Business, Sauder School of
DSpace
UBCV
Chen, Cheng
Doctor of Philosophy - PhD
University of British Columbia
This dissertation is a collection of three essays that study the efficiency of policies targeting environmental and urban transportation issues. The first essay investigates a government incentive that subsidizes the purchase of electric vehicles(EVs) and asks a question of whether subsidizing public charging facility would be more cost-effective. It estimates a discrete choice model of EVs which relies on both EV characteristics and individual demographic information, using micro-level data from the California Clean Vehicle Rebate Program. Results show: (1) EVs with smaller battery capacity are more reliant on the public charging network; (2) consumers with higher income are less price sensitive. Such results support subsidizing more to public charging facility and reducing the EV purchase subsidy to the more affluent consumers. The second essay builds on the literature of road congestion and addresses the importance of schedule delay cost occurred due to uncertain traffic time. We propose the notion of a "reliability standard" that commuters use to calculate their schedule time --- the buffer time added to a commute so as to ensure being at work on time most of the time. With this tool, we conduct an extensive simulation study to gain further insights into the role of commuter composition, time cost differences, and the degree of inflexibility on optimal road tolls. While the cost of commuting time reliability is economically important, we find that the difference between a full-information road toll and a limited-information road toll is smaller than one would expect. Our study points to how future stated preference studies can be designed to elicit more meaningful information that identifies commuter heterogeneity, and in turn will lead to better designs for mobility pricing. The third essay examines the relationship between firms' voluntary disclosure in environmental performance information and their level of institutional ownership. Empirical results indicate that US S&P 500 companies with higher institutional ownership ratio are less likely to disclose to the Carbon Disclosure Project. Moreover, disclosure behavior also leads to a lower ratio of institutional ownership. This negative relationship suggests adverse selection in the disclosure decision, hence such voluntary disclosure policy might be of limited value to the public.
Essays on the Effectiveness of Environmentaland Urban Transportation PoliciesbyCheng ChenB.A., Nanjing University, 2011M.Sc., University of Waterloo, 2013A THESIS SUBMITTED IN PARTIAL FULFILLMENTOF THE REQUIREMENTS FOR THE DEGREE OFDOCTOR OF PHILOSOPHYinTHE FACULTY OF GRADUATE AND POSTDOCTORAL STUDIES(Business Administration)THE UNIVERSITY OF BRITISH COLUMBIA(Vancouver)August 2019© Cheng Chen, 2019The following individuals certify that they have read, and recommend to the Faculty of Graduate and Post-doctoral Studies for acceptance, the thesis entitled:Essays on the Effectiveness of Environmentaland Urban Transportation Policiessubmitted by Cheng Chen in partial fulfillment of the requirements for the degree of DOCTOR OF PHI-LOSOPHY in Business Administration.Examining Committee:Werner AntweilerCo-supervisorSanghoon LeeCo-supervisorRobin LindseyUniversity ExaminerKevin MilliganUniversity ExaminerAdditional Supervisory Committee Members:Sumeet GulatiSupervisory Committee MemberiiAbstractThis dissertation is a collection of three essays that study the efficiency of policies targeting environmentaland urban transportation issues.The first essay investigates a government incentive that subsidizes the purchase of electric vehicles(EVs)and asks a question of whether subsidizing public charging facility would be more cost-effective. It esti-mates a discrete choice model of EVs which relies on both EV characteristics and individual demographicinformation, using micro-level data from the California Clean Vehicle Rebate Program. Results show: (1)EVs with smaller battery capacity are more reliant on the public charging network; (2) consumers withhigher income are less price sensitive. Such results support subsidizing more to public charging facility andreducing the EV purchase subsidy to the more affluent consumers.The second essay builds on the literature of road congestion and addresses the importance of scheduledelay cost occurred due to uncertain traffic time. We propose the notion of a “reliability standard” thatcommuters use to calculate their schedule time — the buffer time added to a commute so as to ensurebeing at work on time most of the time. With this tool, we conduct an extensive simulation study to gainfurther insights into the role of commuter composition, time cost differences, and the degree of inflexibilityon optimal road tolls. While the cost of commuting time reliability is economically important, we findthat the difference between a full-information road toll and a limited-information road toll is smaller thanone would expect. Our study points to how future stated preference studies can be designed to elicit moremeaningful information that identifies commuter heterogeneity, and in turn will lead to better designs formobility pricing.The third essay examines the relationship between firms’ voluntary disclosure in environmental per-formance information and their level of institutional ownership. Empirical results indicate that US S&P500 companies with higher institutional ownership ratio are less likely to disclose to the Carbon DisclosureProject. Moreover, disclosure behavior also leads to a lower ratio of institutional ownership. This negativerelationship suggests adverse selection in the disclosure decision, hence such voluntary disclosure policymight be of limited value to the public.iiiLay SummaryThis dissertation evaluates the efficiency of three existing or proposed policies that target on environmentalor urban transportation issues. First, in order to promote electric vehicle(EV) adoption, improving the publiccharging network is no less important than subsidizing individual purchasers. Investing in charging facilitieswill enhance the attractiveness of EVs with smaller batteries which are also more affordable. Subsidies onluxurious EVs can be reduced because higher-income consumers are less price-sensitive. Second, besidesprolonged travel time, the uncertainty of travel time caused by congestion also occurs cost on commuters,therefore this also needs to be accounted for while designing mobility pricing policies. We propose thatfuture surveys should ask about travelers’ valuation of travel time, inflexibility criteria, and the correlationbetween them. Finally, voluntary disclosure of environmental information might be of limited value tothe public as empirical results show a negative correlation between disclosure decision and institutionalownership.ivPrefaceChapter 2 and 4 are original and independent work by the author, Cheng Chen. Chapter 3 is joint workwith my thesis co-supervisor Professor Werner Antweiler. We divided the work primarily along the linesof theory and empirics and we collaborated on all aspects of the paper. My contributions on the empiricalside include data analysis, empirical estimation, numerical algorithms, and simulations. Professor Antweilertook the lead on the theoretical parts of the paper.vTable of ContentsAbstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiiLay Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ivPreface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vTable of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viList of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ixList of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiAcknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xii1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 Efficient Government Spending on Promoting Electric Vehicles: a Case of California . . . . . 32.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32.2 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52.2.1 Electric Vehicles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52.2.2 Government Incentives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52.2.3 Charging Infrastructure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62.2.4 Related Literature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62.3 Theoretical Framework . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72.3.1 Operational Cost Decomposition . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72.3.2 Factors Affecting EV Operational Cost . . . . . . . . . . . . . . . . . . . . . . . . 112.4 Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122.4.1 Electric Vehicle Adoption in California . . . . . . . . . . . . . . . . . . . . . . . . 122.4.2 National Household Travel Survey . . . . . . . . . . . . . . . . . . . . . . . . . . . 132.4.3 Charging Stations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142.4.4 Demographic Information . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152.5 Empirical Strategy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162.5.1 Discrete Choice Model of EVs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16vi2.5.2 Choice between EVs and ICEVs . . . . . . . . . . . . . . . . . . . . . . . . . . . . 202.5.3 Counterfactual Exercise from Discrete Choice Model . . . . . . . . . . . . . . . . . 252.5.4 Regression with Aggregated Data . . . . . . . . . . . . . . . . . . . . . . . . . . . 262.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 323 The Cost of Commuting Time Reliability: Theoretical Advances using Reliability Standardsand Empirical Findings from Metro Vancouver Traffic Data . . . . . . . . . . . . . . . . . . 343.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 343.2 Travel Time Reliability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 363.3 Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 393.3.1 Approaches to Travel Time Reliability . . . . . . . . . . . . . . . . . . . . . . . . . 393.3.2 Route Choice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 443.3.3 Speed-Volume Relationship . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 453.3.4 Speed-Volume Dispersion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 473.3.5 Optimal Road Toll and Agent Heterogeneity . . . . . . . . . . . . . . . . . . . . . 493.3.6 Commuters’ Buffer Time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 533.3.7 Reliability Pricing in a Road Network . . . . . . . . . . . . . . . . . . . . . . . . . 543.4 Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 543.4.1 Commutes among Census Tract Pairs . . . . . . . . . . . . . . . . . . . . . . . . . 553.4.2 Bridge Data: Volume and Time . . . . . . . . . . . . . . . . . . . . . . . . . . . . 583.5 Empirics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 603.5.1 Travel Time Coefficient of Variation . . . . . . . . . . . . . . . . . . . . . . . . . . 603.5.2 Fre´chet v. Lognormal: which provides a better fit? . . . . . . . . . . . . . . . . . . 643.5.3 Route Choice: is there a speed-reliability trade-off? . . . . . . . . . . . . . . . . . . 653.5.4 Bridge Traffic Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 673.6 Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 723.6.1 Simulation Configuration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 723.6.2 Optimal Toll Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 743.6.3 Results: Single and Dual Toll Scenarios . . . . . . . . . . . . . . . . . . . . . . . . 753.6.4 Distributional Outcomes and Fairness . . . . . . . . . . . . . . . . . . . . . . . . . 783.6.5 Correlation Structure of Time Costs with Inflexibility and Non-Commutes . . . . . . 823.7 Caveats and Extensions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 843.8 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 854 Carbon Emission Disclosure and Institutional Ownership . . . . . . . . . . . . . . . . . . . . 884.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 884.2 Theoretical Framework . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 894.2.1 Motivation of Voluntary Carbon Disclosure . . . . . . . . . . . . . . . . . . . . . . 894.2.2 Impact of Voluntary Carbon Disclosure . . . . . . . . . . . . . . . . . . . . . . . . 904.2.3 Relationship between Voluntary Carbon Disclosure and Institutional Ownership . . . 90vii4.3 Model Specification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 914.3.1 Carbon Disclosure and Institutional Ownership Measures . . . . . . . . . . . . . . . 924.3.2 Instrumental and Control Variables . . . . . . . . . . . . . . . . . . . . . . . . . . 924.4 Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 934.4.1 Carbon Disclosure Project . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 934.4.2 Institutional Ownership . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 944.4.3 Corporate Social Responsibility . . . . . . . . . . . . . . . . . . . . . . . . . . . . 944.4.4 Firms’ Accounting Records . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 954.5 Regression Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 964.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 985 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104A Appendix for Chapter 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110A.1 Proof of Propositions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110A.2 Choice of Vehicles under Baseline Scenario . . . . . . . . . . . . . . . . . . . . . . . . . . 112B Appendix for Chapter 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116B.1 Glossary of Variables in Chapter 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116B.2 Probability Distributions and Random Variables . . . . . . . . . . . . . . . . . . . . . . . . 116B.3 Data Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118B.4 Additional Figures and Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119viiiList of TablesTable 2.1 CVRP Schedule . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6Table 2.2 Frequency of Vehicle Make in Surveyed Sample . . . . . . . . . . . . . . . . . . . . . . 14Table 2.3 Annual Growth of EV Charging Stations and Rebates . . . . . . . . . . . . . . . . . . . 15Table 2.4 Demographic Information . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15Table 2.5 First-Stage Results for Charging Station Equation . . . . . . . . . . . . . . . . . . . . . 19Table 2.6 Nested Logit Reg. of EV Choice with Control Functions . . . . . . . . . . . . . . . . . . 21Table 2.7 Alternative Specifications: Nested Logit Reg. of EV Choice . . . . . . . . . . . . . . . . 22Table 2.8 Logit Regression of Choice between EV/ICEV . . . . . . . . . . . . . . . . . . . . . . . 24Table 2.9 Counterfactual Exercise from Discrete Choice Model . . . . . . . . . . . . . . . . . . . 25Table 2.10 Census Tract - Year Panel Regression, PHEVs . . . . . . . . . . . . . . . . . . . . . . . 27Table 2.11 Census Tract - Year Panel Regression, small BEVs . . . . . . . . . . . . . . . . . . . . . 28Table 2.12 Census Tract - Year Panel Regression, large BEVs (Teslas) . . . . . . . . . . . . . . . . 29Table 2.13 Parameters for Simulating Indirect Network Effects . . . . . . . . . . . . . . . . . . . . 30Table 3.1 Log-Linear Approximation of H(ψ) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44Table 3.2 Determinants of Commuting Speed and Delay . . . . . . . . . . . . . . . . . . . . . . . 58Table 3.3 Traffic Bottlenecks in Metro Vancouver . . . . . . . . . . . . . . . . . . . . . . . . . . . 60Table 3.4 Congestion and Travel Time Coefficients of Variation . . . . . . . . . . . . . . . . . . . 62Table 3.5 Schedule Time Cost [%] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63Table 3.6 Distribution of Route Choices among 2,000 Commutes . . . . . . . . . . . . . . . . . . 66Table 3.7 Speed Limit-Capacity Relationship . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68Table 3.8 Estimation Results Bridge & Tunnel Traffic . . . . . . . . . . . . . . . . . . . . . . . . 71Table 3.9 Simulation Scenario Parametrization . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73Table 3.10 Simulation Scope Parametrization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73Table 3.11 Simulation Results: ‘Lexus Lanes’ Scenario . . . . . . . . . . . . . . . . . . . . . . . . 75Table 3.12 Simulation Results: ‘Asymmetry’ Scenario . . . . . . . . . . . . . . . . . . . . . . . . . 76Table 3.13 Distributional Outcomes: ‘Lexus Lanes’ Scenario . . . . . . . . . . . . . . . . . . . . . 79Table 3.14 Distributional Outcomes: ‘Asymmetric’ Scenario . . . . . . . . . . . . . . . . . . . . . 80Table 4.1 Summary statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95Table 4.2 Cross-correlation table . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96ixTable 4.3 Simultaneous Equations Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97Table 4.4 Disclosure Quality and Institutional Ownership . . . . . . . . . . . . . . . . . . . . . . . 100Table 4.5 Emission Intensity and Institutional Ownership . . . . . . . . . . . . . . . . . . . . . . . 101Table A.1 Characteristics of Representative EVs . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113Table B.1 Glossary of Variables in Chapter 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117Table B.2 Census Tracts in Vancouver Census Metropolitan Area (2016) . . . . . . . . . . . . . . . 118Table B.3 Distributional Outcomes: Average Time Costs by Group in the ‘Lexus Lane’ single-tollscenario with symmetric roads . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120Table B.4 Distributional Outcomes: Average Time Costs by Group in the dual-toll scenario withasymmetric roads . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121xList of FiguresFigure 2.1 Year Trend of Rebate Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12Figure 2.2 Market Share across Regions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13Figure 2.3 Nested Logit Tree Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17Figure 2.4 Ideal Nested Logit Tree Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23Figure 2.5 Indirect Network Effect — Base Case Scenario . . . . . . . . . . . . . . . . . . . . . . 31Figure 2.6 qθ ,t and Nt under Different Scenarios . . . . . . . . . . . . . . . . . . . . . . . . . . . 32Figure 3.1 Travel Time Variability and Travel Time Mark-Up . . . . . . . . . . . . . . . . . . . . 42Figure 3.2 Travel Time Markup Factor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43Figure 3.3 Speed-Volume Function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47Figure 3.4 Effect of Inflexible Commuter Share on Optimal Traffic Volume . . . . . . . . . . . . . 52Figure 3.5 Effect of Schedule Inflexibility on Optimal Traffic Volume . . . . . . . . . . . . . . . . 52Figure 3.6 Census Tract Commuting Trip Sample . . . . . . . . . . . . . . . . . . . . . . . . . . . 56Figure 3.7 Commuting Distance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56Figure 3.8 Commuting Time Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57Figure 3.9 Commuting Speed Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57Figure 3.10 Diurnal Direction Traffic Volume . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59Figure 3.11 Speed Volume Charts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59Figure 3.12 Coefficient of Variation Distribution: Time Markup Tρ . . . . . . . . . . . . . . . . . . 61Figure 3.13 Coefficient of Variation Distribution: Travel Time Tν . . . . . . . . . . . . . . . . . . . 61Figure 3.14 Schedule Time Variation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63Figure 3.15 Log-Likelihood Comparison of Commuting Time Distribution . . . . . . . . . . . . . . 65Figure 3.16 Alternate Route Trade-Offs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66Figure 3.17 Simulation Results: Correlation Structure . . . . . . . . . . . . . . . . . . . . . . . . . 82Figure A.1 Distribution of Daily Driven Distance . . . . . . . . . . . . . . . . . . . . . . . . . . . 113Figure A.2 Operational Cost of Small Vehicles . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114Figure A.3 Operational Cost of Large Vehicles . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114Figure B.1 Comparison of Fre´chet and Lognormal Distribution . . . . . . . . . . . . . . . . . . . . 118Figure B.2 Simulation Results: Correlation Structure . . . . . . . . . . . . . . . . . . . . . . . . . 119xiAcknowledgmentsFirst and foremost I want to thank my advisors Professor Werner Antweiler and Professor Sanghoon Lee fortheir continuous support of my Ph.D. study. Both of them have devoted precious time discussing with meresearch ideas as well as technical details. I learned from them the perseverance, generosity, and enthusiasmof being a researcher. Especially, I owe a lot to Professor Antweiler who collaborates with me in Chapter 3of the thesis and teaches me the rigor of conducting high-quality research.I would also like to thank Professor Sumeet Gulati for joining my committee and providing helpfulfeedbacks on my research. I am also very grateful to Professor Ralph Winter who is willing to offer sugges-tions regarding all aspects. I also thank Professor Robin Lindsey for his suggestions and feedbacks. Manythanks to other faculty members of the Strategy and Business Economics Division and participants in theEnvironmental Economics Reading Group, for their comments and acts of kindness.Special thanks to Xiaonan Sun and Ruoying Wang who have continuously shared their skills and insightswith me without reservation. I also thank many other friends from Sauder School of Business and VancouverSchool of Economics for our interesting discussions. Finally, I owe my survival in the Ph.D. journey to theunconditional support and ultimate understanding from my parents. Thank you.xiiChapter 1IntroductionThis dissertation is a collection of three independent essays that investigate the efficiency of existing orproposed policies targeting on environmental or urban transportation issues. The first essay in Chapter 2investigates whether providing cash subsidies to individual electric vehicle(EV) purchasers is the most cost-effective policy to promote EV adoption. The second essay in Chapter 3 addresses the importance of volatil-ity in commute time and discusses how to induce an optimal mobility pricing scheme that accounts for suchissue. The third essay in Chapter 4 analyzes the effectiveness of a voluntary disclosure policy on firms’environmental performance and suggests that disclosure content is of limited value to the public. In thischapter I will briefly summarize the main methodology and findings of each essay. Because each essaytargets an independent topic, I thus leave a more comprehensive discussion of the research question andliterature review in each chapter.The first essay (Chapter 2) is titled “Efficient Government Spending on Promoting Electric Vehicles:a Case of California”. Various incentives have been carried out by policy makers in order to promoteadoption of electric vehicles(EV), which rely on electricity as an energy source and might generate lessgreenhouse gas compared to conventional vehicles using fossil fuel. This paper aims to analyze factorsthat affect consumers’ taste on different types of EVs, and discuss whether the current U.S. governmentincentives are most efficient. Estimating a discrete choice model using micro-level data from CaliforniaClean Vehicle Rebate Program (CVRP), this paper discovers that access to both private and public chargingfacility contributes to decision of EV purchase. Among various types of EVs, pure battery electric vehicles(BEV) with relatively shorter electric range have the most inelastic demand towards public charging facilitynetwork. Meanwhile, shorter range BEVs have a modest price compared to longer range BEVs, and are moreenergy efficient compared to plug-in electric vehicles (PHEVs). Therefore subsidizing charging facilityinstead of individual EV purchasers might contribute more to energy saving and air pollution reduction,whereas reducing the concern that high-income potential buyers of luxurious longer range BEVs might freeride government subsidy.The second essay (Chapter 3) is titled “The Cost of Commuting Time Reliability: Theoretical Advancesusing Reliability Standards and Empirical Findings from Metro Vancouver Traffic Data”. The literature onroad congestion has long acknowledged the importance of inflexible commuters who incur schedule delaycosts in order to arrive on time. This paper advances a number of new insights into this phenomenon. We1introduce the notion of a “reliability standard” that commuters use to calculate their schedule time—thebuffer time added to a commute so as to ensure being at work on time most of the time. Using two com-peting empirical distribution of commuting travel time (Fre´chet and Lognormal), we develop a tight linearapproximation of the schedule time that neatly separates schedule inflexibility (a commuter characteristic)from the coefficient of variation of travel time (a route characteristic). Our theoretical insights allow us tocharacterize and quantify the cost of commuting time reliability. Empirically, we use two data sets withtraffic flows in the Metro Vancouver area—one with volume and speed of several key congestion points, andone with time distributions across a sample of 2,000 commutes across the entire Metro region—to identifythe links between congestion and the cost of commuting time reliability. The empirical results demonstratethat travel time variability is a function of congestion, but interacts with route characteristics. We also con-duct an extensive simulation study to gain further insights into the role of commuter composition, time costdifferences, and the degree of inflexibility on optimal road tolls. We expand this approach to encompass thecorrelation structure of time costs, degree of inflexibility, and demand response (cutoff time for commutes).While the cost of commuting time reliability is economically important, we find that the difference betweena full-information road toll and a limited-information road toll is smaller than one would expect. Overall, ourstudy points to how future stated preference studies can be designed to elicit more meaningful informationthat identifies commuter heterogeneity, and in turn will lead to better designs for mobility pricing.The title of the third essay (Chapter 4) is “Voluntary Carbon Disclosure and Institutional Ownership”.This study unveils the relationship between firms’ voluntary carbon emission disclosure behavior and thelevel of institutional ownership. The question of interest is whether disclosure of non-financial information isassociated with changes in financial performance. Disclosure improves firms’ transparency to shareholders,and also incurs costs such as to maintain good carbon emission record in the future, therefore disclosure canresult in financial impact of either direction. Empirical results indicate that among US S&P 500 companies,higher institutional ownership ratio causes less disclosure to Carbon Disclosure Project(CDP), an organi-zation which publishes large companies’ self-disclosed information about carbon emission. Moreover thedisclosure behavior also leads to lower ratio of institutional ownership. This negative relationship impliesthat firms’ disclosure behavior does not signal carbon strength, yet might be caused by other motivationsunfavored by institutional investors.2Chapter 2Efficient Government Spending onPromoting Electric Vehicles: a Case ofCalifornia2.1 IntroductionAmong various instruments towards reducing greenhouse gas(GHG) emission, electric vehicles(EVs) havedrawn much attention not only from policy makers but also the general public. Different from conventionalinternal combustion engine vehicles (ICEVs), EVs do not depend on particular sources of energy, whichallows them to use cleaner energy that generates less air pollutants and GHG. According to U.S. EPA, EVsconvert about 59% - 62% of the electrical energy from the grid to power at the wheels, whereas ICEVs onlyconvert about 17% - 21% of the energy stored in gasoline. Many governments have set ambitious goals onreplacing ICEVs with EVs in the future. Britain and France said in 2017 that by 2040 new cars completelyrelying on petrol or diesel will be illegal. China, with the world’s largest EV market, also announced thatICEVs would be banned in the future and required automobile makers with more than 30,000 annual salesto meet a quota of 10% being EVs.From consumers’ point of view, EVs favor potential buyers that they render much lower fuel cost, atabout half of gasoline vehicles.1 Surveys show that EV drivers also appreciate the new technology and envi-ronmental benefit. Despite the superiorities EVs embrace, their adoption are hindered by factors includinghigher prices and concerns on charging. For example, the popular EV Nissan Leaf (2017 model) has a Man-ufacturer’s Suggested Retail Price(MSRP) of $30,680 - $36,790, while a comparable ICE vehicle ToyotaPrius (2017 model) has a much lower MSRP of $23,475 - $30,015. According to EPA’s estimate on annualfuel cost, Nissan Leaf costs $150 less than Toyota Prius per year, which hardly justifies the price differenceof about $6,000. Convenience of charging is another concern to potential EV drivers, as EVs have shorterrange with a full battery compared to ICEVs with a full tank of fuel whereas the charging process takes1U.S. EPA website lists estimated annual fuel cost for each vehicle model. The actual fuel cost savings depends on local priceof gasoline and electricity.3much more time than refueling at gas station. For example, Nissan Leaf (2017 model) has a range of 107miles whereas Toyota Prius (2017 model) has a range of 588 miles, and using fastest charging facility, Leafcan be charged to 80% battery capacity in 30 minutes, which takes way more time than people stay at agasoline pump.Within the family of EVs, there are plug-in hybrid electric vehicles (PHEVs) and battery electric vehicles(BEVs), their difference being that PHEVs have shorter electricity range and would rely on gasoline after itexhausts its battery whereas BEVs use electricity as their sole energy source. Throughout this paper, I usethe word EV to refer to both PHEV and BEV.Policy makers around the world therefore launched combinations of incentives to encourage EV adop-tion, examples including: cash rebates or tax credits upon EV purchasing or leasing, unlimited access tohigh occupancy vehicle(HOV) lanes on highways, utility rate discount for charging EVs, etc. Some localgovernments also subsidize the installation of EV charging stations.The current financial incentives given to EV owners are rather generous. EVs purchased in the USafter year 2010 may be eligible for a federal income tax credit of up to $7,500, depending on the vehicle’sbattery capacity. Under such a scheme, BEVs usually qualify for $7,500 tax credit while PHEVs get $2,500-$4,500. This paper mainly relies on data from California Clean Vehicle Rebate Program (CVRP), which isa state incentive provided by the California Air Resource Board. CVRP provides rebates to various kindsof energy-efficient vehicles including PHEVs, BEVs, and some other alternative fuel vehicles, with PHEVsand BEVs representing about 99% of all the rebated vehicles. Under CVRP, each BEV and PHEV receivesa cash rebate of $2,500 and $1,500 respectively during the time period covered by the dataset used in thisstudy.2 With multiple instruments at hand for the governments to promote EV adoption, a natural questionto ask is how to efficiently allocate limited funding so that maximum amount of total gasoline miles couldbe replaced by electricity miles, leading to most pollution reduction. To answer this question, I proposeto first estimate the utility function of PHEVs and BEVs that explains heterogeneous consumers’ decisionmaking process in EV choice, and then conduct counterfactual exercises to see how consumers would reactunder alternative incentive bundles.The case of California is worth studying due to at least two reasons. First, California is the biggest EVmarket in the US, accounting for about half of US EV sale. Second, compared with other states, Californiasuffers more serious air pollution from ICEVs whereas embraces a cleaner electricity source, bringing EVsgreater environmental benefits (Holland et al., 2016).The contribution of this paper is two-fold. First, it estimates a discrete choice model of EVs whichrelies on both EV characteristics and individual demographic information, whereas the literature mainlyuses aggregated data. Second, this paper provides implication on how to design cost-effective policies topromote EVs, leveraging the heterogeneous tastes of EV owners towards financial incentives and charginginfrastructure.2The CVRP rebate amount adjusted several times since its establishment in 2010, and the details will be presented in a latersection of this paper.42.2 Background2.2.1 Electric VehiclesOver the years, global warming has made increasingly visible impact to our planet. For example, growingarctic temperature has melted glaciers dramatically and resulted in sea level rise, which further threats to in-undate land areas; places around the world experience enlarging variability in temperature and precipitation,which led to conditions like severe wildfires in California during 2017 fall. Increasing GHG emissions suchas carbon dioxide, methane, and nitrous oxide are the dominant cause of climate change.Car driving accounts for one of the largest sources of GHG emissions as traditional cars rely on fossil fuelas sole energy source. Fortunately the invention of EVs provides an opportunity to reduce GHG emissions,since electricity could be generated from cleaner energy sources that emit less GHG. California, for example,mainly uses natural gas, hydro power, solar power, and nuclear power for electricity generation. Such energysources not only lowers GHG emissions compared with gasoline, but also generate less air pollutants suchas particulate matter, nitrogen oxides, sulfur dioxide, etc.EVs first came into existence in mid-19th century, yet the series production of highway-capable EVshappened not until recent decade. In 2008, the first EV available to the general public, Tesla Roadster, waslaunched. It is the first EV using lithium-ion battery cells and has a range greater than 200 miles betweencharges. The production of Roadster was ceased in 2012, when Tesla introduced Model S, a full-sized all-electric luxury car which receives wide popularity. The earliest generation of Model S with a 60 kWh batterypack has an electric range of 208 miles rated by EPA, and 265 miles for the 85 kWh battery pack model.Despite that the price of Model S starts as high as $66,000, it is the top selling EV in year 2014 and 2015,also the second best selling EV model of all the time. In 2010, the Japanese manufacturer Nissan introduceda compact hatchback electric car — Leaf, which is the world’s best selling EV model. First generation ofNissan Leaf comes with a modest electric range at 73 miles (rated by EPA).Tesla Model S and Nissan Leaf are both BEVs which consume electricity as the sole energy source.Another branch of the EV family is PHEV, which carries both a battery and an internal combustion engine.PHEVs function just like BEVs until their battery is exhausted and then they will turn to the gas tank topower the car. PHEVs began available to the public in 2010, and among the most popular models includingthe Chevrolet Volt manufactured by General Motors. The first generation of Chevrolet Volt has an electricrange of 25-50 miles, and it has a total range of 379 miles with full battery and gasoline.2.2.2 Government IncentivesPolicy makers around the globe have tried various tools to promote EV adoption. Federal government ofthe United States carried out tax credit for new EV purchasers since 2008, the amount of which increasesproportionally with battery size and capped at $7,500. The tax credits will phase out after 200,000 EVs havebeen sold by one car manufacturer. Until the end of 2017, the 200,000 subsidy limit has not been reachedby any manufacturer. Charging equipment installed by homes and businesses also receive tax credit through2013, the amount ranging from $1,000 to $50,000, depending on installation scale.In California, the largest EV market of US, additional financial incentives are provided by the Clean5Vehicle Rebate Project (CVRP). The program started in 2010 with $5,000 subsidy to BEVs, and the rebateamount soon decreases to $2,500 after June 2011. PHEVs entered the market in year 2012 with the in-troduction of Toyota Prius PHEV, and PHEV buyers receive a rebate of $1,500 from CVRP. Starting fromMar 29, 2016, the program gives more subsidy to lower-income buyers whereas sets an income cap to re-strict application of rebates from the richer. On Nov 1, 2016, subsidy to lower-income buyers are increasedwhereas the income cap is further lowered. Details are revealed in Table 2.1. Besides financial incentives,local policies such as allowing solo EV drivers access to HOV lanes, free EV parking, discounted utility ratefor EV charging, etc. also contribute to California’s relatively high EV sales.Table 2.1: CVRP ScheduleVehicle Date of Purchase Income Cap Increased RebatePrior to Mar 29 2016 Not Applicable Not ApplicableMar 29 2016 - Oct 31 2016 $250,000 $1,500Nov 1 2016 - Present $150,000 $2,000Increased rebate are eligible to households with income less than 300 % of the federal poverty level.Income Cap are for single filers. Household filers have higher income caps.Other countries leading in EV sales such as Japan, China, United Kingdom, Norway, Netherlands, Swe-den, France, Germany, etc. have also carried out various monetary incentives. The policy instruments theyused include tax reduction, direct subsidies to purchasers or manufacturers, elimination of car registrationfee, etc.2.2.3 Charging InfrastructureThere are several modes of EV charging. It could be as simple as plug in to a non-dedicated 110-volthousehold outlet (Level 1 charging), and it takes about 16 hours to add 100 electric miles.Level 2 charging stations are the most common ones installed by household and public parkades. Theyrequire 240-volt outlet and can charge about 6 times faster than Level 1. Smart features are also availablefor Level 2 charging stations which can schedule charging for off-peak hours. The cost to purchase andinstall Level 2 charging stations at home is about $1,500, while rebates ranging from $500 to $1,000 areavailable for some counties in California. Public Level 2 charging stations cost more than home chargersdue to more features, and installing chargers at curbside costs more than in a garage. Local incentives forpublic or workplace charging stations are also available in some areas.Direct Current(DC) fast charging stations connect EVs to main power grid through an external charger,and can charge most EVs to 80 percent in 20-30 minutes. They are much more expensive to install, costing$50,000 to $100,000 per station.2.2.4 Related LiteratureThis study is built on a growing literature that analyze the factors affecting EV adoption empirically. Liet al. (2017) studied how adoption of EV and deployment of EV charging stations affect each other usingUS vehicle sales data. A feedback loop is found and the authors conclude that policies that subsidize6building charging stations would be twice as effective in promoting EVs compared to the current federaltax incentives for EV purchasers. Studies based on other places around the world also confirmed that EVcharging facility plays an important role in pushing forward EV adoption, examples include Sierzchula et al.(2014), Mersky et al. (2016), Wang et al. (2017), and so on. Bailey et al. (2015) found that the availabilityof home charging has a much more substantial impact than perceived existence of public charging stationson EV demand, using survey of new-vehicle buyers in 2013.This paper is also closely related to the literature discussing the design of government subsidy on cleanvehicles. DeShazo et al. (2017) focuses on designing optimal EV rebate policy that induces more EV saleunder a constraint of total government expense. They illustrated that policies which set a cap on EV price orset different rebate schedule for consumers with heterogeneous income would be more efficient. To supportthis idea, they developed a theory model and tested empirically using data from stated preference surveys.Chandra et al. (2010) estimate the effect of tax rebates offered by Canadian Provinces on the sales of hybridelectric vehicles (HEVs). While confirming the rebate successfully boosted sales of HEVs, they argue thatthe subsidized consumers would have bought either HEVs or other fuel-efficient vehicles in the absence ofthe rebate. Therefore they conclude that reduction of carbon emission is too costly under this rebate scheme.A strand of literature uses stated choice survey data to analyze what factors influence consumers’ deci-sion in EV adoption. Hackbarth and Madlener (2013) used discrete choice model on German survey datato analyze consumers’ preference to BEVs and PHEVs. They found that due to the longer waiting time ofEV charging and higher risk of getting stranded with an empty battery, BEVs are less appealing to con-sumers than PHEVs, since the latter has a backup gasoline tank that allows the PHEV to be refueled asa conventional ICEV. Lieven (2015) conducted survey analysis regarding potential EV purchasers’ prefer-ence to combinations of different government incentives. Based on surveys collected from 20 countries,they claimed that the charging infrastructures are must-haves while expediting EV diffusion, whereas mon-etary incentive and favorable traffic regulations are appealing but not as essential as establishing a chargingnetwork.Several papers apply the random-coefficient discrete choice model which follows the setting of Berryet al. (1995) (referred to as the BLP model) and study the demand for electric vehicles or other new en-ergy vehicles. Zhang et al. (2016) observe the BEV market in Norway and examine how consumers’ BEVchoice vary with government incentives, in addition to price and car characteristics. They find that gov-ernment incentives including bus lane access, toll waiver, and charging station expansion promotes BEVadoption, within them increasing density of charging station has the most significant effects for BEV sales.Beresteanu and Li (2011) use BLP style random coefficients model to analyze demand for hybrid vehiclesunder scenarios of varying gasoline prices and government tax incentives.2.3 Theoretical Framework2.3.1 Operational Cost DecompositionThis section decomposes operational costs of different types of vehicles.Operational cost ci j includes monetary cost and time cost that occur when refueling vehicles. For BEVs,7PHEVs and ICEVs, the general form of their operational costs are similar:ci j = m j +witi jwhere m j stands for dollar fuel cost of driving 1 mile; wi is valuation of time for individual i; ti j is timespent refueling for 1 mile’s driving distance, which includes time searching for refueling stations as well aswaiting. Next I decompose ci j in detail.2.3.1.1 Operational Cost of EVsA major concern for EV adoption is the reliability and convenience of charging. Assume two scenarios ofcharging an EV: regular charging with cost c1,i j and backup charging with cost c2,i j. Upon purchasing an EVj, consumer i has made a decision on her regular charging mode – installing home charging equipment, oruse public chargers located in parkades of workplace or near home, resulting in regular charging cost c1,i j.The consumer is also aware that in some non-regular cases when a BEV is about to exhaust all its batteryaway from her usual charging spot, she would then have to search for public charging station and wait whilethe BEV is being charged. PHEVs, however, enjoy more flexibility when the battery drains thanks to theirbackup fuel tanks. In such non-regular cases, charging cost c2,i j is generated. Last but not least, there existsa possibility that a BEV might get stranded due to completely exhausted battery, with an expected cost ofstranded being c3,i j.Let qi j denote the probability of “backup charging”. The car owners would plan ahead to avoid backupcharging, since that either renders more time cost waiting for a BEV to be charged or more monetarycost to add fuel for a PHEV. Assume daily range driven by person i follows log-normal distribution: ri ∼Lognormal(µi, σ2i ),3 with its probability density function denoted as f (ri). With EV j’s electric range beingR j, qi j can be expressed as the probability that individual i drives distance longer than its maximum electricrange within a day:qB,i j =∫ +∞δR jf (ri)driqP,i j =∫ +∞R jf (ri)driwhere δ ∈ (0,1) is a ratio which means BEV owners recharge their BEVs once they’ve driven a distance ofδR j.4Therefore qi j = q(µi,σi,R j). For simplicity, I assume σi = σ so that f (ri) only depends on µi, the meandaily driving distance. Then qi j = q(µi,R j) and∂qi j∂R j < 0,∂qi j∂µi > 0. The intuition is that EVs with longerelectric ranges will occur less backup charging whereas people who on average drive longer distance perday face higher chance of exhausting battery storage.3To echo the pattern of peoples’ daily driving distance from 2009 National Household Transportation Survey, I set µi = 3.25,σ2i = 0.75. The distribution of ri is skewed to the left with a long right tail.4BEVs suffer from high cost of being stranded therefore BEV owners will not exhaust all of its electric range before recharging,whereas PHEVs do not share such problem.8In the following paragraphs, I discuss the composition of charging costs c1,i j and c2,i j, and strandedcost c3,i j. The cost of regular charging c1,i j varies with the charging mode selected by the EV owner.Specifically, whether or not the EV owner has access to home charging makes a big difference. Having ahome charger guarantees availability and convenience of charging, and does not cause detour to find publiccharging stations. Assume that EV owners who have chargers at home will not use public charging stationsfor regular daily charging, then their regular charging cost would be:c1|HC,i j = PS+PeEjwhere PS is the fixed cost to install a Level 2 charging station amortized to each mile driven by the EV5;E j is energy efficiency of vehicle j, i.e., miles/kWh; Pe is electricity rate6. Note that in the case of homecharging, no time cost occurs to individual i.EV owners without home charging will experience more hassles to regularly charge their EVs due to thephysical distance between charger and home, uncertainty of charging spot availability, and more expensiveelectricity price. The frequency of charging depends on both EV’s electric range R j and EV owner’s averagedaily driving distance ri. Assume that EV owners go to public charging stations only when they expect theleft battery storage would not fully cover the driving distance of the next day, then the days between eachtime charging would be max(⌊δR j/ri⌋,1) for BEVs and max(⌊RPE, j/ri⌋,1) for PHEVs. Then the regularcharging cost per mile of EV owners without home charging c1,i j is:c1|BEV,NHC,i j =wit1(SS,i j)min(ri,R j)max(⌊δR j/ri⌋,1)+PeE jc1|PHEV,NHC,i j =wit1(SS,i j)min(ri,R j)max(⌊RPE, j/ri⌋,1)+PeE jwhere SS,i j is density of level II public chargers7; R j is the electric range of the BEV; RPE, j is the electricrange of PHEV j, wi is individual i’s valuation of time. t1(·) stands for the time spent detouring to a publiccharging station and it is a decreasing function of SS,i j. With greater density of public charging stations, EVowners spare less efforts finding one and less time walking between charging stations and home or office.Also, an EV with a longer electric range can run for more days once fully charged, therefore it reduces thefrequency of charging and time spent on it.With probability qi j, an EV relies on backup charging channels. Since PHEVs have secondary fuelsource as gasoline, PHEVs and BEVs’ backup charging costs differ. For BEVs, such costs include time costof detouring to a charging station and waiting for the EV to be charged, as well as cost of electricity.c2|BEV,i j = qB,i j[wi(t1(SF,i j)δR j+ t2, j)+PeE j]5Level 2 charging uses a regular socket with some EV specification protection arrangement. Most EV models can be fullycharged in 4-6 hours under Level 2 charging. They are most popular in home charging and public charging stations.6For simplicity reason, assume homogeneous electricity rate in baseline case7Charger density differs by geography therefore has subscript i. Compatibility of chargers with EV models may differ thereforesubscript j.9where SF,i j is the density of fast charging stations8, t2, j is charging time of vehicle j under fast chargingmode (minute/mile). Note that in this case, individual i waits for the EV to be charged, because this is nother regular charging spot and she might be in the middle of a trip. DC fast charging stations nowadaysusually can add 80 % of an EV battery in 20-40 minutes, whereas level II chargers take more than 3 hours.Therefore I assume that BEV owners search only for fast charging stations in case of backup charging.For PHEVs, I assume that the owners rely on gasoline as their sole fuel source in cases of backupcharging. Similar to BEVs, PHEVs’ backup charging cost involves time cost of detouring to a gasolinestation and waiting while the gas tank is filled, as well as monetary cost of gasoline.c2|PHEV,i j = qP,i j[wi(t1(SG,i)δRPG, j+ t3, j)+PgG j]where SG,i is the density of gasoline stations; RPG, j is PHEV j’s gasoline range; t3, j is the time of filling thegas (minute/mile); G j stands for miles per gallon and Pg is gasoline price considered as a constant.Furthermore, possibility remains that BEVs will be stranded with an empty battery, which renders un-desired inconveniences such as car towing. The expected cost of being stranded c3,i j only occurs to BEVbut not PHEV, considering the well developed network of gasoline stations. Probability of failure to find apublic charging station, fi j(SS,i j,SF,i j) is a decreasing function of density of public charging stations, i.e.,∂ f∂SS,i j< 0 and∂ f∂SF,i j< 0. BEV owners with accessibility to home charging are only exposed to risk ofstranded in case of backup charging, whereas BEV owners without home charging face the stranded risk inall charging modes. Therefore the expected cost of stranded is as below:c3|PHEV = 0c3|BEV,HC,ij = qB,i j fi j(witsR j+ms)c3|BEV,NHC,ij = fi j(witsR j+ms)where monetary cost occurred and time wasted after a BEV gets stranded is abstracted to ms and ts.To simplify the analysis, I sum up EV’s monetary operational cost and denote it as MB, j for BEVs or MP, jfor PHEVs9. Then the cost term ci j derived from the previous discussion could be summarized as below,differed by being a BEV or PHEV, and having accessibility to home charging (HC) or not (NHC):8Compatibility of fast charging stations differs across EVs, especially Tesla manages their own fast charging network — TeslaSuperchargers, therefore this term has subscript j.9According to EPA, estimated annual fuel cost of a BEV or PHEV varies from $550 to $850, which is a relatively small amountcompared to vehicle prices. PHEVs bear greater fuel cost in general due to higher price of gasoline than electricity.10ci j =(HC,BEV) : PS+MB, j +qi j[wi(t1(SF,i j)δR j+ t2, j + fi jtsR j)+ fi jms](HC,PHEV) : PS+MP, j +wiqi j(t1(SG,i)δRPG, j+ t3, j)(NHC,BEV) : MB, j +wit1(SS,i j)min(ri,R j)max(⌊δR j/ri⌋,1)+wi[qi j(t1(SF,i j)δR j+ t2, j)+ fi jtsR j]+ms fi j(NHC,PHEV) : MP, j +wit1(SS,i j)min(ri,RPE, j)max(⌊RPE, j/ri⌋,1)+wiqi j(t1(SG,i)δRPG, j+ t3, j)(2.1)2.3.1.2 Operational Cost of ICEVsOperational cost for conventional ICEVs is listed below for comparison, the functional form of which issimilar to the backup charging case of PHEVs. It includes time cost of searching for gasoline station andwaiting at the gas pump, and monetary cost of gasoline consumption.cICEV,i j = wi(t1(SG,i)R j+ t3, j)+PgG j2.3.2 Factors Affecting EV Operational CostFor consumers without concerns of environmental impacts, their choices between BEVs, PHEVs, andICEVs with same vehicle attributes depend on trade-off of monetary and time cost of refueling. There-fore efforts to reduce time cost of EV charging is crucial in promoting EV adoption, given that monetarycost of EV charging is relatively fixed.From equation (2.1), one can discover that driving force of EV charging time cost consist of accessibilityto home charging, density of EV charging stations, valuation of time, EV category (BEV or PHEV), and EVrange. This section discusses in general how consumer characteristics and EV attributes affect convenienceof EV charging and hence consumer utility. Several propositions are listed below, with their proves providedin Section A.1.Proposition 1 Accessibility to home charging will lower charging cost in general.Proposition 2 Adding public charging stations will lower charging cost in general, and such impact isgreater for EV owners without home charging.Proposition 3 Within BEVs, those with shorter electric range benefit more from adding public chargingstations.Proposition 4 Greater electric range lowers charging cost, and such impact enlarges with people’s valua-tion of time.The propositions in this section will be tested using individual level EV purchase data. Also, I will useaggregated data to show that smaller BEVs (SBEVs, BEVs with shorter electric range) are more sensitive11Figure 2.1: Year Trend of Rebate Applicationsto the increasing number of public charging stations than larger BEVs (LBEVs, BEVs with longer electricrange). The dataset will be described in Section 2.4, and specification details will be provided in Section 2.5.A baseline scenario (illustrated in Section A.2) compares the operational costs of several currently avail-able car models which are considered to be close substitutes with each other. It shows how individualcharacteristics such as accessibility to home charging, valuation towards time affect operational cost hencechoice of vehicle within categories of BEVs, PHEVs, and ICEVs.2.4 Data2.4.1 Electric Vehicle Adoption in CaliforniaThis paper focuses on the case of California. California Environmental Protection Agency’s Air ResourcesBoard releases information for each EV purchase under CVRP (Center for Sustainable Energy, 2017), in-cluding EV make, time of purchase, Census Tract of residence, etc. I will aggregate this whole sampledataset by Census Tract and year, and then examine the impact of public charging stations on EV adoption.Having detailed geographic information — Census Tract code of the vehicle owner is crucial for this study,for it enables observing how many electric vehicle charging stations are present surrounding the drivers’home address. A total number of 8,058 census tracts are involved in this study.Ever since the CVRP launched in 2010, the number of BEVs and PHEVs10 applying for rebate kept in-creasing. Figure 2.1 below exhibits the trend of rebate applications from different vehicle models11. More-over, figure 2.2 shows the market shares of different EV models across different regions, with the numberon top of each vertical bar indicating the total number of rebates of the region.CVRP also conducted a detailed consumer survey that asks about demographic information. 14,44210PHEVs were launched to sell in year 2012. The data in year 2016 only lasts until September 2016.11For simplicity, BEVs under a single automobile maker are considered as same product, so are PHEVs.12Figure 2.2: Market Share across Regionsquestionnaires have been answered completely, which represent about 10% of all the rebates in CVRP.The following information is unveiled for each questionnaire: (1) rebate application date, (2) rebate dollaramount, (3) vehicle category (e.g. PHEV, BEV, etc.), (4) vehicle make (e.g. Tesla, Nissan, etc.), (5) residencecounty12, (6) income range, (7) housing type, (8) renter/owner of the residence place. With individual EVpurchaser’s demographic information, this survey data can be used to examine consumers’ heterogeneoustaste on EV characteristics.Table (2.2) exhibits vehicles’ type and make frequency that are present in the consumer survey. Notethat in the survey, some less popular EV makers are documented as ”Others”, such as Smart and Volkswa-gen, probably due to privacy reason. Such less popular EV models are excluded from our individual leveldiscrete choice analysis since EV characteristics are unknown. The first column of table (2.2) include allobservations; the second and third columns present observations in counties with higher/lower populationdensity; the last two columns present observations in Northern/Southern California counties. Such split ofsample is in accordance with the empirical analysis in later part of the paper.2.4.2 National Household Travel Survey2017 National Household Travel Survey (NHTS) 13 also provides useful information for this study. Thenationwide survey asks households’ travel decisions including vehicle purchases. One could observe house-12Unfortunately, more accurate Census Tract information is not asked in the individual questionnaire.13Downloaded on March 20, 2018 from https://nhts.ornl.gov.13Table 2.2: Frequency of Vehicle Make in Surveyed SampleType-Make All High Pop. Den. Low Pop. Den. North CA South CABEVBMW 335 186 149 129 206Chevrolet 499 237 262 242 257FIAT 1,482 813 669 681 801Ford 402 164 238 213 189Nissan 2,974 1,369 1,605 1,789 1,185Tesla 2,334 1,207 1,127 1,140 1,194Toyota 352 183 169 173 179PHEVChevrolet 2,890 1,556 1,334 1,101 1,789Ford 1,660 789 871 736 924Toyota 1,514 894 620 618 896Total 14,442 7,398 7,044 6,822 7,620holds’ vehicle choice including both EVs and ICEVs from NHTS, unlike in CVRP where only EV pur-chases are observed. Households’ demographic information such as income, home ownership, householdsize, household vehicle count, etc. are also provided.An important feature of NHTS dataset is that household’s residential state is revealed. This helps identifythe dollar amount of financial incentive a consumer might receive if she purchases an EV. Since financialincentives differ across states and EV models, such variation makes it possible to estimate consumers’preference towards financial incentives.For the purpose of research, there are at least two shortcomings of the NHTS dataset. First, the geo-graphical identifiers of households are at state level, which is too broad to learn the pattern of public chargingstations deployed near each households. Second, since EVs’ market share in the US is about 1%, the samplesize of EV purchasers in this dataset is also relatively small (about 400 EV purchases out of 40,000 totalvehicle purchases surveyed).Nevertheless, I use this dataset to determine households’ choice between category of EVs and ICEVsgiven their demographic information, financial incentives, and density of public charging stations at statelevel.2.4.3 Charging StationsInformation of all electric vehicle charging stations in California are downloaded from Alternative FuelsData Center, U.S. Department of Energy14 on Oct 20, 2015. Charging stations’ location and type informationare contained in this dataset. Unfortunately the dataset unveils opening dates information for merely aboutone third of all stations. However, variation in density of stations is crucial in this study, I rescue the situationby using the earliest date one station appears on on-line EV forums15 to substitute for the actual opening14http://www.afdc.energy.gov/data download15The first source is Plugshare, which comes with a smartphone application to let EV owners to find nearby charging stationsand allow them to leave comments. The date of the first comment is used. The second source is carstations.com, which tells the14date. Yet there are approximately 20% stations still left with unknown opening date, I use Oct 20, 2015 —the day when the list of charging stations is downloaded, to fill in such missing information. The table belowcasts a light on the expansion of EV charging station construction and EV adoption. During year 2011 to2015, the ratio of EVs to charging stations in California increased from 9:1 to 57:1.Table 2.3: Annual Growth of EV Charging Stations and RebatesYear 2010 2011 2012 2013 2014 2015Total # Rebates (BEV&PHEV) 61 4,028 14,679 42,996 85,371 130,276Total # Charging Stations 155 465 960 1,412 1,778 2,296∆ # Rebates (BEV&PHEV) 61 3,967 10,651 42,375 42465 44,905∆ # Charging Stations 155 310 495 452 366 5182.4.4 Demographic InformationTable (2.4) shows the actual EV buyers’ information from the surveys, including: income, whether owninga detached house (as a proxy for ”having access to home charging”), and number of charging stationsnearby. Descriptive statistics are exhibited by buyers of different types of EVs: large BEVs, small BEVs,and PHEVs. Income is given as a range in the original dataset, e.g. $50,000 to $74,999. In our analysis,each individual’s income is assumed to be the mean of the income range he/she belongs to16. Number ofpublic charging stations nearby is derived from the EV buyer’s residence county and purchase year. I firstcalculate for each Census Tract within a county, how many charging stations are within 30km range; then aweighted average is calculated using these numbers, where the weights are given by purchase frequency ofeach Census Tract; the weighted average varies by county and year, and is a used as proxy for number ofcharging stations nearby.Table 2.4: Demographic InformationVariable Mean Std. Dev. Min. Max. NLarge BEV (Tesla) Buyersincome ($1,000) 334.7 185.3 37.5 600 2334own house 0.9 0.3 0 1 2334charging stations in 30km (100) 1.1 0.5 0 2.5 2334Small BEV (Non Tesla BEV) Buyersincome ($1,000) 170.7 110.7 37.5 600 6048own house 0.8 0.4 0 1 6048charging stations in 30km (100) 1.2 0.6 0 2.5 6044PHEV Buyersincome ($1,000) 170.1 110.2 37.5 600 6065own house 0.8 0.4 0 1 6065charging stations in 30km (100) 1.1 0.6 0 2.5 6064concrete date when a station is added on the site. The earliest date of these two data sources will be used as the “opening date”.16The highest income group is documented as ”income greater than $500,000”, no upper limit of income is given. I use $600,000as a proxy for highest income.152.5 Empirical Strategy2.5.1 Discrete Choice Model of EVs2.5.1.1 Model SetupConsumer i makes a discrete choice of EVs from J alternatives. She gains utility ui j from the choice denotedas Yi = j. Utility is composed of a systematic part vi j and a random part εi j which follows generalizedextreme value distribution.ui j = vi j + εi j (2.2)where i and j stand for consumer and EV model respectively. According to EV’s energy source and theirelectric range, I partition the whole set of EVs into groups: PHEVs, longer-range BEVs, and shorter-rangeBEVs. For simplicity, I use the term large BEVs(LBEV)/small BEVs(SBEV) interchangeably with longer-range BEVs/shorter-range BEVs. 17 Until year 2017, Tesla stands out as the only BEV model that has arange greater than 200 miles, whereas other BEVs’ ranges vary from 80 miles to 100 miles. Therefore thecategories large BEVs and small BEVs could also be deemed as Tesla and non-Tesla BEVs respectively.The categorization is demonstrated in Figure 2.3. Then the utility function can be expressed as:ui,g,m = vi,g,m+ εi,g,mwhere subscripts g stand for the group of PHEVs, LBEVs and SBEVs, m is the vehicle make.18 Thereforeeach EV j could be identified by subscript(g,m).vi,g,m depends on both vehicle characteristics zg,m and consumer demographic characteristics xi, and itsfunctional form closely follows predictions from the theoretical model.For vehicle characteristics, I include price, annual fuel cost estimated by US EPA, and electric rangewhich determines the convenience of EV charging, and vehicle size (or volume). To capture the effect thatconsumers with higher income can be less sensitive to EV price change (DeShazo et al. (2017)), I add aninteraction term of income and EV price Pj.As for consumer characteristics, the model estimates the impact of income Ii, owning a detached houseHi, density of public charging stations Si, and an interaction of Hi and Si for each category g: PHEVs,longer-range BEVs, and shorter-range BEVs. Therefore the expression of vi,g,m is as below:vi,g,m = γ1IiPj + γ 2x j +β gziwhere Ii is consumer i’s income; Pj is price of EV j; x j is a vector of EV j’s characteristics except price;zi is a vector of consumer i’s characteristics. In order to draw conclusions on how consumer characteristics17In the robustness analysis, another nesting structure is illustrated where choice is between PHEV and BEVs, and under theBEV category is further partitioned into LBEVs and SBEVs.18I do not differentiate vehicle model for a given vehicle make, which is constrained by our data. Fortunately, most EV producersonly have one model under their production line until year 2017. Exceptions include Ford and Tesla, for which I take the averageof vehicle attributes under each make to represent their EVs.16affect preference to different types of EVs, the coefficients of zi are estimated for each EV group (PHEVs,LBEVs, and SBEVs).The model here follows the standard nested logit model (McFadden, 1978; Berkovec and Rust, 1985;Goldberg, 1995) and assumes that standard error term εi j follows generalized extreme value distribution.Consumers first choose within groups of PHEVs, LBEVs, and SBEVs, and then choose an EV model withinthe group. A tree diagram depicting this decision process is shown in Figure 2.3. The joint probability ofchoosing an EV (g,m) is:Pig,m = Pig×Pim|gwhere Pig,m denotes the joint probability of consumer i choosing EV (g,m); Pig is the probability of choosinga group from the pool of PHEVs, LBEVs, and SBEVs; Pim|g represents probability of choosing an EVconditional on the choice of the previous stage.Figure 2.3: Nested Logit Tree StructureFollowing the research cited above, choice probability of (g,m) will be given by nested logit formulasthat have the following general form:Pig,m = Pig×Pim|g =exp(X igθg+ Iigλg)∑Gk=1 exp(X ikθk + Iikλk)× exp(Xig,mθg,m/λg)∑Mgl=1 exp(Xig,lθg,l/λg)whereIig = log[Mg∑l=1exp(X ig,lθg/λg)]The subscript g and m denote for choice on group g and make m respectively. X ig represents a vector ofexplanatory variables of choice g and θg is the parameter vector specific to group g to be estimated. Mg isthe choice set fo makes given that group g is chosen. Iig measures the expected aggregate utility of subset g.Coefficients λ reflect the dissimilarity of alternatives within a nest. As shown by McFadden (1978), if λ ’s liewithin unit interval, the nested structure is consistent with random utility maximization; as λ approaches 1,the distribution of the error term tends towards an iid extreme value distribution and the choice probabilities17are given by multinomial logit model; λ equaling 0 means the error terms are perfectly correlated. In ourmodel, λ for Tesla in the second stage are constrained to equal 1 since they represent the only choice in thatnest.2.5.1.2 EndogeneityThe previous discussion assumes that explanatory variables in the model are independent of the unobservedfactors. However, the number of public charging stations could be correlated with the error term, castingdoubt on the estimation result from the model previously described. EVs with different electric range havevaried demand on public charging station network, especially, we’ve illustrated that shorter range BEVswould rely on public charging stations more than longer range BEVs and PHEVs. If consumers in a countyprefer shorter range BEVs due to reasons unknown to the researcher, and more charging stations are built dueto high demand brought by the shorter range BEVs, such reverse causal relationship would make “numberof public charging stations” an endogenous explanatory variable.The following section discusses how to deal with the endogeneity issue. Note that since the choicemodel is nonlinear, traditional methods such as instrumental variable could not be used. This paper uses thecontrol function approach (Train, 2009; Petrin and Train, 2010), which alleviates the endogeneity problemby including an extra variable that conditions out the variation of unobserved factors that are correlated withthe endogenous explanatory variable. To elaborate the control function approach, let’s revisit the generalform of the utility function (2.2) from previous section, and revise it so that the deterministic part of theutility vi j is expressed as a function of exogenous variables xi j, endogenous variables yi j, and individualspecific taste parameters βi:ui j = v(xi j,yi j,βi)+ εi j (2.3)Here yi j is the number of public charging stations, which might be correlated with the error term εi j, andwill lead to biased estimation results if the problem left unsolved.First express the endogenous explanatory variables as a function of observed instruments zi j and unob-served factors µi j:yi j = w(zi j,γ)+µi jµi j and εi j are independent of zi j, but µi j is correlated with εi j. Hence yi j is also correlated with εi jwhich is the source of the endogeneity concern. Conditional on µi j, yi j will be independent of εi j under sucha setting, and this is the key to the control function approach. The following paragraphs discuss choice ofzi j.Regarding to the endogenous deployment of public charging stations, two instrument variables are in-cluded. The first one is a dummy variable suggesting whether the EV purchaser’s residence county givesfinancial incentive on installing EV chargers. Such local government policies provides incentives to installmore EV chargers, thus bringing an exogenous shock to the chargers stock. The second IV is constructedbased on Li et al. (2017). They argue that grocery stores and supermarkets are major providers of publicchargers, yet their presence appeared long before the development of EVs, therefore the number of grocerystores and supermarkets brings variation to charger stock and should not be correlated with unobserved vari-18ables in the utility function. For similar reason, other amenities that are potential providers of EV chargingstations should be included in IV construction. Here I use the total number of grocery stores, supermarkets,merchandise stores, and restaurants. This instrument satisfies the exclusion restriction because such ameni-ties are established earlier than massive EV adoption. The decision to install EV charging stations involvesmore than attracting local EV drivers — financial incentives from energy companies and car companiesare also a main driver. Moreover, since the number of such places with amenity remains stable overtimewhereas charging station network expands rapidly over the years, a year trend variable is also included inthe instruments. Suppose consumers’ taste towards different types of EVs does not change across year, thenyear trend should not be correlated with the error terms in the utility function. The first-stage regressionresults could be found in Table 2.5. The coefficients on both government incentives and number of localamenities are both positive and significant at the 1% level.Table 2.5: First-Stage Results for Charging Station EquationVariablegovernment incentive on charging stations 0.683***(0.126)number of local amenities 0.0002***(0.00003)year trend 0.0569*(0.0298)Number of observations is 172.The dependent variable is number of charging stations within 30 km radius of a county in a given year.* p¡0.1, ** p¡0.05, *** p¡0.01Regressing the endogenous explanatory variables yi j on the instruments zi j will give us a residual termµi j, which captures variation of yi j driven by unobserved variables. Further decompose εi j to the partexplainable by µi j (i.e., the control function, CF) and a residual:εi j = CF(µi j;λ )+ ε˜i jPlugging in the above expression of εi j into the utility function (2.3) I will get:ui j = v(xi j,yi j,βi)+CF(µi j;λ )+ ε˜i j (2.4)In the utility function (2.4), the error terms are uncorrelated with the explanatory variables by construc-tion, therefore the model can be estimated following standard steps as described in the previous section.Regarding to the functional form of CF, a straightforward candidate is linear approximation: CF(µi j;λ )=λµi j, as is adopted in this paper.To sum up, the control function approach takes two steps. First, regress the endogenous explanatoryvariables yi j on the exogenous instruments zi j and obtain the residual terms µi j. In the second step, addµi j to the original nested logit model as an extra explanatory variable and estimate the model followingthe standard approach. Note that in the two-step estimation process, the µi j used in the second step is an19estimate from the first step rather than the true µi j, the asymptotic sampling variance of the second stepestimator needs to be corrected (Petrin and Train, 2010). Here the bootstrap method is implemented to fixthis issue.2.5.1.3 ResultsResults using the control function approach is presented in Table 2.6. The first column shows the estimationresult using all observations in the survey (14,420 individuals with 10 EV choices for each person). Theresults are generally as expected: (1) lower price, lower fuel cost, longer electric range, and larger sizewill increase the choice probability; (2) interaction term of price and income is positive and statisticallysignificant, suggesting that higher-income consumers are less price sensitive.The effect of public charging stations is strongest for shorter-range BEVs, which coincides with thetheory prediction. The intuition is that shorter-range BEVs rely on their battery as the sole energy sourceand they have higher probability of getting stranded due to the limited range, hence their reliance on publiccharging network is the most inelastic. The CF of public chargers is positive and statistically significant,indicating that some factor benefiting EV adoption meanwhile also positively affecting public charger de-ployment is omitted from the utility function specification.Owning a detached house gives higher utility for BEVs than PHEVs, which is also intuitive since BEVsrely more on charging facilities than PHEVs and owning a detached house provides the possibility of homecharging.The interaction term of owning a detached house and public charger density is negative, which followsthe theory prediction that public charging matters more for drivers without access to home charging. Thisresult is not statistically significant, and it could be because the sample size of EV purchasers not owning adetached house is too small, only about a quarter of those owning a detached house.The second and third column in Table 2.6 present subsamples containing counties with higher populationdensity (population divided by geographical area) and lower population density respectively. The fourth andfifth column divide the sample to North and South California. The results have similar sign to column (1)using all observations.Table 2.7 shows the estimation results not using alternative specifications. In Table 2.7, column (1) isthe preferred specification same as column (1) in Table 2.6; column (2) drops control function of chargingstations; column (3) drops the interaction of income and price; column (4) adds EV model fixed effects thusdropped EV specific characteristics; column (5) adds an additional level of nest such that consumers choosefrom BEVs and PHEVs first, and the BEV branch is further divided to LBEVs and SBEVs, the rest of themodel being the same. Results remain constant with the preferred specification.2.5.2 Choice between EVs and ICEVsThe above section discusses the question ”Conditional on a consumer decides to purchase an EV, whichone will she choose”. However, one needs to know consumers’ decision rule to choose between EVs andconventional ICEVs. Here I use the NHTS dataset and run a binary logit model to determine the factorsaffecting the choice. Note that ideally one would like to estimate one nested logit choice model with the tree20Table 2.6: Nested Logit Reg. of EV Choice with Control FunctionsChoice ProbabilityAll High Pop. Den. Low Pop. Den. North CA South CAall EVsprice(1,000$) -0.019*** -0.009*** -0.037*** -0.042*** -0.006**(0.003) (0.003) (0.007) (0.007) (0.002)price(1,000$) 0.083*** 0.075*** 0.106*** 0.123*** 0.059***× income (1,000,000$ ) (0.016) (0.025) (0.027) (0.029) (0.023)annual fuel cost -0.983*** -0.891*** -1.284*** -1.898*** -0.469***(0.155) (0.264) (0.228) (0.296) (0.163)electric range 0.903*** 0.827*** 1.147*** 1.575*** 0.463***(0.140) (0.242) (0.200) (0.242) (0.161)size 0.306*** 0.240*** 0.464*** 0.697*** 0.113***(0.048) (0.071) (0.082) (0.108) (0.040)longer range BEVincome(1,000$) 0.004*** 0.004*** 0.003*** 0.002** 0.005***(0.001) (0.001) (0.001) (0.001) (0.001)own house 0.660*** 0.539* 0.826*** 0.595** 0.708***(0.184) (0.325) (0.274) (0.279) (0.248)charger density -0.036 -0.259 0.382 0.079 -0.064(0.205) (0.322) (0.448) (0.329) (0.267)house × charger density -0.041 0.001 -0.128 -0.034 -0.050(0.080) (0.124) (0.169) (0.127) (0.105)CF(charger density) -0.226*** -0.260 0.011 -0.108 -0.418***(0.046) (0.165) (0.151) (0.100) (0.161)constant -16.257*** -15.318*** -19.313*** -24.825*** -9.489***(2.290) (4.109) (3.091) (3.723) (2.702)shorter range BEVincome(1,000$) -0.000 -0.000 0.000 0.000 -0.000*(0.000) (0.000) (0.000) (0.000) (0.000)own house 0.221** 0.814*** 0.071 0.245 0.188(0.097) (0.193) (0.135) (0.153) (0.129)charger density 0.206** 0.690*** 0.659*** 0.576*** 0.131(0.101) (0.177) (0.226) (0.175) (0.127)house × charger density -0.032 -0.208*** 0.007 -0.048 -0.004(0.042) (0.068) (0.088) (0.070) (0.053)CF(charger density) -0.467*** -0.644*** 0.374*** 0.307*** -0.883***(0.032) (0.132) (0.103) (0.073) (0.109)constant -6.051*** -6.424*** -6.979*** -8.321*** -3.625***(0.885) (1.530) (1.197) (1.488) (1.066)shorter range BEV λ 0.634*** 0.522*** 0.891*** 1.103*** 0.347***(0.097) (0.151) (0.151) (0.164) (0.119)PHEV λ 2.360*** 1.865*** 3.774*** 6.209*** 1.041***(0.386) (0.557) (0.764) (1.267) (0.366)N 134491 68846 65645 63626 70865Income is demeaned.Standard errors in parentheses* p < 0.1, ** p < 0.05, *** p < 0.0121Table 2.7: Alternative Specifications: Nested Logit Reg. of EV ChoiceChoice Probability(1) (2) (3) (4) (5)all EVsprice(1,000$) -0.019*** -0.022*** -0.020*** -0.019***(0.003) (0.003) (0.004) (0.004)price(1,000$) 0.083*** 0.095*** 0.199*** 0.083***× income (1,000,000$ ) (0.016) (0.017) (0.005) (0.017)annual fuel cost -0.983*** -1.141*** -0.924*** -0.979***(0.155) (0.156) (0.153) (0.165)electric range 0.903*** 1.043*** 0.854*** 0.899***(0.140) (0.141) (0.140) (0.150)size 0.306*** 0.354*** 0.289*** 0.305***(0.048) (0.049) (0.048) (0.051)longer range BEVincome(1,000$) 0.004*** 0.004*** 0.007*** 0.004***(0.001) (0.001) (0.000) (0.001)own house 0.660*** 0.667*** 0.660*** 0.663*** 0.657***(0.184) (0.184) (0.183) (0.183) (0.188)charger density -0.036 -0.006 -0.034 -0.037 -0.034(0.205) (0.205) (0.205) (0.205) (0.206)house × charger density -0.041 -0.040 -0.041 -0.040 -0.041(0.080) (0.080) (0.080) (0.080) (0.080)CF(charger density) -0.226*** -0.226*** -0.225*** -0.228***(0.046) (0.045) (0.045) (0.050)constant -16.257*** -18.569*** -15.409*** -16.188***(2.290) (2.306) (2.279) (2.518)shorter range BEVincome(1,000$) -0.000 0.000 -0.000** -0.000(0.000) (0.000) (0.000) (0.000)own house 0.221** 0.235** 0.220** 0.232** 0.222**(0.097) (0.097) (0.097) (0.097) (0.098)charger density 0.206** 0.271*** 0.209** 0.208** 0.206**(0.101) (0.100) (0.101) (0.101) (0.101)house × charger density -0.032 -0.028 -0.032 -0.029 -0.032(0.042) (0.042) (0.042) (0.042) (0.042)CF(charger density) -0.467*** -0.467*** -0.474*** -0.467***(0.032) (0.032) (0.032) (0.033)constant -6.051*** -6.981*** -5.760*** -6.026***(0.885) (0.891) (0.886) (0.960)EV model dummy N N N Y NThree level nests N N N N YN 134491 134491 134491 134491 134491Standard errors in parentheses* p < 0.1, ** p < 0.05, *** p < 0.0122structure in Figure (2.4). Unfortunately, the dataset of NHTS and CVRP could not be combined, since theycontain different variables (mainly granularity of households’ geographic location) and the CVRP merelyincludes EV buyers. A nice feature about the NHTS dataset is that households in different states face variousdollar amounts of financial incentives, thus allowing me to identify the impact of financial incentives onchoice probability of EVs.2.5.2.1 Logit ModelUtility of a consumer purchasing an EV is:ui = x′iβ + εiwhere x′i is consumer i specific demographic variable, which includes the dollar amount of financial incentiveprovided in the residential state, relative density of charging stations (measured by number of chargingstations divided by number of gasoline stations in the residential state19), the number of vehicles owned bythe household, household size, home ownership status, income, etc.Assuming (1) consumer i will purchase an EV when ui > 0 or an ICEV when ui <= 0 and (2) ε followslogistic distribution, the probability of consumer i purchasing an EV conditional on buying a new car is:pi =exp(x′iβ )1+ exp(x′iβ )(2.5)Figure 2.4: Ideal Nested Logit Tree Structure19Using state population to normalize the number of charging stations will lead to qualitatively similar results.232.5.2.2 ResultsResults of the logit model described above can be found in Table (2.8), where each column stands for analternative specification. The implications from various specifications are fairly consistent. First, density ofpublic charging stations have a positive impact on EV adoption, and the result stays after dealing with theproblem that charging stations density being endogenous to EV penetration rate. Specification (4) and (5) uselogged value of charging station density to capture the effect that marginal benefit of adding public chargingstations on EV adoption could be decreasing with the installation base of public charging stations. Second,EV subsidy raises the probability of EV adoption. Specification (4) is chosen as the favorite specificationand will be used in counterfactual exercise.Table 2.8: Logit Regression of Choice between EV/ICEVChoice Odds Ratio(1) (2) (3) (4) (5)EVscharging stations 5.470*** 6.101*** 7.267***(0.417) (0.515) (1.083)subsidy ($1,000) 0.176*** 0.114* 0.114* 0.113* 0.113*(0.048) (0.059) (0.059) (0.060) (0.060)home owner 0.522** 0.634*** 0.947** 0.638*** 1.012**(0.232) (0.230) (0.398) (0.229) (0.419)income ($1,000) 0.011*** 0.010*** 0.010*** 0.010*** 0.010***(0.001) (0.001) (0.001) (0.001) (0.001)household vehicle count -0.039 -0.062 -0.061 -0.062 -0.060(0.057) (0.060) (0.060) (0.060) (0.060)household size 0.080 0.062 0.060 0.061 0.059(0.062) (0.062) (0.062) (0.062) (0.062)CF(charging stations) 1.012*** 1.008*** 0.944*** 0.934***(0.328) (0.315) (0.361) (0.348)charging stations × -1.392home owner (1.237)log(charging stations) 7.508*** 9.112***(0.674) (1.373)log(charging stations) × -1.899home owner (1.550)constant -6.863*** -6.417*** -6.690*** -6.501*** -6.830***(0.468) (0.522) (0.578) (0.529) (0.594)N 29047 29047 29047 29047 29047log pseudolikelihood -1.713×106 -1.688×106 -1.687×106 -1.686×106 -1.685 ×106Logit regression is weighted using NHTS sample weight.Number of charging stations of each state is divided by number of gas stations as normalization.Standard errors in parentheses* p < 0.1, ** p < 0.05, *** p < 0.01242.5.3 Counterfactual Exercise from Discrete Choice ModelWith the estimation results from the above sections, we can calculate the choice probability of a specific EVmodel j by multiplying the probability of purchasing an EV Pe with the probability of purchasing model jconditional on choosing from EVs Pj|e:Pe, j = Pe×Pj|e = Pe×Pg|e×Pm|g,eso that the nested logit structure depicted in Graph (2.4) is estimated separately using two datasets. NHTSdataset gives the choice probability of top level (ICEVs vs EVs) whereas the CVRP dataset pins down thechoice probability within the EV class. I conduct several counterfactual exercises by altering the policyprovided and see how the choice probability of different group of EVs would vary.Table 2.9: Counterfactual Exercise from Discrete Choice ModelPanel A: Policy Impact on EV Sharestatus quo Policy (1) Policy (2) Policy(3)EV share 5.7% 25.4% 5.4% 21.8%Panel B: Policy Impact on Choice within EVsstatus quo Policy (1) Policy (2) Policy(3)share(Large BEVs/EVs) 16.2% 13.9% 16.2% 13.9%share(Small BEVs/EVs) 41.8% 48.1% 41.8% 48.1%share(PHEVs/EVs) 42% 42.7% 42% 42.8%Panel C: Policy Impact on EV Choice Conditional on Buying a New Carstatus quo Policy (1) Policy (2) Policy(3)share(Large BEVs) 0.92% 3.53% 0.87% 3.03%share(Small BEVs) 2.38% 12.2% 2.26% 10.5%share(PHEVs) 2.39% 10.8% 2.31% 9.31%Table (2.9) exhibits the counterfactual market share of EVs under alternative scenarios: policy (1):doubling the number of public charging stations; policy (2): eliminate EV subsidies for household withannual income greater than $ 200,000; policy (3): combination of both policy (1) and policy (2). Panel Apredicts the probability of buying an EV conditional on buying a new car, using the estimation result fromthe binary logit model in Section 5.2; Panel B predicts probability of buying a specific group of EV (largeBEV, small BEV, or PHEV) conditional on buying an EV, using the estimation result from the nested logitmodel in Section 5.1; Panel C shows product of Panel A and Panel B, which stands for probability of buyingsome group of EV conditional on buying a new car. Note that the expression ”probability of an individualbuying a car” is interchangeable with ”predicted market share”, under such discrete choice model setting.Results in Table (2.9) Panel C shows that: (1) doubling the number of public charging stations wouldincrease EV shares (of new cars sold) significantly and such effect is stronger with small EVs than large25EVs; (2) removing the EV subsidy given to the more affluent households would cause a slight decrease inEV shares; (3) combining the two policies together would lead to significant boost in EV shares, relative tothe status quo. A back-of-envelope calculation of the cost associated with policy (3) is shown as follows:about 30% of households who purchased EVs have income greater than $200,000 (according to NHTS),eliminating subsidies to such households in California in the year 2015 alone will save about $300 million.20Doubling the number of public charging stations in California from the storage in year 2015 will cost about$75 million. 21 Therefore, my estimation result shows that policy (3) which eliminates EV subsidy tohigher-income consumers and construct more public charging stations not only leads to higher EV sales, butalso costs less than the current subsidy scheme.2.5.4 Regression with Aggregated DataThe previous section estimates consumer’s taste towards different types of EVs, benefiting from the avail-ability of individual level data. Because Census Tract level data are more accurate on EV drivers’ geographiclocation, I test the impact of public charging stations on EV adoption using aggregated Census Tract leveldata.2.5.4.1 Model Setup and Endogeneity IssueFor each group of PHEVs, LBEVs (Teslas), and SBEVs (non-Tesla BEVs), I run regressions on CensusTract(CT)-year level observation:ln(yit) = β0+β1 ln(xit)+X′itγ+δt +σi+ εitwhere yit is the number of rebates of CT i in year t, xit is the number of charging stations within 30kmdistance, Xit are control variables (income, education, household size, travel time to work, etc.), δt is yearfixed effect, and σi is CT fixed effect. The demographic information is averaged at CT-year level, providedby American Community Survey.The issue of endogenous number of charging stations is similar as described in earlier section. I rescuesuch concern in two specifications. First, I added CT and year fixed effects to the regression, thus absorbingunobserved Census Tract level characteristics. Second, I add IVs for number of charging stations nearby.The IVs are number of places with amenity (grocery stores, supermarkets, merchandise stores, restaurants)within 30km multiplied by the total number of charging stations outside of 30km radius of CT i in year t.20Federal tax credits amounts to $7,500 and $4,000 for BEVs and PHEVs respectively. California Clean Vehicle Rebate Programprovides cash subsidy of $2,500 and $1,500 for BEVs and PHEVs respectively. In 2015, the total number of EV purchase inCalifornia is 130,276. Further assume BEVs and PHEVs both occupy half of the EV market share, the total amount of subsidysaved is 130276×30%× (0.5× ($7500+$2500)+0.5× ($4000+$1500)) = $302891700.21In 2015, the stock of public charging stations in California is 2296. Assume 25% of them are DC fast charging stations and75% of them are level II charging stations. The average cost of constructing a typical DC fast charging station is $50,000, and thecost is $27,000 for a level II charging station Li et al. (2017). The total cost to double the public charging stations in California in2015 is thus about: 2296× (0.25×$50000+0.75×$27000) = $75194000.262.5.4.2 ResultsFrom the regressions using aggregated data, one can see that PHEVs and small BEVs benefit most fromdensity of public charging stations. Table 2.10, 2.11, 2.12 exhibit the regression results, in which column(4) is the favorite specification, which includes Census Tract fixed effects, year fixed effects, and IV forcharging station density. Note that the geographic information is boiled down to Census Tract level, leavingthis analysis the one with most accurate estimate on public charging station density surrounding EV owners.Table 2.10: Census Tract - Year Panel Regression, PHEVsOLS OLS OLS GMMVariable (a) (b) (c) (d)log(no. charging stations within 30km) 0.124∗∗∗ 0.043∗∗∗ 0.146∗ 0.610∗∗∗(0.014) (0.009) (0.073) (0.141)log(mean income) 0.135 0.237∗∗ 0.381∗∗∗ 0.264∗∗∗(0.098) (0.111) (0.106) (0.077)log(mean income/median income) 0.245∗∗∗ 0.046 -0.207∗∗∗ -0.169∗∗∗(0.056) (0.054) (0.044) (0.037)log(no. detached house) 0.055∗∗∗ 0.016∗ 0.021∗∗∗ 0.028∗∗∗(0.013) (0.009) (0.006) (0.009)log(adult population) 0.254∗∗∗ 0.246∗∗∗ 0.151 0.137(0.023) (0.024) (0.121) (0.102)percentage(higher education) 1.057∗∗∗ 1.020∗∗∗ 0.233∗∗ 0.161∗(0.182) (0.182) (0.108) (0.095)log(time to work) 0.090∗ 0.171∗∗∗ 0.155∗ 0.114(0.048) (0.052) (0.086) (0.074)percentage(more than 2 vehicles) 0.426∗∗ 0.265 -0.129 -0.193(0.207) (0.241) (0.121) (0.136)year fixed effects No Yes Yes Yescensus tract fixed effects No No Yes YesN 47448 47448 47448 47442adj. R2 0.335 0.501 0.399 0.341Standard errors in parentheses∗ p < 0.1, ∗∗ p < 0.05, ∗∗∗ p < 0.012.5.4.3 Counterfactual Exercise: Indirect Network Effects and Simulation ResultsThe following section conducts counterfactual exercise using the aggregated regression results to analyzehow the EVs and charging stations will evolve under alternative policy bundles.2.5.4.3.1 Model Setup The following model is built on Li et al. (2017). We categorize EVs to PHEVs,small BEVs and large BEVs. Assume that EV sales qθ ,t depend on the number of public charging stations inthe market Nt , the price of the EV pθ ,t , and other product characteristics combined xθ ,t ; where θ ∈ {P,L,S}denotes for EV type (PHEV, large BEV, small BEV respectively), and t denotes for time period. The EVstock of type θ in period t is cumulative EV sale less scrappage, denoted as Qθ ,t = ∑th=1 qθ ,h · st,h, where27Table 2.11: Census Tract - Year Panel Regression, small BEVsOLS OLS OLS GMMVariable (a) (b) (c) (d)log(no. charging stations within 30km) 0.112∗∗∗ 0.036∗∗∗ -0.004 0.634∗∗∗(0.019) (0.012) (0.070) (0.168)log(mean income) 0.127 0.220∗∗ 0.616∗∗∗ 0.455∗∗∗(0.083) (0.096) (0.143) (0.090)log(mean income/median income) 0.146∗∗ -0.049 -0.228∗∗∗ -0.176∗∗∗(0.061) (0.063) (0.038) (0.031)log(no. detached house) 0.069∗∗∗ 0.033∗∗∗ 0.004 0.014(0.014) (0.010) (0.009) (0.012)log(adult population) 0.254∗∗∗ 0.244∗∗∗ 0.166 0.145(0.027) (0.029) (0.121) (0.094)percentage(higher education) 1.269∗∗∗ 1.235∗∗∗ 0.401∗∗∗ 0.302∗∗(0.136) (0.145) (0.129) (0.120)log(time to work) -0.065 -0.003 0.186 0.130(0.052) (0.054) (0.113) (0.095)percentage(more than 2 vehicles) 0.258 0.106 -0.146 -0.234∗(0.162) (0.186) (0.119) (0.131)year fixed effects No Yes Yes Yescensus tract fixed effects No No Yes YesN 47448 47448 47448 47442adj. R2 0.344 0.490 0.373 0.186Standard errors in parentheses∗ p < 0.1, ∗∗ p < 0.05, ∗∗∗ p < 0.01st,h is the survival rate at time t for EVs sold in time h. Assume the survival rate st,h is δ t−h, where δ < 1.The number of charging stations that have been built Nt(QP,t ,QL,t ,QS,t ,zt) depends on the stock of EVs andother variables combined zt that might affect the fixed cost of investment. The EV demand functions andcharging stations installment function are specified as below:ln(qθ ,t) = βθ ,1 ln(Nt)+β2 ln(pθ ,t)+β3xθ ,t , for θ ∈ {P,L,S} (2.6)ln(Nt) = γ1 ln(QP,t +QL,t +QS,t)+ γ2zt (2.7)2.5.4.3.2 Feedback Loop The parameters βθ ,1 and γ1 capture the magnitude of the indirect network effecton two sides. Feedback loop arises if βθ ,1 and γ1 are nonzero. Intuitively, shocks on EV sales in period t willchange the installed base of EVs in period t+1, causing the number of charging stations to adjust, which inturn affect EV sales in period t + 1. If both βθ ,1 and γ1 are positive, then a policy shock that increases thestock of EVs or charging stations will amplify its effect through the feedback loop.28Table 2.12: Census Tract - Year Panel Regression, large BEVs (Teslas)OLS OLS OLS GMMVariable (a) (b) (c) (d)log(no. charging stations within 30km) 0.047∗∗∗ 0.010∗∗∗ 0.118∗∗∗ 0.310∗∗∗(0.007) (0.003) (0.025) (0.079)log(mean income) 0.212∗∗∗ 0.261∗∗∗ 0.258∗∗∗ 0.267∗∗∗(0.055) (0.058) (0.089) (0.087)log(mean income/median income) 0.457∗∗∗ 0.365∗∗∗ -0.112∗∗∗ -0.111∗∗∗(0.048) (0.034) (0.039) (0.039)log(no. detached house) 0.028∗∗∗ 0.011∗ 0.009 0.011(0.009) (0.006) (0.011) (0.013)log(adult population) 0.085∗∗∗ 0.079∗∗∗ 0.001 -0.018(0.017) (0.019) (0.066) (0.061)percentage(higher education) 0.538∗∗∗ 0.512∗∗∗ 0.189∗∗ 0.172∗∗(0.085) (0.089) (0.083) (0.084)log(time to work) -0.022 0.005 0.103∗∗ 0.118∗∗(0.024) (0.026) (0.051) (0.053)percentage(more than 2 vehicles) 0.066 -0.012 -0.202∗∗ -0.245∗∗(0.107) (0.117) (0.101) (0.123)year fixed effects No Yes Yes Yescensus tract fixed effects No No Yes YesN 47448 47448 47448 47442adj. R2 0.271 0.352 0.221 0.186Standard errors in parentheses∗ p < 0.1, ∗∗ p < 0.05, ∗∗∗ p < 0.012.5.4.3.3 Steady State In a longer time span, if a steady state exists where purchases of EVs remainat a certain number cross periods, then qθ ,t = qθ ,t+1 = ... = q∗θ . The equilibrium stock of EV will beQ∗θ = q∗θ/(1− δ ), given Qθ ,t = ∑th=1 qθ ,h · st,h and survival rate being st,h = δ t−h. At the steady state,assume pθ ,t = pθ , xθ ,t = xθ (θ ∈ {P,L,S}), and zt = z. Combining equations (2.7) and (2.6), equilibriumnumbers of EVs (q∗P, q∗S, q∗L) and charging stations (N∗) are defined by the following system of equations:ln(q∗P) = βP,1 ln(N∗)+β2 ln(pP)+β3xPln(q∗L) = βL,1 ln(N∗)+β2 ln(pL)+β3xLln(q∗S) = βS,1 ln(N∗)+β2 ln(pS)+β3xSN∗ = exp[γ1 ln(q∗P+q∗L+q∗S1−δ )+ γ2z](2.8)2.5.4.3.4 Implications on Policy Choices Although difficulties arise when looking for analytical solu-tions to the system of equations (2.8), we can still draw conclusions from the equilibrium conditions listedin (2.8).29We hereby compare the policy effect of subsidizing EV purchase in several initial periods against build-ing more EV charging stations. Subsidizing EV purchase in initial periods is a common strategy adopted bygovernments around the globe. Since it is a limited time discount of EVs, studies have shown that such poli-cies greatly led to EV sales increase in the current period. Yet price of EVs will finally return to the originallevel pθ once the subsidy budget is exhausted. The equilibrium number of periodical EV sales, cumulativeEV stock, number of charging stations would reach the same level as in the case where no subsidy is given.The intuition is that although subsidies in the early periods might speed up EV adoption in the earliest stage,the policy effect will not last as EV stock in the long run is determined by EV characteristics and prices.Consider an alternative policy that aims at promoting EVs by constructing more charging stations.Through the feedback loop illustrated in the model, this policy will also lead to an increase in EV pur-chase. The advantage of this alternative policy is that the beneficial effect will last for all periods after. Thenumber of charging stations in the long term will be raised by the policy instead of converging to naturalequilibrium level N∗ determined in (2.8). The long term EV sales will be higher than the original equilibriumif the number of charging stations with government-enforcing construction surpasses N∗.By fixing the values of pθ ,t , xθ ,t , and zt , and assuming certain values for model parameters as in Li(2017),we conduct simulation to show the effect of feedback loop. The parameters assumed are shown in Table(2.13). The initial EV stock is zero: Qθ ,0 = 0, θ ∈ {P,L,S}. For each period, we sequentially solve functions(2.6) and (2.7) for qP,t , qL,t , qS,t , and Nt , with condition Qθ ,t = qθ ,t +δQθ ,t−1, θ ∈ {P,L,S}.22 Figure (2.5)shows the evolution of three types of EVs and charging stations under this base case.Table 2.13: Parameters for Simulating Indirect Network EffectsCoefficients Values Variables Valuesβ1,P 0.62 pP 30000β1,L 0.32 pL 70000β1,S 0.66 pS 30000β2 -1.2 xP 16β3 1 xL 18γ1 0.6 xS 16γ2 1 z 2δ 0.9To simulate the policy effect of directly subsidizing EV purchase (call it policy A from here), we tem-porarily deduct the subsidy amount from EV prices for the first 10 periods and solve for qP,t , qL,t , qS,t , andNt periodically.23 To mimic the actual policy of Californian EV purchasers, we set the subsidy amount to be$10,000 and $5,500 for BEVs and PHEVs respectively.24In another simulation, we evaluate policy that uses same amount of money to construct charging stations(call it policy B from here) instead. For each period, we first calculate the subsidy amount which equals22Due to the complex functional form, the simulation results are solved numerically using Matlab.23We assume that charging stock accumulates hence the number of charging stations in each period no less than that in the lastperiod.24US Federal Government provides a tax credit of $7,500 for BEV buyers and about $4,000 for PHEV buyers. California CleanVehicle Rebate Program gives cash rebates of $ 2,500 for BEVs and $1,500 for PHEVs.30Figure 2.5: Indirect Network Effect — Base Case Scenario5000qP,t + 10000qL,t + 10000qS,t . Then we calculate number of charging stations that can be built in thisperiod by dividing the subsidy amount by $27,000.25 With such policy interfere, number of charging stationsNB,t will no longer be endogenously determined by (2.6) and (2.7). When the number of subsidized chargingstations surpasses the original equilibrium level, i.e., Ns,t >Nt , the excess number of charging stations are notsupported by the same-period EV stock Q·,t and hence 2.7 does not hold in such case. In the opposite casewhen Ns,t < Nt , then we assume that after Ns,t charging stations have been constructed by the government,private firms will keep building charging stations to the equilibrium number Nt because of positive profit.Therefore, number of EVs q·,t will always satisfy equation (2.6), whereas number of charging stations is thebigger number between Ns,t and Nt .26Figure (2.6) shows the simulated evolution process of EV adoption and charging station constructionunder three scenarios: a base case, policy A that subsidizes EV purchasing, and policy B that subsidizescharging stations. At least two important conclusions can be drawn from this figure.First, policy A has instant effect on EV promotion but does not cause the long run equilibrium of EVsales to increase, whereas policy B’s positive impact on EV sales remains after the policy period (10 years).The reason is that factors determining equilibrium q∗θ and N∗ stay the same under policy A; however, underpolicy B, number of charging stations will be raised exogenously and hence remaining at a higher level thanthe original equilibrium.Second, EVs that are more sensitive to public charging stations would experience highest sales increaseunder policy B.25We follow Li(2017) and assume average cost of building a charging station is at $27,000. Again we assume that chargingstation stock accumulates across periods.26The process of calculating EV sales qB,θ ,t and number of charging stations NB,t for each period is: (1) calculate how manycharging stations can be built with the government subsidy and add it to the existing charging station stock of last period, denotethe resulting number as Ns,t ; (2) calculate qθ ,t and Nt determined by (2.6) and (2.7); (3) if Nt > Ns,t , then NB,t = Nt , qB,θ ,t = qθ ,t ;(4) if Nt ≤ Ns,t , then NB,t = Ns,t , qB,θ ,t = exp(βθ ,1 ln(NB,t)+β2 ln(pθ )+β3xθ ).31Figure 2.6: qθ ,t and Nt under Different Scenarios(a) PHEV sale (b) Large BEV sale(c) Small BEV sale (d) Charging Stations2.6 ConclusionThis paper demonstrates that smaller EVs are more inelastic towards public charging stations than largerEVs, using both individual and aggregated data. The result proves the existence of “range anxiety” of EVdrivers — they are afraid of getting stranded on the road due to an exhausted vehicle battery. Such evidencejustifies the importance of improving EV charging infrastructure network when the policy maker tries topromote EV adoption.Since consumers with higher income are less price sensitive, it makes sense to decrease the amount offinancial incentive allocated to high income consumer group, so that government subsidies won’t be givento “anyway adopters”. After estimating EV demand using discrete choice model, I calculated counterfactualEV sales under alternative policies. The result shows that more EV sales could be achieved by eliminatingsubsidies to high-income consumers and building more public charging stations, meanwhile this policy costsless than the current government subsidy scheme.Using a feedback model, I showed that constructing more charging stations will lead to more EV sales in32the long run as they can benefit EV drivers through all periods, whereas subsidies only affect current periodEV sales.Moreover, shorter range BEVs have a modest price compared to longer range BEVs, and are moreenergy efficient compared to plug-in electric vehicles (PHEVs). Therefore subsidizing charging facilityinstead of individual EV purchasers might contribute more to energy saving and air pollution reduction,whereas reducing the concern that high-income potential buyers of luxurious longer range BEVs might freeride government subsidy.33Chapter 3The Cost of Commuting Time Reliability:Theoretical Advances using ReliabilityStandards and Empirical Findings fromMetro Vancouver Traffic Data3.1 IntroductionDespite its compelling economic benefits, congestion pricing remains under-utilized throughout the world.Few major cities have adopted it, but where it is used—Singapore, Stockholm, and London—it is mostlyquite effective and motorists have adapted to it well. While resistance to congestion pricing remainswidespread in North America, New York is about to introduce congestion pricing in Manhattan (south ofCentral Park) in 2021.1 In addition to tolling some bridges and (private) highway sections, there have beena few experiments involving “Lexus lanes”: differential pricing for different lanes of the same highway.2Hall (2018b) has explored this topic extensively and delivered notable new results that take into accountmotorists’ heterogeneity. This heterogeneity comes in two dimensions: the time cost of commuters, andtheir schedule inflexibility.Theoretical and empirical work has highlighted the fact that motorists care not only about the actualdriving time, but also about the overall travel time that ensures the reliability of the commute. It mattersto commuters that they arrive on time, and thus they choose to arrive early to allow for the dispersion indriving times. Naturally, varying road congestion during different times of the day leads to a distribution ofdriving time. Motorists may have uncertainty about the road conditions that they encounter and the level ofcongestion.Motorists’ preferences for commuting time and reliability have been explored widely in the transporta-1New York Times, March 26, 2019.2Washington State’s SR 167 high occupancy toll (HOT) lanes; tolls range between 50 cents and $9 depending on congestionlevel, 5am to 7pm.34tion economics literature, which will be discussed in detail in the following section. We follow a recentstrand of literature, in particular Hall (2018b), who separates groups of flexible and inflexible commuters.We also expand on Van den Berg and Verhoef (2011), who take commuter heterogeneity into account andexplore distributional outcomes.This paper contributes to this stream of literature both on the theoretical and empirical level. On thetheory side, this paper introduces a novel form of treating the reliability problem. Rather than using aschedule delay3 cost where the time cost of arriving early or being late needs to be made explicit, our modelintroduces a reliability standard which links a measure of schedule inflexibility to the total travel time that isrequired to meet the standard. It turns out that the required buffer time (schedule delay) can be approximatedwell by a linear function of the standard deviation of the road travel (driving) time. Our second innovation isto observe that the standard deviation of the driving time is a function of congestion. Traffic that is slower isalso more variable. We believe that this relationship has not been explored rigorously in the prior literature,4and we provide a new estimation framework to investigate it. With this observation also comes the questionhow road traffic is correlated across a road network.Our empirical work uses data from traffic in the Metro Vancouver area to first identify congestion pat-terns and estimate speed-volume relationships, followed by identifying how the standard deviation (andcoefficient of variation) changes as congestion increases. We find evidence that speed variability increaseswith congestion levels as well. Difference in reliability may lead to different route choices, which playsa role both for competing routes for motorists as well as for the transportation mode choice. A signifi-cant part of our traffic data is obtained from Google’s Distance Matrix interface, which provides real-timeinformation about traffic conditions based on data provided voluntarily by users of their map applicationand Android phones. Our work follows in the growing stream of work that uses geolocation data to infercommuting behaviour (Calabrese et al., 2011; McNeill et al., 2017). In addition to the city-wide analysis,we also focus on a selected number of bottlenecks where we observe speed and volume at hourly intervals.We use a multiplicative heteroskedastic linear model to investigate the effect of congestion on speed and itsvariance. Lastly, we also explore route choice issues in a simulation exercise that explores issues similarto Hall (2018b) and Van den Berg and Verhoef (2011). We are interested in the sorting effect induced bytolling, especially when competing routes offer a trade-off between time and reliability (one route may beslower but less volatile than another route). Our simulation also investigates the correlation structure of timecosts with the degree of schedule inflexibility (for price-inelastic commuters) and with the cutoff time forcommutes that defines the extensive margin for price-elastic commuters.To summarize, our paper makes four novel contributions. First, we introduce a new model using re-liability standards to characterize schedule delay costs, and we demonstrate how to turn this into a veryeffective analytic tool. Second, our empirical work looks at city-wide commuting patterns to identify theimportance of commuting time reliability, and we are able to quantify this importance effectively through3Schedule delay refers to the difference between desired and actual arrival time.4Fosgerau and Fukuda (2012) also investigate the variability of travel time, and they express the random travel time as a functionof the time of day: Tt = µ(t)+σ(t)Xt , where t is time of day, Tt is travel time, µ(t) is mean travel time, σ(t) is interquartile rangeof travel time, and Xt is a standardized travel time. They find that µ(t) and σ(t) are positively correlated and vary strongly with t.Our paper focuses on traffic volume instead of time of travel, as the root cause of such phenomenon.35our theory-based decomposition into road condition and schedule inflexibility. Third, our bridge trafficanalysis demonstrates the effect that the variance of commuting time increases with congestion, and in dif-ferent ways for different types of bottlenecks. Fourth, our simulation analysis stresses that the magnitudeof schedule delay costs can be significant, but that even suboptimal tolls result in strong sorting effects thatdeliver almost all of the welfare gains from tolling. Even imperfect (limited-information) tolls can be highlyeffective tolls.3.2 Travel Time ReliabilityCommuters care not only about how quickly they can get to work, but also how reliably. Being late for workmay come at a significant penalty if it occurs too frequently. Most employees therefore have a reliabilitystandard in mind when they plan how they commute to work, allowing for sufficient buffer time (known as‘schedule delay’ in the literature) to make the journey. Traffic congestion slows down commutes, but it is thevariability of traffic congestion that contributes further to the time required for the commute by advancingdeparture to a time that ensures arrival at the destination at the required time with sufficient likelihood.Our research is predicated on the assumption that commuters have a better understanding of this reliabilitystandard than separate and distinct time cost of arriving early or late. This is a crucial point of departurefrom previous work.Considering the variability of travel time on different routes, there is a trade-off between average traveltime and travel time reliability. Under certain conditions a commuter may prefer the slower but safer route.This argument holds across different route choices as well as across transportation modes. Driving a car towork may be faster on average, but may also come at the greater risk of traffic delays due to congestion oraccidents. Some commuters may thus prefer slower but safer public transit options.Empirical evidence in our paper suggests that increasing congestion not only slows down traffic butalso increases travel time variability. Congestion increases the mean travel time as well as the standarddeviation of travel time. This link has been previously suggested in the literature, but it has not been exploredrigorously in formal models. In this paper we provide empirical evidence about the magnitude of this link,and we explore how it fits with a rigorous micro-economic model of pricing travel time reliability.Our paper is related to at least three strands of literature. The first strand links travel time reliabilityto commuters’ route choice. 5 There are in general two approaches to model travel time reliability in thetransportation literature: the scheduling delay approach and the centrality-dispersion approach.The scheduling delay approach assumes that commuters leave early and keep a safety margin to avoidbeing late. The earliest work can be traced to Gaver (1968) and Knight (1974). Small (1982) formulated amodel based on a utility maximization framework and defined commuters’ utility from travel time and timeof arriving early or late. Small’s work laid the foundation for the α-β -γ model, where α is the value oftravel time, and β and γ are the unit cost of the expected time of arriving early and late, respectively (Arnottet al., 1994). Following this path, Tseng and Verhoef (2008) suggested that value of time varies by time of5In the transportation engineering literature, Iida (1999) is among the earliest to propose the concept of “travel time reliability”,which is defined by the probability that traffic can reach a given destination within a stated time. This literature addresses thereliability of a road network whereas we focus more in heterogeneous commuters’ behavior.36day, with evidence from stated preference data. Taking the uncertain travel time into account, Asensio andMatas (2008) showed that the value of travel time variability is nonnegligible and highly depends on thetime restrictions faced by the individual. Noland and Small (1995) and Noland et al. (1998) extended Small(1982); they further discussed the impact of travel time uncertainty on congestion policies. More recentwork in this line includes Bates et al. (2001), Fosgerau and Karlstro¨m (2010), and Xiao et al. (2017), whichall assume that travel time is a random variable and commuters take an early head start to arrive on time. Ourapproach is similar, but we specifically assume that commuters have heterogeneous schedule inflexibility.Commuters experience different schedule delays because they adhere to different reliability standards. Thetraditional α-β -γ model assumes different unit time cost of travelling, and arriving early or late, therefore itis able to account for how much late the commuter is. Our model does not differentiate the unit time cost andassumes a single time cost for each commuter, with the commuter maintaining some probability of arrivingon time. Commuters might have better knowledge of their schedule inflexibility — how frequent they areallowed to be late at work, instead of their unit time cost of various activities such as driving, and arrivingearly or late. This difference allows us to take the dispersion of commuting time into consideration directly.Our approach also provides a straight-forward extension of theoretical modelling of optimal tolls.Our work has some similarity to Chen and Zhou (2010), who consider both reliability and unreliabilityaspects of travel time variability for route choices. They assume that with a confidence level α the driverswill arrive on time by leaving early and ensure some buffer time, while they also inspect the worst traveltimes in the distribution tail of 1–α . Our work shares the focus on explicit probability distribution functions.The centrality-dispersion approach assumes that commuters have aversion to travel time uncertainty.Related models assume a utility function with a linear combination of mean and variance of travel time.Jackson and Jucker (1982) introduced the mean-variance approach to quantify effects of travel time reli-ability. They used surveys in which subjects were asked to choose among risky trips with random traveltimes and discovered that some commuters prefer the more reliable route, even if the expected travel timeis higher. Abdel-Aty et al. (1997) followed the above method and used standard deviation as the dispersionmeasure instead, and they reached similar conclusion. Small et al. (2005) collected traffic data on CaliforniaState Route 91 in the morning, with both stated and revealed preference data. They estimated a $21.46/hvalue of time, and a $19.56/h value of reliability, where the reliability is defined by the difference betweenthe 80th and 50th percentile travel times.6Recently many researches have investigated the schedule-delay approach together with the centrality-dispersion approach. Carrion and Levinson (2013) showed that reliability of travel time is highly valuedthrough a revealed preference study, using three measures. Engelson and Fosgerau (2016) compared varioustheoretical measures of the cost of travel time variability. Bo¨rjesson et al. (2012) found estimated valuesof travel time variability differ significantly using different models, and they discussed the assumptionsrequired for each model to be justified. Li et al. (2016) proposed an integrated model of both approaches6While our paper does not follow the centrality-dispersion approach, we mention several important contributions to this strandof literature. Using survey data, de Palma and Picard (2005) find that risk aversion is larger for transit users, blue collars, andfor business appointments. Uchida (2014) estimated the value of travel time and reliability based on the risk-averse driver’s routechoice behavior in a road network. More research work following this path includes Polak (1987); Senna (1994); Devarasetty et al.(2012); Kouwenhoven et al. (2014); Beaud et al. (2016).37and justified its use through stated preference experiments. Travel time reliability is also surveyed elsewhere(Noland and Polak, 2002; Small and Verhoef, 2007; Li et al., 2010; Carrion and Levinson, 2012; Taylor,2013).The second strand of related literature focuses on commuter heterogeneity and commuters’ valuationof travel time and reliability. Arnott et al. (1994) argued that opposition to congestion pricing has shiftedthe focus of research from efficiency considerations towards political acceptability (and thus distributionaloutcomes). Road pricing becomes more viable politically when the tolling scheme benefits almost all ur-ban commuters and does not create intensive losses on the minority. Their research thus focuses on theheterogeneity of agents with respect to time cost, following Vickrey (1969). Key insights are related to thedistribution of the drivers with different time costs, notably those with different schedule delay costs. Theirwork laid the foundations for heterogeneity in commuters’ schedule flexibility. Small et al. (2005) estimatedmotorists’ heterogeneous valuation of time and reliability through a discrete choice model, with utility beinga function of toll, travel time, and reliability.Lastly, this paper is also related to the literature on applying tolls to reduce the social cost of congestion.Following the seminal work of Pigou (1920), many have researched how an efficient road tolling systemshould be constructed. Nevertheless, methods for including travel time reliability in road tolling schemeshas not been developed much. Theoretical work on this aspect includes Small and Yan (2001) and Verhoefand Small (2004). Small et al. (2005) and Small et al. (2006) explored toll policy design. Van den Bergand Verhoef (2011) allowed agent preferences to differ across two dimensions: value of time and scheduleinflexibility. They demonstrated the possibility to generate a Pareto improvement by pricing a third of thelanes and forgoing revenue by charging a negative toll off-peak. Hall (2018b)’s theoretical work concludedthat a carefully designed toll that is applied to some of the lanes of a highway could lead to a Pareto im-provement. Hall (2018a) further extended the theory and used survey and traffic data to empirically estimatethe joint distribution of road users’ value of time, schedule inflexibility, and desired arrival time, and foundthat the potential social welfare gains from such tolling scheme are substantial. In line with many studieson traffic congestion, Hall’s research relies on an important premise that hypercongestion exists (Walters,1961; Keeler and Small, 1977; Small and Chu, 2003) so that a toll can increase traffic throughput. However,Anderson and Davis (2018) casted doubts on the existence of hypercongestion. Our research approach doesnot require hypercongestion.7The allocation of welfare gains also remains a central theme in policy discussions about mobility pricing.Classic tolling schemes consider only commuters’ value of time, and many researchers concluded that com-muters with higher valuation of time would gain by paying efficient tolls, whereas commuters with lowervaluation of time could suffer a loss prior to toll revenue redistribution (Cohen, 1987; Arnott et al., 1994).7The notion of hypercongestion was introduced by Vickrey to refer to situations where traffic flow is inversely related to trafficdensity. Network flow follows an inverse U-shape relationship with respect to network density. Network flow first increases asnetwork density rises, reaches a peak, and as network density rises further leads to a fall in network flow and possibly completegridlock. Travel on the positively-sloped portion of the inverse-U is considered ‘congested,’ and on the negatively-sloped portion itis considered ‘hypercongested.’ There is a new class of models that address hypercongestion issues. Arnott (2013) introduced thebathtub model for heavily congested downtown areas where traffic jams cause traffic flow to fall, and in which traffic density (thelevel of the bathtub) is experiencing either normal (low-level congestion) or hypercongested traffic. Traffic velocity is negativelycorrelated to traffic density. Time-varying congestion pricing can convert traffic jams into queues for entering into the downtownarea.38More recently, Van den Berg and Verhoef (2011) consider bivariate continuous distributions of value of timeand schedule delay in their tolling scheme. They found that a majority of users could be left better off evenbefore toll revenue redistribution, with the commuters with intermediate value of schedule delays and lowervalue of time suffering the greatest loss. Eliasson (2016) discussed the fairness of congestion charges fromdistinct perspectives. Besides the traditional consumers’ perspective which includes monetary and time costin traveling, the author also discussed the citizens’ perspective that consider whether individuals’ views ofsocial issues are aligned with policy makers’ objective. The conclusions from both perspectives are similarand suggest that middle-income groups win the most. Ke and Gkritza (2018) employed the Suits Index toinvestigate impact of congestion tolling on urban and rural households. They found that congestion pricingcan be progressive on income for urban households, whereas regressive with regards to rural households,with the difference caused by driving distance and income. Our simulation process will also use Suits Indexto inspect the equity aspect of the tolling scheme.To sum up, we provided empirical evidence that increasing traffic volume increases not only the traveltime, but also (in most instances) its standard deviation. The estimation of this relationship using real-timetraffic data contributes to the literature of travel time reliability. Theoretically, our paper introduces an in-novative measure of how travel time reliability affects commuters’ cost function. Our model of schedulingdelay specifically allows for heterogeneity of commuters’ time value and schedule inflexibility, which en-ables us to assess the welfare impact of tolling on different groups of commuters. The welfare effects fromtolling reveal that the inflexible group of commuters benefit more than the flexible group in general, and thatmore affluent commuters benefit more either by paying an efficient toll or through receiving a per-capita tollrefund when they abandon commutes.3.3 TheoryDeveloping theory that is useful for empirical work typically requires choosing appropriate functional formsthat lead to tractable and estimable algebraic expressions. While much work has been done on the theoreticalfoundations of optimal road tolling, we employ a set of assumptions that on one hand allow for sufficientflexibility and on the other hand lead to empirically testable implications.3.3.1 Approaches to Travel Time ReliabilityThe pertinent literature on travel time reliability refers to the travel time cost as the α-β -γ model (Arnottet al., 1994), where α is the unit cost of expected travel (driving) time, β is the unit cost of the expected timeof arriving early and γ is the unit cost of the expected time of arriving late. Following the approach pioneeredby Vickrey (1973) for heterogeneous groups, the ratios α/β and α/γ are assumed identical across groups.Van den Berg and Verhoef (2011) provides a recent application of this type of model, which provides forvery convenient interpretations of tolls when the heterogeneous commuters follow uniform distributions.This approach circumvents an important complication: what is the empirical distribution of commutingtime and schedule delay costs? There are two parts to this question: how to quantify the cost per unit oftime, and how to quantify the probability of being late or arriving early. Essentially, there are different wayson how to approach the γ part for the cost of arriving late.39First, a motorist may incur a per-minute cost for arriving late that is (significantly) higher than theordinary time cost. For this one needs to model explicitly the tail of the distribution for late arrival. Themotorist minimizes total cost, which is the sum of (1) driving time priced at ordinary time cost, (2) early-arrival time priced at a early-arrival cost, and (3) late-arrival time priced at the late-arrival cost. This may bedubbed the “variable-cost lateness model” that is common in the literature.Second, a motorist may incur a fixed penalty each time when arriving late. This again requires identi-fying the tail of the distribution for late arrival. The motorist minimizes total travel cost, but the late-arrivalcomponent is the product of late-arrival probability and penalty. This is the “fixed-cost lateness model.”Third, a motorist may simply adhere to a reliability standard: plan driving so that arriving late occursinfrequently and meets the motorist’s schedule inflexibility. This is the “reliability standard model.” Wechoose to take this third route because it (a) does not require explicit knowledge of the late cost (either fixedor variable), and (b) leads to particularly intuitive solutions. Our model shares the important features withLo et al. (2006) which they called “travel time budget model”.8 While they assume travel time follows anormal distribution, we use log-normal and Fre´chet distributions that have long right tails and fit the databetter. We arrive at a linearization technique that disaggregates the time mark-up factor into a route-specificcoefficient of variation and a multiplier that reflects commuters’ inflexibility. Our cleaner functional formlends itself more readily to empirical work.We begin by defining a motorist’s schedule inflexibility ψ ≥ 0 so that a ψ = 0 indicates that a commuterdoes not care about being late and any positive number indicates increasing schedule inflexibility. In prob-abilistic terms, a value of ψ = 0 will be associated with the median travel time. The odds of being late aregiven by once in (ψ+2). We assume that travel time T is distributed with a cumulative distribution functionΦ(T ). Thus, the motorist chooses time to depart before desired arrival time T ∗ (driving time T plus ‘buffertime’ to ensure timely arrival) so that the probability of arriving on time isΦ(T ∗)≤ ψ+1ψ+2∈ [1/2,1) (3.1)Specifically, we assume that travel times follow the long-tailed Fre´chet distribution with minimum traveltime T ◦ > 0, shape parameter a ∈ (0,1), and scale parameter S > 0 so thatΦ(T ;T ◦,a,S) = exp(−[T −T ◦S]−1/a)(3.2)The Fre´chet distribution has the mean T¯ = T ◦+S ·Γ(1−a) and the variance σ2 = S2(Γ(1−2a)−Γ2(1−a)).A commuter facing the schedule inflexibility ψ will therefore choose a travel time T ∗ that obeysT ∗ = T ◦+S ·χa with χ ≡[ln(2+ψ1+ψ)]−1(3.3)8In Lo et al. (2006), the travel time budget is defined as sum of expected travel time and travel time margin: bp = E(Tp)+λσTp ,where Tp is the random variable of travel timeon route p, E(Tp) and σTp are mean and standard deviation of Tp, λ is a parameterthat can be related to the probability that a trip arrives within the travel time budget. P{Tp ≤ bp = E(Tp)+λσTp}= ρ , where ρ isthe probability that the actual trip time is within the travel time budget.40where the buffer time is the difference between T ∗ and the mean travel time T¯ . The transformation of ψ intoχ is nearly linear for large schedule inflexibility ψ; for example, for ψ=250 the value of χ=251.5 is just0.006% larger than ψ .Consider the following numerical example. A commuter’s mean travel time is 45 minutes, with a stan-dard deviation of 6 minutes, and a best feasible travel time of 30 minutes. Then S= 12.38 and a= 0.24.The parameters a and S can be recovered numerically from solving the two equations for mean and vari-ance of the Fre´chet distribution. Assuming that the commuter has a reliability requirement of ψ=50 (thecommuter can afford to be late to work five times a year), then T ∗ = 30+12.38(51.5)0.24 = 61.8 minutes.The commuter should allow for an extra 17 minutes for the typical 45-minute commute in order to arrive ontime.The distributional parameters T ◦, S and a are all functions of road congestion v˜ ∈ [0,1) and thereforeneed to be extracted from the estimated values of mean, variance, and skewness as functions of v˜, wherev˜ equals traffic volume divided by road capacity. We note that observing standard deviation and mean oftravel time — Tσ and Tµ , given T ◦, allows backing out a < 1/2 directly through1+T 2ρ =Γ(1−2a)Γ2(1−a) =⇒ a(Tρ) (3.4)where the coefficient of variation is defined asTρ ≡ TσTµ −T ◦ (3.5)The value of a increases with Tρ . Having solved for a numerically immediately reveals S= (Tµ−T ◦)/Γ(1−a). (N.B.: Γ(1−a) ∈ [1,1.772] for a ∈ [0,0.5].) The optimal time to depart before the desired arrival time isT ∗ = T ◦+(Tµ −T ◦) χaΓ(1−a) (3.6)We revisit this equation after introducing the speed-volume relationship.The Fre´chet distribution is only one among many plausible choices. The shifted log-normal distributioncan be parameterized similarly with three parameters asΦ(ln(T −T ◦)−µσ)≤ 1+ψ2+ψ(3.7)where Φ(·) is the standard normal cumulative distribution function and so thatln(T ∗−T ◦) = µ+σ · χ˜ with χ˜ ≡Φ−1(1+ψ2+ψ)(3.8)and moments µ = ln(Tµ)−σ2/2 and σ2 = ln(1+T 2σ /(Tµ −T ◦)2) = ln(1+T 2ρ ) that can be obtained fromthe observational mean Tµ and and standard deviation Tσ . Thus, using the coefficient of variation Tρ for41simplification,T ∗ = T ◦+(Tµ −T ◦)exp(χ˜ ·√ln(1+T 2ρ ))√1+T 2ρ(3.9)Consider again the numerical example with a commuter’s mean travel time of 45 minutes, with a stan-dard deviation of 6 minutes, and a best feasible travel time of 30 minutes. Then Tρ = 0.4. With ψ=50 thestandard normal cumulative distribution function yields χ=2.07. Then T ∗= 30+(45−30)(2.220/1.077)=60.9 minutes, or about 16 minutes more than the average trip time. The log-normal and Fre´chet distributionsgive very similar results.Figure 3.1: Travel Time Variability and Travel Time Mark-Up0255075100125150175200225Travel Time Markup (T∆) in %0 5 10 15 20 25 30 35 40 45 50Travel Time Variability (Tρ) in %ψ=10ψ=50ψ=250Note: based on log-normal distributionIt is helpful to illustrate the relationship between congestion variability and trip time. The coefficient ofvariation Tρ is a dimensionless number. Similarly, the dimensionless metricT∆ ≡ T∗−T ◦Tµ −T ◦ −1 =T ∗−TµTµ −T ◦ (3.10)is a measure of the travel time reliability mark-up: how much extra time is added for reliability relative tothe mean-to-minimum time difference. Figure 3.1 shows the mark-up for three values of ψ , 10 (late onceevery two weeks), 50 (5 times late per year) and 250 (once late per year), for the log-normal distribution. Inthe numerical example with Tρ=40%, the markup for ψ=50 is 106%. The fact that T∆ is a dimensionlessnumber proves to be helpful with the theoretical analysis but doesn’t immediately tell how much time acommuter needs to add. The more intuitive and practical measure of the time markup over average travel42time isTΛ ≡ T∗−TµTµ= T∆(1− T◦Tµ)≈ H(ψ) · TσTµ= H(ψ) ·Tν (3.11)where Tν ≡ Tσ/Tµ is the ordinary coefficient of variation. In the above numerical example with H(ψ)=2.65and Tν=0.133, the time markup is 35.3%, or 16 minutes on top of the average 45 minutes.For empirical research as well as further theoretical modelling it is helpful to observe that the relationshipbetween Tρ and T∆ is nearly linear for any given ψ . Therefore, one may use an approximation:Theorem 1 (Travel Time Reliability Markup) The travel time markup T∆ for commuters with scheduleinflexibility ψ is related to the parameters T ◦, Tµ , and Tσ of the full-trip travel time distribution (andimplicitly the coefficient of variation Tρ ) approximately throughT∆ ≈ H(ψ) ·Tρ ⇐⇒ T ∗ ≈ Tµ +H(ψ) ·Tσ = Tµ(1+TΛ) (3.12)where H(ψ) is a positive and increasing function in ψ . The full travel time is larger than the mean drivingtime by an amount that is proportional to the standard deviation of driving time by the factor H(ψ).The above theorem suggests a particular schedule delay cost in the notation of the α-β -γ travel costmodel. It replaces the late cost with a reliability standard and treats the early arrival period the same as thecommuting period.Figure 3.2: Travel Time Markup Factor11.522.533.544.555.5Travel Time Markup Factor H(ψ)10 20 50 100 200Schedule Inflexibility (ψ)Log−normalFréchetThis linearization is extremely useful for practical applications, and at the same time it is highly intuitive.But how good it is this approximation empirically? The R2 statistics for the underlying regressions arebetter than 0.99, which means that the linearization is easily justified. However, the different empiricaldistributions deliver different H(ψ), as is illustrated in figure 3.2, which shows the schedule inflexibility43measure ψ on a logarithmic scale on the horizontal axis and the empirically-estimated travel time markupfactor H(ψ) on the vertical axis. For very low levels of schedule inflexibility the markup factor is near oneand rises to below 4 for the log-normal distribution and above 5 for the Fre´chet distribution.The link between ψ and H(ψ) is nearly perfectly log-linear for the log-normal distribution, and onlyslightly less so for the Fre´chet distribution.The Fre´chet distribution provides a link between ψ and H(ψ) thatis slightly steeper than the log-normal distribution and it delivers larger values of H(ψ) than the log-normaldistribution when ψ gets large. Table 3.1 provides approximations for the log-linear relationship between ψand H(ψ) for both distributions and estimation ranges of [10,250] and [50,250] respectively, correspondingto figure 3.2.Table 3.1: Log-Linear Approximation of H(ψ)Distribution Approximation Fit (R2) Range (ψ)Lognormal H(ψ) = 0.7656 · ln(ψ)−0.3698 0.9997 [10,250]Lognormal H(ψ) = 0.7824 · ln(ψ)−0.4534 1.0000 [50,250]Frchet H(ψ) = 1.3229 · ln(ψ)−2.2870 0.9894 [10,250]Fre´chet H(ψ) = 1.4998 · ln(ψ)−3.1711 0.9975 [50,250]To summarize, the theoretical model yields insightful links between the statistics T∆ and Tρ through themarkup factor H(ψ), while practical applications will use the direct link between effective time markup TΛand the simple coefficient of variation Tν . Empirical work therefore needs to establish (1) which distribu-tional assumption (Fre´chet, Log-normal) provides a better approximation in order to choose the appropriateH(ψ) approximation; and (2) how large the coefficient of variation Tν is in order to quantify the buffertime that commuters add to their journeys. The two coefficients of variation Tν and Tρ are empirically quitedifferent in nature. Our empirical analysis shows that Tν and Tρ are virtually uncorrelated because the de-nominators are quite different in nature. While Tρ measures the time variation Tσ with respect to the averagedelay Tµ −T ◦, Tν measures it with respect to the average time Tµ . Our theoretical analysis that suggestslinearization hinges on the properties of Tρ rather than Tν , while the practical implications for the extraschedule time hinges on Tν .3.3.2 Route ChoiceCommuters take their entire travel route into account. Their total travel time is the sum of road segmentsk ∈K in route K so that ∑k∈K Tk with variance ∑k∈K ∑l∈K σkσlρkl with standard deviation σk of roadsegment k and ρkl the correlation coefficient between individual road segments along route K . The natureof this correlation is important. It can be positive when high traffic volume is spread throughout the roadsystem. It can also be negative when congestion at an “upstream” bottleneck is holding back traffic flow andis thus relieving congestion “downstream”. For the commuter it is the total variance that matters, not thepartial variance at a particular road segment.The commuter faces a choice between competing routes and will take both speed and reliability into44account. First consider two untolled roadsK ∈ {1,2} connecting A and B. The commuter chooses routeargmaxK {T ∗K } (3.13)which may or may not be the same as choosing the route that is faster on average argmaxK (TKµ ). Using theapproximation (3.12), it is possible to describe the choice between two routes 1 and 2 where we assume thatroute 1 is, on average, faster than route 2: T 1µ < T2µ . If a commuter chooses routes only based on averagetravel time, that commuter will always choose route 1. However, when variability comes into play, thecommuter may prefer route 2 if it is more reliable than route 1 even though it is slower on average. ThenT ∗2 > T∗1 implies T2µ +H ·T 2σ > T 1µ +H ·T 1σ . Then the following result holds:Theorem 2 (Route Choice with Schedule Inflexibility) If route 1 is on average faster than route 2 so thatT 1µ < T2µ , then a commuter prefers route 2 over route 1 if the ratio of the difference in standard deviation tothe difference in mean travel time exceeds the inverse of H(ψ):T 1σ −T 2σT 2µ −T 1µ' 1H(ψ)(3.14)As schedule inflexibility ψ increases and 1/H gets smaller, the commuter will prefer route 2 for eversmaller differences in travel time variability. The numerical values for 1/H range from 0.82 (Fre´chet distri-bution and ψ=10) to 0.19 (Fre´chet distribution and ψ=250).Route choice involves multiple road segments. For the commuter only the entire trip matters, and in-dividual road segments influence the overall trip planning. The main empirical complication arises fromthe fact that studying total travel time requires looking at entire trips rather than road segments individuallybecause of the correlation structure that is captured by the correlation coefficients ρkl . The implication forempirical work is that it is not sufficient to merely investigate the variability effect of road congestion atindividual points in the road network, but also the entire correlation structure.3.3.3 Speed-Volume RelationshipThe starting point for modelling congestion is a relationship between travel time T and traffic volume v ona particular road. Travel time (T ) and speed (V ) are linked through the relationship V = L/T where L isthe length of the road. Thus travel time and speed can be used interchangeably. Empirical work mostlyuses speed, as this is easier to measure, while theoretical work prefers time, as this is more meaningfulconceptually.Speed-volume relationships have been studied extensively and there are numerous functional forms thathave been explored. For theoretical purposes, an important choice is about whether to account for hyper-congestion. The presence of hypercongestion leads to a backward-bending speed-volume relationship thatallows for two speed points for a given traffic volume: a (normal) congestion speed and a hypercongestionspeed. The presence of hypercongestion is a critical element in some models, especially in models thatfollow the Arnott (2013) “bathtub” model and capture traffic flows in dense urban cores.In our paper we work with Metro Vancouver traffic data that does not show strong evidence of hyper-45congestion at key bottlenecks. We focus our analysis on situations with moderate levels of congestion, butwe acknowledge that our results will not extend to hypercongestion scenarios. We do not require hypercon-gestion as a condition for deriving our results.We explore two functional forms for the speed-volume relationship that avoid hypercongestion andmerely allow for congestion to approach the capacity limit, at which point travel speed approaches zero.9The first functional form is taken from Pipes (1967). For a given road capacity c, travel time T is afunction of uncongested travel time T , the road capacity utilization rate v˜≡ v/c ∈ [0,1], and the curvaturecoefficient ξ > 0 so thatT (v) = T (1− v/c)−ξ (3.15)The curvature ξ determines the congestivity of the road. As ξ increases, the roadway is easier and easierto congest. In this version of the equation, values for ξ will be between zero and one, and in practice arequite small. However, while this type of speed-volume equation and its cousins can be fitted relatively easilyto the data when it comes to the mean travel time, we are interested in dispersion and thus need to be carefulabout how individual speed observations are scattered above or below the mean for a particular volume. Wewill therefore need to adjust this equation to fit our empirical distribution functions and allow for a minimumtravel time T ◦. Conceptually, there is a “safe limit” on speed, which may well be above the posted speedlimit as the latter is set to control speed in traffic and not at free flow when the road is nearly empty.The second functional form we consider is a generalization of the bureau of public roads(BPR) function(Bureau of Public Roads, 1964):T (v) = T [1+κ(vc)λ](3.16)By virtue of having three parameters, this form can provide a better fit for the data. However, it turnsout that estimating it in our framework will require non-linear techniques.Our modelling is predicated on the assumption that there is a minimum travel time T ◦ < T .Even when a road is completely uncongested, there is variation around the travel time because of weatherconditions, time of day and lighting, or other factors. Our empirical travel time distribution thus requiresseparating minimum and average travel time, and allowing this to vary under congestion. We thereforereformulate (3.15) as a stochastic equationT (vt)−T ◦T −T ◦ =(1− vtc)−ξexp(εt) (3.17)where εt is an error term that is distributed normally with mean zero. The variance of the error term isassumed to be independent of congestion, but when we turn to our empirical work we allow it to varywith congestion as well. In equation (3.17), the new variable T (roughly, the average speed without anycongestion) becomes an estimable parameter in addition to ξ . This formulation allows us to link up thecongestion function directly with our log-normal distribution function. When ln(T (v)−T ◦) is distributednormally, we can estimate a congestion function for the mean commuting time, and we can additionally9We have also tried fitting Vancouver bridge traffic data using other functional forms illustrated in Greenshields et al. (1935);Drake and Schofer (1966), which are outperformed by the two models we finally choose.46allow for the variance of commuting time to depend on congestion.The modification in equation (3.17) is of significance. Effectively, we shift the coordinates of the distri-bution so that ∀t : T (vt) ≥ T ◦. Comparing (3.17) with (3.15), the power term on the right hand side scalesup T −T ◦ rather than T ◦, and the former is much smaller in magnitude than the latter. The result is thatwe can expect much higher estimates of ξ when we estimate (3.17).Figure 3.3: Speed-Volume FunctionV°=100km/h V⊕=90km/h0102030405060708090100Speed [km/h]0 10 20 30 40 50 60 70 80 90 100Road Congestion [% of Capacity]ξ=0.4ξ=0.7ξ=1.0Equation (3.17) can also be written in terms of speed rather than time, as showing speed in a diagram isoften more insightful than showing time for a given distance. Ignoring the effect of the stochastic term εt ,the velocity V (v) as a function of traffic volume v is given byV (v) =V ◦[1+(V ◦V −1)(1− vc)−ξexp(εt)]−1(3.18)The speed-volume chart in figure 3.3 illustrates the relationship between v˜ and speed for V ◦=100km/hand V =90km/h and three different ξ . When we estimate equation (3.17), our dependent variable willbecome ln(Tt/T ◦−1), and as we observe speed, we replace this (identical in value) with ln(V ◦/Vi−1).3.3.4 Speed-Volume DispersionA central theme in this paper is the empirical fact that congestion not only increases average travel time butalso increases the variability of travel time. The key metric for dispersion is the standard deviation of traveltime Tσ , or its normalized cousin, the coefficient of variation Tρ as defined in (3.5).The analysis in the preceding section introduces functional forms (3.15) and (3.16) that capture theeffect of congestion on travel time. We have modified (3.15) to capture variation in commuting time andbe consistent with log-normal distributions through (3.17). This new formulation allows us to draw a link47between variance and mean by assuming that Tρ , the coefficient of variation for commuting time mark-up,is approximately constant. Then Tσ = Tρ(Tµ −T ◦). Using the linearization insight expressed in theorem 1and equation (3.12) with H(ψ) as a function of the schedule inflexibility parameter, we are able to derive atheorem about the commuting time under congestionTheorem 3 (Commuting Time with Congestion and Schedule Infexibility) The commuting time for com-muters facing schedule inflexibility ψ and travel time coefficient of variation Tρ is approximated byT ∗(v˜) = T ◦+(T −T ◦) ·G(Tρ ,v) · (1+TρH(ψ)) (3.19)if the traffic congestion follows (3.17) and the coefficient of variation of travel time Tρ is approximatelyindependent of the level of congestion.As we will show in the empirical discussion of the paper further below, the function G is derived fromthe properties of the log-normal distribution function and is given byG(Tρ ,v) =√1+T 2ρ(1− v/c)ξ (3.20)and follows from the assumption of log-linearity of T −T ◦. Equation (3.19) compares directly to the com-muter who is flexible. The log-linear distribution implies that the mean commuting time (without schedulinginflexibility) isTµ(v˜) = T ◦+(T −T ◦) ·G(Tρ ,v) (3.21)The difference of time that is added to the commute as buffer time is therefore given by (T − T ◦) ·G(Tρ ,v) ·Tρ ·H(ψ). Quantifying this will be important to gauge the effect that scheduling inflexibility hason the total cost of commuting.The assumption that Tρ is independent of the level of congestion is perhaps strong. We find empiricalevidence that supports this notion for across-city commutes. However, we find some traffic bottleneckswhere road congestion also increases variance more than proportionally and thus Tρ may increase withcongestion.The discussion above only accounts for one dimension of dispersion: namely that for a given level ofcongestion there are varying speed outcomes. There are several sources for this type of dispersion. Thecomposition of traffic can be different in terms of trucks and cars. There can be differences in weatherconditions that interact with the level of congestion. These physical reasons can all contribute to dispersionthat varies with the level of congestion.There is also a second type of dispersion, which could be described as “congestion uncertainty.” Assumethat the speed-volume relationship does not exhibit dispersion in the time dimension. Rather, the commuterdoes not know which volume of traffic she will encounter on a given day due to random demand shifters.This means that a commuter may expect a certain amount of traffic on average, but with random dispersion.Observationally, this does not make any difference for the planning by the commuter. Whether the dispersionis caused by speed dispersion or volume dispersion, ultimately it is the commuting time that varies.483.3.5 Optimal Road Toll and Agent HeterogeneityThe optimal road toll problem has been described extensively, and what is added here is a more involvedtreatment of agent heterogeneity in the presence of time cost dispersion and schedule inflexibility dispersion.There are several ways of modelling the commuter’s choice problem: as a welfare maximization problem,as a travel cost minimization problem, or a utility maximization discrete choice problem. Our starting pointis a travel cost minimization problem to derive the optimal tolls.The planner’s objective is to choose a vector τ of optimal link tolls to minimize total travel cost forthe i ∈ {1, ..,n} individuals, each choosing an individual route Ri with path elements δik = 1(k ∈ Ri), andchoosing to travel pii(τ )∈{0,1} or not, so that the total social cost reflects individuals’ time costωi, scheduleinflexibilityψi, and cost zi of not travelling. The non-travel cost can also be viewed as the maximum durationT∅i that a commuter is willing to spend on this trip, which implies T∅i = zi/ωi. All toll revenue is returnedto commuters, so from the point of view of the planner the toll revenue does enter into the cost problem.This is an important consideration as otherwise the toll revenue could influence the commuting decision.It is practical to group commuters into those with a flexible schedule (ψ = 0) and those with an inflexibleschedule (and a common ψ 0) so that the first group has an extensive margin and respond to prices, whilethe second group will always commute. Let α denote the fraction of inflexible commuters and 1−α thefraction of flexible commuters. Further denote as pi(τ )∈ [0,1] the fraction of flexible commuters that chooseto drive after seeing posted tolls.Aggregating these groups and averaging them yields the social cost functionC = minτ[αω¯∗T¯ ∗(τ )+(1−α)ω¯ (pi(τ )T¯ (τ )+(1−pi(τ ))T¯∅)]n (3.22)where ω¯ is the average time cost of flexible commuters and ω¯∗ is the average time cost of inflexible com-muters, and where vk = ∑i δik is the number of commuters who take road k. Furthermore, T¯ ∗ and T¯ are theaverage travel times of the inflexible commuters (including their schedule delay) and the flexible commuters(who choose to travel), respectively. We also introduce T¯∅ under the assumption that zi and ωi are uncor-related, an assumption we will relax in our empirical work. However, for expositional purposes we use thisassumption to derive analytically tractable results.Total traffic volume is v= n[α+(1−α)pi(τ)]. Therefore, the share of flexible commuters that commutesispi(τ) =(v/n)−α1−α (3.23)Inflexible commuters choose route RiRi = argminδik{ω∗i T∗ (v(τ ),ψ)+∑kδikτk}(3.24)while flexible (inframarginal) commuters choose route RiRi = argminδik{ωiT (v(τ ))+∑kδikτk}(3.25)49conditional on making the trippii = 1(ωiT (v(τ ))+∑kδikτk < zi+ εi)(3.26)The above implies that a commuter makes the trip when the total cost of making the trip (travel timecost and tolls) is smaller than the cost of avoiding the trip. This is simply another way of putting the discretechoice problem and could be expressed similarly in utility terms.If εi is assumed to be distributed as an independent and identical type I extreme value (i.e., Gumbel), theconditional logit model emerges with an aggregate probability of making trips given bypi =[1+ exp(u(ω¯(T¯∅− T¯ (pi))− τ¯))]−1 (3.27)This provides a solution to the optimal traffic flow v. Inverting the above demand function yields the optimaltoll:τ¯ = ω¯(T¯∅− T¯ (pi))− 1uln(pi1−pi)(3.28)Unambiguously, the optimal toll increases when a lower travel volume (lower pi) is required in optimum.The cost minimum for C is found from the first-order condition for the optimal traffic volume v. Inturn, the travel demand function v(τ) reveals the optimal toll given optimal traffic volume v. It is importantto acknowledge the economic intuition underlying this principle of minimizing cost with respect to trafficvolume rather than optimal toll. The size of the toll does not matter for welfare because all revenue isreturned to economic agents. As long as the returned funds do not influence commuting behaviour, thetwo-stage process of minimizing costs with respect to traffic volume and then finding the optimal toll for therequired volume is economically sound.Before returning to the general case of a road network, consider the simple case of a single road. Toobtain a closed-form solution for the first-order condition, it is useful to introduce the variable travel time(T −T ◦) elasticityη ≡ d(T −T◦)dvvT −T ◦ = ξ[v˜1− v˜](3.29)with respect to traffic volume v. We also introduce the time cost ratio ϕ ≡ ω¯∗/ω¯ to capture asymmetric timecosts. Note that ϕ > 1 when inflexible commuters have a higher time cost than flexible commuters.We also make use of our congestion function (3.17), and we introduce a functionU(v)≡[T∅−T ◦T −T ◦](1− v/c)ξ√1+T 2ρ−1 (3.30)which decreases with congestion v. The term in square brackets is a time ratio: the difference betweennon-commute threshold and minimum time relative to the difference between average free-flow time andminimum time. Further recall that η(v) increases in v, and thus U(v)/η(v) decreases with v. Thus thefirst-order condition for a cost minimum reveals the following theorem:50Theorem 4 (Optimal Single-Road Traffic Volume) For a single road travelled by α inflexible commuters(with average time cost of ω¯∗ and average travel time T¯ ∗) and 1−α flexible commuters (with average timecost of ω¯ , average travel time T¯ , and maximum trip time T¯∅), the optimal traffic volume is given byvn= α[ϕ(1+H(ψ)Tρ)−1U(v)/η(v)−1](3.31)which can be solved for v numerically.We are interested in understanding how changes in the share α of inflexible commuters, as well aschanges in their degree of inflexibility ψ , affect the optimal traffic volume. We are also interested to knowhow differences in travel cost between the two types of commuter matter. Is it reasonable to assume thattime costs are the same (ϕ=1), or will they differ substantially? It is clear that an increase in ϕ has a similareffect as an increase in α , as both enter multiplicatively in the numerator.The expression in square brackets in (3.31) must be greater than one because the share α of inflexiblecommuters always commutes. For v/n > α , it must hold that ϕ(1+TρH(ψ))>U(v)/η(v). This says thateither the schedule inflexibility or the time cost ratio for the inflexible commuters must be large enoughto generate a solution that reduces the commutes of flexible commuters. Furthermore, we require thatnumerator and denominator are both positive. For the numerator, this means that the schedule inflexibilityψ must be large enough to compensate for a time cost ratio ϕ < 1 where the flexible commuters have ahigher cost than the inflexible commuters.10Equation (3.31) is nonlinear in v and thus the effect of key parameters on optimal traffic volume canonly be identified through implicit function calculus. Defining (3.31) as F(v,α) = 0, it follows thatdvdα=−∂F/∂α∂F/∂v< 0 anddvdψ=−∂F/∂ψ∂F/∂v< 0 (3.32)Figure 3.4 illustrates the effect of inflexible commuter share on optimal traffic volume. It shows that asthe share of inflexible commuters increases, the optimal traffic volume decreases gently. However, as theproportion of flexible commuters 1−α gets smaller and smaller, a larger and larger number of them have torefrain from commuting to enable the optimal traffic volume to be attained. When α reaches about 58% inthis numerical simulation, it is optimal to induce all flexible commuters to stop commuting.Figure 3.5 depicts the effect of an increase in schedule inflexibility on the optimal traffic volume. Ituses the same parameters as before except that α is fixed at one-half, and the factor H(ψ)Tρ is varied from0 to the point where all inframarginal commuters stop commuting. As schedule inflexibility increases, therelative importance of the inflexible commuters increases because these commuters add more and more extratime to ensure timely arrival. As a result, the number of inframarginal commuters is pushed towards zero,while the total share of commuters approaches the lower bound of α .When there are no inflexible commuters (α = 0), there is a particularly simple solution for the optimal10If the time cost of flexible commuters is high and the schedule inflexibility of the other commuters is low, then it makes noeconomic sense to curtail the commutes of flexible drivers.51Figure 3.4: Effect of Inflexible Commuter Share on Optimal Traffic Volume010203040506070Percent0 5 10 15 20 25 30 35 40 45 50 55Share of Inflexible Commuters (α) in %Traffic Volume (v/n)Inframarginal commuters (pi)Parameters: n=1900, c=2000, κ=2, λ=4, ω¯=ω¯∗=25, H(ψ)=6, Tρ=0.25, T ◦=30, T¯∅=90.Figure 3.5: Effect of Schedule Inflexibility on Optimal Traffic Volume010203040506070Percent0 .4 .8 1.2 1.6 2 2.4 2.8 3.2 3.6Inflexibility Factor (H(ψ)Tρ)Traffic Volume (v/n)Inframarginal commuters (pi)Parameters: n=1900, c=2000, κ=2, λ=4, ω¯=ω¯∗=25, α=0.5, T ◦=30, T¯∅=90.52vehicle flow:vc=[11+ξ/U(v)]=pi(τ)nc(3.33)This non-linear equation can be solved for v.3.3.6 Commuters’ Buffer TimeA planner who fails to take into account the buffer time (the time mark-up) of inflexible commuters willsolve a cost minimization problem where the planner falsely assumes that H = 0. Because of (3.31), thelinearization result that is implied there suggests that the numerator is treating changes in the time cost ratioϕ and changes in the mark-up factor 1+TρH(ψ) exactly the same. This means that there is a fundamentalequivalence in the way a researcher can treat the time mark-up for inflexible drivers and their time cost:Theorem 5 (Reliability Pricing Equivalence) The optimal traffic volume (and thus optimal toll) dependsdirectly onϕ∗ ≡ (ω¯∗/ω¯) · [1+TρH(ψ)] = ϕ(1+T∆) (3.34)and therefore a higher time cost of inflexible drivers is observationally equivalent with a higher time-markupT∆.The implication is that a road toll that only allows for the differential time cost of inflexible drivers,but not their time mark-up, will result in a suboptimal outcome as if the time cost of inflexible drivers hadbeen underestimated by a factor of 1+T∆. This result has important implications for empirical research.Researchers need to estimate the “effective time cost” of inflexible commuters by estimating their nominaltime cost ω¯∗ and the degree of their schedule inflexibility ψ .We can use theorem 1 about travel time reliability markup to characterize the total cost, noting thatT¯ ∗ = T¯ [1+H(ψ)Tν ], where Tν = T¯σ/T¯ is the ordinary coefficient of variation of commuting time. ThenC = nω¯T¯ [αϕ(1+H(ψ)T¯ν)+(1−α)(pi+(1−pi)Ω)] (3.35)where Ω ≡ T¯∅/T¯ > 1 is the ratio of the threshold time for non-commuting to average commuting time.Road tolls determine the share of flexible commuters pi entering the road and decrease average travel timeT¯ and the coefficient of variation T¯ν . In the absence of tolling, pi = 1. Then we can compare the cost withreliability costs against the case where reliability costs are ignored (and thus H(ψ) = 0). Dividing the twocost measures yields a measure of the schedule time cost:Theorem 6 (Schedule Time Cost) Given the share of inflexible commuters α , schedule inflexibility ψ ,commuting time coefficient of variation T¯ν , and time cost ratio ϕ of inflexible to flexible commuters, theextra cost (in percent) induced by the presence of schedule time is given byA ≡ 100% ·H(ψ) · T¯ν[1+1−ααϕ]−1(3.36)in the absence of road tolls.53Effectively, equation (3.36) allows us to put an upper limit on the extra cost due to schedule inflexibility;it is H(ψ)T¯ν . Furthermore, when the time cost of flexible and inflexible commuters is the same, thenthe extra cost due to schedule time is simply proportional to the share of inflexible commuters so thatA = 100% ·αH(ψ)T¯ν .3.3.7 Reliability Pricing in a Road NetworkThe results obtained so far paint a very simple picture about how reliability pricing can be brought into aframework for optimal road tolling in a road network, which itself has been well established in the literaturealready. The key modifications derived from the analysis in this paper is that researchers need to identify:(a) the composition of commuters (the share α of inflexible commuters);(b) the relative time cost (ϕ) of inflexible and flexible commuters;(c) the schedule inflexibility (ψ) of commuters; and(d) the coefficient of variation (Tν ) of commuting trip time.It is the latter that is specific on individual routes, and thus empirical research will need to identify thereliability of each road segment and identify how the variance of individual road segments adds up across themultitude of trip patterns in a region. This is where the empirical research in this paper attempts to providesome novel insights by studying commuting patterns in the Metro Vancouver region. Just how large arethese coefficients of variation across commuting trips? While our study does not identify the three other keyparameters (α , ϕ , and ψ), which require other microeconomic data sets from surveys, we aim to identify Tρand Tν from observed traffic flows.3.4 DataWe utilize data from a variety of sources. From Statistics Canada’s National Household Survey 2016 weobserve commuting patterns among pairs of census tracts (CTs). A CT is a small areas that captures between2,500 and 8,000 persons in census metropolitan areas (CMA). We employ data for the Metropolitan Van-couver area (CMA code 933) area that encompasses the cities listed in table B.2 with a total of 482 censustracts. The commuting patterns in the household survey only identifies 43,763 CT pairs with a minimumnumber of commutes. We restrict our analysis to commutes with origin and destination CT both in MetroVancouver and exclude those trips that start or end outside Metro Vancouver.We obtain travel time information from the Google Maps Distance Matrix API. This Application Pro-grammer Interface (API) provides information on distance, normal travel time, and time in traffic for origin-destination pairs, which we identify by longitude and latitude as the mid-points of census tracts. The APIemploys a specific traffic model for calculating the time in traffic. Google employs live traffic data, whichit acquires from users of their navigation applications that share location information in real time. We usetheir “best guess” model, whose reported duration in traffic is their best estimate of travel time given whatis known about both historical traffic conditions and live traffic.In addition to the region-wide commuting pairs we also focus on several bottlenecks of traffic flows—bridges and tunnels—which are well known to experience high levels of congestion during rush hour. Onlyone of these, the Port Mann Bridge, was tolled between 2012 and 2017. We employ post-toll data, but note54that the removal of the toll on September 1, 2017 led to a significant increase (about 30%) in traffic volume.The main feature of our bottleneck data is our ability to match travel time through these bottlenecks in bothdirections with volume measurements from the BC Ministry of Transportation Traffic Data Program.3.4.1 Commutes among Census Tract PairsWe sample 2,000 “typical” commuting trips and ensure that the sampling frequency is matched to the volumeof commutes reported in the Household Survey. Thus CT pairs with many commuters will be sampledproportionally more than those with fewer commuters. Figure 3.6 shows the cumulative distribution of CTpairs in descending order of traffic volume reported by the household survey. We sample by taking 2,000routes so that the frequency with which we sample routes is weighted by the traffic volume.11Figure 3.7, 3.8 and 3.9 describe the overall distribution of the sampled routes of census-tract pairs. Thedistributions for distance and commuting time are noticeably right-skewed and thus have means that arehigher than their medians. In our sample the mean commuting distance is 13.5km (8.4mi) and takes 21minutes. The average speed that we observe is about 35.6km/h (22.2mi/h); however some commutes can beas slow as 10km/h and as fast as 70km/h.Our commuting data lends itself to summarizing and analyzing region-wide patterns. We first look ataverage commuting speed and commuting delay and try to explain how it varies during rush hour. Oursample of 2000 trips across Metro Vancouver during seven half-hour intervals between 06:30 and 10:00provides estimates of how the log of average speed and the average delay (measured as the log of the ratioof observed travel time to normal travel time as reported by the Google API) depends on distance, time ofday, and day of week. Table 3.2 summarizes the results.Column (A) in table 3.2 reveals that average speed increases with distance so that a 10% increase indistance increases average speed by 2.4%. This effect is a result of longer commutes containing longersections of highway driving. The time of day effect is captured by a linear and square time effect thatsuggests that speed is lowest (and delay is highest) around 08:30. Delays increase very little with distance.A 10% increase in distance is associated only with an 0.5% increase in delay. The best days for commutingare Mondays and Fridays, whereas other days of the week are slower. Weekends are excluded from theanalysis. We cluster standard errors in our analysis.Column (B) in table 3.2 captures the delay, the log ratio of travel time in traffic to normal travel time.Both figures are provided directly by the Google API. This means that under ideal conditions the observedtravel time may be higher or lower than the normal travel time. We again find a link to distance, but muchweaker than for speed. A 10% increase in distance increases delays by about half a percent. Delays aresmaller on Mondays and Fridays compared to the three other weekdays.We use the available time distribution data in several ways. For each commuting trip we calculateminimum travel times, and for each CT pair and time slot (2,000 times 7) we calculated mean and standarddeviation in order to obtain empirical estimates of Tν and Tρ that we analyze further. We also use the CT-pairtime-slot data set to estimate the parameters of the underlying Fre´chet and Lognormal distributions in order11We split the cumulative distribution into 2,000 segments by taking a route sample each time we cross the next 0.05% thresholdof cumulative volume.55Figure 3.6: Census Tract Commuting Trip Sample0102030405060708090100Cumulative Share of Commuters [%]0 2000 4000 6000 8000 10000 12000 14000 16000 18000 20000Rank of Census Tract Pair by Commuter VolumeCommuting Volume Distribution − Census Tract PairsNote: census tract pairs are sorted in descending order of traffic volume. Source: Statistics Canada, NationalHousehold Survey (2016).Figure 3.7: Commuting DistanceMedian: 10.9 kmMean: 13.5 km01234567Percent0 5 10 15 20 25 30 35 40 45 50 55 60Commuting Distance [km]Commuting Distance DistributionNote: representative sample of 2000 trips across census tract pairs.56Figure 3.8: Commuting Time DistributionMedian: 18.3 min.Mean: 20.8 min.01234Percent0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90Commuting Time [minutes]Commuting Time DistributionNote: representative sample of 2000 trips across census tract pairs.Figure 3.9: Commuting Speed DistributionMedian: 35.2 km/hMean: 36.0 km/h012345Percent0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80Commuting Speed [km/h]Commuting Speed DistributionNote: representative sample of 2000 trips across census tract pairs.57Table 3.2: Determinants of Commuting Speed and Delay(A) (B)Dependent Variable¸ Speed DelayIntercept¸ 2.951c (246.) −0.042c (8.85)Distance ln(d) 0.242c (50.3) 0.045c (20.7)Time of Day (linear) h−8 −0.053c (46.1) 0.056c (53.0)Time of Day (squared) (h−8)2 0.055c (75.6) −0.054c (76.4)Implied Peak Time [hour] 8.478c (828.) 8.524c (844.)Monday¸ 0.021c (38.4) −0.020c (40.0)Tuesday¸ −0.013c (27.0) 0.008c (22.2)Thursday¸ −0.018c (30.4) 0.012c (26.1)Friday¸ 0.026c (41.5) −0.023c (42.0)Regression fit (R2)¸ 0.559 0.290Observations¸ 685,993 685,993Note: Statistical significance at the 95%, 99%, and 99.9% level of confidence is indicated by superscriptsa, b and c, respectively. Standard errors are clustered for the 2,000 commutes. Numbers in brackets aret-statistics. The dependent variables are the log of observed speed and the log of the ratio of travel timein traffic to normal travel time. The implied peak is the hour of minimum speed or maximum delay.Wednesday is the base day for the regressions and thus is omitted. Weekends are excluded.to determine which distribution describes the data more accurately. The result from this analysis allows usto decide whether H(ψ) is more suitable based on either of the two distributions.3.4.2 Bridge Data: Volume and TimeThe commuting pattern data faces one important limitation: we do not observe traffic volumes directly.The BC Ministry of Transportation collects data on traffic volumes at a number of measurement stationsacross the region, including key bottlenecks (Opus International Consultants, 2014). Table 3.3 identifies thelocations we study. We obtain hourly data for one full year from October 2017 through September 2018.12Two of our routes have alternating counterflow lanes. The Lions Gate Bridge has three lanes in totaland switches back and forth between 2+1 and 1+2 lanes in each direction. The George Massey Tunnel hasfour lanes in total and switches between 1+3, 2+2, and 3+1 configurations. Our study of these routes tries tocontrol carefully for the times of day in which they are operated in a particular configuration as they followa set schedule during the day.We have also obtained speed information through the Google Distance Matrix API in real time for roadsegments of a few kilometers in length. We have sampled speeds in 5-minute intervals between 06:00 and21:55, and at 15-minute intervals during the night. We have averaged the data at the hourly level to matchour bridge volume data.Figure 3.10 shows the diurnal traffic volume for four of our bridges. The northbound and southboundtraffic can show significant asymmetries. While the traffic on the Second Narrows Bridge (connecting12The publication of volume data for some bridges is lagging or has suffered from technical outages. We are missing datafor the Second Narrows Bridge in November 2017 and parts of July 2018. Our data for the Alex Fraser Bridge is missing fromMarch-September 2018.58Figure 3.10: Diurnal Direction Traffic VolumePANEL A PANEL B01,0002,0003,0004,0005,000Median Traffic Volume [vehicles/hour]0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23Intraday Traffic Volume: Alex Fraser BridgeNorthboundSouthbound01,0002,0003,0004,0005,000Median Traffic Volume [vehicles/hour]0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23Intraday Traffic Volume: Port Mann BridgeNorthboundSouthboundPANEL C PANEL D01,0002,0003,0004,0005,000Median Traffic Volume [vehicles/hour]0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23Intraday Traffic Volume: Second Narrows BridgeNorthboundSouthbound01,0002,0003,000Median Traffic Volume [vehicles/hour]0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23Intraday Traffic Volume: Oak Street BridgeNorthboundSouthboundFigure 3.11: Speed Volume ChartsPANEL A PANEL B2030405060708090100110Speed in Traffic [km/h]0 1000 2000 3000 4000 5000Traffic Volume [vehicles]NorthboundSouthboundSpeed & Volume: Alex Fraser Bridge2030405060708090100110Speed in Traffic [km/h]0 1000 2000 3000 4000 5000Traffic Volume [vehicles]NorthboundSouthboundSpeed & Volume: Port Mann BridgePANEL C PANEL D2030405060708090100Speed in Traffic [km/h]0 1000 2000 3000 4000 5000Traffic Volume [vehicles]NorthboundSouthboundSpeed & Volume: Second Narrows Bridge2030405060708090Speed in Traffic [km/h]0 1000 2000 3000Traffic Volume [vehicles]NorthboundSouthboundSpeed & Volume: Oak Street Bridge59Table 3.3: Traffic Bottlenecks in Metro VancouverCode Name Direction Lanes∗ LimitPMB-N Port Mann Bridge Northbound (west) 2+3 90 km/hPMB-S Port Mann Bridge Southbound (east) 2+3 90 km/hGMT-N George Massey Tunnel Northbound 1/3 80 km/hGMT-S George Massey Tunnel Southbound 1/3 80 km/hAFB-N Alex Fraser Bridge Northbound 3 90 km/hAFB-S Alex Fraser Bridge Southbound 3 90 km/hLGB-N Lions Gate Bridge Northbound 1/2 60 km/hLGB-S Lions Gate Bridge Southbound 1/2 60 km/hSNB-N Second Narrows Bridge Northbound 2 70 km/hSNB-S Second Narrows Bridge Southbound 2 70 km/h∗ a/b indicates counterflow lanes minimum/maximum; a+b indicates separated lanesVancouver to North Vancouver) is quite balanced in both directions, the Alex Fraser Bridge has strongnorthbound traffic in the morning and southbound traffic in the afternoon. The Oak Street Bridge connectingRichmond to Vancouver has stronger northbound than southbound traffic in the morning.Important for our research is the relation between traffic volume and commuting time. In figure 3.11 weshow scatter plots of hourly volume and speed for the same routes as in figure 3.10.13 They illustrate thetypical speed-volume link, although there is no clear prima facie evidence of hypercongestion. The new PortMann Bridge show few signs of significant congestion. Given its significant capacity, only traffic accidentsseem to slow down traffic noticeably.3.5 Empirics3.5.1 Travel Time Coefficient of VariationFigures 3.12 and 3.13 provide histograms of the distribution of the two coefficients of variation Tρ =Tσ/(Tµ − T ◦) and Tν = Tσ/Tµ . The first coefficient of variation is measured with respect to the averagedelay Tµ −T ◦ and the second coefficient is measured with respect to the average time Tµ . We construct the“best” travel time T ◦ for commuting trip i from observations across different times t, and then we allow fora 10% faster drive under optimal conditions in order to allow for individual variation in driving behaviour.T ◦i = 0.9mint {Tit} (3.37)This procedure ensures that T ◦i is truly providing a floor for the travel time.Empirically, we find that both measures are strongly positively correlated (about 0.88), as one wouldexpect when both measures share the same numerator. Both distributions have a long right tail. The traveltime markup coefficient of variation Tρ has a mean of 24%, whereas the commuting time coefficient ofvariation has a mean of about 6.1%. Recall that each data point was sampled to represent roughly equal13We show speed rather than time because of convention in the transportation literature.60Figure 3.12: Coefficient of Variation Distribution: Time Markup TρMedian: 22.50%Mean: 24.53%censored at 90%012345Percent0 10 20 30 40 50 60 70 80 90Travel Time Markup Coefficient of Variation (Tρ) in percentTravel Time Markup Coefficient of Variation DistributionNote: representative sample of 2000 trips across census tract pairs.Figure 3.13: Coefficient of Variation Distribution: Travel Time TνMedian: 5.24%Mean: 6.39%censored at 30%012345Percent0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30Travel Time Coefficient of Variation (Tν) in percentCommuting Time Coefficient of Variation DistributionNote: representative sample of 2000 trips across census tract pairs.61number of commuters.We observe seven half-hour time blocks of morning commutes in Metro Vancouver, but we have onlytime but no volume data. Therefore we construct a road congestion index (RCI) based on the average delaythat commuters incur:RCIkt = 100% ·(T¯ktT ◦k−1)(3.38)This proxy for actual traffic volume is zero when average travel time does not exceed the minimum (best)travel time. It has a mean of 21.8% and median of 17.8%, and the 5th and 95th percentiles are 3% and 53%,respectively.Table 3.4: Congestion and Travel Time Coefficients of Variation(A) (B) (C)Dependent Variable¸ 100%Tν 100%Tρ 100%TρRoad Congestion Index¸ 0.093c (35.8) −0.148c (17.9)Timeslot 07:00¸ −0.861c (5.08)Timeslot 07:30¸ −3.659c (19.3)Timeslot 08:00¸ −3.026c (13.2)Timeslot 08:30¸ −1.579c (6.14)Timeslot 09:00¸ 0.754b (2.58)Timeslot 09:30¸ 1.029b (3.09)Regression fit (R2)¸ 0.266 0.065 0.065Observations¸ 14,000 14,000 14,000CT Pair Fixed Effects¸ yes yes yesNote: Statistical significance at the 95%, 99%, and 99.9% level of confidence is indicated by superscriptsa, b and c, respectively. Standard errors are clustered for the 2,000 commutes. Numbers in brackets aret-statistics.We are interested in identifying the extent to which the coefficients of variation increase or decreasewith the level of congestion. In Table 3.4 we report three regression specifications that link our observedcoefficients of variation to the RCI measure defined in (3.38). Column (A) finds that the ordinary coefficientof variation Tν increases slightly with our road congestion index measure defined in (3.38). The empirical fit(the R2 statistic) is somewhat weak at 0.266, but the intuition that variance increases with congestion morethan the average is intuitive. The estimated coefficient is relatively small, moving the RCI by 10%-pointsshifts Tν by less than 1%-point.The effect of congestion on Tρ is somewhat weaker and actually negative, reported in column (B). Weconclude from this that there is no case to be made that Tρ increases with congestion. The negative pointestimate rules that out convincingly. The estimation in column (B) is slightly sensitive to the choice of T ◦in (3.37).14 The larger magnitude of the estimate is not surprising given that the mean Tρ is several timeslarger than Tν . However, the fit in column (B) is much weaker than in column (A), and we conclude that itis not unreasonable to assume that Tρ is not strongly influenced by congestion.In column (C) we also use dummy variables to proxy for the effect of road congestion during different14It is possible to find a T ◦ that would bring the estimate close to zero.62time slots, with 06:30 as the baseline time slot. Tρ , with an average of about 21%, is slightly lower duringpeak congestion. The overall explanatory power of road congestion with respect to Tρ is not very high.There is a weak effect of congestion on Tρ , but the magnitude is not large enough to negate the theoreticalassumption to hold Tρ constant in our theoretical modelling.Table 3.5: Schedule Time Cost [%]Q1 Median Q3Tν 3.89 5.24 7.93ψ=16 6.82 9.19 13.90ψ=40 9.55 12.86 19.46ψ=100 12.26 16.51 24.97ψ=250 15.05 20.27 30.66Our analysis is also able to provide an evaluation of the overall cost of scheduling time as we are ableto estimate Tν for the Metro Vancouver region and match it with assumptions about schedule inflexibility ofcommuters, the share of inflexible commuters, and the time cost ratio. Table 3.5 reports the median, as wellas first and third quartile (Q1 and Q3) of our empirical findings of Tν . We combine this information withfour assumptions of ψ , spaced apart at a factor of 2.5 from each other. A schedule inflexibility of ψ=16 israther low and can be considered the lowest plausible point. At ψ=40, the commuter is aiming to be lateno more than once every 8 weeks. At ψ=100 and ψ=250, the commuter does not want to be late late morethan once every 20 weeks and once a year, respectively. Our cautious “best estimate” is the median of Tν atψ=40, which suggests a schedule time cost of 12.3%. Individual commuters may experience more or lessschedule time. A very inflexible commuter (ψ=250) at the third quartile point may incur time costs closeto 30%.Figure 3.14: Schedule Time VariationH(ψ)⋅Tν = 0.123.5.63.811.251.582Time Cost Ratio (ω*/ω) − logarithmic scale0 .2 .4 .6 .8 1Share of inflexible commuters (α)0123456789101112Extra Commuting Cost [percent]The schedule time factor TΛ that we calculate in table 3.5 is the maximum attainable individually, butthe overall time cost increase across all commuters—flexible and inflexible—depends also on the share ofinflexible commuters α and the time cost ratio ϕ of inflexible to flexible commuters. The contour plot in63figure 3.14 illustrates how our key estimate of schedule time (forψ=40 and median Tν ) varies with these twoparameters, based on our Schedule Time Theorem expressed in equation (3.36). The effect of differences inϕ are relatively modest as we explore a range from 1:2 to 2:1 in our diagram. A higher ϕ leads to a slightlyhigher extra commuting cost. The stronger effect comes from the composition of commuters. When ϕ=1,then A = αTΛ; the time cost increase is directly proportional to the share α of inflexible commuters.3.5.2 Fre´chet v. Lognormal: which provides a better fit?Our discussion of the reliability standard hinges empirically on the choice of distribution for commutingtime. Our analysis employs both Fre´chet and log-normal distributions as these are obvious choices fornon-negative distributions. However, there are important differences in the shape of these distributions:for identical moments of mean and standard deviation, the Fre´chet distribution has a more compressed andfocused shape than the log-normal distribution. (Figure B.1 in the appendix illustrates it.) The empiricalconsequence of the choice of distribution function is reflected in our linear approximation H(ψ) of scheduleinflexibility as illustrated in figure 3.2. The Fre´chet distribution has a higher slope of H(ψ), and has highervalues of H(ψ) when schedule inflexibility is high (roughly when ψ > 40). We are therefore interested inproviding empirical evidence about the relative merits of the distributional choice. Our commuting patterndata enables us to do so as we observe distributions of commuting time across census tract pairs and timeslot.Because our time dimension is limited (we only have 50 days), we exploit the fact that Tρ is not de-pendent on the level of road congestion, and pool our data across the 7 different time slots. This meansthat for every of our 2,000 census tract pairs (except the 50 that show no commuting time variation) wehave 7×50=350 observations at our disposal. Specifically, we estimate the following two log-likelihoodfunctions for the two distributionsLLFr =−∑it{ln(a∑kskδkt)+[∑k skδktTit −T ◦i]1/a−(1+1a)ln(∑k skδktTit −T ◦i)}(3.39)andLLLn =−∑it{ln(σ(Tit −T ◦i )√2pi)+[ln(Tit −T ◦i )−∑k µkδkt ]22σ2}(3.40)where δkt ≡ 1(k= t) is an indicator variable that is one when time period t matches the variable numberk. There are K + 1 parameters: one for each time slot and a “shape” parameter for the distribution. Ouridentification strategy, which is based on Tρ being independent of road congestion, allows us to estimate asingle shape parameter for each CT pair while estimating one scale or locational parameter for each of the 7time slots. Recall that in the Fre´chet distribution the shape parameter a is a function of Tρ ; see equation (3.4).64Figure 3.15: Log-Likelihood Comparison of Commuting Time Distribution Median: 22.20Lognormal preferredFréchet preferredcensored at −150 censored at +1500123456Percent−150 −125 −100 −75 −50 −25 0 25 50 75 100 125 150AIC Difference: 2[ln(LLognormal)−ln(LFréchet)]Commuting Time Distributions: Fréchet v. LognormalNote: representative sample of 2000 trips across census tract pairs.It is not possible to directly test one distribution against the other using a test statistic. We employ theAkaike information criterion AIC = 2K−2lnL, a measure of the relative quality of statistical models for agiven set of data. When comparing two models, the lower AIC indicates the better fit. Because both modelshave the same number of parameters K, the measure we use to characterize the relative performance of thetwo distributions is the metric∆AIC≡ (−2LLFr)− (−2LLLn) (3.41)Fre´chet is preferred over lognormal if ∆AIC is negative, and lognormal is preferred over Fre´chet if ∆AICis positive. We report the results of our analysis from running 2,000 pairs of regressions in figure 3.15,a histogram of each of the ∆AIC we compute from our regression pairs. As is visible, the bulk of theestimation results favour the lognormal distribution over the Fre´chet distribution. We conclude, therefore,that generally the lognormal distribution provides a better fit for commuting time distributions than theFre´chet distribution.The important implication of our analysis is therefore that our H(ψ) linear approximation of commutingtime mark-up as a function of schedule inflexibility (ψ) should be based on the lognormal distribution, andthus the lower H(ψ) that are implied by this choice for larger ψ .3.5.3 Route Choice: is there a speed-reliability trade-off?We sample 2,000 commutes seven times a day across Metro Vancouver. How often do commuters take thesame route, and how many times will they find a better alternative on a different route? Our data set is able toanswer these questions. Table 3.6 shows the distribution of the number of routes commuters may take. Eventhough the Google API will not provide the exact route, it provides the distance of the route recommended.65We granularize the data by considering a route as different if the integer number of kilometers is different.So routes that are 3.3km and 4.2km would be considered different, while routes that are 3.8km and 4.1kmwould be considered roughly the same. This granularization is meant to suppress minute differences inroutes and focus instead on major route choice differences.Table 3.6: Distribution of Route Choices among 2,000 CommutesRoutes 1 2 3 4 5 6 7 8 9 10+Frequency 27.9% 27.3% 15.7% 9.7% 6.2% 4.5% 2.8% 1.8% 1.7% 2.6%Roughly one third of commuters will only take one route, while about 60% take no more than two routes.As the data in the table shows, there are some commutes that are much more variable, and some commuteseven observe more than ten routes. On average, commuters take 2.7 different routes. As commutes getlonger, obviously there are also more permutations of route segments. The table above does not revealthe intensity of alternative route choices: when commuters take alternative routes, they may do so moresparingly. We see that 70% of commutes are on the first route choice, and another 17% on the second routechoice, and another 6% on the third route choice. About 93% of commuters thus occur on the top threeroute choices.We also regress the number of routes on the log of distance. We employ a count regression using thePoisson distribution and find a positive coefficient (0.64) that is highly statistically significant. It confirmsthat route choices become more complex with greater distance.Figure 3.16: Alternate Route Trade-Offs−.6−.4−.20.2.4Variability Difference Tρ (alternate minus base)−.2 0 .2 .4 .6 .8Slowness Difference Tφ (alternate minus base)Alternate Route vs. Base RouteThe focus of our paper is on commuter time reliability, and our line of inquiry thus takes us to thequestion how a commuter’s usual route (defined as the route most often taken on a given commute) compareswith that commuter’s alternate routes (defined as all the routes taken less frequently). Our theoretical worksuggests that the coefficient of variation Tρ is the right measure to compare route performance in terms of66variability, and thus we construct the difference ∆Tρ ≡ T Aρ −T Bρ as the metric that compares the alternate (A)routes against the base (B) route. We construct a similar measure for the slowness of each of our commutingroutes: Tφ ≡ (T¯ − T ◦)/T ◦. This measures captures the markup of average travel time over fastest traveltime. To compare alternate (A) routes against base (B) routes, we construct ∆Tφ ≡ T Aφ −T Bφ as our measureof difference in slowness. Some of our 2,000 commutes never use alternate routes or have no time variation,which leaves us with 1,215 observations. In our diagram 3.16 we ignore eight outliers with unusually highor low ∆Tφ and show a simple linear fit. The green lines divide the diagram into four quadrants.On average, it is unsurprising that alternate routes are slower than preferred routes. What is less obviousis how the route choice is related to the time variability of the route, our Tρ measure. The correlation infigure 3.16 is striking: slower routes are associated with a reduction in variability. This means, as a stylizedfact, that alternate routes are slower but less risky. The mean ∆Tφ is about 0.12 (an increase from 0.37 forbase route to 0.49 for alternate route) and the mean ∆Tρ is about –0.11 (a drop from 0.40 for base route to0.29 for alternate route). The conclusion from this exercise is that route choice is not just about speed, butalso about reliability. If it wasn’t, there should be no correlation in figure 3.16.3.5.4 Bridge Traffic AnalysisIn our citywide analysis we only have a rough proxy for congestion as we do not have flow data for allsegments of our sampled commutes. However, the BC Ministry of Transportation publishes hourly volumedata for a number of select bridges and tunnels that we have described in our data preview section. Thisdata enables us to link volume and speed data to answer the question how increasing congestion affects thedispersion of commuting time. While this analysis allows us to observe the dispersion characteristics atthese bottlenecks, these findings are not representative of the entire commute. Bottlenecks are obviouslyhighly important for the overall commuting time and its dispersion, but queueing in front a bottleneck andother spillovers are influencing the effect on the total commuting time. Commuters’ route choice and traveldecision depends on the total commuting time, including buffer time, but not on the travel time througha bottleneck alone. Our empirical analysis reveals the magnitude of two key parameters: how congestionincreases travel time through the bottleneck, and how congestion increases (or decreases) the variance oftravel time. It is the latter that is a novel contribution of our paper.In estimating the effect of congestion on commuting time and its dispersion, we employ a log-linearversion of (3.17). However, this approach requires us to introduce the minimum travel time T ◦ and roadcapacity c as constants. The minimum travel, or analogously maximum speed V ◦, constrains the empiricaldistribution. We define the maximum speed asV ◦ ≡ bmaxt{Vt}/0.9c (3.42)which mirrors (3.37). We report this speed as an integer number and consider this 10% increase overthe highest observed speed as a plausible limit on what is still feasible under completely ideal conditions.Naturally, this maximum speed is much higher than the average speed and the speed limit (V¯ ).1515Nevertheless, there are always drivers who may exceed even what we consider a “generous” upper limit. In May 2018 it was67We also need to define the capacity of each of our bridges and tunnels. There is an extensive literature onrating road capacity. We rely on Hall (1975) and Federal Highway Administration (2016, 2017) to determinethe capacity of our multilane highways asc = max{2200,1000+12.427 ·FFS} · Lanes1+HV/200(3.43)where HV is the percentage of heavy traffic on the route, and with the free-flow speed (FFS) given byFFS = 121.32− fLW− fLC [km/h] (3.44)Here, fLW and fLC are adjustment factors for lane width and right shoulder later clearance, respectively.The adjustment factor for lane width are 3.6m (0.00 km/h); 3.3m (3.06 km/h); 3.0m or less (10.62 km/h).The adjustment factor for right shoulder lateral clearance is zero for grater than 1.8m, and a maximum of5.8 km/h and 3.9 km/h for 2-lane and 3-lane roads, respectively, when no right shoulder is present. Wehave rather incomplete information on the adjustment factors that are needed for our bridges and tunnelsbecause of widely different design characteristics. However, the posted speed limit V¯ reflects many of thesecharacteristics such as narrow lane width, absent shoulders, or concrete barriers on the side. We fall back ona classic calculation by Johannesson (1931)c =⌊24001+18.3/V¯⌋·Lanes (3.45)that provides a remarkably sturdy approximation of lane capacity. We show the results of this formula intable 3.7.Table 3.7: Speed Limit-Capacity RelationshipSpeed Limit [km/h] 50 60 70 80 90 100 110 120Lane Capacity [vehicles] 1756 1839 1902 1953 1994 2028 2057 2082We use multiplicative heteroskedastic linear regression (MHLR) to analyze our bridge traffic data anddetermine how dispersion and travel time vary with the level of congestion. We estimate a linear model ofthe form yi = xiβ + εi with dependent variable yi and a vector of independent variables xi and i.i.d. errorswith mean zero and variance σ2i . The variance function σ2i = exp(ziγ ) is parametric and is explained byvariable vector zi. Equivalently, ln(σ2i ) = ziγ is linear. Thus we can estimate the MHLR log-likelihoodfunctionLL =−12[n ln(2pi)+n∑i=1ziγ − (yi− xiβ )2ziγ](3.46)Stata, the statistical software that we use, has implemented this type of regression through the commandhetregress for the linear case. It is straight-forward to generalize this to the non-linear case.reported that a Ferrari driver was fined $750 for clocking 210 km/h on Lions Gate Bridge. The posted speed limit is 60 km/h. Thereis no limit to recklessness.68We start out by noting that ln(Ti − T ◦) is normally distributed, and because T ◦ is a constant, yi ≡ln(Ti/T ◦− 1) is also normally distributed. Empirically we normalize distance for our bridge and tunnelanalysis and thus we observe velocities Vi and infer V ◦. Therefore, for any distance, it holds that Ti/T ◦ =V ◦/Vi. Thus we calculate yi = ln(V ◦/Vi−1). The mean is expected to follow a congestion function of thetypes proposed in (3.15) and (3.16),16 and implemented in (3.17) as a stochastic version that fits with ourlog-normality assumption for Ti−T ◦. The error term εi in (3.17) is distributed normally with mean zero andvariance σ2, which we allow to grow analogously to the mean. Thus we can estimate the linear systemyi = ln(T /T ◦−1)−ξ ln(1− vi/c)+ εi (3.47)ln(σ2i ) = ln(Σ )−ζ ln(1− vi/c) (3.48)which provides estimates of T and ξ in the mean equation, and Σ and ζ in the variance equation. Hence,we calculate the observational mean asTµ(v˜) = T ◦+[T −T ◦(1− v˜)ξ]· exp(Σ /2(1− v˜)ζ)(3.49)and the standard deviation asTσ (v˜) = (Tµ(v˜)−T ◦)√exp(Σ (1− v˜)ζ)−1 (3.50)and thereforeTρ =TσTµ −T ◦ =√exp(Σ (1− v˜)ζ)−1 (3.51)Note that when ζ = 0, the expression on the right turns into a constant√exp(Σ )−1 and thus becomesindependent of congestion. This means that Tσ increases proportional to Tµ −T ◦ as congestion increases.In the ζ =0 case,Tµ(v˜) = T ◦+T −T ◦(1− v˜)ξ√1+T 2ρ (3.52)When we interpret the results, it is useful to express T as a speed equivalent, knowing that T /T ◦ =V ◦/V . Thus, using the estimate of the intercept in the mean equation aˆ = ln(T /T ◦− 1), it follows thatV = V ◦/(1+ exp(aˆ)). Similarly, when we interpret the constant aˆ = ln(Σ ) in the variance equation, wereport the corresponding initial T ρ at v˜=0 as√exp(exp(−aˆ))−1.If ζ is positive, then the coefficient of variation will decrease with congestion. However, if ζ is negative,then the coefficient of variation will in fact increase with congestion. Both are possible outcomes. Both ξand ζ determine the travel time in (3.49). When ζ is positive, it reinforces the effect of ξ ; however, whenζ is negative, it dampens the effect of ξ . The intuition is that a positive ζ increases the variance σ2 of thelog-normal distribution when congestion increases, while a negative ζ decreases that variance. Because of16There is no log-linearization of the Pipes-Munjal congestion function because ln(1+κ(1− v˜)λ ) does not allow separating κ andλ . It is therefore necessary to estimate this version non-linearly. We leave this exercise for future study as the small improvementsin fit do not change our qualitative results in this section.69the right-skewed shape of the log-normal distribution, increasing variance pulls up the arithmetic mean.Table 3.8 reports the results of our estimation for several of our bridges, opposing traffic directions,and different lane numbers due to counterflow traffic: the Alex Fraser Bridge northbound and southbound(AFB-N and AFB-S); the Oak Street Bridge (OSB-N and OSB-S); the Second Narrows Bridge (SNB-N andSNB-S); the Lions Gate Bridge (LGB-N and LGB-S) in two-lane mode; and the George Massey Tunnel(GMT-N and GMT-S) in 2-lane normal mode and 3-lane counterflow mode. We are not presenting resultsfor the Massey Tunnel or the Lions Gate Bridge when only a single lane is in operation because thesephases are heavily driven by lane merging and queuing. Similarly, we do not show results for the Port MannBridge because the bridge has distinct express and local lanes, while the volume data is aggregate. For thisbridge we are not able to discern separate volumes for the long-distance and local traffic, and the northbounddirection also has a complicated lane merger that results in capacity curtailment.Table 3.8 first shows the relevant fixed parameters for our bridges and tunnels: the number of lanes,posted speed limit, maximum speed inferred by (3.42), and road capacity inferred by (3.45). There aretwo blocks of regression estimates in each column: the first for the mean equation (3.47), and the secondfor the variance equation (3.48). The congestion effect estimates identify ξ and ζ , respectively. The twoconstants are difficult to interpret without transformation. Therefore, we report the initial speed V forthe mean equation and the initial Tρ for the variance equation. “Initial” means that these are the speeds(or coefficients of variation) with zero congestion. We finally report the number of observations and theAikaike Information Criterion (AIC) for model selection purposes (noting that smaller AICs are better).Our result for the Lions Gate Bridge northbound has a negative ξ estimate, which we attribute to a ratherhigh maximum speed compared to the initial speed. We discard this set of estimates as unreliable.Overall, we find strong evidence that the congestion parameter ξ for the mean equation varies betweenabout 0.6 and 1.0. This means that, as can be expected, congestion strongly increases travel times. Theeffect is somewhat more pronounced in some places than others. The Oak Street Bridge northbound hasmuch stronger congestion behaviour than southbound. This observation is consistent with the fact that thenorthbound traffic transitions freeway traffic to urban (signal) traffic, while southbound a string of trafficlights regulate the traffic volume onto the bridge.Our key result concerns the variance equation and fully justifies our choice of using an MHLR model:variance is strongly influenced by congestion. Our estimates of ζ generally tend to be mostly highly posi-tive (in seven of twelve cases), and sometimes negative (in three of twelve cases). In some cases the resultsare insignificant. The case of the Oak Street Bridge southbound is particularly interesting because it char-acterizes transition from urban (signal) traffic to freeway traffic, so inflow to the bridge is throttled by thesignal phases. This results in the coefficient of variation being essentially constant. Where we see relativeunimpeded traffic flow, such as on the Alex Fraser Bridge, the variance also does not seem to increase withcongestion. The variances effect kicks in much stronger in the cases where some amount of queuing takesplaces (northbound traffic on Oak Street, the Massey Tunnel, but also on the Second Narrows Bridge thathas strong on-ramp traffic merging onto it.There are three key takeaways from this section. First, variance matters—a lot. Second, variance appearsto increase with congestion when traffic has strong “bottleneck” features, while the coefficient of variation70Table 3.8: Estimation Results Bridge & Tunnel TrafficRoute AFB-N AFB-S OSB-N OSB-SLanes¸ 3 3 2 2Speed Limit [km/h]¸ 90 90 60 60Max. Speed [km/h]¸ 108 111 88 91Road Capacity¸ 5982 5982 3678 3678Constant (Mean Eq.)¸ −1.633c (158.) −1.648c (147.) −1.650c (361.) −1.719c (384.)Congestion Effect¸ 0.669c (57.1) 0.692c (44.7) 1.010c (171.) 0.777c (89.3)Initial Speed [km/h]¸ 90.355c (593.) 93.080c (553.) 73.820c (1359) 77.166c (1470)Constant (Var. Eq.)¸ −1.607c (43.7) −1.644c (43.0) −2.933c (124.) −2.958c (107.)Congestion Effect¸ −0.450c (8.96) −0.078 (1.39) 0.718c (32.4) −0.095 (1.74)Initial Tρ¸ 0.471c (49.3) 0.462c (47.6) 0.234c (82.3) 0.231c (70.2)Observations¸ 3,550 3,550 8,635 8,635AIC¸ 3487.46 4098.71 4256.52 -1382.5Route GMT-N GMT-S SNB-N SNB-SLanes¸ 2 2 3 3Speed Limit [km/h]¸ 80 80 70 70Max. Speed [km/h]¸ 103 102 101 99Road Capacity¸ 3906 3906 5706 5706Constant (Mean Eq.)¸ −1.515c (265.) −1.707c (320.) −1.683c (254.) −1.646c (247.)Congestion Effect¸ 0.581c (51.0) 0.710c (73.0) 0.841c (76.6) 0.778c (74.1)Initial Speed [km/h]¸ 84.437c (971.) 86.339c (1221) 85.176c (963.) 82.995c (928.)Constant (Var. Eq.)¸ −2.657c (98.8) −2.823c (103.) −2.321c (83.1) −2.381c (85.3)Congestion Effect¸ 0.918c (24.5) 0.815c (22.5) 1.227c (43.2) 1.090c (37.6)Initial Tρ¸ 0.270c (71.8) 0.247c (70.8) 0.321c (68.2) 0.311c (68.5)Observations¸ 5,821 5,821 7,560 7,560AIC¸ 3839.87 2741.97 11339.3 9904.03Route GMT-N GMT-S LGB-N LGB-SLanes¸ 3 3 2 2Speed Limit [km/h]¸ 80 80 60 60Max. Speed [km/h]¸ 102 95 67 50Road Capacity¸ 5859 5859 3678 3678Constant (Mean Eq.)¸ −1.759c (86.0) −1.731c (44.7) −0.541c (18.8) −1.361c (146.)Congestion Effect¸ 0.896c (48.1) 0.764c (26.8) −0.352c (14.9) 0.344c (49.6)Initial Speed [km/h]¸ 87.014c (333.) 80.712c (172.) 42.340c (94.7) 39.798c (526.)Constant (Var. Eq.)¸ −2.289c (23.7) −1.072c (9.06) −1.478c (16.4) −3.221c (57.1)Congestion Effect¸ 0.730c (10.6) −0.480c (4.95) −0.386c (5.02) 0.250c (8.35)Initial Tρ¸ 0.327c (19.7) 0.639c (14.3) 0.506c (19.8) 0.202c (34.8)Observations¸ 1,090 1,456 1,456 1,074AIC¸ 1606.55 1769.55 1387.28 -78.424Note: Statistical significance at the 95%, 99%, and 99.9% level of confidence is indicated by superscriptsa, b and c, respectively. Standard errors are clustered for the 2,000 commutes. Numbers in brackets aret-statistics.71remains relatively flat when congestion is less driven by merging traffic and queueing effects. Third, whenvariance and mean both increase with congestion, the variance effect intensifies the mean effect becauseof the right-skewed shape of the log-normal distribution. This in turn matters for reliability calculations:schedule-sensitive drivers will avoid the roads that are getting excessively unpredictable and in tendencyfavour alternative routes that trade-off more reliability against slower speed. This is one of the two topicsthat we explore more deeply in our next section, which simulates route choice.3.6 SimulationThe purpose of our simulation exercise is to explore competing routes where commuters can choose amongtwo options that differ in terms of volume, speed, and dispersion characteristics. As commuters can chooseroutes, this problem is inherently more difficult to describe algebraically and instead is best addressedthrough simulation. We have at the minimum two distributions to draw from randomly, and this makesanalytic solutions very difficult if not impossible to obtain. To focus on the essence of our model we simu-late a simple two-road system. The framework we use can be used easily for more complex networks, butby focusing on two competing routes we are able to better identify the sorting effect between flexible andinflexible commuters. Our two routes can be envisioned either as two separated lanes of the same highway(the “Lexus Lane” model), but they can also be envisioned as the choice between two transportation modes(public transit and cars). Our analysis is applicable to either type of interpretation.The interpretation of our analysis as a transportation mode choice requires some modification, however.A car-owning commuter only decides between competing routes. A commuter choosing between competingtransportation modes will take the difference in transportation cost into account, which includes the variablecost of an individual trip as well as the levelized fixed cost of the transportation mode. If ownership of acar is treated as a sunk cost, the decision at the margin compares fuel cost against transit fare. In MetroVancouver, transit fares are divided into three zones ($2.95, $4.20, $5.70, respectively, for a single trip). Atypical 13.5km commute by car in Vancouver would cost about $2.00-$2.50, depending on the fuel efficiencyof the vehicle and the price of gasoline. In most instances, the car will be the cheaper option at the margin.However, the difference in cost is negligible in comparison to the time cost difference, and we thus focus onthis alone in our simulation for route choice. We capture the cost trade-off by focusing on the asymmetry inthe route choice—slower but more reliable versus faster but more volatile—and using identical tolls on bothroutes: identical per-trip prices regardless of commuting mode.3.6.1 Simulation ConfigurationOur simulation explores two scenarios that characterize the effect of reliability on commuting.• Two symmetric roads with one road tolled. This configuration mirrors the ‘Lexus lane’ approachstudied by Hall (2018b). We are exploring how introducing a toll on one of two routes will improvethe allocation efficiency by sorting inflexible and flexible commuters.• Two asymmetric roads with both roads tolled. With this configuration we are interested in thetrade-off between a slower but more predictable route (or mode) and a faster but more volatile route72(or mode). One of the routes has a significantly higher Tρ than the other (double). Even without a toll,commuters sort themselves so that inflexible commuters prefer the slower but safer route (or mode)over the alternative. However, how much more sorting is induced by tolling?The two scenarios allow us to determine how route choice is affected by policy (congestion pricing) andby self-sorting based on route characteristics. The two scenarios are parameterized as shown in table 3.9.We refer to the two competing routes as ‘A’ and ‘B’, where route ‘A’ is the tolled road in the ‘Lexus Lane’scenario, and the slow-but-certain route in the ‘Asymmetry’ scenario.Table 3.9: Simulation Scenario Parametrization‘Lexus Lane’ ‘Asymmetry’(Toll: A) (Toll: Both)Parameter Symbol Unit A B A BLane Capacity c [vehicles/hr] 2200 2200 2200 2200Minimum Travel Time T ◦ [min] 15 15 18 12Initial Average Travel Time T [min] 20 20 23 17Congestivity ξ [–] 0.50 0.50 0.50 0.50Coefficient of variation Tρ [–] 0.25 0.25 0.20 0.40Table 3.10: Simulation Scope ParametrizationHigh Medium LowParameter Symbol (H) (M) (L)Share of Inflexible Commuters α 0.8 0.6 0.4Schedule Inflexibility ψ 250 100 40Time Cost Ratio ϕ 1.25 1.00 0.80For the time cost distribution we employ Canadian census data that identifies the individual incomein the Metro Vancouver region as CAD 44,700 and CAD 33,600 for mean and median, respectively, inthe year 2016. Following Small and Verhoef (2007), we assume that time cost is 50% of income. Basedon OECD estimates17 of 1,706 average annual hours actually worked per worker for Canada in 2016 wedetermine a mean and median time cost of $13.10/h and $9.85, which we transform through the momentsof the lognormal distribution into µ = ln(median)= 2.0894 and σ =√2ln(mean/median)= 0.75567. Inaccordance with the theoretical consideration, the cutoff time T∅i that determines the cutoff cost throughthe mean time cost ω¯ so that zi = ω¯T∅i is drawn from an extreme value type I (Gumbel) distribution. Wecalibrate this distribution by choosing a mean and median of 50 and 47 minutes, respectively.18In table 3.10 we define the base parameterizations for our simulation. We explore our three key parameters–the share of inflexible commuters, the schedule inflexibility, and the time cost ratio—at three levels thatcharacterize the low end, mid range, and high end of plausible parameterizations.For the share of inflexible commuters (α) we argue that during the morning rush hour it likely exceeds50% and think that 60% is a conservative estimate, but allow for a 40% and 80% alternatives. We thus have17OECD.Stat time data table ANHRS.18See details in the mathematical appendix.73a bracketing of 20% between steps. For the degree of inflexibility we assume that a ψ of 100 (being late towork 2-3 times per work year) is a reasonable standard, but also allow for a stricter level (once per year) anda weaker level (once every 8 weeks). There is a ratio of 2.5:1 between each of the two steps for ψ . For thetime cost difference between the two commuter groups we start with a neutral assumption of 1:1, and allowfor a 25% deviation in either direction.We thus have 3×3×3=27 cases that we explore. For each of these 27 scenarios we begin by dispatchingall commuters to fill up both routes, which provides our baseline against which we compare the results froman optimal toll. We explore two optimal tolls: the full-information optimal toll that takes schedule delaycost of the inflexible commuters into account, and the limited-information (sub-)optimal toll that only takesobservable driving time into consideration. For ease of reference, we call them ‘optimal’ and ‘classic’ tolls.Where we need to distinguish between the two, we denote these outcomes with an asterisk (∗) or a bullet (•)superscript. We describe the algorithm for computing the toll optimum below. Once we have computed thetwo toll optima, we are interested in a number of different outcomes:(a) the schedule delay premium A , expressed as a percentage, when everyone commutes (no toll);(b) the optimal toll τ;(c) the percentage share pi of flexible commuters who decide to commute (with 1− pi the share of non-commuters;(d) the utilization rates of both routes, v˜A and v˜B, as a percentage;(e) the percentage share of inflexible commuters who prefer the tolled or slow-but-certain route φ IA and thepercentage share flexible commuters who prefer the untolled or fast-but-volatile route φFB ;(f) the cost savings ∆C achieved through the toll as a percentage reduction over the no-toll case.Additionally, we will also explore distributional outcomes that we define further below.3.6.2 Optimal Toll AlgorithmWe have implemented our simulations both in C++ and Python code in order to cross-verify our simulationmethodology. This dual implementation strategy has reassured us that our algorithm is reliable. We use themore-efficient C++ code for our high-replication results. Our optimal toll algorithm consists of five steps:1. assign random time cost ωi and cutoff cost zi to each commuter (and in the expanded version, alsodraw a random schedule inflexibility ψi);2. dispatch all commuters sequentially, letting them choose optimal routes conditional on current levels;3. reoptimize route choices until the choices of all commuters are stable;4. find the optimal toll through golden section search (GSS)19 using a cost function that includes com-muting time including schedule delay, but excludes tolls (as they are rebated uniformly per capita).Each search step consists of assigning a new toll level, reoptimizing the route choices, and calculatingthe cost function; and5. find the ‘classic’ toll in the same way using a cost function that only includes travel time.We are able to speed up the simulation runs by computing in advance the travel times, or the key partsthereof, that correspond to each of the discrete capacity utilization points for each route. This means that19We choose this method because it is robust even when the cost function is not smooth.74we can rely on inexpensive additions and multiplications to compute final travel and commute times, ratherthan computing power functions and square roots. This simple trick allows us to run between 30 and 70simulations per second in our C++ code.3.6.3 Results: Single and Dual Toll ScenariosThe first aim of our simulation exercise is the characterization of optimal tolls in the presence of distinctcommuter groups (flexible and inflexible) with different time costs, and where the degree of inflexibility(the reliability standard) of the inflexible commuters may vary. Tables 3.11 and 3.12 present the results ofour simulation for the ‘Lexus Lane’ and ‘Asymmetry’ scenarios, respectively, where we interpret the secondscenario also as as a potential mode choice. Both tables show the results of the average of 1,000 simulationruns.Table 3.11: Simulation Results: ‘Lexus Lanes’ ScenarioParameters Optimal Toll Classic Tollα ψ ϕ A τ pi v˜A v˜B φ IA φFB ∆C τ pi ∆CL L L 11.21 1.19 81.3 77.9 90.8 60.0 65.2 −2.69 1.00 81.7 −2.64L L M 12.78 1.32 80.7 76.7 91.3 66.3 71.4 −3.36 1.05 81.3 −3.26L L H 14.37 1.46 79.8 75.2 91.8 72.1 77.6 −4.23 1.12 80.8 −4.06L M L 14.38 1.31 81.0 77.4 91.0 63.0 68.1 −3.02 1.03 81.6 −2.90L M M 16.40 1.45 80.3 76.1 91.5 69.1 74.3 −3.81 1.07 81.2 −3.61L M H 18.46 1.61 79.4 74.5 92.0 74.6 80.4 −4.82 1.15 80.7 −4.52L H L 17.66 1.44 80.7 76.8 91.2 65.6 70.7 −3.40 1.05 81.5 −3.20L H M 20.13 1.59 79.9 75.4 91.7 71.5 76.9 −4.30 1.10 81.1 −3.97L H H 22.64 1.77 78.9 73.7 92.3 76.7 82.9 −5.43 1.18 80.6 −4.96M L L 18.00 1.61 78.8 80.9 92.9 56.1 71.6 −3.71 1.36 79.3 −3.64M L M 19.61 1.84 77.6 79.8 93.2 60.0 80.8 −4.59 1.52 78.5 −4.48M L H 21.11 2.12 76.4 78.5 93.5 63.2 88.8 −5.61 1.72 77.6 −5.47M M L 23.09 1.79 78.2 80.4 93.0 58.0 75.9 −4.18 1.44 79.0 −4.05M M M 25.17 2.06 77.1 79.2 93.3 61.6 84.7 −5.18 1.60 78.3 −4.99M M H 27.08 2.37 75.8 78.0 93.6 64.3 91.9 −6.29 1.83 77.3 −6.06M H L 28.33 2.01 77.7 79.9 93.2 59.6 79.8 −4.68 1.51 78.9 −4.47M H M 30.87 2.31 76.5 78.6 93.5 62.8 88.0 −5.78 1.68 78.1 −5.46M H H 33.26 2.65 75.4 77.5 93.8 65.2 94.4 −6.94 1.94 77.2 −6.60H L L 26.11 2.11 74.6 85.5 94.9 52.3 78.9 −4.67 1.91 75.2 −4.64H L M 27.20 2.45 73.2 84.8 95.0 53.8 89.1 −5.44 2.19 74.0 −5.39H L H 28.15 2.78 72.3 84.4 95.1 54.8 95.7 −6.11 2.53 73.0 −6.07H M L 33.51 2.38 74.0 85.2 94.9 53.1 83.9 −5.17 2.07 74.8 −5.11H M M 34.91 2.76 72.7 84.6 95.1 54.3 92.7 −5.92 2.39 73.7 −5.85H M H 36.12 3.13 71.9 84.2 95.1 55.0 97.6 −6.57 2.78 72.8 −6.51H H L 41.12 2.67 73.4 84.9 95.0 53.7 88.1 −5.65 2.23 74.5 −5.54H H M 42.85 3.05 72.4 84.4 95.1 54.7 95.2 −6.41 2.58 73.5 −6.30H H H 44.34 3.49 71.7 84.1 95.2 55.1 98.6 −6.99 3.04 72.7 −6.91Note: Initial schedule delay cost markup A in percent. Optimal toll τ in dollars. Flexible com-muters commuting pi in percent. Route utilization rates v˜ in percent. Share of commuter types Iand F taking routes A and B in percent. Cost savings over baseline ∆C in percent. Average of1,000 simulation runs.75Table 3.12: Simulation Results: ‘Asymmetry’ ScenarioParameters Optimal Toll Classic Tollα ψ ϕ A τ pi v˜A v˜B φ IA φFB ∆C τ pi ∆CL L L 7.33 3.92 70.1 76.0 79.9 100. 100. −5.35 3.92 70.1 −5.35L L M 8.35 3.51 70.1 76.0 79.9 100. 100. −5.16 3.51 70.1 −5.16L L H 9.39 3.14 70.1 76.0 79.9 100. 100. −4.96 3.14 70.1 −4.96L M L 9.39 3.92 70.1 76.0 79.9 100. 100. −5.39 3.92 70.1 −5.39L M M 10.70 3.51 70.1 76.0 79.9 100. 100. −5.18 3.51 70.1 −5.18L M H 12.04 3.14 70.1 76.0 79.9 100. 100. −5.01 3.14 70.1 −5.01L H L 11.54 3.92 70.1 76.0 79.9 100. 100. −5.40 3.92 70.1 −5.40L H M 13.15 3.51 70.1 76.0 79.9 100. 100. −5.22 3.51 70.1 −5.22L H H 14.79 3.14 70.1 76.0 79.9 100. 100. −5.05 3.14 70.1 −5.05M L L 15.98 5.84 57.1 79.4 78.0 69.7 100. −9.73 5.23 61.3 −9.57M L M 17.28 5.70 53.3 77.8 76.8 68.2 100. −11.04 5.05 58.5 −10.83M L H 20.04 5.57 49.1 75.9 75.4 66.6 100. −12.41 4.85 55.5 −12.13M M L 22.35 6.17 55.3 80.3 75.8 70.4 100. −10.99 5.32 61.2 −10.69M M M 25.17 6.02 51.2 78.6 74.3 69.0 100. −12.41 5.09 58.6 −11.99M M H 27.77 5.89 46.6 76.8 72.6 67.4 100. −13.96 4.92 55.5 −13.45M H L 29.54 6.48 53.4 80.9 73.6 71.0 100. −12.17 5.33 61.4 −11.62M H M 32.99 6.34 49.0 79.3 71.9 69.6 100. −13.73 5.13 58.7 −13.05M H H 35.96 6.19 44.2 77.5 70.1 68.0 100. −15.44 4.95 55.6 −14.64H L L 28.36 9.02 31.8 83.1 81.0 54.6 100. −13.23 7.37 42.9 −12.76H L M 29.96 9.03 25.4 81.7 79.9 53.8 100. −14.75 7.26 37.8 −14.23H L H 31.35 9.11 18.9 80.4 78.8 52.9 100. −16.31 7.19 32.0 −15.78H M L 37.42 9.63 28.4 83.7 79.1 55.1 100. −14.80 7.47 42.7 −14.04H M M 39.47 9.69 21.9 82.5 77.9 54.2 100. −16.43 7.35 37.5 −15.63H M H 41.22 9.81 15.5 81.2 76.7 53.4 100. −18.03 7.28 31.7 −17.22H H L 47.08 10.23 25.2 84.2 77.3 55.4 100. −16.20 7.53 42.6 −15.11H H M 49.57 10.31 18.6 83.1 76.0 54.7 100. −17.94 7.41 37.4 −16.80H H H 51.74 10.54 12.5 82.0 74.8 53.9 100. −19.62 7.32 31.7 −18.49Note: Initial schedule delay cost markup A in percent. Optimal toll τ in dollars. Flexible commuterscommuting pi in percent. Route utilization rates v˜ in percent. Share of commuter types I and F takingroutes A and B in percent. Cost savings over baseline ∆C in percent. Average of 1,000 simulation runs.Both tables characterize 27 scenarios of combinations of the α , ψ , and ϕ parameters defined in table 3.10as low (L), medium (M) and high (H). We consider the MMM scenario as our baseline—but we do not havedata to reliably identify any of the three parameters.The column presenting the A measure reveals the empirical importance of the schedule delay cost.When all vehicles are dispatched (no toll), the extra time due to schedule delay ranges from about 13% inthe LLL scenario to abut 46% in the HHH scenario in table 3.11 and about 7% to 52% in table 3.12. Onaverage, our model suggests that schedule delays add about 27% cost to inflexible commuters. For a 20-minutes driving time, schedule delay adds another 5–6 minutes. It is immediately apparent thatA increaseswith all three parameters: a larger share of inflexible commuters, higher degree of inflexibility, and highertime cost of inflexible commuters all increase the economic importance of schedule delay.The full-information optimal toll (‘Optimal’ in both tables) is characterized in both tables with dollarfigures. In the single-toll case they range from $1.19 to $3.49, a significant range in relative terms (2.9:1).76The toll induces a number of flexible drivers to cease commuting, and thus the share of flexible commuterswho continue to commute (pi) varies between about 72% and 81%. A drop of traffic volume of up to 30%due to tolls is perfectly within the range of what has been found in practice. As the costA of schedule delayincreases, so does the toll, which in turn reduces pi . The tolls that our model finds look quite reasonable interms of magnitude.It may surprise at first glance that the utilization rate of roads is increasing when A goes up, but notethat as α goes up, the share pi applies to a smaller cohort of commuters. So in the HHL scenario route Awill get utilized much more than in scenario LLH. What is clearly apparent, though, is that route A alwayshas a lower utilization rate of route B, a direct result of the toll. This wedge in utilization makes route Afaster than route B, allowing sorting of high-value commuters and low-value commuters. This result agreeswith Small and Yan (2001) and Verhoef and Small (2004) who address that commuter heterogeneity playsan important role for such “Lexus Lane tolling” to work. The beneficial effect of tolling comes both fromreducing demand (a scale effect) and from sorting commuters (a composition effect). This becomes evenclearer when we turn to the question which commuter takes which route. Without tolling, commuters ofboth types are perfectly indifferent between taking route A and B and we start with a 50:50 mix. Tollingensures that a higher fraction of inflexible commuters takes the tolled route A, and more flexible commuterstake the untolled route B. This sorting effort is strongest, unsurprisingly, win the HHH scenario.The column ∆C shows the cost savings of the tolled equilibrium over the untolled equilibrium. Theoverall cost savings that we find from tolling range from about 3% to 7%. They are highest in our MHH andHHH scenarios: inflexibility is pronounced and inflexible commuters have higher time cost than flexiblecommuters. Our cost measure assumes that all toll revenue is returned in full to commuters.The limited-information optimal toll (‘classic’ in both tables) where the social planner sets the tollbased on observable driving time, but where commuters choose route based on their full information aboutschedule delay, shows some rather important features that have strong implications for policy design. Thedemand response from the ‘classic’ toll (identified by the magnitude of pi) is rather similar to the full-information optimal toll case. So even though the classic toll is always a bit too small and thus the inducedscale (demand) effect is a little less, the cost savings (∆C ) are quite comparable to the full-information case.The conclusion is thus that even the suboptimal toll induces a sufficiently strong sorting effect that generatesmost of the gains for commuters. In other words, even when schedule delay costs are large, incompleteinformation about them does not result in hugely inefficient tolls.We now turn to the dual-toll case where the routes are highly asymmetric. Recall that route A is slowbut predictable, and route B is fast but unpredictable. We make route A 6 minutes slower than route B (23versus 17 minutes), but also make route A twice as reliable as route B by choosing appropriate Tρ values.Table 3.12 shows the results. We now find that much higher tolls are needed to get the desired sortingeffect. For our low-α scenarios we find perfect sorting: inflexible commuters take route A, and flexiblecommuters take route B. All the gains come from the demand (scale) effect, as the dual toll has a neutralsorting effect. The self-sorting for the flexible types remains in place throughout our range of parameters.Flexible commuters always prefer the faster route. However, as the toll increases, an increasing numberof low-time-cost inflexible commuters chooses to switch from A to B because route B is now less busy.77The tolls that we compute cover again a wide range, and because they tend to be significantly higher thanin our first scenario, the demand response is much stronger. When schedule delay costs are high, the tollstrongly favours policies that benefit the group of inflexible commuters and starves off commutes fromflexible commuters.We note again a key result with respect to cost savings (∆C ): there is hardly any difference between the‘optimal’ and ‘classic’ tolls, which suggests again that the beneficial effect from tolls with respect to sortingis induced very effectively even when the toll level is suboptimal. While perfect sorting occurs for the low-αscenario, classic and optimal toll are actually the same because the tolls do not induce any sorting. Onlywhen the share of inflexible commuters is large enough to allow additional sorting, do we see a gap openingbetween classic and optimal tolls.Our Asymmetry scenario generates welfare gains from a demand effect, rather than through sorting. Thecommuters are already self-sorting because of the asymmetry in road conditions, and thus there is not muchthat can be gained from differential tolls. One key insight therefore is that asymmetric tolling is useful whenroad conditions are similar, while symmetric tolling is useful when road conditions are dissimilar.The results in table 3.12 can also be interpreted as mode choice: flexible commuters commute by car,and most inflexible commuters prefer the (slower but more reliable) train. As the toll rises, some of theinflexible commuters also commute by car because now the traffic density on route B decreases sufficientlyto make this route fast enough to remain competitive for inflexible commuters with low time cost. Tollingincreases the use of the reliable but slower route A and at the same time reduces congestion on the faster butvolatile route B.What we have gained from comparing our two scenarios is one key insight: optimal tolling inducessorting (composition) and demand (scale) effects. When conditions are similar across routes, the benefitsfrom tolling arrive more from the sorting effect and required tolls tend to be low. When conditions aredissimilar across routes with a strong negative correlation of reliability and speed, then larger tolls areneeded to induce a stronger demand respond to relieve congestion because the heterogeneous commutergroups self-select into the optimal routes already—it isn’t necessary to create the selection effect artificially.3.6.4 Distributional Outcomes and FairnessThe distributional outcome of mobility pricing have received much attention because perceived unfairnessof such a pricing scheme is perhaps the most formidable obstacle to its implementation (Eliasson, 2016).We pursue two strategies to characterize the distributional outcome. The first method looks at the netgains of different commuter groups relative to our baseline no-toll scenario for the commuters in each offive groups:1. Inflexible commuters taking (tolled or slow-but certain) route A, W IA.2. Inflexible commuters taking (untolled or fast-but-volatile) route B, W IB.3. Flexible commuters taking (tolled or slow-but certain) route A, W FA .4. Flexible commuters taking (untolled or fast-but-volatile) route B, W FB .5. Flexible commuters who are not commuting because the commuting cost exceeds their cutoff cost,W F∅ .78Table 3.13: Distributional Outcomes: ‘Lexus Lanes’ ScenarioParameters Optimal Toll Classic Tollα ψ ϕ SI◦ R W IA WIB WFA WFB WF∅ SI R WIA WIB WFA WFB WF∅ SIL L L 45.9 122 93 10 1 18 116 44.2 104 89 12 9 19 101 44.5L L M 46.9 133 121 5 −9 21 123 45.0 108 114 9 4 22 103 45.4L L H 48.1 144 156 −2 −21 25 130 45.8 114 145 6 −2 26 107 46.3L M L 45.8 133 110 8 −3 20 126 44.1 107 103 12 9 21 103 44.4L M M 47.0 145 143 2 −15 24 133 44.9 110 131 9 4 25 105 45.4L M H 48.3 158 183 −6 −30 29 140 45.8 117 167 6 −2 29 109 46.5L H L 45.8 145 129 6 −8 23 135 43.9 109 118 12 9 24 105 44.4L H M 47.1 158 168 −1 −22 27 143 44.9 113 149 9 4 27 107 45.5L H H 48.6 172 213 −11 −39 32 150 45.9 120 189 6 −2 32 112 46.7M L L 46.9 171 114 22 −5 34 159 44.8 147 111 24 6 33 139 45.1M L M 48.0 193 146 20 −19 46 173 45.6 162 143 24 −2 44 150 46.0M L H 49.1 219 183 17 −38 64 190 46.3 181 180 23 −13 59 163 46.7M M L 46.9 189 134 22 −12 41 173 44.6 155 130 25 5 39 146 45.0M M M 48.1 214 171 19 −29 56 189 45.5 171 166 25 −3 52 157 46.0M M H 49.2 243 212 16 −50 78 209 46.2 193 207 25 −15 69 173 46.8M H L 46.9 211 156 22 −20 49 189 44.4 162 149 27 5 45 152 45.0M H M 48.2 238 197 19 −40 68 208 45.4 179 188 27 −3 60 164 46.1M H H 49.4 270 240 15 −64 95 230 46.2 205 234 28 −16 81 184 47.0H L L 48.3 238 139 44 −12 62 214 45.7 216 139 44 −1 60 197 45.9H L M 49.0 274 173 49 −30 91 240 46.2 246 174 50 −15 86 220 46.5H L H 49.7 309 207 54 −48 129 269 46.7 283 208 55 −32 121 250 46.9H M L 48.3 267 162 48 −21 78 237 45.5 234 162 49 −4 73 212 45.8H M M 49.1 307 198 54 −42 113 267 46.1 268 199 55 −20 104 239 46.5H M H 49.8 347 233 59 −62 160 302 46.7 310 235 61 −39 146 275 47.0H H L 48.2 298 186 53 −31 96 261 45.3 252 186 54 −7 88 227 45.8H H M 49.2 338 225 59 −51 138 294 46.0 290 225 61 −23 124 258 46.5H H H 49.9 386 259 66 −76 194 338 46.6 339 262 68 −46 174 303 47.0Note: Suits Index (SI), with superscript ◦ for baseline; average annual rebate (R); welfare gain (W ) forinflexible (I) and flexible (F) commuters taking routes A and B, or not commuting (∅). Optimal toll: fullinformation; classic toll: limited information. Average of 1,000 simulation runs. See appendix table B.3for corresponding measures of average time cost by commuter group.These five groups are strongly sorted by time costs. The commuters with the highest time cost prefer totake the tolled route, while the commuters with the lowest time cost prefer to take the untolled route. TheW metrics are scaled up to 250 commutes per year in order to capture the annualized dollar value of thechanges in welfare. A positive W represents a gain over the untolled scenario, and a negative W representsa loss over the untolled scenario.In order to calculate distributional effects, we need to make a specific assumption about how the revenuefrom the tolls are recycled. We assume that all commuters receive an equal share of the toll revenue.20Our second approach follows a familiar approach for investigating the regressivity or progressivity oftax policies, the Suits index. This method is also used in Ke and Gkritza (2018), who apply this measure to20It would be easy to explore alternative assumptions such as not returning revenue to commuters, or only returning a fraction ofrevenue to commuters.79Table 3.14: Distributional Outcomes: ‘Asymmetric’ ScenarioParameters Optimal Toll Classic Tollα ψ ϕ SI◦ R W IA WIB WFA WFB WF∅ SI R WIA WIB WFA WFB WF∅ SIL L L 45.8 805 −119 0 0 35 651 38.2 805 −119 0 0 35 651 38.2L L M 46.7 721 −94 0 0 32 583 39.7 721 −94 0 0 32 583 39.7L L H 47.8 644 −70 0 0 29 521 41.2 644 −70 0 0 29 521 41.2L M L 45.8 805 −114 0 0 36 651 38.3 805 −114 0 0 36 651 38.3L M M 46.8 720 −89 0 0 32 583 39.8 720 −89 0 0 32 583 39.8L M H 47.9 644 −63 0 0 29 521 41.4 644 −63 0 0 29 521 41.4L H L 45.8 805 −109 0 0 35 652 38.4 805 −109 0 0 35 652 38.4L H M 46.9 720 −82 0 0 32 582 40.0 720 −82 0 0 32 582 40.0L H H 48.1 644 −57 0 0 29 521 41.7 644 −57 0 0 29 521 41.7M L L 47.1 1,209 178 −19 0 −103 749 37.5 1,104 180 3 0 −68 724 38.2M L M 48.4 1,159 268 −8 0 −125 683 38.8 1,052 261 21 0 −82 664 39.5M L H 49.6 1,109 311 138 0 −150 619 40.0 997 301 172 0 −95 604 40.8M M L 47.1 1,266 192 109 0 −121 758 37.4 1,123 198 128 0 −69 729 38.3M M M 48.6 1,212 250 220 0 −146 689 38.8 1,063 250 245 0 −81 666 39.8M M H 49.9 1,159 325 333 0 −174 622 40.0 1,010 317 368 0 −96 607 41.1M H L 47.0 1,318 192 287 0 −141 764 37.3 1,127 204 297 0 −68 729 38.5M H M 48.6 1,261 251 426 0 −170 693 38.7 1,071 258 441 0 −81 667 40.0M H H 50.1 1,203 341 550 0 −200 622 40.0 1,018 337 582 0 −95 606 41.4H L L 48.4 1,948 214 120 0 −134 1,103 37.0 1,632 234 160 0 −58 986 38.1H L M 49.3 1,922 279 183 0 −173 1,062 38.1 1,589 301 232 0 −80 929 39.3H L H 50.0 1,908 358 252 0 −216 1,042 39.0 1,554 383 314 0 −106 881 40.3H M L 48.3 2,063 240 207 0 −163 1,143 36.9 1,653 270 250 0 −58 989 38.4H M M 49.3 2,044 311 286 0 −208 1,113 38.0 1,608 344 341 0 −82 932 39.6H M H 50.1 2,038 392 372 0 −255 1,106 39.0 1,570 430 445 0 −108 882 40.6H H L 48.3 2,174 259 306 0 −196 1,187 36.8 1,667 300 349 0 −60 991 38.6H H M 49.4 2,158 334 405 0 −245 1,164 38.0 1,620 380 463 0 −83 931 39.8H H H 50.2 2,174 416 509 0 −299 1,185 39.0 1,580 474 592 0 −109 883 40.9Note: Suits Index (SI), with superscript ◦ for baseline; average annual rebate (R); welfare gain (W ) for inflexible (I)and flexible (F) commuters taking routes A and B, or not commuting (∅). Average of 1,000 simulation runs. Seeappendix table B.4 for corresponding measures of average time cost by commuter group.data from Oregon. The Suits index (scaled up by 100 for easier use) is calculated asSI = 100[1− 12∑i[T (yi)−T (yi−1)](yi− yi−1)]∈ [−100,+100] (3.53)where yi is the cumulative share of income, which we proxy for by the time cost ωi, and the correspondingcumulative time cost T (yi). Also, y0 = 0 and T (0) = 0. The Suits Index is negative when the policy isregressive, and positive when the policy is progressive. We find that in all our simulations the Suits Index ispositive: the cost of commuting is progressive—time is more valuable to high-income earners.The results of our analysis are reported in tables 3.13 and 3.14. We compare the Suits Index in thebaseline scenario S◦ against the corresponding outcomes for the ‘optimal’ and ‘classic’ tolls, and we reportthe five W statistics for both types of tolls.80So who gains, and who loses? As a reference point, it is useful to report the average rebate (R in thetables) from the tolls, which is necessarily considerably more in the ’asymmetry’ case than the ’Lexus lane’case because both routes are tolled. This amount is redistributed among the various commuter groups sothat on average nobody gains or loses because our setup mandates that all toll revenue goes back to allcommuters. Consider the baseline case in table 3.13. The average commuter pays $215 in tolls and getsjust as much back in rebates, for a net zero gain. However, the different commuter groups fare differently.The affluent inflexible commuters who pay the toll and take route A tend to gain much more than the lessaffluent inflexible commuters who end up taking the untolled route. The toll-induced sorting effect benefitsthem the most. In some cases, especially when the overall proportion of inflexible commuters is small, theless affluent group of inflexible commuters ends up with net losses in some cases. The mid-affluent flexiblecommuters who take the tolled route A tends to lose as well, while the less affluent commuters who stay onroute B gain slightly—but this group is large. The most affluent flexible commuters will cease commuting,and thus their gains tend to be the highest because they benefit from the rebate the most as their losses areconstrained by their cutoff time (reservation cost). The picture for the ‘classic’ toll case is qualitativelysimilar, although the magnitudes are somewhat smaller.The Suits Index summarizes the total distributional effect: there is a small drop in progressivity of thecost of commuting, typically not more than a few percentage points. In other words, tolling does not radicallychange the distributional outcomes in table 3.13. However, the picture in table 3.14 for the ‘asymmetry’case reveals a different picture as the Suits Index drops about up to 10 percentage points. Tolling reducesthe progressivity of commuting costs much more noticeably.The results in the Asymmetry scenario in table 3.14 differ in some important ways from those in ta-ble 3.13. When the share of inflexible commuters is low, this group stands to lose, but when their share ishigh, they gain significantly regardless of which route they take. Tolling clearly benefits the inflexible com-muters, and it also benefits the flexible commuters with high time cost who cease commuting. Who paysfor it are the large number of flexible commuters who all take route B and pay the full toll, but increasinglyshare their route with the less affluent inflexible commuters. Note that in table 3.14 there are many zeros,which is because there are no travellers under such category, for example, no flexible travellers will evertake the slower but more reliable route A.If we interpret the Asymmetry scenario as a mode choice problem, then the inflexible commuters whoneed to get to work are the ones that gain as long as they are the majority of commuters. Then the tollingsystem works in their favour. The flexible commuters who can choose to commute or not will gain if theyare induced to stay home and lose if they still commute. That does not seem such an unfair outcome atfirst because it shifts the burden from the inflexible commuters (who need to get to work) to the flexiblecommuters (who could perhaps delay their trips). The only caveat is that the burden falls disproportionatelyon the less affluent flexible commuters with the lowest time value. This is what shows in the large drop ofthe Suits Index.813.6.5 Correlation Structure of Time Costs with Inflexibility and Non-CommutesOur baseline simulation explored variations in the time cost and inflexibility in a limited fashion by consid-ering high, medium, and low scenarios for the time cost ratio ϕ of inflexible to flexible commuters, and thedegree of inflexibility of the former group. We kept the decision about non-commutes “neutral” by keepingthe distribution of the cutoff time for non-commutes, T∅i , uncorrelated with the time cost ωi.The correlation between time cost and cutoff cost has not been explored systematically. We use oursimulation to vary the correlation of time cost with inflexibility, ρω,ψ and the correlation of time cost withcutoff cost, ρω,z systematically between −1 and +1. We use 51 steps of 0.04, and thus 2,601 points in thespace spanned by the two correlation coefficients. We use 100 replications for each correlation point, for atotal of 260,100 simulations, and average over these replications. We illustrate our results in contour plotsfor four key variables: the optimal toll, the share of flexible commuters commuting, the cost savings, andthe change in the Suits Index.Figure 3.17: Simulation Results: Correlation StructurePanel A Panel B−1−.8−.6−.4−.20.2.4.6.81Time Cost − Inflexibility Correlation (ρ ω,ψ)−1 −.8 −.6 −.4 −.2 0 .2 .4 .6 .8 1Time Cost − Cutoff Time Correlation (ρω,z)1.522.533.544.555.56Optimal toll (τ) in dollars−1−.8−.6−.4−.20.2.4.6.81Time Cost − Inflexibility Correlation (ρ ω,ψ)−1 −.8 −.6 −.4 −.2 0 .2 .4 .6 .8 1Time Cost − Cutoff Time Correlation (ρω,z)707274767880828486889092Commuting demand (pi) in percentPanel C Panel D−1−.8−.6−.4−.20.2.4.6.81Time Cost − Inflexibility Correlation (ρ ω,ψ)−1 −.8 −.6 −.4 −.2 0 .2 .4 .6 .8 1Time Cost − Cutoff Time Correlation (ρω,z)−8−7.5−7−6.5−6−5.5−5−4.5−4Cost savings due to toll (∆C) in percent−1−.8−.6−.4−.20.2.4.6.81Time Cost − Inflexibility Correlation (ρ ω,ψ)−1 −.8 −.6 −.4 −.2 0 .2 .4 .6 .8 1Time Cost − Cutoff Time Correlation (ρω,z)−6−5.5−5−4.5−4−3.5−3−2.5−2Change in Suits Index of Progressivity82Figure 3.17 summarizes our results. Panel A shows the optimal toll τ; panel B shows the commutingdemand pi of flexible commuters; panel C shows the cost savings ∆C from baseline (non-tolled) to optimal(tolled) scenario; and panel D shows the change in the Suits Index between baseline (non-tolled) and optimal(tolled) scenario. The four quadrants in each chart identify the four combinations of positive and negativecorrelations. If we had data on the distributions for our individual commuters we could pin down a singlepoint in each diagram. By exploring the entire feasible range we hope to gain a better understanding howmuch these correlations matter.Overall, the correlation ρω,z of time cost with reservation price (cutoff time) for the flexible commutersis the dominant influence, which is visible in the strong vertical patterns in panels A and B for the optimaltoll and demand response. The correlation ρω,ψ of time cost with the degree of inflexibility of inflexiblecommuters matters much less in general.For the optimal toll, the influence of a strong positive correlation between time cost and cutoff time isvisible in Panel A in figure 3.17. When affluent flexible commuters also have high cutoff costs, tolls needto be higher. Consider the extreme case of perfect positive correlation when zi = ωiT¯∅ and all flexiblecommuters have the same cutoff time for their trips. To induce commuters to stay at home, ever higher tollsare needed to get a demand respond. If there is no (i.e., zero) correlation, on the other hand, this means thatcommuters simply have a reservation price for each trip that is independent of their income and time cost.In that case, tolls are just about half of what is needed as when ρω,z approaches perfect positive correlation.Panel B corresponds to this and shows clearly that higher ρω,z correlation generates less and less of a demandresponse.Panels C and D in figure 3.17 explore the welfare implications of the correlation structure. Panel Cshows the cost reduction ∆C when going from no toll to optimal toll. The cost savings range from about4 percent in the negative/negative quadrant to to over 7 percent in the positive/positive quadrant. Here, thecorrelation structure of ρω,ψ between time cost and schedule inflexibility comes into play much stronger, asthe cost function is strongly influenced by the size of ψ .Panel D shows the change in progressivity (∆SI) as captured by the change in the Suits Index whengoing from no toll to optimal toll. The pattern in panel D is quite similar to the pattern in panel C. Thesmallest changes to the progressivity of congestion occur again in the negative/negative quadrant, and thelargest changes in the positive/positive quadrant. The economic logic of what we find in panels C and Dis closely tied to the need to have higher tolls when the correlation coefficients increase to get the desiredoutcome.The main conclusion of our correlation structure analysis is that it matters significantly. In order todesign effective policy, we need to know more than just averages of the time cost, inflexibility, and reserva-tion prices. Effective mobility pricing requires knowledge of the distribution of time cost, inflexibility, andreservation prices, as well as the two correlations. Based on what we found in panel A for the optimal toll,if we had incorrectly assumed zero correlations when in fact we had strong positive correlations, tolls wouldbe much too low.833.7 Caveats and ExtensionsThis empirical work in this paper explores commuting patterns in the Metro Vancouver region and demon-strated the importance of schedule delay costs. We have been able to quantify this importance, and ourresults also emphasize the importance to allow for congestion effects on the variance of commuting time.But there are important limitations on our results, and these limitations lay out an agenda for future empiricalwork in this area.Our traffic data focuses on vehicle commutes. While this is a significant part of the overall commutes, itdoes not account for public transit and other forms of transportation. Work on road tolls has often sufferedfrom an exclusive focus on road traffic without being able to quantify the substitution effects. In order toaddress commuting reliability, we need to know the entire choice set of commuters. An obvious extensionof the work in this paper would be to investigate the reliability of public transit commuters where they areavailable. Where are there margins of substitutions?The biggest caveat of our empirical work is that we know little about the commuters making theirmorning commutes. We do not know which part is truly inflexible, having to get to work, and whichpart is flexible, being able to delay or cancel trips. We also do not know the degree of inflexibility—thereliability standard that inflexible commuters adhere to. While we are able to make reasonable and plausibleassumptions about this standard (a big improvement over guessing parameters in the α-β -γ model), we donot know the distribution of this measure ψ and how it is correlated with income or time cost ω . We also donot know how the reservation price (cutoff time) for flexible commuters is distributed and could be correlatedwith time cost ω . Our research shines a bright light on these gaps in our knowledge. Future empiricalwork, especially stated preference work, needs to explore these distributions and their correlation structurerigorously. Our work yields a better understanding of what to ask individual commuters in surveys,21 gainingdeeper insights into the crucial distributions of ω , ψ , and z, and the composition α of commuters.With respect to designing road tolls and their distributional outcomes, our work highlights the impor-tance of pinning down the aforementioned distributions. Almost inevitably, road tolls generate benefits tosome commuters and losses to other commuters. Our work shows clearly that these gains and losses de-pend not only on the heterogeneity of the commuters, but also on the heterogeneity of road conditions (andcompeting mode choices). If anything, our work suggests that the frontier of transportation research lies inmicroeconomic studies of individual commuting behaviour. The literature on mobility pricing has come farin demonstrating that such pricing is hugely beneficial—and London, Singapore, and Stockholm show thatthis is not just a theoretical point. However, to overcome resistance to adopting mobility pricing especiallyin North America, we need to gain a better understanding of the distributional outcomes region-wide and inthe presence of greater limitations on mode choice.A major caveat in some of our theoretical and empirical work is the lack of allowing for variation acrossdeparture times. We focus on morning commutes, but as our data from Metro Vancouver shows, congestionfollows a well-established pattern around a peak. Tolls that vary by time of day are the obvious answer to this21Lo et al. (2006) has surveyed for the risk averse parameter λ in their paper, which is a similar measure to our reliability standardψ . We would like to conduct similar surveys and ask individuals their expected frequency of being late, which would be even moreintuitive.84issue. We do not explore the mix of commuters that are at different points of their journey and the resultingdynamics. However, we duly note that variation around departure times will also change the compositionof commuters: our key variables α , ψ , ϕ , and the various correlations associated with ω , ψ , and z areall time dependent. An obvious extension of our work would involve exploring the dynamics effects ofcomposition changes. If the composition changes, the tolls need to change accordingly. Even if (untolled)traffic volume were constant over time, the optimal toll could still change over time if the composition ofcommuters changes.We acknowledge other important caveats of our approach. We assume in our optimal-toll simulationthat motorists and toll-setters have full information on traffic conditions and commuter preferences (timecost, schedule inflexibility). Research work such as Lindsey (2009) and Boyles et al. (2010) explores howinformation asymmetry between motorists and toll-setters can affect the traffic outcome. Lindsey (2009)showed in theory that with uncertain capacity, tolls could be justified for optimal capacity only if tolls areset using information no less than drivers have. Boyles et al. (2010) discussed how optimal tolling schemecan be designed for cases where travelers have either full information on traffic network or only know theprobability distributions, and tolls being static or could response to realized traffic. We acknowledge theexistence of information asymmetry by exploring a classic (limited information) toll scheme in comparisonto the full information optimal toll. We still allow for motorists to gain full information about the distributionmoments of traffic flow.3.8 ConclusionsWhen commuters plan their work-daily trips, a significant share of them needs to allow for additional buffertime to ensure that they arrive on time for work. This means that they need to take the dispersion of theircommuting time into account. Just how large is the cost that is added to commutes as a result of this scheduledelay? How much does the existence of this additional schedule delay affect optimal road tolling? If policymakers do not take this extra cost into consideration, will policies based on incomplete information aboutthe true commuting time turn out to be significantly suboptimal?The literature on congestion pricing has long acknowledged the importance of commuter heterogeneity.This paper deviates from the conventional assumption of schedule delay costs and replaces this with a traveltime reliability standard that introduces an explicit metric of schedule inflexibility. This metric provides foran economically intuitive relationship between the standard deviation of travel time and the total travel timethat allows sufficient buffer time upon arrival to meet the reliability standard. The notion of a reliabilitystandard has several advantages. It allows us to employ two empirical distributions of travel time—Fre´chetand log-normal—and link a measure of schedule inflexibility with the time mark-up on driving time. Thissetup also lends itself very effectively to empirical work we conduct in our paper. The reliability standardleads to a linearization technique that disaggregates the time mark-up factor into two separate components:a route-specific coefficient of variation, and a multiplier that reflects the schedule inflexibility. This decom-position technique allows us to model commuting time reliability very succinctly and derive new theoreticalinsights about optimal road tolls.Empirically, our paper explores three separate avenues. First, we have assembled data from real-time85Google traffic data to determine commuting time across a sample of 2,000 commutes across the Metro Van-couver region over a 10-week period. Second, we have also used such data to measure speeds at numerouscongestion points in the region: high-traffic bridges and tunnels. The latter we are able to link to trafficvolume measurements that allow us to infer speed-volume relationships and dispersions. Third, we usesimulation techniques to infer the effect of route characteristics on optimal tolling, and the effect of tolls ondistributional outcomes.Our analysis of region-wide commuting patterns provides an estimate of the economic importance ofschedule delay cost, which we put at about 13% as our preferred estimate and an upper bound of 30%.The overall importance of schedule delay costs depends significantly on the share of inflexible commuters,which we are unable to ascertain. We also find evidence for a speed-reliability tradeoff: alternate routes areslower but less risky.Analysis of our bridge traffic data through multiplicative heteroskedastic linear regression reveals thatthe variance of crossing time is related to the level of congestion, and not just the mean crossing time.However, while we find a strong positive congestion effect on variance for several bridges, there are some forwhich this pattern does not hold because of idiosyncracies in traffic management or differences in networktopology. Overall, we believe that our results reinforce the notion that the second-order effect of congestionon the variance of travel time is important and in previous contributions to the literature has almost alwaysbeen ignored.Our simulation explores route choice under two different scenarios: one where two roads are symmetricbut only one is tolled, and another one where two roads are asymmetric (one road is slower but more reliable)but both are tolled. Optimal tolls induce both a scale (demand) effect and a composition (sorting) effect.When route conditions are similar, even low-ish tolls can generate significant benefits from inducing sorting.When route conditions are dissimilar and are negatively correlated in terms of speed and reliability (whichhas similarities to transportation mode choice), we find that most of the traction comes from the demandresponse and little additional sorting.We also investigate the welfare effects by studying who would gain and lose from a toll. Commutingcosts are strongly progressive, and we find that tolls have a benign effect and tend to reduce progressiv-ity as captured by the Suits Index. Overall, inflexible commuters stand to gain the most along with theflexible commuters induced to stay home, based on the notion that toll revenue is distributed equally to allcommuters.Our simulation study also sheds light on the use of a limited-information optimal toll in comparison to afull-information optimal toll. The limited-information case involves information asymmetry between com-muters and social planner, where the social planner only observes driving time and determines an optimaltoll without taking schedule delay into consideration, while commuters use their full private information todetermine route choice. We find, surprisingly, that an imperfect toll is not as bad as feared. In our ‘LexusLane’ scenario even a toll that is somewhat too low will induce a strong sorting effect that will benefit com-muters almost as much as the perfect full-information toll. In the asymmetric route case, the full-informationtoll does generate benefits, but they are small in magnitude. These results are encouraging news: mobilitypricing does not have to be perfect as long as it induces a fair bit of sorting.86Our paper makes several novel contributions. We introduce the notion of a reliability standard as aviable and practical alternative to conventional α-β -γ cost models. Our modelling allows us to take thedispersion of commuting time into consideration directly, and it provides for a straight-forward extensionof theoretical modelling of optimal tolls. The simplicity of our linearization approach makes this tool veryuseful for future work in this area. Our empirical work based on Metro Vancouver commutes shows clearlythat dispersion matters, and we can put forward plausible estimates of the extra cost added by reliabilityconsiderations. Our congestion points analysis allows us to estimate key characteristics of the speed-volumerelationship in the presence of dispersion. Simulation results also demonstrate that reliability considerationscan lead to strong self sorting of commuters across routes, and that optimal congestion prices don’t needto be perfect to achieve the desired outcome. Even limited-information tolls can generate beneficial sortingeffectively.Our research also suggests how future stated preference studies can better identify commuting behaviourfor empirical work: we need to ask commuters whether (or how many) trips are flexible or inflexible, andhow important it is to arrive on time. Asking people about how often they can afford to be late is muchmore intuitive than asking them about the cost of being late or arriving early, which most commuters willbe unable to quantify. In order to gauge demand, it is also easier to ask flexible commuters at what durationthey would rather not make a trip in order to gauge the distribution of cutoff times. Importantly, our researchdemonstrates the importance of the correlation of time cost with the measure of inflexibility (for inflexiblecommuters) and cutoff cost (for flexible commuters).We conclude our paper with two policy recommendations. First, to better understand the welfare im-plications of mobility pricing, we need to study commuter heterogeneity better. Our paper has concretesuggestions about the questions we need to ask commuters in order to determine their type, inflexibility,and demand response. Second, policy makers need to address commuting reliability by providing options(e.g., rapid public transit that is immune to road congestion) or by allowing commuters to self-sort throughprices. In addition to tackling congestion in urban cores (e.g., as is proposed for Manhattan), turning High-Occupancy Vehicle (HOV) lanes into High-Occupancy Toll Lanes (HOT) lanes is probably among the mostpractical options in North America.87Chapter 4Carbon Emission Disclosure andInstitutional Ownership4.1 IntroductionWith a growing attention on the global warming issue, legislation gradually emphasizes limiting the emissionamount of greenhouse gas (GHG). Carbon pricing mechanisms have been well established and implemented,including cap-and-trade programs and carbon tax systems. Besides these legislation that explicitly sets aprice on carbon emission, non-pricing mechanisms also came into being to motivate companies to reduceGHG emission, among which carbon reporting mechanism is one good example. Mandatory emissionreporting mechanisms such as US EPA’s greenhouse gas inventory track emission from individual facilitiesand suppliers of certain fossil fuels and industrial gases. This study focuses on a voluntary carbon emissiondisclosure program initiated by a global non-for-profit organization — Carbon Disclosure Project (CDP).The objective of CDP is to raise more public attention towards big companies’ environmental impact andto motivate companies to reduce their emission. CDP sends its annual report to more than 767 institutionalinvestors such as mutual funds, banks, insurance companies, etc., and it hopes that institutional investorswould take into account companies’ carbon footprints when they make investment decisions. If institutionalinvestors, upon receiving CDP reports, actually modify their portfolio to invest more on carbon efficientcompanies, firms might take actions to gradually reduce their emission. In CDP’s news reports, it claimedthat companies that did a better job in disclosing carbon emission information to CDP experienced a superiorfinancial return, compared to the companies that do not disclose, or those disclose limited information. Thecausal relationship between voluntary carbon emission disclosure and firms’ financial success, however, isdubious, because such correlation could be driven by many other forces. For example, if cautious managersare more likely to disclose their carbon emission and also more capable to bring profit to their firms, thenthe financial success would not be caused merely by the carbon emission disclosure behavior.The questions asked are: (1) whether higher institutional ownership ratio induce stronger incentive toparticipate in such voluntary disclosure program, and (2) whether such disclosure cause a greater share ofinstitutional ownership. The reasons to focus on institutional ownership are as follows. First, institutional88investors have more expertise in analyzing stock performance and hold a relatively stable number of shares,as a result, it is generally better for a company to have higher institutional ownership ratio. Therefore insti-tutional ownership is an indicator of firms’ financial success, and provides implication whether disclosing isa signal of better future financial performance. Second, since CDP devotes to inform institutional investorsabout large companies’ carbon emission information, it makes sense to analyze whether the disclosed in-formation affects companies’ institutional ownership. Third, Kim and Lyon (2011) studied the relationshipbetween CDP disclosure and stock price, and found no evidence suggesting participation in CDP wouldincrease share prices. They further inferred that participation in CDP was not entirely voluntary but dueto pressure from shareholders, regulators, and the institutional investors involved in the CDP. Their workprovided a motivation to analyze institutional investors’ responses to CDP disclosure reports.In order to answer the two questions, this study builds a simultaneous equations model which capturesthe feature that both institutional ownership and CDP participation are endogenously determined and couldaffect each other. The results show that within US S&P 500 companies, (1) higher institutional ownershipratio lead to less disclosure to CDP, and (2) disclosure to CDP cause lower institutional ownership ratio.4.2 Theoretical Framework4.2.1 Motivation of Voluntary Carbon DisclosureVoluntary disclosure of carbon emission information can be costly. First, by disclosing such information,the company might lose its green consumers or green investors if its performance does not meet their ex-pectations. Second, the company might be giving away its production information to its competitors, sincecarbon emission is highly correlated with production activities. Third, the company seems to commit itselfto maintain its carbon emission level near its currently disclosed emission amount, by making the gestureto participate in the CDP program. Why do some companies still disclose to CDP voluntarily, consideringsuch unnecessary costs? Do the disclosing companies really have superiority in carbon efficiency, or do theydo so mainly due to shareholder pressure?Lyon and Maxwell (2004) provided several candidate models to unveil the true motivation for firms toconduct voluntary environmental activities. First, this effort might be taken to attract green consumers orgreen investors. If this motivation dominates, firms’ altruistic environmental activities should be followedby their financial success either due to more profit raised from green consumers or more favored capitalinvestment from green investors. Second, this could be a strategic behavior to preempt the regulation makersabout the future environmental standard to be set for the industry. After firms indicate their current emissionlevel, it will become a benchmark when future regulations are designed. If firms claim that their efforts tovoluntarily reduce emission involve major capital investment, this sunk cost would become firms’ bargainingpower to persuade the regulation makers to loosen the environmental standard that was planned to be set.In this case, such voluntary environmental activities might not be associated with superior environmentalperformance or financial success. In one of their later studies, Lyon and Maxwell (2011) indicate that firmsengage in more self-regulation when they perceive a greater threat of government regulation. They focusedin firms’ disclosure behavior in US Department of Energy’s Voluntary Greenhouse Gas Registry and their89actual emission. This program allows firms to choose to report emission amount at aggregate level or atproject level. Empirical results show that participants in this program engage in highly selective reporting— the participants actually increase total emission during the reporting period while they report reductionper project, however non-participants decrease aggregate emission over time.Reid and Toffel (2009) verified the hypothesis that firms voluntarily disclose environmental informationdue to shareholder pressure using CDP data. More specifically, firms will be more likely to participate inCDP if it is targeted by a shareholder resolution on related topics such as environmental disclosure or climatechange. They also found that firms subject to greater regulatory threats will be more likely to participate inCDP.4.2.2 Impact of Voluntary Carbon DisclosureAnother question to ask is what impact will follow after a company discloses its carbon emission informationto the public. The positive effect of carbon disclosure is to increase the company’s transparency to thepublic, therefore reducing its long term risk in case of future regulation towards carbon emission changes.Meanwhile, the actual investment to reduce carbon emission might be against the company’s objectiveof maximizing shareholders’ value. Therefore the financial impact of voluntary carbon disclosure can beambiguous.On one hand, a related literature investigates the relationship between firms’ social responsibility (CSR)and their financial performance, including stock return and institutional ownership, and suggests that suchvoluntary environmental activities benefit companies’ financial performance. CSR counts for companies’ re-sponsibility to the stakeholders in many aspects, including environment protection. Heiner (1983) suggestedthat institutional investors are more capable than individual investors to assimilate and act upon informationabout socially responsible corporate practices. Graves and Waddock (1994) found a positive relationshipbetween a company’s CSR and the number of institutions holding the company’s shares, yet the relationshipbetween CSR and the percentage of shares owned by institutions is not statistically significant. Taking onestep ahead, Cox et al. (2004) discovered that long-term institutional investment (defined by the shares heldby pension funds, life insurance companies, etc.) is positively related to CSR. They concluded that CSRcan be viewed as a significant determinant of firm exposure to long-term risks, therefore CSR can affectlong-term investors’ portfolio choice decision.On the other hand, some studies suggest that voluntary carbon reduction activity leads to negative fi-nancial impact. Fisher-Vanden and Thorburn (2011) assert that corporations that commit to reduce GHGemission appear to be more likely to experience negative stock return, based on an empirical test regard-ing companies announcing membership in EPA’s Climate Leaders. Jacobs et al. (2010) also found thatannouncements of voluntary emission reductions are associated with significant negative market reaction.4.2.3 Relationship between Voluntary Carbon Disclosure and Institutional OwnershipResponding to CDP is not mandatory, therefore firms will evaluate their benefits and potential risks whendeciding to disclose their carbon emission information. As explained above, firms’ decision to voluntarilydisclose their carbon emission, as a managerial strategy, and firms’ institutional ownership, as one aspect of90financial performance, can affect each other simultaneously.Firms’ disclosure in carbon emission might cause change in its institutional investors’ holding volumeand hence its institutional ownership. Such voluntary environmental activity could affect companies’ futurefinancial performance because it reveals information to its investors. If investors take such voluntary disclo-sure activity as a good signal that the company is confident about its carbon emission amount and thus facingless financial risk in case of future regulation change, they would be more likely to appreciate such disclo-sure behavior. However, the reverse consequence might arise if either of the following situations happen.First, heavy emitters in the past could easily reduce its emission intensity and pick the low-hanging fruit,however the companies that have always been making investment to maintain low level of carbon emissionface more difficulties to further reduce their emission intensity. Second, heavy emitters might have moreincentive to preempt policy makers to loosen emission restriction level before any legislation is finalized,therefore they could be more likely to disclose to CDP. If such adverse selection phenomenon indeed existsand is recognized by the investors, the financial impact of voluntary disclosure could be negative. Besides, ifdisclosing firms are exposed to higher regulation risk, the disclosure behavior might also imply future finan-cial burden from investors’ perspective. Since CDP sends its annual reports to more than 767 institutionalinvestors which manage assets of more than US$ 92 trillion, a natural question to ask is whether institutionalinvestors of the S&P 500 companies react to whether they disclose to CDP. The reason that this study limitswithin S&P 500 companies is that CDP currently only sends out questionnaires to the biggest companiesaround the world, therefore within all US companies only S&P 500 companies are surveyed.Meanwhile, institutional ownership could also affect firms’ disclosure decision. If the institutional in-vestors demand more transparent information about the companies’ environmental performance which mayor may not cause the firm future legislation risk, then we would expect higher institutional ownership leadsto greater probability of disclosure. If instead, the institutional investors communicate directly with the com-panies, requesting and analyzing their carbon emission amount, then the companies with high institutionalownership would be less willing to disclose such information.4.3 Model SpecificationAs described above, this study is mainly concerned with the relationship between companies’ decision involuntary disclosure of carbon emission information and their ratio of institutional ownership. To accountfor the endogeneity between the disclosure decision and institutional ownership, I formulate a simultaneousequations model and treat both of the variables as endogenous. Two equations are contained in this model,one explaining the impact of disclosure on institutional ownership ratio, the other one explaining the causalrelationship from the opposite direction. Instrumental variables are added in both equations to identify thetrue impact of the two endogenous variables. The model setup is as below.InstOwnit =β0+β1Disclit +β2IV1it +β3controls+year dummies+ industrydummies+uit(4.1)91Disclit =γ0+ γ1InstOwnit + γ2IV2it + γ3controls+year dummies+ industrydummies+ vit(4.2)The measure of the variable InstOwn (institutional ownership) and Discl (disclosure dummy) will bedefined in the next section. Equation (4.1) measures how the disclosure dummy variable influences thecompany’s institutional ownership, and equation (4.2) measures how different levels of institutional own-ership affect the likelihood that a company would participate in CDP’s voluntary disclosure program. Thissimultaneous equations model takes into account the endogeneity generated from reverse causal relation-ship, with both equations containing the endogenous variables on both sides. The variables IV1 and IV2serve as IVs for InstOwn and Discl correspondingly. In equation (4.1), the model assumes that Discl af-fects InstOwn, however InstOwn also influences Discl reversely, if firms with different levels of institutionalownership have various level of motivation to disclose to CDP. Adding an exogenous variable IV1 that onlycorrelates with InstOwn to the equation will minimize the reverse causality bias and helps identify the directimpact of Discl on InstOwn. The explanation for equation (4.2) is similar. The objective of equation (4.2)is to find out how institutional ownership ratio affects the decision to disclose to CDP, yet causality couldalso arise from the opposite direction. The exogenous variable IV2 only correlates with Discl, and adding itto equation (4.2) eliminates the reverse causality bias. Candidates for IVs will be discussed in the followingsection.4.3.1 Carbon Disclosure and Institutional Ownership MeasuresThe variable InstOwnit stands for stock i’s institutional ownership in year t, and institutional ownershipis defined by number of shares held by institutional investors divided by the total number of outstandingshares. The dummy variable Disclit equals 1 if company i chose to answer the questionnaire from CDP inyear t, and equals 0 otherwise. The data source will be discussed in Section 4.4.4.3.2 Instrumental and Control VariablesInstrumental variables need to be highly correlated with the regressors they serve as instruments for, butunrelated to the error terms in the equation those regressors are used.To select for an IV for Institutional Ownership, I use the conclusion from Falkenstein (1996) and Gom-pers and Metrick (2001) that institutional investors prefer stocks with better liquidity and higher stockprices. Therefore the IV chosen here is the share turnover (trading volume within a year/number of out-standing shares at the end of the year) and stock price at the end of each year. These two variables shouldbe exogenous to firm’s disclosure decision, since there is no clear link between firm’s stock liquidity andenvironmental performance or disclosure tradition.The IV for Disclosure is “state greenness”, which will be defined and justified in the following. Stategreenness is supposed to measure the environmental consciousness of the state that the company’s head-quarter locates in. The more one state cares about environmental sustainability, the more likely firms locat-92ing in that state would participate in such voluntary disclosure programs. However, where the company’sheadquarter locates should be independent of the company’s institutional ownership. To measure the stategreenness, I use the online searching frequency of “global warming” of each state from Google. Googlepublishes the regional searching frequency of popular phrases on Gtrend, which is publicly available. An-other IV used is firm’s clean energy strength which is a dummy variable taken from the KLD dataset. Iassume that firms known of using clean energy devote more to environment protection, therefore they couldbe more likely to disclose to the public about their carbon emission.The control variables that appear in both equations include accounting records such as firm size (mea-sured by company market value and number of employees), revenue (measured by annual sales), and finan-cial risk (leverage ratio, defined as total debt divided by total equity). Firms’ past environmental performanceand management skills could affect both the disclosure decision and institutional ownership, and therefore,should be controlled. As a candidate, corporate social responsibility (CSR) characterizes firms’ true envi-ronmental performance and management skills, however the data for some firms are missing. Therefore Irun regression models both with and without CSR data. In regression model 1, I include CSR data of: thenumber of environmental strengths, the number of environmental concerns, the number of corporate gover-nance strengths, and the number of corporate governance concerns. Regression model 2 does not includeCSR ratings in the control variables, and keeps all other variables the same as model 1.4.4 Data4.4.1 Carbon Disclosure ProjectCarbon Disclosure Project(CDP) is an international organization that sends out annual surveys to the biggestcompanies around the world to ask about their carbon emission information. Each year more than half com-panies respond to the questionnaires and provide details about their carbon emission generated from pro-duction process, energy use, or supply chain. From year 2006, CDP has gained attention from an increasingnumber of institutional investors who subscribe for CDPs annual report at no charge or pay an annual fee toachieve enhanced access to the dataset. The main difference of CDP compared to other disclosure programsare that (1) it includes global carbon emission of a company, not just within a single country, and (2) thisemission data is at company level instead of facility level, and involves companies from all industries insteadof merely the emission intensive ones.This study uses annual CDP reports containing US S&P 500 companies’ self-disclosed informationfrom year 2006 to 2013. In each year, every US S&P 500 company receives a questionnaire from CDP, andsome of them choose to respond to CDP voluntarily. CDP then compiles the annual report and makes thedata available to the public. Not only does CDP report the information provided by those companies whoanswered the questionnaire, it also lists out which companies failed to participate in this voluntary disclosureprogram. I use a disclosure dummy variable to indicate whether a company has replied to the questionnairein a specific year. The dummy variable equals 1 if the company disclosed its carbon emission informationto CDP in the referred year and it equals 0 otherwise.In addition to studying firms’ disclosure decision, I also investigated the disclosure quality and the ac-93tual carbon emission amount of those companies that gave back the questionnaire. In order to encouragethe companies to deliver high quality questionnaires, CDP assigns a disclosure score to each completedquestionnaire and highlights the companies with the highest scores. The more questions the company hasanswered in the questionnaire, the higher its disclosure score is. Moreover, companies can gain credit in dis-closure score if they manage to seek for external verification institution to verify their disclosed information.I use this disclosure score to proxy for companies’ disclosure quality. The actual emission amount data isused to calculate emission intensity which is defined by emission per employee. The emission accounted inthis study only includes emission generated from the actual production process but not that generated fromsupply chain, because the latter information is disclosed by only a few companies.4.4.2 Institutional OwnershipData of stock holding volume and stock price information all comes from Thompson Reuter database. Foreach stock, the database provides quarterly data of institutional ownership, share turnover, etc. Institutionalownership of a stock is defined by the total amount of stock held by institutional investors (such as banks,pension funds, charity funds, etc.) divided by the total number of outstanding shares. To create annual datafrom quarterly data, I use the fourth quarter’s data as a representation. Stock turnover is the total number oftransactions of a stock within one year divided by the number of outstanding shares at year end.4.4.3 Corporate Social ResponsibilityKinder, Lydenberg, Domini Research & Analytics (KLD) dataset provides annual rating of companies’ per-formance in environment, employee relationships, governance, etc., which are known as corporate socialresponsibility (CSR). The ratings come from a comprehensive research of firms’ financial statements, popu-lar press, government reports, etc., and the database is widely used by institutional investors and scholars toevaluate firms’ impact on the environment and stakeholders such as consumers, employees, communities,etc.This study mainly concerns with two aspects of CSR, environment and corporate governance. Whenfirms are making the decision of whether to voluntarily disclose their carbon emission information, whichis an environmental concern, their decisions are clearly depending on their true environmental performance.Also, management skills, which can be captured by KLD dataset’s corporate governance rating, influencesa company’s disclosure behavior in general.Each year, the KLD dataset gives a 1/0 score for firms strengths and concerns in some specific aspects.The involved categories include environmental strengths, environmental concerns, corporate governancestrengths, and corporate governance concerns.1 The data is available from year 1995 to 2012.The variables used in the regression model include: clean energy strength, transparency strength, number1 Environmental strengths include: a. environmental beneficial products and services; b. pollution prevention; c. recycling;d. clean energy; e. communications; f. property, plant, and equipment; g. others. Environmental concerns include: a. hazardouswaste; b. regulatory problems; c. ozone depleting chemicals; d. substantial emissions; e. agricultural chemicals; f. climate change;g. other concerns. Corporate governance strengths include: a. limited compensation; b. ownership strength; c. transparencystrength; d. political accountability strength; e. public policy strength; f. others. Corporate governance concerns include: a. highcompensation; b. ownership concern; c. accounting concern; d. transparency concern; e. political accountability concern; f. publicpolicy concern; g. governance structures controversies; h. others.94of environmental strengths other than clean energy, number of environmental concerns, number of corporategovernance strength other than transparency strength, and number of corporate governance concerns.4.4.4 Firms’ Accounting RecordsThe regression model controls for some of the firms’ financial and accounting characteristics such as firmsize, profitability, industry. This data comes from Compustat North America database. The variables usedin this study include number of employees, equity, market value, financial leverage ratio, global industrialcode (GIC), revenue, etc.Table 4.1 shows summary statistics and Table 4.2 shows cross correlations of the variables.Table 4.1: Summary statisticsVariable Mean Std. Dev. Min. Max. Ndisclosure 0.656 0.475 0 1 3300institutional ownership 0.787 0.178 0 1 4871state greenness 4.297 0.126 3.951 4.533 4363log share turnover 0.562 0.811 -6.977 3.334 4863clean energy strength 0.293 0.455 0 1 3517transparency strength 0.21 0.408 0 1 2918# environmental strengths 0.579 0.905 0 4 3517# environmental concerns 0.522 1.013 0 5 3574# corporate governance strengths 0.092 0.305 0 2 2918# corporate governance concerns 0.679 0.746 0 4 3574log employee number 2.827 1.449 -3.297 7.696 4467log market value 9.315 1.123 2.724 13.348 4108log financial leverage ratio 1.096 0.695 0.044 6.899 4394log sales 8.926 1.248 0.443 13.07 4517log stock price 3.551 0.967 -4.605 7.058 428695Table 4.2: Cross-correlation tableVariables (1) (2) (3) (4) (5) (6)disclosure Institutional state log share clean transparencyOwnership greeness turnover energy strength(1) disclosure 1.000(2) Inst. Ownership -0.113 1.000(0.000)(3) state greenness 0.063 -0.031 1.000(0.000) (0.041)(4) log share turnover -0.106 0.324 -0.014 1.000(0.000) (0.000) (0.376)(5) clean energy strength 0.282 -0.204 0.051 -0.162 1.000(0.000) (0.000) (0.004) (0.000)(6) transparency strength 0.246 -0.208 0.030 -0.181 0.474 1.000(0.000) (0.000) (0.115) (0.000) (0.000)4.5 Regression Results and DiscussionTable 4.3 exhibits the regression results of the model defined by Equation (4.1) and Equation (4.2).From Table 4.3, one can observe that both coefficients of disclosure dummy and institutional ownershipare negative and statistically significant, in both models. The results of model 1 directly reveals that: (1)controlling the other characteristics of a firm, it would have 6.82 percent points less institutional ownershipif it changed from not disclosing to disclosing to CDP, and (2) controlling the other characteristics, theprobability that a firm voluntarily discloses its carbon emission information would decrease by 8.83 percentpoints if its institutional ownership increased by 1 percent point. The coefficient given by model 2 is veryclose to that of model 1.An advantage of using simultaneous equations model is that one can learn the feedback effects of en-dogenous variables. When the institutional ownership percentage changes, the probability of disclosure willalso modify, which again leads to variations in institutional ownership. Taking this feedback effect into ac-count, the marginal effects of the two variables have on each other are different from the coefficients directlyread from the regression result table.Considering the feedback effects, the results indicates: (1) controlling the other characteristics of a firm,it would have 7.26 percent points less institutional ownership if it changed from not disclosing to disclosingto CDP, and (2) controlling the other characteristics, the probability that a firm voluntarily discloses itscarbon emission information would decrease by 9.40 percent points if its institutional ownership increasedby 1 percent point.Results show that higher institutional ownership does not lead to greater probability of disclosing. Thisfinding somehow contradicts the conjecture in the literature that firms might be voluntarily disclosing theircarbon emission information due to pressure from institutional investors (Kim and Lyon, 2011), althoughCDP is designed to share firms’ carbon emission information with institutional investors. One possiblereason that firms with higher institutional ownership tend to hide their carbon emission information from96Table 4.3: Simultaneous Equations ModelVARIABLES Model 1 Model 2Discl InstOwn Discl InstOwninstitutional ownership -0.883*** -0.882**(0.334) (0.310)state greenness 0.154** 0.227***(0.0759) (0.0694)clean energy strength 0.129*** 0.158***(0.0267) (0.0224)number of environmental concerns 0.00216 -0.00948***(0.0128) (0.00296)number of environmental strengths 0.0168 0.00219(0.0144) (0.00363)transparency strength 0.0858***(0.0268)number of corporate governance strengths -0.0380 0.00619(0.0331) (0.00773)number of corporate governance concern 0.0208 0.00530(0.0145) (0.00346)log employees 0.0107 0.00294 0.0124 0.00311(0.0151) (0.00361) (0.0130) (0.00314)log market value 0.0310 -0.0346*** 0.0199 -0.0335***(0.0195) (0.00480) (0.0182) (0.00476)log leverage ratio 0.0160 -0.00149 0.00589 -0.00162(0.0190) (0.00459) (0.0182) (0.00435)log sale 0.00512 -0.00438 -0.0073 -0.0069(0.0197) (0.00477) (0.0198) (0.0047)disclosure -0.0682** -0.0684**(0.0346) (0.0286)log share turnover 0.0526*** 0.0487***(0.00588) (0.0052)log stock price 0.0360*** 0.0363***(0.00434) (0.00399)Constant 0.0565 1.052*** -0.267 1.073***(0.578) (0.0371) (0.545) (0.0326)Observations 2,013 2,013 2487 2487R-squared 0.121 0.333 0.0987 0.3356Standard errors in parentheses2-digit industry FE, and year FE are included.*** p<0.01, ** p<0.05, * p<0.197the public could be that firms communicate directly with their institutional investors about every aspect oftheir business, therefore disclosing to the rest of the investors becomes less necessary.Another result demonstrates that more disclosure leads to lower institutional ownership, which means thedisclosure behavior is not appreciated by institutional investors. If firms’ disclosure behavior are not drivenby philanthropic environmentalism, but by the motivation to manipulate the standard of future regulationon GHG emission, then disclosure does not serve as a signal of greater possibility of financial successin this case, therefore would not attract more institutional investment. This type of motivation amplifiesin states where environmental regulations are generally stricter and are more likely to charge for GHGemissions in the future. That being the case, such regression result favors the perspective in existing literaturethat companies who disclose more details face stronger regulatory threat. The IV “state greenness” bringsvariation across different states, therefore distinct levels of state regulatory threat. If institutional investorsbelieve that disclosing firms will likely encounter unfavorable GHG regulation changes and incur financialburden, the phenomenon that voluntary carbon disclosure results in lower institutional ownership could beeasily understood.The relationship between institutional ownership with (1) disclosure quality (measured by the disclosurescore evaluated by CDP) and (2) emission intensity (emission from production process and energy usedivided by number of employees) is also examined using the same method — simultaneous equations model.The regression results are in Table 4.4 and Table 4.5. The results indicate that these relationships are notstatistically significant. Therefore no conclusion can be drawn to say that the level of institutional ownershipwould affect disclosure quality or actual emission intensity. This again strengthens the argument that suchvoluntary disclosure behavior might not be due to pressure coming from institutional investors, since higherinstitutional ownership ratio does not lead to better disclosure quality or lower emission intensity.Nevertheless, comparing Table 4.3, Table 4.4 and Table 4.5, one can find that firms with greater numberof environmental strengths tend to have better disclosure quality, and that firms with greater number ofenvironmental concerns have higher level of emission intensity. The observations in these two regressiononly include the firms that have responded to CDP. Therefore, although the voluntary disclosure activityinvolves self-selection, the disclosed information can still reveal the firms’ true environmental performance.4.6 ConclusionThis study looks at the causal relationship between firms’ decision in voluntarily disclosing its carbon emis-sion information to CDP, a global non-for-profit organization that collects biggest firms’ carbon emissiondata and publishes annual reports to make the data publicly available, and firms’ level of institutional own-ership. A simultaneous equations model is used to capture the endogenous characteristic of this question.The results show that the impact is negative and statistically significant, from both directions — the impactof disclosure on institutional ownership and the impact of institutional ownership on the probability of dis-closure. This suggests that disclosing firms might not be the most carbon efficient ones, but rather thosedisclosing with other motivations such as preempting the regulators, and they could be subject to higher reg-ulation risk. Therefore voluntary carbon disclosure mechanism such as CDP is sub-optimal in the attemptto unveil firms’ environmental footprints to the public. Considering this point, firms’ voluntary disclosure98to CDP can not serve as a positive signal of their greenness status or financial success potential. Mandatorymechanisms should be considered in the future to realize the objective of disclosing firms’ carbon footprintsand motivating them to take action to reduce emission. If disclosure is mandatory, the information releasedwould directly inform investors of firms’ environmental performance, and there would be no selection prob-lem in this case. Nevertheless, if investors want to learn some knowledge about firms’ true environmentalperformance from CDP reports, they can specifically inspect the firms’ self-disclosed emission amount andtheir disclosure quality, which is available only from the companies that chose to participate in CDP.This study still faces a lot of challenges, and the most important one being finding a stronger instrumentalvariable for the disclosure dummy variable. In cases where the companies’ headquarter location state affectsits institutional ownership, the IV would not be valid. This might happen if stocks of companies from somespecific states consistently show superior financial performance and are favored by institutional investors,or if more institutional investors are located in some states and they tend to invest in companies that arephysically close to them because of lower information costs.Another potential improvement of this research is to decompose institutional holding by various typesof institutional investors. For example, public investors might value more in corporate social responsibilityof the stocks they invest in, therefore more likely to invest in companies that are willing to disclose theirenvironmental performance. Moreover, some institutional investors, such as pension funds, may have longerinvestment horizon than the others that favor short-term appreciation in stocks. If better environmentalperformance requires higher operational cost in the short-term but brings cost-saving in the long-term, theninstitutional investors with longer investment horizon would value more for firms that disclose to CDP.As legislation changes, UK has launched a mandatory carbon reporting project and the legislation cameinto effect in October 2013. All quoted companies in the UK are subject to this new regulation. An inter-esting follow-up research could be conducted to discover this mandatory carbon reporting project and seewhether the companies that already participated in CDP emit more or less compared to the companies thatfailed to respond to CDP. A better idea of whether there is adverse selection problem in participation in CDPcan be elicited with the new data from the UK’s mandatory reports.99Table 4.4: Disclosure Quality and Institutional OwnershipVARIABLES disclosure quality institutional ownershipInstitutional Ownership -15.44(19.33)state greenness 2.305(5.116)clean energy strength 6.499***(1.589)number of environmental concerns 0.234 -0.0118***(0.788) (0.00393)number of environmental strengths 2.606*** 0.00377(0.853) (0.00604)transparency strength 3.866**(1.610)number of corporate governance strengths 0.494 0.0174*(2.025) (0.0105)number of corporate governance concerns -0.825 -0.00437(0.915) (0.00478)log employees 0.775 0.00404(0.984) (0.00513)log market value 2.180* -0.0287***(1.150) (0.00595)log leverage ratio 0.982 0.00103(1.135) (0.00610)log sale -2.017 -0.0105(1.292) (0.00677)disclosure score -0.00143(0.00100)log share turnover 0.0709***(0.00872)log stock price 0.0334***(0.00593)Constant 47.31 1.080***(34.65) (0.0619)Observations 994 994R-squared 0.197 0.384Standard errors in parentheses2-digit industry FE, and year FE are included.*** p<0.01, ** p<0.05, * p<0.1100Table 4.5: Emission Intensity and Institutional OwnershipVARIABLES emission intensity institutional ownershipinstitutional ownership -2.232(1.875)state greenness -0.202(0.505)clean energy strength 0.255*(0.149)number of environmental concerns 0.380*** -0.00193(0.0693) (0.0145)number of environmental strengths 0.0295 -0.00141(0.0769) (0.00515)transparency strength 0.0273(0.138)number of corporate governance strengths -0.191 0.00676(0.183) (0.0134)number of corporate governance concerns 0.0944 -0.00492(0.0888) (0.00657)log employees -0.790*** -0.0107(0.0956) (0.0285)log market value -0.0194 -0.0317***(0.114) (0.00786)log leverage ratio 0.0709 -0.00403(0.113) (0.00782)log sale 0.193 -0.00815(0.119) (0.0108)emission intensity -0.0160(0.0348)log share turnover 0.0726***(0.0107)log stock price 0.0303***(0.00892)Constant 5.953 1.107***(3.709) (0.103)Observations 717 717R-squared 0.536 0.453Standard errors in parentheses2-digit industry FE, and year FE are included.*** p<0.01, ** p<0.05, * p<0.1101Chapter 5ConclusionIn this dissertation, we investigate the efficiency of three existing or potential policies targeting on environ-mental or urban transportation issues.Chapter 2 suggests that in order to promote the adoption of electric vehicles (EVs), the governmentshould invest on building more public charging stations, in addition to providing cash incentives to individ-ual EV purchasers. Meanwhile, subsidies giving to luxurious EVs or affluent consumers could be cut down.Empirical results demonstrate that smaller EVs are more inelastic towards public charging stations thanlarger EVs, because of a greater possibility of exhausting their batteries during a trip. Larger EVs, on theother hand, are much more expensive and would be affordable by higher-income consumers. Empirical re-sults show that more affluent consumers are less price sensitive, meaning that some of them would purchaseluxurious EVs with or without subsidies. Therefore, sizing down subsidies to higher-income EV purchasersor to luxurious EVs while building more charging stations could contribute more to induce EV purchasing,meanwhile reducing the concern that potential buyers of luxurious EVs might free ride government subsidy.Chapter 3 characterizes the cost of travel time reliability and discusses the optimal tolling scheme thatconsiders for such cost. When commuters plan their work-daily trips, a significant share of them needs toallow for additional buffer time to ensure that they arrive on time for work. Deviating from the conventionalassumption of schedule delay costs, we propose a travel time reliability standard that introduces an explicitmetric of schedule inflexibility. This setup allows linearization technique that disaggregates the time mark-up factor into two separate components: a route-specific coefficient of variation, and a multiplier that reflectscommuter’s schedule inflexibility. This decomposition technique allows us to model commuting time relia-bility very succinctly and derive new theoretical insights about optimal road tolls. Empirical results indicatethat schedule delay cost is economically important and that both mean and variation of travel time increasewith congestion level. Our simulation explores route choice of a two-road system under two different sce-narios: (1) symmetric roads with one road being tolled, and (2) asymmetric roads with both being tolled.Optimal tolls induce both a scale (demand) effect and a composition (sorting) effect. When route conditionsare similar, even low-ish tolls can generate significant benefits from sorting. When route conditions aredissimilar and negatively correlated in speed and reliability, the most of the traction comes from the demandresponse and little additional sorting. Through a welfare analysis we find that tolling reduces progressivityof commuting cost.102Chapter 4 looks at the causal relationship between firms’ decision in voluntarily disclosing its carbonemission information and their level of institutional ownership. Although environmental performance doesnot directly indicate financial success, it might put companies at risk in case of policy change, such ascarbon tax. Institutional investors are more sophisticated and might account for such risk in their investingdecisions. Moreover, due to the larger share of stocks held by institutional investors, they might put pressureon companies to improve their environmental performance. To capture the endogenous characteristics of thisquestion (that comes from reverse causality), the study employs a simultaneous equations model. The resultsshow negative influence from both directions — the impact of disclosure on institutional ownership and theimpact of institutional ownership on the probability of disclosure. This suggests that disclosing firms mightnot be the most carbon efficient ones, but rather those disclosing with other motivations such as preemptingthe regulators, and they could be subject to higher regulation risk. Therefore voluntary carbon disclosuremechanism is sub-optimal in the attempt to unveil firms’ environmental footprints to the public. 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The intuition is that having a reliable charging spot saves the troublelooking for public chargers meanwhile largely reducing the risk of getting stranded.Proof of Proposition 2:To simplify the analysis, assume that time to find a slow charging station (with level I&II chargers)t1(SS,i j) and time to find a DC fast charging station t1(SF,i j) are both decreasing functions of total number ofcharging stations Si in this region, i.e.,∂ t1(SS,i j)∂Si< 0 and∂ t1(SF,i j)∂Si< 0. The probability of failure to finda public charging station is also assumed to be a decreasing function of Si, i.e.∂ fi j(SS,i j,SF,i j)∂Si< 0. Theinfluence of number of charging station having on EV operational cost is as below:∂ci j∂Si=(HC,BEV) : qi j[wiδR j∂ t1,F∂Si+(witsR j+ms)∂ fi j∂Si](HC,PHEV) : 0(NHC,BEV) :wimin(ri,R j)max(⌊δR j/ri⌋,1)∂ t1,S∂Si+wiqi jδR j∂ t1,F∂Si+(witsR j+ms)∂ fi j∂Si(NHC,PHEV) :wimin(ri,RPE, j)max(⌊RPE, j/ri⌋,1)∂ t1,S∂Si(A.1)From equation (A.1) it is easy to see that∂ci j∂Siis non-positive in every case, and that∂cNHC,BEV,i j∂Si<∂cHC,BEV,i j∂Si,∂cNHC,PHEV,i j∂Si<∂cHC,PHEV,i j∂Si, i.e.,∂ci j∂Sihas greater absolute value for non home owners inboth cases of BEV and PHEV. The intuition is that EV owners without home chargers rely more on public110chargers, whereas EV owners with access to home charging seldomly need to seek public chargers. There-fore adding public charging stations bring most benefit to those without opportunity of home charging.Proof of Proposition 3:To prove Proposition 3, one needs to calculate derivative of∂ci j∂Siregarding to R j. For home owners, onecan see:∂ 2ci j∂Si∂R j=∂qi j∂R j[wiδR j∂ t1,F∂Si+(witsR j+ms)∂ fi j∂Si]−qi j wiδR2j∂ t1,F∂Si−qi j witsR2j∂ fi j∂SiThe above term is positive because∂qi j∂R j< 0,∂ t1,F∂Si< 0,∂ fi j∂Si< 0, and all other parameters are positive.Similarly, for non home owners, this term would be:∂ 2ci j∂Si∂R j=− wig(R j)2g′(R j)∂ t1,S∂Si+∂qi j∂R j(wiδR j∂ t1,F∂Si)−qi j wiδR2j∂ t1,F∂Si− witsR2j∂ fi j∂Siwhere g(R j) = min(ri,R j)max(⌊δR j/ri⌋,1) and g′(R j) > 0, assuming fixed ri. Together with condition∂qi j∂R j< 0,∂ t1,S∂Si< 0,∂ t1,F∂Si< 0,∂ fi j∂Si< 0, and other parameters positive, one would reach conclusion thatthe term above is positive.Therefore, with or without access to home charging, a greater electric range would increase∂ci j∂Si, whiledecreasing its absolute value, i.e., the cost reduction effect brought by adding public charging stations de-crease with BEV’s electric range.Proof of Proposition 4:For BEV owners with home charging:∂ci j∂R j=∂qi j∂R j[wi(t1(SF)δR j+ t2, j + ri jtsR j)+ ri jms]−qi jwi( t1(SF)δR2j+ri jtsR2j)∂ 2ci j∂R j∂wi=∂qi j∂R j(t1(SF)δR j+ t2, j + ri jtsR j)−qi j( t1(SF)δR2j+ri jtsR2j)Since∂qi j∂R j< 0 and other parameters are all positive, it follows that∂ci j∂R j< 0 and∂ 2ci j∂R j∂wi< 0.For PHEV owners with home charging:∂ci j∂RPE, j= wi∂qi j∂RPE, j(t1(SG)δRPG, j+ t3, j)111∂ 2ci j∂RPE, j∂wi=∂qi j∂RPE, j(t1(SG)δRPG, j+ t3, j)With∂qi j∂RPE, j< 0, one can see∂ci j∂RPE, j< 0 and∂ 2ci j∂R j∂wi< 0.For BEV owners without home charging:∂ci j∂R j= wi[− t1(SS)g(R j)2g′(R j)+∂qi j∂R j(t1(SF)δR j+ t2, j)− (qi j t1(SF)δR2j+ ri jtsR2j)]∂ 2ci j∂R j∂wi=− t1(SS)g(R j)2g′(R j)+∂qi j∂R j(t1(SF)δR j+ t2, j)− (qi j t1(SF)δR2j+ ri jtsR2j)where g(R j) = min(ri,R j)max(⌊δR j/ri⌋,1). With∂qi j∂R j< 0 and g′(R j) > 0, one can see∂ci j∂RPE, j< 0and∂ 2ci j∂R j∂wi< 0.For PHEV owners without home charging:∂ci j∂RPE, j= wi[− t1(SS)gP(RPE, j)2g′P(RPE, j)+∂qi j∂RPE, j(t1(SG)δRPG, j+ t3, j)]∂ 2ci j∂RPE, j∂wi=− t1(SS)gP(RPE, j)2g′P(RPE, j)+∂qi j∂RPE, j(t1(SG)δRPG, j+ t3, j)where gP(RPE, j) = min(ri,RPE, j)max(⌊RPE, j/ri⌋,1). With∂qi j∂RPE, j< 0 and g′P(RPE, j) > 0, one can see∂ci j∂RPE, j< 0 and∂ 2ci j∂RPE, j∂wi< 0.Therefore, operational cost decreases with electric range, and such effect enlarges with wi — valuationof time. The intuition is that EVs with longer electric range need to be charged less frequently and havelower probability of getting stranded, thus reducing time cost of driving, and such characteristic would beappreciated more by people with higher valuation of time.A.2 Choice of Vehicles under Baseline ScenarioThe choices within BEVs, PHEVs, and ICE vehicles rely on trade-off between time cost and monetary cost,when price and vehicle attributes are the same. Using currently available car model attributes data listedin Table 1 and assuming distribution of peoples’ daily driving distance ri follows log normal distributionwith µi = 3.25, σ2i = 0.75, this section presents how the valuation of time can affect the operational cost ofBEVs, PHEVs, and ICEVs, thus flipping preference towards them.The vehicles in Table A.1 are divided to two groups, within each group the vehicles are deemed assubstitutes with similar price and amenity. The vehicles in the same group are assumed to differ only in theway they are refueled. The first group represents for energy efficient small vehicles which has one modelof ICEV, PHEV, BEV respectively, whereas the second group represents for luxurious vehicles which only112includes an ICEV and a BEV1.Table A.1: Characteristics of Representative EVsMake-Type price electric range gas range mi/kWh mi/gallon refuel timeToyota Prius $24,200 - 571 mi - 47.6 5 minChevrolet PHEV $25,185 38 mi 342 mi 2.9 37.1 5 minNissan BEV $22,065 84 mi - 3.3 - 30 minBMW 740i $74,000 464 mi 22.2 5 minTesla BEV $59,900 208 mi - 2.9 - 40 minPrices are MSRP deducting government tax incentives and tax rebates.Refuel time is time to fill up the gas tank (PHEVs); for BEV it is to charge 80% of its battery capacityunder DC fast charging. The time is a coarse estimate with unit being minutes.The cumulative distribution function of ri is shown in Figure A.1. With the currently popular EV fleets,Chevy PHEV’s electric range can satisfy about 60% of the daily trips. BEV models Nissan and Tesla ModelS’s electric range cover 90% and 99% of daily trips respectively.Figure A.1: Distribution of Daily Driven DistanceUsing baseline assumptions on density of public chargers, I draw graphs (as shown in Figure A.2) thatshow the impact of evaluation of time on vehicle choice, with cases differentiated by whether or not homecharging is available.1PHEVs are currently absent in the luxurious vehicle class113Figure A.2: Operational Cost of Small Vehicles(a) with home charging (b) without home chargingIn Figure A.3, I compare the operational cost of three popular small vehicle models: Nissan Leaf,Chevrolet Volt, and Toyota Prius, each representing categories of BEV, PHEV, and ICEV. With home charg-ing available, EV owners save time detouring for refueling, therefore EVs’ operational cost cuts lower thanICEVs. PHEVs superior in quickly refuel with gasoline after its battery drains therefore they are more fa-vored than BEVs for people with higher valuation of time. Without home charging, however, the time spenton looking for public charging stations hinders EV adoption, leaving ICEVs the dominant choice for peoplewith valuation of an hour higher than 5$.Figure A.3: Operational Cost of Large Vehicles(a) with home charging (b) without home chargingThis pair compares popular large vehicle models: Tesla Model S (BEV) and BMW 740i (ICEV). Lack-ing for a large PHEV model, I include the Chevrolet Volt (PHEV) as a comparison. As Tesla’s luxury carshave a long electric range that greatly reduce possibility of running out of battery, people with home charg-ing will always find Tesla’s operational cost lowest. For people without access to home charging, those whovalue an hour of time greater than 120$ will find BMW 740i, which serves as Tesla’s luxury counterpart,114occur lower operational cost.This section considers a baseline scenario where density of public charging stations is fixed and repre-sentative vehicle models from category of BEV, PHEV, and ICEV are compared. One can intuitively findthat EV range and accessibility to home charging can make a big difference on EV’s operational cost.115Appendix BAppendix for Chapter 3B.1 Glossary of Variables in Chapter 3B.2 Probability Distributions and Random VariablesOur work makes extensive use of probability distributions. At times we calibrate our distributions to real-world data such as mean and median income. For a random variable x that is distributed log-normallywith location and shape parameter µ and σ , it is straight forward to back out these parameters from theobservational mean (x¯) and median (x˜) with x˜ < x¯:µ = ln(x˜) and σ =√2ln(x¯/x˜) (B.1)and therefore the standard deviation sx and coefficient of variation cvx of x is given bysx = x¯√(x¯/x˜)2−1 and cvx = sx/x¯ =√(x¯/x˜)2−1 (B.2)We use a similar method to calibrate the Gumbel (extreme value type I) distribution. Using the Euler-Mascheroni constant E = 0.57721566490153286 and the constant ln(ln(2)) =−0.366513, it follows thatσ = (x¯− x˜)/(E + ln(ln(2)) and µ = x¯−σE (B.3)and the standard deviation as sx = σ ·pi/√6 = 1.28255 ·σ .Figure B.1 below shows the shapes of the Fre´chet and Log-normal distributions for comparison foridentical empirical mean Tµ and standard deviation Tσ , as well as left boundary T ◦. The Fre´chet distributionhas a more compact shape than the lognormal distribution for the same moments.116Table B.1: Glossary of Variables in Chapter 3Variable Descriptionψ Motorist’s schedule inflexibilityT Travel timeT ∗ Optimal time to depart before desired arrival timeT ◦ Distributional parameter: minimum travel timeS Distributional parameter: scale parametera Distributional parameter: shape parameterT¯ Mean of travel timeσ2 Variance of travel timev˜ Road congestion: traffic volume divided by road capacityTµ Observed mean of travel timeTσ Observed standard deviation of travel timeTρ Coefficient of variation of travel time, Tρ ≡ TσTµ−T ◦µ Parameter in the shifted log-normal distributionσ Parameter in the shifted log-normal distributionT∆ Measure of travel time mark-up, T∆ ≡ T∗−TµTµ−T ◦TΛ Measure of travel time mark-up, TΛ ≡ T∗−TµTµTν Ordinary coefficient of variation, Tν ≡ Tσ/TµV Travel velocityL Length of the roadv Traffic volumec Road capacityT Uncongested travel timeξ Curvature coefficientV ◦ Maximum possible velocityV Uncongested traffic velocityτ Optimal link tollsω Individual time costz Cost of not travellingT∅ Maximum duration that a commuter is willing to spend on a trippi(τ ) Fraction of flexible commuters that choose to drive after seeing posted tollsα Fraction of inflexible commutersn Number of potential commutersη Travel time elasticity, η ≡ d(T−T ◦)dv vT−T ◦ω¯ Average time cost of flexible commutersω∗ Average time cost of inflexible commutersϕ Time cost ratio117Figure B.1: Comparison of Fre´chet and Lognormal DistributionEmpirical MeanTµ=45 Tσ=6 T°=300.02.04.06.08.1.12Probability Density30 35 40 45 50 55 60 65 70 75 80Driving Time [minutes]LognormalFréchetB.3 Data DescriptionTable B.2: Census Tracts in Vancouver Census Metropolitan Area (2016)Municipality #Burnaby 42Coquitlam 25Delta 19Greater Vancouver A 5Langley 30Maple Ridge 15New Westminster 13North Vancouver 27Pitt Meadows 4Port Coquitlam 9Port Moody 8Richmond 39Surrey 95Vancouver 117West Vancouver 8White Rock 5All Other 21Total 482118B.4 Additional Figures and TablesFigure B.2: Simulation Results: Correlation StructurePanel A Panel B−1−.8−.6−.4−.20.2.4.6.81Time Cost − Inflexibility Correlation (ρ ω,ψ)−1 −.8 −.6 −.4 −.2 0 .2 .4 .6 .8 1Time Cost − Cutoff Time Correlation (ρω,z)7677787980818283848586Utilization rate of route A, in percent−1−.8−.6−.4−.20.2.4.6.81Time Cost − Inflexibility Correlation (ρ ω,ψ)−1 −.8 −.6 −.4 −.2 0 .2 .4 .6 .8 1Time Cost − Cutoff Time Correlation (ρω,z)9192939495969798Utilization rate of route B, in percentPanel C Panel D−1−.8−.6−.4−.20.2.4.6.81Time Cost − Inflexibility Correlation (ρ ω,ψ)−1 −.8 −.6 −.4 −.2 0 .2 .4 .6 .8 1Time Cost − Cutoff Time Correlation (ρω,z)606162636465Share of inflexible commuters on route A (φ A)−1−.8−.6−.4−.20.2.4.6.81Time Cost − Inflexibility Correlation (ρ ω,ψ)−1 −.8 −.6 −.4 −.2 0 .2 .4 .6 .8 1Time Cost − Cutoff Time Correlation (ρω,z)767880828486889092Share of flexible commuters on route B (φ B)The four figures above show the results of the 51× 51× 100 simulation runs for the correlation space for ρω,ψ and ρω,z, thecorrelation between time cost and inflexibility for the inflexible commuters and the correlation between time cost and cutoff time(reservation price) for the flexible commuters. Panels and A and B show the utilization rates of routes A and B (tolled and untolled,respectively), and panels C and D show the share of inflexible commuters taking route A and the share of flexible commuters takingroute B, respectively.119Table B.3: Distributional Outcomes: Average Time Costs by Group in the ‘Lexus Lane’ single-tollscenario with symmetric roadsParameters Groups Optimal Toll Classic Tollα ψ ϕ ω¯ I ω¯F ω IA ωIB ωFA ωFB ωF∅ ω IA ωIB ωFA ωFB ωF∅L L L 11.72 14.65 16.48 4.58 17.56 6.87 32.30 16.42 4.56 17.49 6.84 32.60L L M 13.10 13.10 17.40 4.66 16.62 6.54 28.51 17.31 4.61 16.50 6.50 28.93L L H 14.65 11.72 18.46 4.71 15.78 6.20 25.06 18.34 4.65 15.62 6.15 25.59L M L 11.72 14.65 16.02 4.39 18.01 7.07 32.12 15.94 4.35 17.89 7.02 32.57L M M 13.10 13.10 16.97 4.45 17.06 6.72 28.30 16.85 4.39 16.89 6.66 28.89L M H 14.65 11.72 18.11 4.51 16.28 6.36 24.89 17.95 4.42 16.03 6.29 25.58L H L 11.72 14.65 15.66 4.21 18.46 7.26 31.88 15.55 4.16 18.30 7.20 32.47L H M 13.10 13.10 16.63 4.27 17.53 6.89 28.07 16.49 4.19 17.29 6.81 28.83L H H 14.65 11.72 17.76 4.32 16.78 6.51 24.62 17.57 4.21 16.42 6.43 25.48M L L 11.72 14.65 17.09 4.85 18.11 7.20 30.73 17.03 4.82 18.03 7.17 31.10M L M 13.10 13.10 18.40 5.12 17.80 7.01 27.02 18.31 5.08 17.68 6.99 27.46M L H 14.65 11.72 20.00 5.46 17.82 6.77 23.73 19.87 5.40 17.61 6.76 24.22M M L 11.72 14.65 16.80 4.72 18.86 7.50 30.53 16.72 4.69 18.75 7.46 31.03M M M 13.10 13.10 18.15 5.01 18.69 7.27 26.81 18.03 4.95 18.50 7.25 27.41M M H 14.65 11.72 19.79 5.37 18.89 6.98 23.62 19.60 5.28 18.57 6.98 24.21M H L 11.72 14.65 16.53 4.61 19.67 7.77 30.31 16.41 4.56 19.49 7.73 31.01M H M 13.10 13.10 17.93 4.91 19.63 7.51 26.58 17.76 4.83 19.32 7.48 27.37M H H 14.65 11.72 19.64 5.30 20.08 7.15 23.49 19.39 5.18 19.61 7.16 24.20H L L 11.72 14.65 17.75 5.11 18.57 7.47 28.83 17.71 5.10 18.53 7.46 29.11H L M 13.10 13.10 19.53 5.60 19.06 7.35 25.36 19.48 5.57 18.99 7.35 25.65H L H 14.65 11.72 21.66 6.18 19.95 7.03 22.54 21.60 6.15 19.85 7.06 22.76H M L 11.72 14.65 17.60 5.06 19.73 7.82 28.55 17.54 5.04 19.65 7.82 28.94H M M 13.10 13.10 19.45 5.56 20.42 7.59 25.26 19.38 5.53 20.30 7.62 25.63H M H 14.65 11.72 21.62 6.16 21.59 7.17 22.45 21.54 6.12 21.45 7.22 22.73H H L 11.72 14.65 17.50 5.02 20.95 8.12 28.40 17.42 4.99 20.84 8.13 28.89H H M 13.10 13.10 19.38 5.53 21.90 7.81 25.14 19.28 5.49 21.73 7.85 25.56H H H 14.65 11.72 21.60 6.15 23.41 7.27 22.44 21.50 6.11 23.21 7.33 22.75Note: This table shows the average time cost by commuter groups corresponding to the welfare analysisin table 3.13, the ‘Lexus Lane’ scenario. The group means are shown first, followed by the average timecost for the five groups of commuters under an ‘optimal’ and ‘classic’ toll regime.120Table B.4: Distributional Outcomes: Average Time Costs by Group in the dual-toll scenario withasymmetric roadsParameters Groups Optimal Toll Classic Tollα ψ ϕ ω¯ I ω¯F ω IA ωIB ωFA ωFB ωF∅ ω IA ωIB ωFA ωFB ωF∅L L L 11.72 14.65 11.72 9.84 25.90 11.72 9.84 25.90L L M 13.10 13.10 13.10 8.81 23.15 13.10 8.81 23.15L L H 14.65 11.72 14.66 7.88 20.73 14.66 7.88 20.73L M L 11.72 14.65 11.70 9.85 25.89 11.70 9.85 25.89L M M 13.10 13.10 13.09 8.81 23.18 13.09 8.81 23.18L M H 14.65 11.72 14.63 7.88 20.70 14.63 7.88 20.70L H L 11.72 14.65 11.72 9.84 25.89 11.72 9.84 25.89L H M 13.10 13.10 13.11 8.80 23.19 13.11 8.80 23.19L H H 14.65 11.72 14.66 7.88 20.71 14.66 7.88 20.71M L L 11.72 14.65 13.63 7.36 9.26 21.80 13.53 7.28 9.40 22.93M L M 13.10 13.10 15.66 7.58 8.19 18.70 15.44 7.58 8.32 19.82M L H 14.65 11.72 16.22 11.52 7.24 16.02 15.87 11.93 7.36 17.13M M L 11.72 14.65 12.35 10.18 9.26 21.33 12.29 10.19 9.44 22.86M M M 13.10 13.10 13.33 12.61 8.18 18.27 13.15 13.01 8.35 19.83M M H 14.65 11.72 14.59 14.79 7.23 15.63 14.25 15.62 7.40 17.09M H L 11.72 14.65 11.09 13.24 9.24 20.85 11.05 13.56 9.48 22.90M H M 13.10 13.10 11.98 15.64 8.14 17.87 11.83 16.44 8.37 19.82M H H 14.65 11.72 13.33 17.41 7.21 15.28 13.01 18.75 7.43 17.08H L L 11.72 14.65 12.76 10.47 8.42 17.55 12.65 10.54 8.63 19.17H L M 13.10 13.10 14.12 11.93 7.47 15.03 13.92 12.10 7.64 16.43H L H 14.65 11.72 15.72 13.45 6.60 12.90 15.41 13.73 6.74 14.05H M L 11.72 14.65 12.03 11.34 8.42 17.10 11.93 11.44 8.67 19.08H M M 13.10 13.10 13.32 12.84 7.44 14.66 13.12 13.07 7.66 16.34H M H 14.65 11.72 14.81 14.45 6.61 12.67 14.50 14.81 6.78 14.03H H L 11.72 14.65 11.34 12.17 8.41 16.77 11.25 12.34 8.70 19.09H H M 13.10 13.10 12.56 13.75 7.42 14.41 12.36 14.07 7.69 16.33H H H 14.65 11.72 13.97 15.44 6.59 12.44 13.67 15.90 6.78 13.99Note: This table shows the average time cost by commuter groups corresponding to the welfare analysisin table 3.14, the ‘Asymmetry’ scenario. The group means are shown first, followed by the average timecost for the five groups of commuters under an ‘optimal’ and ‘classic’ toll regime.121
Thesis/Dissertation
eng
Business Administration - Strategy and Business Economics
Vancouver : University of British Columbia Library
Attribution-NonCommercial-NoDerivatives 4.0 International
Graduate
Essays on the effectiveness of environmental and urban transportation policies
Text