Choice and Allocation Models for the Housing Market

325 Pages·1989·15.78 MB·English

by  Jan Rouwendal (auth.)

CHOICE AND ALLOCATION MODELS FOR THE HOUSING MARKET
STUDIES IN OPERATIONAL REGIONAL SCIENCE
For a complete list of volumes in this series see final page of this volume_
Choice and
Allocation Models
for the Housing Market
by
Jan Rouwendal
Free University, Amsterdam, The Netherlands
KLUWER ACADEMIC PUBLISHERS
DORDRECHT / BOSTON / LONDON
Library of Congress Cataloging in Publication Data
Rouwendal. Jan. 1959-
Choice and allocation models for the housing market / Jan
Rouwendal.
p. cm. -- (Studies in operational region sciences; 8)
Includes bibliographical references.
1. Housing--Mathematlcal models. 2. Demand (Economic theory)
-Mathematical models. 3. Utility theory--Mathematical models.
I. Title. II. Series.
HD7287.5.R65 1989
338.4·76908·OI5118--dc20 89-19973
ISBN-13: 978-94-010-7613-5 e-ISBN-13: 978-94-009-2468-0
DOl: 10.1007/978-94-009-2468-0
Published by Kluwer Academic Publishers,
P.O. Box 17, 3300 AA Dordrecht, The Netherlands.
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to my parents
CONTENTS
Preface xiii
Chapter 1 Introduction
1.1 The Prob1eJ11 1
1.2 The Analytical Tools 2
1.3 A Sw.&ry of the Book 4
PART A GENERAL
Chapter 2 INDIVIDUAL CHOICE BEHAVIOUR
2.1 Introduction 9
2.2 Additive Rando. Utility Models 9
2.2.1 Discrete Choices: A Stepwise Approach, 2.2.2 Random
Utility Theory, 2.2.3 Additive Random Utility Models, 2.2.4
Continuity and Differentiability of the Choice Probability
Functions, 2.2.5 Gross Substitutability, 2.2.6 Price Sensitivity
2.3 Examples of Discrete Choice Models 25
2.3.1 Probit Models, 2.3.2 Generalized Extreme Value Models,
2.3.3 Discussion
2.4 Discrete Choice in a Dynamic Context 30
2.4.1 State Dependence, 2.4.2 Deterministic Variation versus
Stochastic Instability, 2.4.3 Alternative Interpretations, 2.4.4
Discussion, 2.4.5 Inertia
2. 5 Conclusion 36
Notes 38
Chapter 3 UNCERTAINTY AND THE CONSISTENCY OF DISCRETE CHOICE MODELS
3.1 Introduction 41
3.2 Discrete Choice under Uncertainty 41
3.2.1 Utility Maximization under Uncertainty, 3.2.2 Three
Conditions, 3.2.3 Derivation of a Generalized Choice Model,
3.2.4 Discussion
3.3 Evaluation 52
3.3.1 Comparison with Conventional Demand Theory, 3.3.2 The
Modified Logit Model, 3.3.3 Discussion, 3.3.4 Are there
Alternative Models ?
viii
3.4 The Welfare Economics of Discrete Choice Theory 60
3.4.1 Expected Maximum Utility, 3.4.2 Invariance of Expected
Utilities, 3.4.3 The Case of Uncertainty
3.5 Conclusion 65
Notes 67
Chapter 4 FROM MICRO TO MESO CHOICE ANALYSIS
4.1 Introduction 69
4.2 Complete Description of the Market 72
4.2.1 Introduction, 4.2.2 One Class of Actors, 4.2.3 Multiple
Classes of Actors, 4.2.4 Interaction between Classes, 4.2.5
Origin· Dependent Choice Probabilities, 4.2.6 Entry and Exit,
4.2.7 Discussion
4.3 Aggregation 79
4.3.1 Stochastic Processes, 4.3.2 The Markov Assumption, 4.3.3
The Master Equation, 4.3.4 Convergence to an Interactive Markov
Chain
4.4 Relationship with Spatial Interaction Models 89
4.4.1 Introduction, 4.4.2 Entropy Maximization, 4.4.3 Discussion
4.5 Conclusion 94
Notes 96
Chapter 5 ALLOCATION OF ACTORS WITHIN THE MODEL
5.1 Constraints on Aggregate Behaviour 99
5.1.1 Allocation Mechanisms, 5.1.2 Preliminaries
5.2 Price Equilibrium 102
5.2.1 Introduction, 5.2.2 Market Demand Function, 5.2.3
Existence and Uniqueness of Price Equilibrium, 5.2.4 A Necessary
and Sufficient Condition for Uniqueness, 5.2.5 Review of the
Literature, 5.2.6 Interpretation of the Price Equilibrium, 5.2.7
Conclusion
5.3 Rationing 116
5.3.1 Introduction, 5.3.2 Preliminaries, 5.3.3 Individual Choice
Behaviour and Market Demand, 5.3.4 Uniform Rationed Equilibrium,
5.3.5 Mixed Equilibrium, 5.3.6 Class and Origin-Specific
Realization Probabilities, 5.3.7 An Additional Assumption, 5.3.8
Uniqueness, 5.3.9 Discussion
ix
5.4 Some Final Remarks 135
Notes 138
Chapter 6 TIlE MESO-MODEL AND ITS DYNAMICS
6.1 Introduction 141
6.2 The General Model 141
6.2.1 Description, 6.2.2 Movements from One State to Anocher,
6.2.3 Further Specification, 6.2.4 An Alternative Formulation,
6.2.5 Discussion
6.3 Dynamics : Perron-Frobenius Theory and its Extensions 148
6.3.1 Introduction, 6.3.2 The Linear Case, 6.3.3 Extensions 0
the Original Theorem: Homogeneous Systems, 6.3.4 Discussion
6.4 Dynamics : Related Approaches 155
6.4.1 Introduction, 6.4.2 Brouwer's Fixed Point Theorem and
Existence of Steady States, 6.4.3 The Global Univalence Theorem
and Uniqueness of Steady States, 6.4.4 Stability of Steady
States, 6.4.5 Nonlinear Dynamics
6.5 Concluding Remarks 162
Notes 165
Appendix 166
PART B TIlE HOUSING MARKET
Chapter 7 TIlE HOUSING MARKET SPECIFICATION OF A MODEL
7.1 Introduction 171
7.2 A Rationed Market with Homogeneous Demanders 171
7.2.1 Introduction, 7.2.2 The Allocation Process, 7.2.3 The
Dynamic System, 7.2.4 Steady-State Solution of the Model,
7.2.5 Features of the Steady-State, 7.2.6 Conclusion
7.3 Extensions of the Basic Model 185
7.3.1 Introduction, 7.3.2 Heterogeneous Households, 7.3.3
Changes in the Rationing Procedure
7.4 Simulation Exercises 192
7.4.1 Introduction, 7.4.2 The One-Class Model,7.4.3 A
Heterogeneous Population, 7.4.4 Various Allocation Procedures
x
7.S Conclusion 203
Notes 204
Chapter 8 HOUSEHOID DEKOGRAPHY
8.1 Introduction 207
8.2 The Limits of the Fixed Transition Rates Approach 208
8.2.1 Introduction, 8.2.2 The Leslie Model, 8.2.3 The Two
Sex Problem, 8.2.4 Some Household Models with Fixed
Transition Rates
8.3 Interactive Markov Chains and Household Del80graphy 214
8.3.1 Introduction, 8.3.2 The Two-Sex Problem Revisited,
8.3.3 Additional Requirements, 8.3.4 The Generalized Harmonic
Mean as a Possible Specification, 8.3.5 The Generalized
Harmonic Mean and the Six Requirements, 8.3.6 Further
Extensions of the Model
8.4 Economic Influences on Household Formation 222
8.4.1 Introduction, 8.4.2 Influence of Economic Variables on
Household Formation, 8.4.3 Conclusion
8.S Conclusion 224
Notes 226
Chapter 9 OPTIMAL HOUSEHOID BEHAVIOUR AND HOUSING CHOICE
9.1 Introduction 229
9.2 Intertemporal Utility Maximization and Housing Choice 230
9.2.1 Preliminaries, 9.2.2 The Model, 9.2.3 Intertemporal
Separability, 9.2.4 An Alternative Two-Stage Procedure,
9.2.5 Discussion
9.3 Discrete Choice, Costs of Nobility and Disequilibrium 239
9.3.1 Notation, 9.3.2 The Adapted Model, 9.3.3 Intertemporal
Separability Revisited, 9.3.4 Disequilibrium, 9.3.5 Discussion
9.4 Consequences of Queueing 245
9.4.1 Introduction, 9.4.2 Effects on the Utility Values, 9.4.3
Effects on the Observed Choice Probabilities, 9.4.4 Conclusion
Notes 252
Chapter 10 CHOICE BEHAVIOUR IN THE DUTCH HOUSING MARKET
10.1 Introduction 253
xi
10.2 Unobserved Heterogeneity of Dwelling Types 256
10.2.1 Introduction, 10.2.2 Influence on Utility, 10.2.3
Relationship between Utility and Rent
10.3 Discussion of the Data Set 260
10.3.1 The Housing Needs Survey, 10.3.2 The Classification
of the Housing Stock
10.4 Determination of the Realization Probabilities 264
10.4.1 Introduction, 10.4.2 The Rented Sector, 10.4.3 The
Owner-Occupied Sector, 10.4.4 Specific Circumstances in 1981
10.5 Specification and Estimation Results 271
10.5.1 Introduction, 10.5.2 Specification of the Utility
Function for the Rented Sector, 10.5.3 Effects of Uncertainty
and Queueing, 10.5.4 Results of Estimation, 10.5.5 The
Owner-Occupied Sector, 10.5.6 The First Stage of the Decision
Process
10.6 Conclusion 287
Notes 292
Appendix 293
Chapter 11 Evaluation and Conclusion
11.1 The General Part of the Study 297
11.1.1 The Individual Actor as a Cornerstone of the Analysis,
11.1.2 General Discussion of Discrete Choice Models, 11.1.3
Problems with the Development of Alternative Models, 11.1.4
Aggregation, the Master Equation and Entropy Maximization,
11.1.5 Allocation, 11.1.6 Long Run Dynamics
11.2 The Application to the Housing Market 305
11.2.1Some Relatively Simple Models, 11.2.2 Household
Demography
11.2.3 Optimizing Behaviour and Housing Choice, 11.2.4
Empirical Research
11. 3 Some Final Reaarks 309
List of References 311