Spatial Interaction Modelling

Prologue.- I Context and Methodology.- 1 Geographical Roots of Spatial Interaction.- 1.1 Analogies with Newtonian Gravitation.- 1.1.1 Gravity Effect Identification.- 1.1.2 Retail Gravity Models.- 1.1.3 Gravity and Commodity Flows.- 1.2 Bases in Entropy, Constrained Optimization and Time Geography.- 1.2.1 Entropy Basis for Gravity Models.- 1.2.2 Intervening Opportunities Models.- 1.2.3 Activities, Time Budgets and Travel.- 1.2.4 Entropy in Continuous Space.- 1.2.5 Other Entropies and Their Physical Significance.- 1.3 Further Enhancements.- 1.3.1 The More General Information Theory Approach.- 1.3.2 A Retail Equilibrium Model.- 1.3.3 Probabilistic Entropy vs Random Utility for Individual Choice.- 1.3.4 Cost Minimization with Entropy Constraint(s).- 1.3.5 Some Key Conceptual Contributions.- 1.3.6 Characterization of Model Errors and Robustness.- Appendix 1.1.- 2 Key Insights in ‘Space’ and Microeconomics.- 2.1 Some Important Theoretical Advances.- 2.1.1 Urban/Rural Model and Urban Land Models.- 2.1.2 Agglomeration in Linear Markets for Single and Comparison Goods.- 2.1.3 Linear Model of Production Location and Transport Flows.- 2.1.4 Imperfect Competition in Linear Space.- 2.2 From Theory to Applications.- 2.2.1 National, Interregional and Multi-Regional Input-Output Models.- 2.2.2 Spatial Price Equilibrium.- 2.3 Some New Directions.- 2.3.1 Increasing Returns and Monopolistic Competition.- 2.3.2 Knowledge Exchange and Space.- 3 Spatial Interaction Modelling Embracing Microeconomics.- 3.1 Evaluation of Relevant Previous Efforts.- 3.1.1 Re-Interpretation of a Retail Equilibrium Model.- 3.1.2 Dispersed Spatial Price Equilibrium.- 3.2 Comprehensive Specification of a Unifying Framework.- 3.2.1 Entropy in a Decision-Theoretic Context.- 3.2.2 Different Entropies for Different Decision Contexts.- 3.2.3 Fundamental Role of Constraints in Modelling Supply and Demand.- 3.2.4 Calibration of Open Models Adding Information via Constraints.- 3.2.5 Nesting, Clustering and Independence from Irrelevant Alternatives.- 3.2.6 Inequality and Logistic Short Run Capacity Constraints.- 3.2.7 Properties of Models under Aggregation.- 3.2.8 Surplus Evaluation by Simple Transformations of Entropy Lagrangian.- 3.2.9 Fulfilment of Key Economic Lemma.- 3.2.10 Non-Homogeneous Supply and Demand Functions.- 3.2.11 Brief Summary.- Appendix 3.1.- II Some Examples of Urban Modelling.- 4 Activities as Generators of Spatial Interaction.- 4.1 Elements of an Activity Demand Framework.- 4.1.1 Characterisation of the Demand for Activities.- 4.1.2 The Huff Model and its Extensions.- 4.1.3 A Comprehensive Activity-Based Model.- 4.2 Supply, Equilibrium and Imperfect Competition.- 4.2.1 Short Run Goods/Services Supply Model with Congestion.- 4.2.2 Short Run Demand/Supply Equilibrium.- 4.2.3 Movement Towards Long Run Supply Equilibrium.- 4.2.4 Observations on Imperfect Competition.- 5 Knowledge Exchange and Agglomeration.- 5.1 Fundamentals of the Contact Process.- 5.1.1 Preliminary Matching.- 5.1.2 Face-to-Face Contacts Among the Matched Pairs.- 5.2 An Elementary Modelling Framework for Firms.- 5.2.1 Elements of a Short Run Probabilistic Knowledge Supply Model.- 5.2.2 Long Run Adjustment Processes.- 5.3 Concluding Remarks.- 6 Imperfect Competition in Land/Housing Markets.- 6.1 Introduction.- 6.2 The Economic Structure of the Models.- 6.2.1 Market Structure.- 6.2.2 The Behavioural Model.- 6.3 A Competitive Land Market.- 6.3.1 Unconstrained Models for Competitive Markets.- 6.3.2 Constrained Models for Competitive Markets.- 6.3.3 Hotelling’s Lemma.- 6.4 Imperfect Competition.- 6.4.1 Unconstrained Models for Imperfect Competition.- 6.4.2 Constrained Models for Imperfect Competition.- 6.5 Final Comments.- III Some Interregional Contributions.- 7 Trade under Changing Networks and Technology.- 7.1 Trade under a Changing Transport Network with Given Technology.- 7.1.1 An Enhanced Deterministic Interregional Model.- 7.1.2 Probabilistic Multi-Regional Flows with Multi-Regional Data.- 7.1.3 Probabilistic Interregional Flows with Multi-Regional Data.- 7.1.4 Implementation Issues.- 7.1.5 Some Further Developments.- 7.2 Changes in Both Transport Networks and Production Technology.- 7.2.1 Motivation for Model.- 7.2.2 Proposed Interregional Model.- 8 Illustration of Imperfect Competition.- 8.1 Introduction.- 8.2 A General Equilibrium Framework.- 8.2.1 A Model of Producer Behaviour.- 8.2.2 A Model of Buyer/Consumer Behaviour.- 8.2.3 Characterisation of the Equilibrium.- 8.3 Consideration of Imperfect Competition.- 8.3.1 Specification of an Equilibrium.- 8.3.2 Elements of a Stackelberg Approach.- 8.3.3 Elements of a Solution Procedure.- 8.3.4 Surplus Evaluation.- 8.4 Future Directions.- Appendix 8.1.- 9 Interregional Migration.- 9.1 Introduction.- 9.1.1 Market Segmentation.- 9.1.2 Choice Hierarchy.- 9.1.3 Reliability of Projections.- 9.1.4 Net Migration vs Gross Migration Models.- 9.1.5 Exogenous and Endogenous Quantities.- 9.1.6 Updating of Regional Populations.- 9.1.7 Properties of the Migration Flow Pattern.- 9.2 Comparative Static Migration Model.- 9.2.1 Notation.- 9.2.2 Model Estimation.- 9.2.3 Use of Estimated Model for Projection.- 9.2.4 Empirical Performance.- 9.3 A Two-Stage Dynamic Estimation Procedure.- 9.3.1 Relevant Previous Work.- 9.3.2 New Model Specification and Estimation.- 9.3.3 Simple Application of the Two-Stage Model.- 9.3.4 Future Issues.- Future Challenges.- References.