Regional Science is now more than 50 years old; in the last two decades,
significant advances in methodology have occurred, spurred in large part by access to
computers. The range of analytical techniques now available is enormous;
this books provides a sampling of the toolkit that is now at the disposal
of analysts interested in understanding and interpreting the complexity of the spatial
structure of sub- national economies. The set of tools ranges from the more traditional
(input-output) to new developments in computable general equilibrium models, nonlinear
dynamics, neural modelling and innovation.
Table of Contents
Contributors xiii
1 Introduction Michael Sonis 1
2 Complex Socio-Economic Systems in Regional Science Reconsideration of Theories
of Linear Spatial Analysis Michael Sonis 5
2.1 Introduction 5
2.2 Catastrophe Effects in Linear Programming 7
2.2.1 Cone-Wedge Presentation of the Domain of Structural Stability of Optimal Solutions 7
2.3 Structure of Optimal (Minimum Cost) Transportation Flows 9
2.3.1 Domains of Structural Stability and Boundaries of Structural Change in Optimal
Transportation Networks 9
2.3.2 Behavioral Competition Between Suppliers and Demanders within the Minimum Cost
Transportation Problem 12
2.4 Superposition Principle: The Inverted Problem of Multi-Objective Programming 12
2.4.1 Connection Between the Weber Principle of Industrial Location and the
Möet;bius Barycentric Calculus 14
2.4.2 The Caratheodory Theorem and the Inverted Problem of Multi-Objective Programming 15
2.4.3 Decomposition Formalism for Multi-Objective Analysis Based on Minkovsky-Caratheodory
Theorem 17
2.5 Polyhedral Catastrophic Dynamics of the Push-Pull States of Migration Streams 21
2.5.1 Description and Geometrical Interpretation of the Decomposition Procedure 21
2.5.2 Normalized Space of Admissible Migration States 23
2.5.3 Example of the Decomposition Analysis 24
2.5.4 Interconnections Between Pull and Push Analyses 27
2.5.5 Polyhedral Catastrophic Dynamics 28
2.6 Reconstruction of Central Places Geometry on the Basis of Barycentric Calculus 30
2.6.1 Main Assumptions of the Classical Theory of the Central Places 31
2.6.2 Barycentric Coordinates in the Möet;bius Plane 36
2.7 The Superposition Model of Central Place Hierarchy 40
2.7.1Hierarchical Structures of the Central Place System 40
2.7.2 Polyhedron of Admissible Central Place Hierarchies for an Actual Central Place
System 42
2.7.3 Decomposition of an Actual Central Place Hierarchy 43
2.7.4 Best Fitting Approximation Procedure and the Algorithm of Decomposition 44
2.7.5 Hierarchical Analysis of the Christaller Original Central Place System in Munich,
Southern Germany 45
2.7.6 Structural Stability, Structural Changes and Catastrophes in Central Place
Hierarchical Dynamics 47
2.8 Transportation Flows in Central Place Systems 48
2.8.1 Spatial Structure of the Minimum Cost Flows in a Bounded Beckmann-McPherson Central
Place System 48
2.8.2 Aggregated Schemes and Transportation Tables for Derivation of Rotationally
Invariant Flows 49
2.8.3 Structurally Stable "Top-Down" Transportation Flows in Bounded Three-Tier
Beckmann-McPherson Central Place Hierarchies 50
2.8.4 Optimal Extensions of the Transportation Network in Growing Urban Systems 54
2.9 Feedback Loop Decomposition Analysis of Spatial Economic Systems: Hierarchy of
Spatial/Functional Feedback Loop Production Cycles 57
2.9.1 Quasi-Permutation Matrices and Closed Feedback Loops of the Intra-Regional
Production Cycles 58
2.9.2 Superposition of Intra-Regional Production Feedback Loop Cycles: Decomposition
Algorithm 60
2.9.3 Vertical Specialization of Production and the Economic Meaning of the Multi-Regional
Aggregated Spatial Feedback Loop Production Cycles 61
2.9.4 The Matrioshka Imbedding Principle for the Nested Disaggregated Hierarchy of Spatial
Feedback Loop Production Cycles 62
2.9.5 Spatial Production Cycles in the European Common Market, 1965-1980 63
3 New Developments in Input-Output Analysis Fields of Influence of Changes, the
Temporal Leontief Inverse and the Reconsideration of Classical Key Sector Analysis
Michael Sonis Geoffrey J. D. Hewings 69
3.1 Introduction: Coefficient Change in Input-Output Models 69
3.1.1 Three Approaches to Input Coefficient Change 71
3.2 Basic Results of the Theory of Field of Influence of Changes in Direct Inputs 74
3.2.1 Temporal Multipliers and Temporal Increments 74
3.2.2 Multiplicative and Additive Forms of the Temporal Leontief Inverse 75
3.2.3 The Fine Structure of the Temporal Increments 77
3.3 Direct (First Order) Fields of Influence of Coefficient Change: Matrix Form of the
Sherman-Morrison approach 80
3.3.1 Definition of Direct (First Order) Field of Influence of Changes 80
3.3.2 Cross Structure of the First Order Fields of Influence 81
3.3.3 Change in One Row (Column) 84
3.4 Reconsideration of Classical Key Sector Analysis 85
3.4.1 Intensity of Direct Field of Influence and the Global Intensity Matrix as Multiplier
Product Matrix (MPM) 85
3.4.2 Backward and Forward Linkages of Economic Sectors and Key Sector Analysis 86
3.4.3 Multiplier Product Matrix (MPM) and Structural Economic Landscapes 88
3.4.4 Minimum Information Property of MPM 90
3.5 Synergetic Second Order Fields of Influence 93
3.5.1 Definition of Second Order Field of Influence 93
3.5.2 Structure of Fields of Influence of the Second Order 95
3.5.3 Intensity of the Second Order Synergetic Fields of Influence 95
3.5.4 Distribution Span of Fields of Influence of the Second Order 96
3.5.5 Numerical Distribution Span of Intensities of Fields of Influence of the Second
order 98
3.5.6 Simonovits' Error Rectangles and the Decomposition of Leontief Inverse 99
3.6 Minimum Information Decomposition of Leontief Inverse 101
3.6.1 Structure of Synergetic Interactions Between Economic Sectors 102
3.7 Key Sector Analysis of the Chinese Economy, 1987, 1990 104
3.7.1 The Chinese National Economy, 1987 104
3.7.2 Changes in the Chinese Economy, 1987-1990 111
3.7.3 Comparative Analysis: China and the Metropolitan Economies 112
4 Interregional Computable General Equilibrium Models Eduardo Haddad 119
4.1 Introduction 119
4.2 A Stylized Theoretical Interregional General Equilibrium Model 120
4.2.1 Regions 121
4.2.2 Commodities 121
4.2.3 Consumers 121
4.2.4 Firms 121
4.2.5 Endowments 122
4.3 Social Accounting Matrices as the Basis for Modeling 125
4.3.1 Scaffolding 127
4.4 The State-of-the-Art: Common Features, Common Issues 127
4.4.1 Regional Setting and Data Constraints 128
4.4.2 Bottom-Up and Top-Down Approaches 129
4.4.3 Interregional Linkages 131
4.4.4 Production and Consumption Systems 134
4.4.5 Transportation Services 137
4.4.6 Calibration 138
4.4.7 Sensitivity Analysis 139
4.4.8 Closure 140
4.4.9 Intertemporal Analysis 142
4.4.10 Solution Method 142
4.4.11 Operational Models 143
4.5 The Road Ahead: Challenges and New Directions 146
5 Optimality versus Stability: Pattern Formation in Spatial Economics
Töet;nu Puu 155
5.1 Optimality and Linearity in Economics 155
5.2 Flows and Areas 156
5.3 An Illustrative Case from Solid Geometry 157
5.4 Hexagonal Patterns: Optimality of Shape 157
5.5 On Boundary Conditions 158
5.6 Transversality 158
5.7 Further Research Agenda 160
6 Urban and Hinterland Evolution Under Growing Population Pressure
Wolfgang Weidlich 163
6.1 General Design Principles 163
6.2 The Integrated Model for Urban and Population Evolution 164
6.2.1 The Key-Variables 164
6.2.2 Motivation-Driven Probabilistic Transition Rates 165
6.2.3 Evolution Equations 166
6.3 A Simple Implementation of the Population-Sector: Global Treatment of City- and
Hinterland-Population 168
6.3.1 The Global Population and Capacity Variables 168
6.3.2 Global Personal Utilities and Transition Rates 169
6.3.3 Evolution Equations for the Population Configuration 170
6.3.4 The Case of Equal Net Birth Rates in City and Hinterland 171
7 Socio-Spatial Dynamics and Discrete Non-Linear Probabilistic Chains
Michael Sonis Dimitrios S. Dendrinos 177
7.1 Introduction: University of Discrete Socio-Spatial Dynamics 177
7.2 Definition and Elementary Properties of Probabilistic Chains 178
7.3 Types of Discrete Probabilistic Chains Describing Relative Socio-Spatial Dynamics 181
7.3.1 Fractional-Linear Probabilistic Chains 181
7.3.2 Linear Probabilistic (Markov) Chains 182
7.3.3 Logistic Growth Probabilistic Chain 182
7.3.4 Statistical Procedure for Estimation of Rates of Change and Initial State of the
Logistic Growth Probabilistic Chain (Sonis, 1983, Sonis, 1987a) 184
7.3.5 Interpolation-Extrapolation Dynamics of the Logistic Growth Probabilistic Chain 185
7.3.6 Applications to Analysis of Israeli Regional Employment Co-Influence 186
7.3.7 Log-Linear Probabilistic Chains 189
7.3.8 Application of Log-Linear Probabilistic Chain Model to the Analysis of Regional
Competition and Complementarity 190
7.3.9 Interdependence Interpreted from the Viewpoint of Discrete Relative Dynamics 192
7.4 Concluding Comments and Future Directions 195
8 Principles of Neural Spatial Interaction Modeling Manfred M. Fischer
199
8.1 Introduction 199
8.2 The Context 201
8.3 Network Learning and Model Performance 202
8.4 Local and Global Search Procedures 204
8.5 Bootstrap Estimation 208
8.6 Model Complexity 210
8.7 Assessing the Generalization Performance 211
8.8 Concluding Remarks 212
9 Quick but no so Dirty ML Estimation of Spatial Autoregressive Models
Daniel A. Griffith 215
9.1 Background 215
9.2 The Normalizing Constant Approximation: History, Description and Generalization 217
9.2.1 History 218
9.2.2 Derivation of Griffith and Sone's Approximation Specification 220
9.2.3 Extensions of Griffith and Sone's Approximation 222
9.2.4 Alternatives to the Griffith-Sone Jacobian Approximation 225
9.3 Implementation of the Jacobian Approximation 228
9.3.1 The Jacobian Approximation when all of the Eigenvalues are Known 229
9.3.2 The Jacobian Approximation when the n-1 Nonprincipal Eigenvalues are Unknown but can
be Approximated 232
9.3.3 The Jacobian Approximation when the n-1 Nonprincipal Eigenvalues are Unknown and
Lack a Known Approximation 233
9.4 Implications for Standard Error Estimates 235
9.5 Discussion and Future Directions 239
10 Innovation Diffusion Theory: 100 Years of Development Michael Sonis
243
10.1 Introduction 243
10.2 Major Actors in the Analysis of the Innovation Diffusion Process 246
10.3 Socio-Ecological Mechanisms of Innovation Spread 248
10.3.1 Empirical Regularities of Innovation Spread: Competition Between Adoption and
Non-Adoption 248
10.3.2 Many Competitive Innovations 250
10.3.3 Qualitative Analysis of the Innovation Diffusion Process: Some Examples 252
10.4 The First Principle of Individual Choice Within the Collective 256
10.4.1 Choice Behavior of Homo Oeconomicus 256
10.4.2 Choice Behavior of Homo Politicus 257
10.4.3 Choice Behavior of Homo Socialis 257
10.4.4 Adopter as a "Collective Being" in Innovation Choice 258
10.5 Innovators and Innovating Elites 258
10.5.1 Duality Between Supply Push and Demand Pull: Meso-Level Competition Between Social
Elites vs. Micro-Level Social Contacts 259
10.5.2 Captive Manipulation Power of Elites Influence: Ten Commandments of Aggressive
Intolerance 261
10.6 Active Environment and Socio-Ecological Niches 262
10.6.1 Adoption and Non-Adoption Niches in Innovation Diffusion Process 263
10.6.2 Case of Many Competitive Innovations and their Niches 264
10.7 Conclusion and Future Directions of Development 265
11 Urban Economics at a Cross-Road Recent Theoretical and Methodological
Directions and Future Challenges Roberta Capello Peter Nijkamp 273
11.1 Urban Economics in Regional Science 273
11.2 Recent Theoretical Directions 276
11.3 Recent Methodological Directions 280
11.4 Urban Economics and Regional Science Transition 283
11.5 Future Challenges 286
11.6 Conclusions 287
12 Conclusion Theories and Models Inspired by Empirical Regularities of Socio-Economic
Spatial Analysis Michael Sonis 293
12.1 Introduction 293
12.2 First Meta-Theoretical Principles in Socio-Economic and Socio-Ecological Sciences 296
12.2.1 Principle of Collectivity 297
12.2.2 Principle of Complication 297
12.2.3 The principle of Superposition 298
12.2.4 The Duality Principle 299
Index 303
305 pages, 38 illus., Hardcover
