ISBN: 3540205284
TITLE: Spatial Interaction Modelling
AUTHOR: Roy
TOC:

Prologue 1
Part I CONTEXT AND METHODOLOGY
1 Geographical Roots of Spatial Interaction 9
1.1 Analogies with Newtonian Gravitation 9
1.1.1 Gravity Effect Identification 9
1.1.2 Retail Gravity Models 10
1.1.3 Gravity and Commodity Flows 13
1.2 Bases in Entropy, Constrained Optimization and Time Geography 14
1.2.1 Entropy Basis for Gravity Models 14
1.2.2 Intervening Opportunities Models 19
1.2.3 Activities, Time Budgets and Travel 21
1.2.4 Entropy in Continuous Space 24
1.2.5 Other Entropies and Their Physical Significance 26
1.3 Further Enhancements 29
1.3.1 The More General Information Theory Approach 29
1.3.2 A Retail Equilibrium Model 33
1.3.3 Probabilistic Entropy vs Random Utility for Individual Choice 34
1.3.4 Cost Minimization with Entropy Constraint(s) 36
1.3.5 Some Key Conceptual Contributions 40
1.3.6 Characterization of Model Errors and Robustness 47
Appendix 1.1 50
2 Key Insights in `Space' and Microeconomics 51
2.1 Some Important Theoretical Advances 51
2.1.1 Urban/Rural Model and Urban Land Models 51
2.1.2 Agglomeration in Linear Markets for Single and Comparison Goods 56
2.1.3 Linear Model of Production Location and Transport Flows 58
2.1.4 Imperfect Competition in Linear Space 60
2.2 From Theory to Applications 63
2.2.1 National, Interregional and Multi-Regional Input-Output Models 63
2.2.2 Spatial Price Equilibrium 67
2.3 Some New Directions 68
2.3.1 Increasing Returns and Monopolistic Competition 68
2.3.2 Knowledge Exchange and Space 71
3 Spatial Interaction Modelling Embracing Microeconomics 74
3.1 Evaluation of Relevant Previous Efforts 74
3.1.1 Re-Interpretation of a Retail Equilibrium Model 74
3.1.2 Dispersed Spatial Price Equilibrium 75
3.2 Comprehensive Specification of a Unifying Framework 77
3.2.1 Entropy in a Decision-Theoretic Context 77
3.2.2 Different Entropies for Different Decision Contexts 78
3.2.3 Fundamental Role of Constraints in Modelling Supply and Demand 80
3.2.4 Calibration of Open Models Adding Information via Constraints 86
3.2.5 Nesting, Clustering and Independence from Irrelevant Alternatives 91
3.2.6 Inequality and Logistic Short Run Capacity Constraints 95
3.2.7 Properties of Models under Aggregation 97
3.2.8 Surplus Evaluation by Simple Transformations of Entropy Lagrangian 99
3.2.9 Fulfilment of Key Economic Lemma 100
3.2.10 Non-Homogeneous Supply and Demand Functions 101
3.2.11 Brief Summary 101
Appendix 3.1 102
Part II SOME EXAMPLES OF URBAN MODELLING
4 Activities as Generators of Spatial Interaction 107
4.1 Elements of an Activity Demand Framework 107
4.1.1 Characterisation of the Demand for Activities 107
4.1.2 The Huff Model and its Extensions 110
4.1.3 A Comprehensive Activity-Based Model 116
4.2 Supply, Equilibrium and Imperfect Competition 126
4.2.1 Short Run Goods/Services Supply Model with Congestion 126
4.2.2 Short Run Demand/Supply Equilibrium 128
4.2.3 Movement Towards Long Run Supply Equilibrium 128
4.2.4 Observations on Imperfect Competition 130
5 Knowledge Exchange and Agglomeration 131
5.1 Fundamentals of the Contact Process 131
5.1.1 Preliminary Matching 131
5.1.2 Face-to-Face Contacts Among the Matched Pairs 134
5.2 An Elementary Modelling Framework for Firms 136
5.2.1 Elements of a Short Run Probabilistic Knowledge Supply Model 136
5.2.2 Long Run Adjustment Processes 144
5.3 Concluding Remarks 149
6 Imperfect Competition in Land/Housing Markets 150
6.1 Introduction 150
6.2 The Economic Structure of the Models 151
6.2.1 Market Structure 151
6.2.2 The Behavioural Model 153
6.3 A Competitive Land Market 156
6.3.1 Unconstrained Models for Competitive Markets 156
6.3.2 Constrained Models for Competitive Markets 159
6.3.3 Hotelling's Lemma 162
6.4 Imperfect Competition 163
6.4.1 Unconstrained Models for Imperfect Competition 163
6.4.2 Constrained Models for Imperfect Competition 165
6.5 Final Comments 166
Part III SOME INTERREGIONAL CONTRIBUTIONS
7 Trade under Changing Networks and Technology 171
7.1 Trade under a Changing Transport Network with Given Technology 172
7.1.1 An Enhanced Deterministic Interregional Model 174
7.1.2 Probabilistic Multi-Regional Flows with Multi-Regional Data 176
7.1.3 Probabilistic Interregional Flows with Multi-Regional Data 180
7.1.4 Implementation Issues 182
7.1.5 Some Further Developments 185
7.2 Changes in Both Transport Networks and Production Technology 186
7.2.1 Motivation for Model 186
7.2.2 Proposed Interregional Model 187
8 Illustration of Imperfect Competition 190
8.1 Introduction 190
8.2 A General Equilibrium Framework 191
8.2.1 A Model of Producer Behaviour 191
8.2.2 A Model of Buyer/Consumer Behaviour 194
8.2.3 Characterisation of the Equilibrium 196
8.3 Consideration of Imperfect Competition 198
8.3.1 Specification of an Equilibrium 199
8.3.2 Elements of a Stackelberg Approach 200
8.3.3 Elements of a Solution Procedure 201
8.3.4 Surplus Evaluation 202
8.4 Future Directions 202
Appendix B.1 203
9 Interregional Migration 205
9.1 Introduction 205
9.1.1 Market Segmentation 205
9.1.2 Choice Hierarchy 206
9.1.3 Reliability of Projections 206
9.1.4 Net Migration vs Gross Migration Models 207
9.1.5 Exogenous and Endogenous Quantities 208
9.1.6 Updating of Regional Populations 208
9.1.7 Properties of the Migration Flow Pattern 209
9.2 Comparative Static Migration Model 209
9.2.1 Notation 210
9.2.2 Model Estimation 211
9.2.3 Use of Estimated Model for Projection 214
9.2.4 Empirical Performance 216
9.3 A Two-Stage Dynamic Estimation Procedure 216
9.3.1 Relevant Previous Work 217
9.3.2 New Model Specification and Estimation 219
9.3.3 Simple Application of the Two-Stage Model 222
9.3.4 Future Issues 224
Future Challenges 227
References 229
Subject Index 237
END
