Spatial Interaction Modelling

In this book, the author's strong commitment to the multi-disciplinary field of regional science emerges to provide a unifying framework between spatial modelling traditions from quantitative geography and those from spatial economics, whereby each is enhanced. Starting with a detailed discussion of each field illustrated with numerical examples, the two traditions are brought together by either making the economic models probabilistic or transforming the objectives of the geographic models to reflect both utility theory and production theory. The ideas are applied to develop urban models of activity analysis, face-to-face contacts and housing supply, as well as regional models in the areas of input-output analysis, imperfect competition and interregional migration.

Contenu

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.