGEMENTS CHAPTER I: INTRODUCTION AND OVERVIEW 1.1 On the interface between economics anddemography 1 1.2 Historical review of population theories 9 CHAPTER II: INTERACTION BETWEEN DEMOGRAPHY AND ECONOMICS 2.1 Introduction 16 2.2 The logistic model 17 2.3 The Lotka-Volterra model 20 2.4 Economic fertility theories 28 CHAPTEFt III: A STUDY OF CONTINUOUS ECONOMIC SPATIO- TEMPORAL MODELS FOR POPULATION ANALYSIS 3.1 An overview of selected models 38 3.2 Hotelling's model 41 3.2.1 A historical note 41 3.2.2 A primer on vector calculus 42 3.2.3 Population dispersal in two-dimensional space 47 3.2.4 Population growth 52 3.2.5 Derivation of the logistic equation 55 3.2.6 The basic model 56 3.2.7 Later investigations of Hotelling's equation 58 3.2.8 Causes of migration 61 3.2.9 Concluding comments 62 3.3 Puu's model 63 CHAPTER IV: PURE DEMOGRAPHIC MODELS 4 Introduction 74 4.2 Models considering age and time 76 4.2.1 The life table 76 4.2.2 The one-region growth model 82 4.3 Models considering age, time, and space 89 4.3.1 The multiregional life table 89 4.3.2 The multiregional demographic model 94 4.4 Interacting populations: two-sex models 97 IV page CHAPTER V: APPLICATION OF THE MULTIREGIONAL DEMOGRAPHIC MODEL TO SWEDEN 5.1 Regional subdivisions of Sweden 102 5.2 A general outline of regional population growth m 104 Sweden 5.2.1 Historical trends in regional population development 104 5.2.2 Current trends m regional population growth 107 5.3 A test projection and conclusions 115 5.4 Critigue of the multiregional demographic model 122 CHAPTER VI: THE THEORETICAL STRUCTURE OF THE SYNERGETIC MODEL 6.1 Introduction 133 6.2 Assumptions 134 6.3 The model 135 6.4 Continuous and discrete approximation approaches 142 6.5 The estimation of parameters 150 CHAPTER VII: APPLICATION OF THE SYNERGETIC MODEL TO SWEDEN 7.1 Causal factors in migration 154 7.1.1 Labour market 154 7.1.2 The housing market of Sweden 176 7.2 Regional utilities, variance of regional utilities, 178 regional preferences and migratory stress 7.2.1 Regional utilities 178 7.2.2 Regional preferences 181 7.2.3 Migratory stress 182 7.3 Choice of socio-economic variables 183 7.4 Representation of global mobility and regional 185 utilities of key causal factors 7.4.1 Representation of global mobility 185 7.4.2 Representation of regional utility 189 7.5 Test projections 192 7.6 A critigue of the synergetic model and a brief 197 comparison with related models EPILOGUE AND DIRECTIONS FOR FUTURE RESEARCH BIBLIOGRAPHY - 1 - CHAPTER I INTRODUCTION AND OVERVIEW 1.1 On the interface between economics and demography ParaUel _ a2L1£ m Given, in a plane, a line L and a point. P not on L. "Through P there exists one and only one line parallel to L." Euclid "There are at least two lines through P parallel to L." Lobatschewsky "There are no lines trough P parallel to L." Riemann Public opinion holds that the economist's main task is the analysis of price adjustment mechanisms, unemployment and balance of payments problems. Anything beyond these main professional areas may in the eyes of the layman be interpreted in two different ways: a economics has an imperialistic ambition in relation to different social sciences b the diminishing returns to economic research Even among economists, economics is considered an imperial science with a position among the social sciences analogous to that of mathe­ matical physics or biology in the natural sciences, a view extensively supported among others by Samuelson (1985) and Stigler (1984). The main examples include Coase's theorem (1960) and Becker's 'crime and punishment' approach (1974) in law; Becker's family theory (1981) in sociology; Becker's (1960), Leibenstein's (1957) and Easterlin's fertility analysis (1962) in demography; the 'public choice' school in politics; Fogel'8 (1974) slavery analysis in history; and H.
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