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Congestion Pricing With Heterogeneous Travellers Vincent A.C. van den Berg
CONGESTION PRICING WITH HETEROGENEOUS TRAVELLERS
ISBN 978 90 3610 232 2 Cover design: Crasborn Graphic Desingners bno, Valkenburg a.d. Geul This book is no. 496 of the Tinbergen Institute Research Series, established through cooperation between Thela Thesis and the Tinbergen Institute. A List of books which already appeared in the series can be found in the back.
CONGESTION PRICING WITH HETEROGENEOUS TRAVELLERS
ter verkrijging van de graad Doctor aan de Vrije Universiteit Amsterdam, op gezag van de rector magnificus
prof.dr. L.M. Bouter, in het openbaar te verdedigen
ten overstaan van de promotiecommissie van de faculteit der Economische Wetenschappen en Bedrijfskunde
op woensdag 8 juni 2011 om 13.45 uur in de aula van de universiteit,
De Boelelaan 1105
Vincent Adrianus Cornelis van den Berg
geboren te Woerden
promotoren: prof.dr. E.T. Verhoef
prof.dr. P. Rietveld
Foreword This PhD thesis concludes four years of research at the Department of Spatial Economics of the VU University. Without the support and help of many persons I would never have been able to get this far. I would like to thank my parents for their love and support during the 4 years I worked on my thesis and before that. I would like to thank my friends and family for patiently listening to me complaining—or, worse yet, being enthusiastic—about my work.
I have great appreciation for the support and insightful comments of my supervisors Erik Verhoef, Eric Kroes, and Piet Rietveld, as well as for their work on our papers. I would like to thank them for giving me the freedom in my research I needed, but also for being there when I needed help. I am also thankful to Frank van Oort for bringing me into contact with Piet Rietveld, which led to my job interview at the VU in January of 2007.
Thanks also to my committee members: Serge Hoogendoorn, Robin Lindsey, Stef Proost, Jan Rouwendaal, and Harry Timmermans for the substantial time they invested in my thesis and their very helpful comments.
I am grateful for the help and support of my all colleagues. A special mention goes to Eva Gutiérrez-i-Puigarnau for her great efforts in improving my papers and thesis, to Muhammed Sabir, Vincent van der Goes, and Ferdinand Paraguas for their helpful comments on my papers, Yin-Yen Tseng for helping me getting started with the empirical analysis, and Paul Koster for our discussions. I would like to express my great appreciation for the editors and referees of the papers that were submitted for publication. Their comments—although at times frustrating, especially when they led to a rejection—did improve my papers greatly. I also thank Mrs Ellman for her work on proofing the English of this thesis.
This thesis uses Stated Preference datasets of the Dutch Railways (NS). I would like to thank the NS for allowing me to use these great datasets, and for their helpful comments. I am especially thankful for the support of Menno de Bruyn, Freek Hofker, Maurice Unck, and Theo van der Star from the NS. I appreciate the effort and care Steer Davies Gleave has put in collecting the data.
My thesis project was financially supported by the “Betrouwbaarheid van transportketens” project of Transumo. Transumo (TRANsition SUstainable MObility) is a Dutch platform for companies, governments, and knowledge institutes that cooperate in the development of knowledge with regard to sustainable mobility. There was also financial support from the AdG Grant #246969 OPTION of the European Research Council (ERC). I thank Transumo and ERC for their support. Finally, I am grateful for the support of the Tinbergen Institute.
CHAPTER 1: 1 INTRODUCTION
1.1 Motivation 2 1.1.1 Heterogeneity and congestion pricing 3
1.2 Objectives and Structure of the Thesis 5 1.3 Limitations 8
PART I: THEORETICAL PART
CHAPTER 2: 15 CONGESTION TOLLING IN THE BOTTLENECK MODEL WITH HETEROGENEOUS VALUES OF TIME
2.1 Introduction 16 2.2 The Generalised Price and Demand Surface 17 2.3 Discrete Heterogeneity 18 2.4 Numerical Set-Up 19 2.5 No-Toll Equilibrium 22
2.5.1 The Analytical Model 22 2.5.2. Numerical Base-Case Results 24
2.6 First-Best Public Toll 25 2.6.1 The Analytical Model 25 2.6.2 Numerical Results 26
2.7 A Private Monopoly Controlling the Road 28 2.7.1 The Analytical Model 28 2.7.2 The Numerical Model 28
2.8 Second-Best Tolls 30 2.8.1 The Analytical Model for a Pay-lane 30 2.8.2 The Analytical Model for the Public Time-Invariant Toll 32 2.8.3 The Numerical Models for the Second-Best Policies 32 2.8.4 Conclusion 34
2.9 Sensitivity Analyses 35 2.9.1 NT Equilibrium with a Uniform Value of Time Distribution 35 2.9.2 Welfare Effects of an FB Toll with Different Value of Time Distributions 36
2.9.3 Second-Best Policies with Different Value of Time Distributions 36 2.9.4 Detailed Analysis of the Sensitivity Analysis for the Public Pay-Lane 37 2.9.5 Second-Best Policies with Different Price Elasticities 39 2.9.6 The Pay-Lane with Different Shares of Total Capacity 39 2.9.7 Concluding the sensitivity analysis 40
2.10 Conclusion 41 Appendix 2A: Description of Some of the Symbols Used 42 Appendix 2B: Discrete Heterogeneity and the No-Toll Equilibrium Price 42 Appendix 2C: Derivation of the Pay-Lane Equilibrium 43 Appendix 2D: Numerical Solutions for Pay-Lane and Time-Invariant Toll 44
CHAPTER 3: 47 WINNING OR LOSING FROM CONGESTION PRICING
3.1. Introduction 48 3.2. The demand and generalised price functions 50
3.2.1. The Basics 50 3.2.2. Homogeneous Users 51 3.2.3. Proportional Heterogeneity: an Example with Two Discrete Groups 53 3.2.4. Ratio Heterogeneity: an Example with Two Discrete Groups 54 3.2.5. Proportional and Ratio Heterogeneity: an Example with discrete Groups 55
3.3. The Full Model and Its No-Toll Equilibrium 56 3.3.1 Analytical No-Toll (NT) Model 57 3.3.2 Congestion Externalities and Heterogeneity 58 3.3.3 Base Case Numerical Model for the No-Toll (NT) Equilibrium 58
3.4. Continuous Heterogeneity and First-Best Public (FB) Tolling 60 3.4.1 Analytical Model for the First-Best Public (FB) Equilibrium 61 3.4.2 Numerical Base Case Model for the First-Best Public (FB) Equilibrium 61
3.5. Continuous Heterogeneity and the Pay-Lane 63 3.5.1 Analytical Pay-Lane Model 63 3.5.2 Base Case Numerical Model for the Public Pay-Lane (PL) 64 3.5.3 Base Case Numerical Model for the Private Pay-Lane (PPL) 65 3.5.4 Concluding the Pay-Lane Models 66
3.6. Sensitivity Analyses 66 3.6.1 Effect of Heterogeneity on the No-Toll (NT) Case 67 3.6.2 Heterogeneity and First-Best Public (FB) Tolling 67 3.6.3Effect of Heterogeneity on the Public (PL) Pay-Lane 69 3.6.4 Effect of Heterogeneity on the Private (PPL) Pay-Lane 69 3.6.5 Concluding the sensitivity analysis 71
3.7. Conclusion 71 Appendix 3A: Numerical Solution Method for a Pay-Lane Equilibrium 72
CHAPTER 4: 75 CONGESTION PRICING ON RAIL AND ROAD WITH HETEROGENEOUS VALUES OF TIME AND SCHEDULE DELAY
4.1 Introduction 76 4.2. Analytical Road Model 78
4.2.1. Ratio Heterogeneity and Road Pricing 79 4.2.2. Proportional Heterogeneity and Road Pricing 81
4.3. Analytical Rail Model 83 4.3.1. Ratio Heterogeneity and Road Pricing 83 4.3.2. Proportional Heterogeneity and Road Pricing 85
4.4. Set-Up Numerical Models 86 4.5. Numerical Pricing Model with Proportional Heterogeneity 87
4.5.1. Base Case No-Congestion-Pricing (NCP) Equilibrium 88 4.5.2. Base Case Congestion Pricing Equilibria and Proportional Heterogeneity 88 4.5.3. Sensitivity Analysis 90 4.5.4. Conclusions on Proportional Heterogeneity 92
4.6. Numerical Pricing Model with Ratio Heterogeneity 92 4.6.1. Base case no-congestion-pricing and first-best equilibria with ratio heterogeneity 93 4.6.2. Sensitivity Analysis 95 4.6.3. Conclusions on Ratio Heterogeneity 96
4.7. Some Further Sensitivity Analyses 96 4.7.1 Fixed Cost 96 4.7.2 Price Elasticities 97 4.7.3 Crowding Costs 97
4.8. Conclusion 97
PART II: EMPIRICAL PART
CHAPTER 5: 103 BIASES IN WTP ESTIMATES FROM MNL DUE TO HETEROGENEITY
5.1. Introduction 104 5.2. Literature Discussion 105 5.3. Non-Symmetric Marginal Utilities 106
5.3.1. Set-Up of the Dataset Simulations 106
5.3.2. Results of the Dataset Simulations with Non-Symmetric Heterogeneity 109
5.4. Correlation between two heterogeneous marginal utilities 111 5.4.1. Examples of Correlated Heterogeneity in Marginal Utilities 111 5.4.2. Set-up Dataset Simulations with Correlated Heterogeneity 111 5.4.3. An Decreasing Relation Between Simulated Marginal Utilities 112 5.4.4 An Increasing Relation Between Simulated Marginal Utilities 114 5.4.5 Conclusions on the Effect of Correlated Marginal Utilities 115
5.5 Conclusion 115
CHAPTER 6: 119 CHOICE OF TRAIN TICKET
6.1 Introduction 120 6.2 D