Dynamic Decision Theory: Applications to Urban and Regional Topics

ISBN-13: 9789401069120 / Angielski / Miękka / 2011 / 268 str.

G. Haag

Opis

Choice processes appear in all spheres of society. Hitherto ruling paradigms in the modelling of choice problems have presumed a competitive general equi- librium which, however, proves insufficient for dynamic processes. This contribution aims at providing a general coherent and closed frame- work for the dynamic modelling of decision processes. It was one of my main interests to build a bridge between the pure model building concepts and their practical applications. Therefore all given examples are related to empirical work. Solution algorithms for the estimation of trend parameters as well as the numerical simulation in concrete applications therefore playa central role in this contribution. Friendly relations with a number of colleagues from many universities in Europe, and the U.S. have emerged during the different applications. I wish to thank all of them. The international cooperations were mainly initiated and supported by conferences and workshops organized and financed by the International Institute for Applied Systems Analysis (lIASA), the Istituto Ricerche Economico-Sociali Del Piemonte (I RES). the Institut National D 'Etudes De'mographiques (I NED), the Centre for Regional Science Research UmeJ. (CERUM) and the Projets de Cooperation et D'Echange avec France (Procop>' Special thanks go to the Volkswagen Stiftung for financial support of this work over the years. Thanks also go in particular to my friend and mentor Prof.W.Weidlich for his encouragement and for the many suggestions he made in fruitful discus- sions and common work that have taken place over the years.

Spis treści

1. Introduction.- 2. A Dynamic Theory of Decision Processes.- 2.1 The Panel Data-Based Discrete Choice Approach.- 2.2 The Master Equation View in Dynamic Choice Processes.- 2.3 The Decision Process.- 2.3.1 Decision Space and Decision Configuration.- 2.3.2 Individual Decision Processes and Conditional Probability.- 2.3.3 Individual and Configurational Transition Rates.- 2.3.4 Some Functional Forms of the Individual Transition Rates.- 2.4 The Equations of Motion.- 2.4.1 The Master Equation for the Decision Configuration.- 2.4.2 The Translation Operator.- 2.4.3 The Mean Value Equations of the Dynamic Decision Theory.- 2.5 Parameter Estimation.- 2.5.1 Parameter Estimation via Comparison of Transition Rates.- 2.5.2 Parameter Estimation via Comparison of Decision Configurations.- 2.5.3 The Dependence of Trend Parameters on Motivating Factors.- 2.5.4 Scheme of Model Building for Dynamic Decision Processes.- 2.6 Selection Criteria for the Examples.- 3. Shocks in Urban Evolution.- 3.1 Introduction.- 3.2 A Stochastic Model on Shocks in Urban Evolution.- 3.2.1 The Configurational Transition Rates.- 3.2.2 The Master Equation.- 3.2.3 The Individual Transition Rates.- 3.2.4 The Stationary Solution of the Master Equation.- 3.2.5 Equations of Motion for Mean Values and Variances.- 3.2.6 Estimation of the Utility Function and Mobility.- 3.2.7 Regression of Trend Parameters on Socio-Economic Data.- 4. Intra — Urban Migration.- 4.1 Introduction.- 4.2 A Stochastic Model on Intra-Urban Dynamics.- 4.2.1 The Configurational Transition Rates.- 4.2.2 The Master Equation.- 4.2.3 The Stationary Solution of the Master Equation.- 4.2.4 The Mean Value Equations.- 4.2.5 The Parameter Estimation Procedure.- 4.2.6 Empirical Testing of the Land Use Density-Rent Model.- 5. Inter-Regional Migration.- 5.1 Introduction.- 5.2 The Stochastic Migration Model.- 5.2.1 The Individual Transition Rates for the Migration Process.- 5.2.2 The Configurational Transition Rates.- 5.2.3 The Stochastic Equations of Motion.- 5.2.4 The Stationary Solution of the Migratory Master Equation.- 5.2.5 Quasi-Deterministic Equations of Motion.- 5.2.6 The Stationary Solution of the Quasi-Deterministic Equations.- 5.2.7 Determination of Utilities and Mobilities from Empirical Data.- 5.3 Comparative Analysis of Inter-Regional Migration.- 5.3.1 Choice of Comparable Socio-Economic Variables.- 5.3.2 The Global Mobility under Comparative Aspects.- 5.3.3 The Regional Utilities and Preferences of the Federal Republic of Germany.- 5.3.4 Comparison of the Variance of Utilities.- 5.3.5 Comparison of the Migratory Stress.- 6. Chaotic Evolution of Migratory Systems.- 6.1 Introduction.- 6.2 The Migratory Master Equation and Mean Value Equations for Interacting Populations.- 6.2.1 Inter-Group and Intra-Group Interactions of Individuals.- 6.2.2 The Master Equation for Interacting Subpopulations.- 6.2.3 The Deterministic Equations for Interacting Subpopulations.- 6.2.4 The Exact Stationary Solution of the Deterministic Equations.- 6.3 Chaotic Behaviour of Migratory Trajectories.- 6.3.1 A Numerical Simulation.- 6.3.2 Lyapunov Exponents and Fractal Dimensions.- 6.4 Conclusion.- 7. Spatial Interaction Models and their Micro-Foundation.- 7.1 Introduction to Spatial Urban Theory.- 7.2 A Service System as the Basis of the Model.- 7.3 A Master Equation Approach.- 7.3.1 The Total Transition Rates for the Service Sector Model.- 7.3.2 Consumer Dynamics.- 7.3.3 Decision Processes of Developers, Retailers and Land Owners.- 7.4 The Quasi-Deterministic Equations to the Dynamic Service Sector Model.- 7.5 The Stationary Solution of the Service Sector Model.- 7.5.1 Relation between Expenditure Flows and Transportation Costs.- 7.6 Dynamic Simulations and their Interpretation.- 7.6.1 The Influence of Low Transportation Costs.- 7.6.2 The Influence of High Transportation Costs.- 7.7 Concluding Comments.- 8. Further Applications and Extensions.- 8.1 Knowledge, Innovation, Productivity.- 8.1.1 Knowledge as an Endogeneous Input of the Growth Process.- 8.1.2 Regional Decisions about the Investment Ratio.- 8.1.3 Decision Processes Concerning the Percentage Share of Research Investment.- 8.1.4 Some Conjectures.- 8.2 Economic Cycles.- 8.2.1 Short-Term Cycles.- 8.2.2 Long-Term Cycles.- 8.3 Housing and Labour Market.- 8.4 Concluding Remarks.- 9. Appendix: The Master Equation.- 9.1 Deterministic and Probabilistic Description of Systems.- 9.2 Some General Concepts of Probability Theory.- 9.3 The Derivation of the Master Equation.- 9.4 The Stationary Solution of the Master Equation for Detailed Balance.- 9.5 The Stationary Solution of the Master Equation of Chapter 4.- 9.6 The Stationary Solution of the Master Equation of Chapter 5.- 9.7 The Embedding of Random Utility Theory.- 9.7.1 The Multinomial Logit Model.- 9.7.2 The Multinomial Logit Model as Limiting Case of our Dynamic Theory.- 9.8 The Construction of Configurational Transition Rates via Panel Data.- References.