Interregional Migration: Dynamic Theory and Comparative Analysis

In part I of this book a dynamic migratory model connecting the microlevel of individual migration trends with the macrolevel of interregional migration is developed. Its derivation makes use of the master equation method. Applying a ranking regression analysis, the trend parameters of the model are correlated to regional socio-economic key factors. In part II the model is applied to interregional migration within the countries Federal Republic of Germany, Canada, France, Israel, Italy and Sweden. In part III a comparative analysis of the results is given. In part IV a selfcontained derivation of the master equation and of solutions relevant for the migratory system is given, the ranking regression analysis is exemplified and a computer program for the estimation of trendparameters is added.

I. General Theory.- Synopsis of Part I.- 1 Concepts of the Dynamic Migration Model.- 1.1 Population Configuration and Migration Matrix.- 1.2 The Decision Process.- 1.3 Transition Probabilities as Functions of Dynamic Utilities and Mobilities.- 2 The Migratory Equations of Motion.- 2.1 The Master Equation for the Population Configuration.- 2.2 The Meanvalue Equations.- 2.2.1 Derivation of their General Form.- 2.2.2 Separation of the Birth/Death Processes.- 2.2.3 The Stationary Solution.- 3 The Estimation of Parameters.- 3.1 The Regression Analysis for Trendparameters.- 3.1.1 Log-Linear Estimation of Trendparameters.- 3.1.2 Nonlinear Estimation of Trendparameters.- 3.1.3 Comparison of the Quality of Estimates.- 3.2 The Dependence of Trendparameters on Socio-Economic Key-Factors.- 3.2.1 The Space of Variables.- 3.2.2 The Standard Regression.- 3.2.3 Ranking of Relevance of Key-Factors and Representation of the Utility Vector.- II. Interregional Migration in Individual Countries.- Synopsis of Part II.- 4 Federal Republic of Germany.- 4.1 The Regional System and the Registration of Population and Migration.- 4.1.1 The Division of the Country into Federal States.- 4.1.2 The Volume and Registration of Migration.- 4.1.3 Choice of the Period of Evaluation.- 4.1.4 Assumption of One Homogeneous Population.- 4.1.5 Total Population Growth.- 4.2 Transition Probabilities, Mobilities and Utilities.- 4.2.1 Form of Transition Probabilities.- 4.2.2 Decomposition of the Mobility Matrix.- 4.2.3 Regional Utilities and Preferences.- 4.2.4 Migratory Stress.- 4.3 Choice of Socio-Economic Variables.- 4.3.1 Identification of Influences on the Global Mobility and Utilities.- 4.3.2 Classification of Socio-Economic Variables.- 4.4 Selection of Key-Factors.- 4.4.1 The Key-Factor Analysis of the Global Mobility.- 4.4.2 The Key-Factor Analysis of the Regional Utilities.- 4.4.3 Transition Rates in Terms of Key-Factors.- 5 Canada.- 5.1 Introduction.- 5.1.1 Historical Patterns of Spatial Population Growth.- 5.1.2 Current Patterns of Spatial Population Growth.- 5.1.3 Spatial Differentials in Residual Population Growth.- 5.2 Global Mobility, Utilities and Preferences.- 5.2.1 Global Mobility.- 5.2.2 Regional Utilities.- 5.2.3 Regional Preferences.- 5.2.4 Migration Stress.- 5.3 Socio-Economic Analysis.- 5.3.1 Analysis of the Global Mobility.- 5.3.2 Analysis of the Regional Utilities.- 5.4 Conclusion.- 5.5 Appendix: Tables and Figures.- 6 France.- 6.1 Population and the Regional System.- 6.2 The Data.- 6.3 Evolution of Global Mobility.- 6.4 Regional Utilities.- 6.5 Regional Preferences.- 6.6 Socio-Economic Key-Factors.- 6.7 Comparison with a Gravity Model.- 7 Israel.- 7.1 Introduction.- 7.2 Sources and Limitations of Data.- 7.3 Impact of Internal Migration on Israeli Population Redistribution.- 7.4 Spatial Organization of Temporarily Stable Migration Streams.- 7.5 Global Mobility.- 7.6 Regional Utilities and Preferences.- 7.7 Explanatory Socio-Economic Key-Factors.- 7.8 Concluding Remarks.- 8 Italy.- 8.1 The Study Area.- 8.1.1 Introduction.- 8.1.2 The Country and its Subdivision into Regions.- 8.1.3 Brief Overview of the Italian Demographic Situation and of its Roots.- 8.1.4 Migration Pattern.- 8.2 Design of the Application.- 8.2.1 Choice of the Zoning System.- 8.2.2 Uncertainties of Demographic Input Data.- 8.3 Demographic Trendparameters of Migration.- 8.3.1 Global Mobility.- 8.3.2 Regional Utilities and their Variance.- 8.3.3 Regional Preferences and their Variance.- 8.3.4 Migratory Stress.- 8.4 The Key-Factors of Migration.- 8.4.1 Choice and Availability of Economic Data.- 8.4.2 Key-Factor Analysis of the Global Mobility.- 8.4.3 Key-Factor Analysis of the Regional Utilities.- 8.4.4 A General Concluding Comment.- 9 Sweden.- 9.1 Regional Subdivisions of Sweden.- 9.2 A General Outline of Regional Population Growth in Sweden.- 9.2.1 Historical Trends in Regional Population Development.- 9.2.2 Current Trends in Regional Population Growth.- 9.3 Reasons for Migration.- 9.3.1 Labour Market.- 9.3.2 The Housing Market of Sweden.- 9.4 Regional Utilities, Variance of the Regional Utilities, Regional Preferences and Migratory Stress.- 9.4.1 Regional Utilities.- 9.4.2 Regional Preferences.- 9.4.3 Migratory Stress.- 9.5 Choice of Socio-Economic Variables.- 9.6 Representation of Global Mobility and Regional Utilities in Terms of Key-Factors.- 9.6.1 Representation of the Global Mobility.- 9.6.2 Representation of the Regional Utility.- III. Comparative Studies.- Synopsis of Part III.- 10 Comparative Analysis of Population Evolution Models.- 10.1 Introduction and Survey of Modelling Approaches.- 10.2 Linear Evolution of Age Groups in Regions ― Classical Demographic Analysis.- 10.3 Economy and Demography.- 10.3.1 Logistic Evolution.- 10.3.2 Population and Production.- 10.3.3 Models Combining Economic and Demographic Change.- 10.4 Economy, Demography and Migration.- 10.4.1 Logistic Population Growth and Migratory Diffusion.- 10.4.2 Migration and Public Resources.- 10.5 Stochastic Choice Theory and Migration.- 10.6 The Master Equation Approach to Population Analysis.- 10.6.1 Comparison of Two Approaches.- 10.6.2 The Model of this Book and its Relation to Economics.- 11 Comparative Analysis of Interregional Migration.- 11.1 Purposes and Problems of the Comparison of Interregional Migration in Different Countries.- 11.1.1 Interregional Migration and Total Population Evolution.- 11.1.2 Problems in the Choice of Regions.- 11.1.3 General Conclusions from the Comparison of Mobilities and Utilities.- 11.1.4 Problems in the Choice of Comparable Socio-Economic Factors.- 11.2 Comparative Analysis of Quantitative Results.- 11.2.1 Synopsis of Definitions, Tables and Figures.- 11.2.2 Comparative Interpretations: The Global Mobility.- 11.2.3 Regional Utilities and Preferences.- 11.2.4 Migratory Stress.- IV. Mathematical Methods.- Synopsis of Part IV.- 12 Derivation of the Master Equation.- 12.1 Some General Concepts of Probability Theory.- 12.2 The Master Equation.- 12.3 Individual and Configurational Probability Transition Rates.- 13 Solutions of the Master Equation.- 13.1 Detailed Balance.- 13.1.1 Stationary Solution of the Master Equation.- 13.1.2 Proof of Detailed Balance for the Migratory System.- 13.2 The Stationary Solution for the Migratory Master Equation.- 13.3 H-Theorem and Entropy.- 13.4 Time Dependent Solutions.- 14 Tests of Significance in the Ranking Regression Analysis.- 14.1 The Coefficient of Multiple Correlation (R2).- 14.2 The F-Test.- 14.3 The t-Test.- 14.4 The Durbin-Watson Test.- 15 Ranking Regression Analysis of the Global Mobility.- 15.1 The General Procedure.- 15.2 An Explicit Example.- 16 A Computer Program for the Estimation of Utilities and Mobilities.- References.