Choice and Allocation Models for the Housing Market

It is generally agreed that food, clothing and shelter are the three basic material needs of all people. A simple test for the successfulness of any economic system may therefore be the extent to which it succeeds in providing the population with these commodities. One would conjecture that in the countries that are generally considered as highly developed there would be no problems at all with their availability. And although this conjecture is to a large extent, confirmed by the evidence, it is nevertheless surprising that in western economies with the high per capita incomes housing is still an important object for public concern. Food and clothing are abundantly available in these countries, but the provision of housing is often an object of serious policy concern. To mention one striking example : in the Netherlands there still exist official figures that mention housing shortages of ten thousends of dwellings. This state of affairs is not mentioned here to motivate an exaggerated view on housing problems in Western countries. The situation in the Netherlands and comparable countries is indeed much better than that in underdeveloped countries and a comparison with developing countries would presumably show figures which are comparable to those for food or clothing. The point I want to make is that even in highly developed market economies where the availability of food and clothing is quite satisfactory, the availability of dwellings often is not.

1 Introduction.- 1.1 The Problem.- 1.2 The Analytical Tools.- 1.3 A Summary of the Book.- A: General.- 2 Individual Choice Behaviour.- 2.1 Introduction.- 2.2 Additive Random Utility Models.- 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.- 2.3.1 Probit Models.- 2.3.2 Generalized Extreme Value Models.- 2.3.3 Discussion.- 2.4 Discrete Choice in a Dynamic Context.- 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.- Notes.- 3 Uncertainty and the Consistency of Discrete Choice Models.- 3.1 Introduction.- 3.2 Discrete Choice under Uncertainty.- 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.- 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 ?.- 3.4 The Welfare Economics of Discrete Choice Theory.- 3.4.1 Expected Maximum Utility.- 3.4.2 Invariance of Expected Utilities.- 3.4.3 The Case of Uncertainty.- 3.5 Conclusion.- Notes.- 4 From Micro to Meso Choice Analysis.- 4.1 Introduction.- 4.2 Complete Description of the Market.- 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.- 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.- 4.4.1 Introduction.- 4.4.2 Entropy Maximization.- 4.4.3 Discussion.- 4.5 Conclusion.- Notes.- 5 Allocation of Actors within the Model.- 5.1 Constraints on Aggregate Behaviour.- 5.1.1 Allocation Mechanisms.- 5.1.2 Preliminaries.- 5.2 Price Equilibrium.- 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.- 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.- 5.4 Some Final Remarks.- Notes.- 6 The Meso-Model and its Dynamics.- 6.1 Introduction.- 6.2 The General Model.- 6.2.1 Description.- 6.2.2 Movements from One State to Another.- 6.2.3 Further Specification.- 6.2.4 An Alternative Formulation.- 6.2.5 Discussion.- 6.3 Dynamics: Perron-Frohenius Theory and its Extensions.- 6.3.1 Introduction.- 6.3.2 The Linear Case.- 6.3.3 Extensions o the Original Theorem: Homogeneous Systems.- 6.3.4 Discussion.- 6.4 Dynamics: Related Approaches.- 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.- Notes.- B The Housing Market.- 7 The Housing Market: Specification of a Model.- 7.1 Introduction.- 7.2 A Rationed Market with Homogeneous Demanders.- 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.- 7.3.1 Introduction.- 7.3.2 Heterogeneous Households.- 7.3.3 Changes in the Rationing Procedure.- 7.4 Simulation Exercises.- 7.4.1 Introduction.- 7.4.2 The One-Class Model.- 7.4.3 A Heterogeneous Population.- 7.4.4 Various Allocation Procedures.- 7.5 Conclusion.- Notes.- 8 Household Demography.- 8.1 Introduction.- 8.2 The Limits of the Fixed Transition Rates Approach.- 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 Demography.- 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.- 8.4.1 Introduction.- 8.4.2 Influence of Economic Variables on Household Formation.- 8.4.3 Conclusion.- 8.5 Conclusion.- Notes.- 9 Optimal Household Behaviour and Housing Choice.- 9.1 Introduction.- 9.2 Intertemporal Utility Maximization and Housing Choice.- 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 Mobility and Disequilibrium.- 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.- 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.- 10 Choice Behaviour in the Dutch Housing Market.- 10.1 Introduction.- 10.2 Unobserved Heterogeneity of Dwelling Types.- 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.- 10.3.1 The Housing Needs Survey.- 10.3.2 The Classification of the Housing Stock.- 10.4 Determination of the Realization Probabilities.- 10.4.1 Introduction.- 10.4.2 The Rented Sector.- 10.4.3 The Owner-Occupied Sector.- 10.4.4 Specific Circumstances in.- 10.5 Specification and Estimation Results.- 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.- Notes.- 11 Evaluation and Conclusion.- 11.1 The General Part of the Study.- 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.- 11.2.1 Some 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 Remarks.- List of References.