Andrew Curran 11084979 Master’s Thesis in Economics Industrial Organization, Regulation and Competition Policy Supervisor: Dr. A.M. (Sander) Onderstal
Welfare Enhancing Alternatives to
Congested Highways:
How Carpool Lanes Can be Hybridized
to Increase Welfare and Efficiency
This document is written by Andrew Curran who declares to take full responsibility for the contents of this document.
I declare that the text and the work presented in this document is original and that no sources other than those mentioned in the text and its references have been used in creating it.
The Faculty of Economics and Business is responsible solely for the supervision of completion of the work, not for the contents.
Table of Contents
1. Introduction 2. Background 2.1 Toronto & Congestion 2.2 Traffic As An Externality 2.3 Previous Regulations & Shortcomings 2.3.1 407 ETR 2.3.2 HOV Lanes 2.3.3 Pan Am Games 2.4 HOT Definition 2.5 How They Can Be Implemented 2.6 When are HOT preferred to HOV 2.7 Toll Types 2.7.1 Monthly Toll 2.7.2 Flat Mileage Toll 2.7.3 Dynamic Mileage Toll 3 Theoretical Model 3.1 Calculation of Driver Costs 3.2 Costs not included 3.3 What range of values will sustain carpooling for HOV? 3.4 What range of values will sustain carpooling for HOT? 4 Simulation 5 Results 5.1 Impacts on Congestion 5.2 Impacts on Driver Welfare 6 Conclusion 7 Appendix 7.1 Derivation of Elasticity 7.2 Explanation of Simulation Values 7.2.1 Hourly Income Mean and SD 7.2.2 Average Commute Distance 7.2.3 Coordination Time Mean and SD 7.2.4 Critical Traffic Level and Marginal Cost of Congestion 7.2.5 Gas Consumption 7.2.6 Individuals Value for Driving 7.2.7 Random Value Generation 7.3 Stata Code 8 Sources1. Introduction
In recent years the urban population of Toronto has expanded rapidly as a result of economic growth and high standards of living. With this growth has come an increase in roadway demand as the local population is largely dependent on driving to meet transportation needs. Largely, highway demand is fueled by the transportation of goods across the country as well as the urban commute and as congestion increases so too does the necessity for highway management and regulation. In this paper I will discuss regulatory frameworks for highway management, contrasting current and proposed systems with a focus on improving the overall welfare of those who participate in this market. I will base my investigation on the work of Lou (2011) and their investigation of Optimal Dynamic Pricing Strategies For HighOccupancy/Toll lanes as well as that of Berry (1994) and their paper on Estimating DiscreteChoice Models of Product Differentiation. My aim is to determine the relative performance of High Occupancy Toll (HOT) and High Occupancy Vehicle (HOV) lanes in terms of road congestion and user welfare. This will be accomplished first with an analysis from a theoretical perspective on what conditions will be required to benefit from HOT lane introduction followed by a simulation testing relative performance levels.
2. Background
2.1 Toronto & Congestion
In Canada, highways have a significant economic importance due to the population’s dependence on them for trade, commuting and leisure. When these interests overlap on a particular highway, such as many of the highways that traverse Toronto, the ability to manage highway infrastructure and reduce congestion is of particular importance. With regional development simultaneously limiting opportunities for highway expansion and increasing the strain on current infrastructure, regional planners will need to look towards progressive solutions to ensure the future economic viability of transportation within the Greater Toronto Area (GTA).
As is the case in many urban areas across the world, GTA highways see large daily fluctuations in demand during morning and afternoon rushhour commutes. This is a symptom of decades of urban sprawl in the area, creating a landscape that is inefficient and poorly suited to largescale transit infrastructure. As a result, for many residents it is not viable for them to reach their workplace by any other means aside from their personal vehicles. In the 2010 General Social Survey, GTA residents indicated that on average, daily
commutes for public transit users were 20 minutes longer than those who travelled by car (Turcotte, 2011), leaving many to face commuter traffic without a practical substitute.
The highways that traverse the GTA play a more significant role than commuting alone, serving as trade corridors between Eastern Canada and the United States. These highways account for a sizeable portion of the Continental Gateway, which links Quebec in the North to Windsor in the South and are estimated to support upwards of $560B CAD in trade yearly(Lévesque, 2010). Any level of excess congestion will increase shipping costs for these goods and ultimately have a negative impact on consumers through higher prices and a negative impact on the region, as manufacturing there will be perceived as less appealing.
2.2 Traffic As An Externality
There is an incentivization problem when it comes to roadways and congestion, each individual feels the impact of traffic loads but most likely will not work towards reducing their impact as it is not compatible with their own utilitymaximizing behavior. The root of this problem lies in the fact that the private costs inflicted on any driver as a result of entering the highway are likely to be different from the social costs inflicted on the rest of the highway. When there is a distinction like this between private and social costs, the consumption decision of any individual will likely not be aligned with the socially optimal outcome, as they do not consider the extra congestion felt by all other roadway users when determining their own behavior. This behavior was recently outlined in a research study conducted in the GTA by Metrolinx (2008). The organization estimated that on a yearly basis, excess congestion above a socially optimal level resulted in additional congestion costs of $2.9B$3.8B CAD for commuters alone.
In order to align private and social costs there must be a mechanism that charges drivers as a result of the added congestion they are inflicting on existing highway users. This can be achieved through the introduction of a road toll, serving as a tool to bridge the gap between costs and align drivers’ consumption decisions with a sociallypreferred outcome. This toll would have to be set with care, otherwise an overcharge or undercharge may leave society in a worse outcome than before regulation. Since highway demand in the GTA can fluctuate greatly over the course of a day, the toll would need to be dynamic in order to safeguard against this problem. While regular toll roads have a strong economic backing, the public discontent that arises when drivers are asked to pay to use a road that their tax dollars initially built is undesirable from a political perspective and because of this a more progressive solution is required.
2.3 Previous Regulations & Shortcomings
Past efforts to regulate traffic on the GTA highways have targeted incentivization for carpooling, capacity expansion and the management of periods of extraordinary demand.
While each has enjoyed its own level of success it is important to acknowledge their shortcomings in order to understand the necessary requirements of a solution to the current problem.
2.3.1 407 ETR
The oldest of the three examples is Highway 407 Express Toll Route (ETR), which first opened in 1997 and has since expanded to cover a 108 km stretch between Burlington and Pickering (407 ETR, 2015A). The main purpose of the 407ETR was to provide relief to highway 401, Toronto’s busiest highway, and was the first in the world to have all electronic tolling systems (407 ETR, 2015B). Just one year after its launch, an operating lease for the highway was put up for international public tender and has since been jointlyowned by Cintra Infraestructuras, Canada Pension Plan Investment Board and SNCLavalin.
The tolling mechanism of 407ETR charges a flat toll per kilometer based on the time of day, section of road and type of vehicle (407 ETR, 2015C). While this is certainly an improvement on static tolls, which do not change over the course of the day, it still leaves much to be desired since the toll is not directly impacted by current congestion levels. Another drawback is the current management structure of the highway itself. Being operated by a private organization, 407ETR has an incentivization problem, as toll management will be influenced by the profitmaximizing behavior of the firm and will often not achieve socially optimal outcomes. In the absence of public ownership it will be difficult to ensure toll management which will be in the public’s best interest. In the case of the 407ETR this would take the form of significantly reducing tolls during offpeak periods to ensure a greater distribution of traffic among the GTA highways. Currently, tolls do not fluctuate significantly over the course of the day, with a trip costing $0.2162/km at 2:00 and $0.3754/km at 8:00 (407 ETR, 2015C).
2.3.2 HOV Lanes
The second example I would like to highlight of previous regulation of GTA highways is the introduction of HighOccupancy Vehicle (HOV) lanes. HOV lanes allow access to drivers of vehicles with two or more occupants, and in certain cases service vehicles such as busses and taxis (Ontario Ministry of Transportation, 2016). The incentivization effect created by HOV lanes to reduce congestion on GTA highways and the resulting fuel savings for drivers have been highlighted by the government as some of the most important factors for introducing them. While HOV lanes alone may work some of the time, there will always be periods of the day where traffic congestion is not significant enough in regular lanes to compensate drivers for the cost of arranging a carpool. During these periods in the day, HOV lanes will likely be underutilized and could be causing unnecessary strain on the remainder of the highway.
2.3.3 Pan Am Games
The last example I would like to highlight of traffic regulation in the GTA is the ability of the government to manage congestion in extraordinary circumstances such as when a city is hosting a major sporting event or convention. This was demonstrated in 2015 when Toronto hosted the PanAmerican Games, a sporting event open to competitors across the Americas. While hosting the games there was an influx of traffic as both locals and visitors travelled to one of 30 venues across the city (Government of Ontario, 2015). This extra load on existing infrastructure was managed in a variety of ways including adjusting transit operations and most notably the addition of many temporary HOV lanes across GTA highways. While the additional HOV lanes may have served those attending the events well, it was widely reported in the media for causing traffic chaos during peak commute hours.
The main problem with this solution to temporary increases in traffic is very similar to the problems presented by using HOV lanes for regular congestion. The temporary HOV lane will provide a great deal of relief to the intended audience during the specific period in the day when it is necessary but there will be a large portion of the day where there is little or no demand. When this is the case, the highway as a whole will not be efficiently managed, resulting in unnecessary congestion on the remaining lanes and an opportunity for a better distribution of traffic.
2.4 HOT Definition
The regulatory structure that I propose for better highway management in the GTA is a hybridization of traditional toll highways with the carpooling incentivization of HOV lanes. This lane structure is known as a HighOccupancy Toll (HOT) lane and is implemented in a similar fashion to traditional HOV lanes. Occupying the far left lane of any given highway HOT lanes allow the admission of tollpaying, singleoccupant vehicles in addition to the free entrance of multioccupant vehicles.
While HOT lanes are not a new concept in road planning, there is plenty of opportunity to adapt rules and regulations to fit the particular needs of the GTA’s highways. For instance, when it comes to vehicle exemption rules, the Government of Ontario currently allows any bus, emergency vehicle, airport taxi or electric vehicle to have free access to use current HOV lanes regardless of the number of occupants (Ontario Ministry of Transportation, 2016). This could be adapted or implemented in its current form for any lane converted to the HOT system as these choices are justified given current regulation. In addition to this, highway management could be further empowered with the option of changing required occupant levels from 2 to 3 or more in extraordinary circumstances. While this provides important trafficreducing incentivization, it would be important to implement this in a dynamic manner, to avoid unnecessary restrictions during offpeak periods.
2.5 How They Can Be Implemented
With the implementation of such intricate highway regulation comes the inevitable issue of enforcement. It is crucial for the success of a HOT lane system to have reliable enforcement in order to deter any misuse of the lanes, otherwise the highway will eventually deteriorate to the point of its original form. The concept of enforcement is no easy task, as automation will be required to ensure efficiency in the system, the question of how to implement this must be addressed. Recently there has been substantial technological advancement in this area and through harnessing some of these new technologies we may now have a reasonable way to enforce this proposed regulation.
As documented by Robert Poole of the Reason Foundation (2011), we now have the capability to observe occupant levels in vehicles through the use of multiband infrared systems. This technology allows enforcement agencies to observe passenger levels at speeds upwards of 140km/h(VODC, n.d.A), in a variety of environmental conditions, with an accuracy comparable to that of the human eye. Most importantly, this form of detection can make the distinction between human skin and other materials, narrowing the opportunity for drivers to cheat the system. On the website for one of the companies developing this technology, Vehicle Occupancy Detection Corporation (VODC), they claim to have reached a 96% accuracy for multioccupant detection in a trial conducted by the California Department of Transportation (VODC, n.d.B).
With the automatic detection of multioccupant vehicles seemingly covered by current technologies, there is the issue of toll collection to be resolved for the successful implementation of automated HOT lane enforcement. Unlike the previous example, the technology for automated toll collection has been widely used since the introduction of 407 ETR in 1997. In order to manage toll payments there would need to be a system of cameras and radio transponders at the entrance and exit of HOT lanes. The transponders would interact with personal devices installed in each vehicle to communicate through radiofrequency ID (RFID) and automatically calculate and charge each singleoccupant vehicle for their trip. In the absence of a working radio transponder, cameras would be placed to capture licence plate information and could be used in combination with vehicle registration databases to manually bill all other vehicles.
2.6 When are HOT preferred to HOV
With the question of enforcement resolved we next need to consider what elements of a roadway make it suitable for HOT lane implementation. First I will consider why the HOV component is necessary and what it provides. When congestion on any roadway has gone beyond an acceptable level it becomes necessary to incentivize drivers to reduce traffic loads. This can be accomplished in a number of ways such as additional infrastructure development and transit promotion to name a few. In the case of the GTA however, where
transit may not always be an option due to urban sprawl, it becomes crucial to incentivize drivers to carpool and increase occupant density in order to reduce highway traffic loads.
One problem that arises from having only an HOV lane is that many drivers may not be able to efficiently coordinate their behavior. When this is the case an HOV lane may be underutilized, resulting in unnecessary excess traffic loads on the remainder of the highway. This leads to the next component of the HOT lane design, the singleoccupant vehicle toll. If HOV lanes are being underutilized for a significant portion of the day it would be beneficial to permit access to some of the remaining traffic. Unfortunately, in the absence of a toll system too many drivers would enter this lane and the traffic reducing incentives created by the HOV system would be negated. Conversely, if there is a toll and it is set too high, there will be little or no relief to regular lanes and the HOT lane will still be underutilized. This will lead into the next section where I will discuss a few proposed toll mechanisms, their drawbacks and benefits.
2.7 Toll Types
In this section I will compare and contrast toll models in order to gain insight on which type is preferred for implementation in Toronto and to point out the benefits and shortcomings of each. The three toll systems I will focus on are monthly access tolls, flat mileage tolls and dynamic mileage tolls. The first toll model is structured so that a highway driver can pay for access to a HOT lane one month at a time and have unlimited usage for the duration of the month. The second toll system, flat mileage tolls, allows drivers to pay a previously specified toll per kilometer of HOT lane travel. This toll may change over the course of the day but is not directly linked to current road usage and will always be posted ahead of time. The last system, dynamic mileage tolls, updates in real time as a predetermined function of traffic levels on the highway and charges HOT lane drivers a toll per kilometer of usage.
2.7.1 Monthly Toll
While monthly toll systems are the least sophisticated of the options I will present, they offer some benefits to drivers that the remaining systems cannot provide. The main benefit to drivers is the simplicity of the system itself. In fact, it is this type of toll that the Government of Ontario is now considering to implement across the GTA with trials beginning this September (Spurr, 2016). Drivers can pay a fee upfront that is known to them, allowing for budgeting as well as sufficient time to make an informed decision about their consumption behavior. From a regulatory perspective however, the benefits are limited to the low implementation cost of the system. Since the toll will not fluctuate with time or highway usage, regulators will be forced to target a specific period of day, most likely rush hour commuting. They will aim to sell a quantity of monthly access equal to the amount of additional space left over from carpool users during this time period in order to preserve carpooling incentivization.
The shortcomings of this approach to HOT lane management go a long way to discredit monthly tolls as a viable mechanism. The primary concern with this system is that it does not make any attempt to deal with fluctuating demand over the course of a day. As highway use changes dramatically throughout the day in the GTA it would be natural to have a toll that encapsulates this, which is not the case with the monthly access. At best, it would distribute traffic optimally during commuting hours, still resulting in HOT lane underutilization during offpeak hours. In addition, access pricing will need to be updated over time to account for changes in traffic demand and would most likely need a sophisticated model to attend to this to avoid the costs of employing regulators on a fulltime basis.
2.7.2 Flat Mileage Toll
An improvement from monthly toll systems would be flat mileage tolls, allowing regulators to target multiple time periods while still providing toll transparency and predictability for highway users. By implementing a system of this structure specific sections of highways could be isolated, each having their own toll costs to meet changes in demand across the length of the highway. A preferred distribution of traffic could be attained during offpeak periods compared with the monthly system, since regulators could monitor average demand during these periods and set rates accordingly. The last major advantage of this system, especially when compared to the previous example, is that drivers could pick and choose how many times they would like to use the lane without needing to commit to an entire month of access.
While having more opportunity for refinement, thanks to the ability to set separate tolls based on time period and highway segment, there are still some major drawbacks of the flat mileage toll system. The absence of realtime feedback to the system leads to a loss of control for regulators as they cannot ensure the important traffic reducing incentivization is maintained. If at any period too many cars choose to make use of the HOT lane, there could potentially be a loss to credibility of any benefits from carpooling, leading to uncertainty for carpoolers and possibly a decrease in carpooling behavior in the future.
2.7.3 Dynamic Mileage Toll
The way I propose to remedy the shortcomings of the toll structures above is through a dynamic mileage toll for the GTA. With the implementation of an accurate demand estimation model and a traffic monitoring system, regulators could retain traffic reduction incentivization while raising the carrying capacity of the highway. This method would be flexible enough to accommodate periods of extraordinary demand with little to no intervention by policy makers since the toll would be actively updating itself based on current highway usage. Due to this active monitoring and feedback, the toll would presumably outperform the models mentioned previously during off peak periods as well and would give regulators the option of temporarily reducing the toll to zero. This would be beneficial in circumstances where traffic levels are low enough that drivers would not be incentivized to carpool anyways, leading to a preferred distribution of traffic across the highway.
Of course, there will be drawbacks to introducing a system of this nature. It is relatively easy to foresee that the dynamic model would outperform the previous systems during offpeak periods, but with the vast majority of demand occurring during peak periods it is most important to understand how it will perform then. Additionally, since rates would not be announced far in advance, drivers would face a level of uncertainty when using the highway which could hinder their consumption decisions. Lastly, there would most likely need to be a period for calibration, where the model reveals drivers’ willingness to pay and progresses towards a steady state. While certainly not negligible, these drawbacks are significantly less severe than those of the monthly and flat mileage systems which is why I will investigate the performance of this system in the coming sections.
3 Theoretical Model
3.1 Calculation of Driver Payoff
I hope to demonstrate the efficiency gains of progressing to HOT lanes from HOV lanes through two separate methods. The first will be a theoretical model testing parameter ranges where HOT is likely to outperform HOV from a driver welfare perspective. The second method will contrast relative performance of HOT and HOV by means of a simulation. This theoretical model will determine the interactive effect of a driver’s inherent value, cost of coordinating a carpool, cost of gas, and the impact of congestion and traffic volume. I will determine this by investigating the results of utility maximizing behaviour under the presumption that driver payoffs are determined as follows:
+
P ayoff from Drivingi= CCongestion* Vi+ CCoordination, i* Vi+ CGas CToll− VDriving, i
In the above function CCongestion is a variable with time units, signifying the time cost for each individual as a function of traffic quantity for that given lane. Multiplying this by their individual value (hourly wage) provides the opportunity cost incurred by driver Ci. Coordination, i is similarly a variable with time units, representing the amount of time each individual requires to organize a carpool. CGasand CToll is the average cost of gas per kilometer of driving and the cost of the toll incurred if applicable. V Driving, iis the individual’s value for driving and represents the time savings they receive from commuting by car compared with transit. Driver welfare will then be calculated as the sum of all driver payoffs.
3.2 Costs not included
While I aimed to include as many applicable costs as possible associated with highway driving in HOV and HOT systems there were a few which I had to omit for reasons I will defend below. Each individual driver on the road is unique and has their own beliefs, some may be more naturally drawn to concepts such as carpooling and may receive some sort of warm glow effect from the good deed of reducing traffic congestion than others. Alternatively, others may be negatively impacted by the concept of this and may genuinely
dislike the company of another person during their highway trip. These benefits and costs are hard to quantify as they are intangible, unlike the monetary cost incurred from something such as gas consumption, and due to this it would be very difficult to include within the scope of this paper.
Similarly, drivers may be impacted very differently from congestion. While each driver has a value to their time, allowing for a monetary calculation of how much each minute of excess congestion will cost, it is difficult to quantify the stress on a driver or wear and tear on car components. It is not entirely unreasonable to also think of some circumstances where drivers may even benefit from congestion, for example, if there is a task waiting for the driver at the destination of their trip which they are not looking forward to reaching. As a result, the only impact from congestion that I chose to include is the cost associated with delays incurred.
The last immediately obvious cost which I chose to omit is any environmental costs that result from highway driving. These were omitted due to the sheer difficulty of quantification as well as the inherent variability across both vehicles and drivers. Not only will each vehicle model pollute at a different rate, but depending on the driver, could have vastly different levels of pollution for the same model as a result of differences in driving habits. In addition, it may not even be that large of a stretch to say that for most drivers the environmental toll has little or no effect on their consumption decisions on a regular basis. In fact, it may be quite unreasonable to presume that a driver even considers the excess pollution they may create by not entering the HOT lane through carpooling or tolling.
3.3 What range of values will sustain carpooling for HOV?
In order for carpooling to be a viable option for any individual highway driver within this model the payoff resulting in entering the HOV lane must be larger than the payoff in the regular lane. If driver payoff is derived as stated above the resulting condition must hold for carpooling to be appealing.
PHOV > PNormal
C 1/2)V MC C 1/2)C C MC
Vi CongestionHOV + ( i Congestion + Vi Coordination, i+ ( Gas− VDriving, i> Vi CongestionNormal + Vi Congestion + CGas− VDriving, i
ViCCongestionHOV − ViCCongestionNormal > (1/2)CGas+ (1/2)V MCi Congestion − Vi Coordination, iC
1/2) 1/2)MC
CCongestionHOV − CCongestionNormal > ( V i CGas+ ( Congestion− CCoordination, i − /2) dVi
d(CCongestionHOV −CCongestionNormal )= ( 1
V2i
CGas
*Note: Marginal cost of carpooling in normal lane is the impact of one additional car to current traffic loads. Marginal cost of carpooling in HOV lane is the impact of adding half of a car since each car will consist of two occupants.
As driver income increases the difference between congestion in HOV and normal lanes that sustains carpooling is smaller. This would suggest that high income individuals would be the least likely to carpool as the possible distributions that lead to a beneficial outcome are much fewer.
3.4 What range of values will sustain carpooling for HOT?
In order for carpooling to continue as a viable option within HOT framework the above condition must hold in addition to carpooling being a preferred choice to paying the toll.
PCarpoolHOT > PTollHOT
C 1/2)V MC C 1/2)C C MC
Vi CongestionHOT + ( i Congestion + Vi Coordination, i+ ( Gas− VDriving, i> Vi HOTCongestion+ Vi Congestion + CT oll− VDriving, i
C 1/2)V MC 1/2)C
Vi Coordination, i− ( i Congestion+ ( Gas> CToll 1/2)MC δVi δCT oll = CCoordination, i− ( Congestion
After the introduction of HOT the subset of the population that will carpool is likely to decrease as there is now a second condition which will need to hold in order for a driver to benefit from carpooling. The impact of driver income on this condition is much more ambiguous and is entirely influenced on their ability to arrange a carpool. If this cost of coordinating a carpool (in time) is greater than half the marginal cost of an additional vehicle of traffic (in time), then the toll required to maintain carpooling behaviour will need to increase with driver income. Conversely, if a driver is efficient at arranging a carpool the toll required to maintain carpooling behaviour will decrease with value. This signifies that when it comes to HOT lane introduction, the individual cost of coordinating a carpool has a significant impact on carpooling behaviour leading to an ambiguous effect of driver income.
4 Simulation
The specific dynamic toll model I would like to test is an extension of a logit demand model specified by Lou (2011) . Their proposed system utilizes monitoring devices which can detect traffic levels in both regular and HOT lanes in real time, then use this information along with the current toll to directly observe a driver’s willingness to pay. This information is recursively fed back into the model to update the toll for the next iteration of the current time interval.
Where my model will depart from that specified by Lou (2011) is the introduction of heterogeneity of driver values instead of homogeneity, the introduction of costs and benefits to carpooling such as time spent coordinating a ride as well as the potential gas savings, and the introduction of the impact of congestion on driver utility. I believe these model extensions are crucial to the external validity of the results as they strive to consider all possible
monetary incentives associated with highway use and potentially lead to a different result than previously found. To incorporate these changes I will follow the structure proposed by Berry (1994) and use this to build upon the proposed mechanism of Lou (2011).
The primary method I would like to implement for determining possible efficiency gains from my proposed model is a simulation. Through the simulation I will be able to generate a set of drivers that will react in line with an individual who is maximizing their own utility and then observe the impact of the toll model on this population. This simulation will be carried out within the statistical software package Stata and will be helpful in the future for stress testing the proposed logit demand model of Berry (1994) in this context.
Within the simulation there will be a few assumptions I will have to make. Firstly, that drivers can observe their surroundings in a way to determine which option provides the highest payoff. While this may not be true in practice as humans are imperfect it is an assumption that is widely made within the study of economics and I believe is reasonable in this setting. Secondly, I will have to impose characteristics in the model such as the cost of gas and the marginal impact of an additional vehicle on congestion. These characteristics will be determined using physical indicators wherever possible such as required stopping distance for a given speed and average gas consumption of highway traffic. Specific parameter values that were used in the simulation will be discussed in the appendix.
The structure of the toll estimation model will make use of ownprice elasticity and information obtained through the logit demand model proposed by Berry (1994). In this model it is important to specify not only the market share of each product being investigated, in my case HOT lane use, but also the market share of the outside good, which would be the regular lane traffic levels. This outside market share would change over time in the simulation if the costs of consumption exceed the benefits for each individual, allowing the option for driver’s not to consume. The structure of this model in the context of my thesis is as follows: x p uij= β j− α j+ ξj+ εij − ηj= αp (1j − sj )
Where and are model parameters,β α uij is the utility of person i derived from product xj, jis the observable characteristics of product pj,jis the price of product ξj,jis the unobservable characteristics of product εj, ijis difference between consumer i’s preference for good j
compared to the mean, ηjis the ownprice elasticity of good j, and sjis the market share of product j. A derivation of the ownprice elasticity equation is provided in the appendix.
In the context of my simulation different lane choices will represent different consumption products for drivers. They will be distinctly different as they provide differing levels of congestion, costs and underlying benefits. The price paid for each lane will differ, with carpoolers paying the cost of carpooling, toll payers paying the toll and regular lane users avoiding costs all together. Observable characteristics in this context would take the form of congestion levels and unobservable characteristics would cover anything like warmglow feelings of carpooling.
What I aim to simulate with my program is the effect of adding a HOT system as described above on a population relative to that of a HOV system. This program will be tested as if it was a single segment of a larger HOT lane network within a highway, facing the same interval of time within a given day over multiple iterations. This makes the assumption that driver characteristics during a specific period of the day will be relatively similar on a subsequent day. If traffic is cyclical on a daily basis throughout the week this would represent the same period of the day, over multiple days. Alternatively, if there is a large difference between demand characteristics across weekdays in the GTA, this model could be implemented to determine the optimal toll for one period of a single weekday.
Drivers in the simulation are programmed in a manner where they can observe their own payoffs once their choices have been made. In addition, they will also observe based on traffic levels in each of the lanes what their payoffs would have been if they had selected any of the other available options. If a driver observes that they would have been better off with another choice, in a following iteration that driver will make that choice instead, with a predetermined probability. The probability at which a driver changes to a preferential lane will be strictly less than 1 as to avoid unnecessary cycles and promote convergence to an equilibrium.
The simulation itself will look to determine the relative performance of HOT to HOV by testing driver costs for each system over multiple generated sets of drivers. Within each set of drivers the simulation will run for a number of iterations of the HOV system until drivers have settled into a steady state distribution across lanes. Once consumption choices become stable for a number of periods the results will be stored and the same set of drivers will be introduced to HOT. This will progress in a similar manner and store the results under the HOT framework next. Once a single set of drivers has been exposed to both regulatory frameworks and the performance data has been stored a new set of drivers will be generated and the simulation will repeat as before.
5 Results
5.1 Impacts on Congestion
While decreasing overall traffic levels is a primary concern for GTA highway regulation the distribution of this traffic can have a significant impact on the costs inflicted on drivers. When everything else is held constant, an increase in traffic on the road will arguably have a negative impact on existing users as it will only increase congestion. However, when the overall distribution can be impacted through regulation it may be possible to increase traffic while decreasing costs on average. This will only be possible if the initial traffic is poorly distributed across lanes since regulatory intervention will take advantage of the misallocation of drivers.
This is demonstrated nicely within the data generated by the simulation as I observed an average increase in traffic on the road from 283 to 287 while having a beneficial impact on average costs. This increase in traffic is a direct result of allowing singleoccupant vehicles into the HOT lane, as congestion increases in the HOT lane a portion of carpoolers no longer benefit from the relative lack of congestion and will move to one of the two singleoccupant consumption options. Average traffic levels for each of the three consumption possibilities is summarized below in Table 1.
Normal Lane Carpool Toll
HOV 265 17.5
HOT 166 13.5 107
Table 1 Average Traffic Levels
What is interesting about the impact of this form of regulatory intervention is that the overall carrying capacity of the road will have increased. Since the cost of driving has decreased on average for highway users there may now be the possibility of additional drivers entering the road who were previously travelling by another method such as transit. While this may be a negative side effect if transit in the area is already underutilized it may conversely be advantageous if transit was previously struggling to meet demand.
5.2 Impacts on Driver Welfare
While the redistribution of traffic and increased carrying capacity is desired by regulators, it will only be accepted by the population if it can have a positive overall impact on driver welfare. This impact on drivers is crucial politically for the successful implementation of HOT lane regulation as it will otherwise face criticism from both the public as well as the political opposition. Almost more important than the overall impact is the impact on different social classes. As HOT lanes have already been framed in the media as solely benefiting the rich, with some dubbing them “Lexus lanes” (CBC News, 2015), one of the main goals of my simulation was to demonstrate the potential benefit to lowincome users. While the cost of singleoccupancy tolling will be arguably more expensive for lowincome drivers, many fail to recognize the positive impact of moving wealthier drivers into the HOT lane. As more drivers choose to toll, the remainder of singleoccupant drivers will receive a benefit from the reduced congestion in their lane.
This has been nicely demonstrated in Table 2, as we observe a relative cost of driving for HOT compared with HOV less than 1 for both high and low income types. This table demonstrates the relative cost of driving in a HOT lane system compared to a HOV lane system, with values greater than 1 indicating an increase in average costs from the introduction of HOT lanes and values less than 1 indicating a decrease. Column 1 shows the overall impact on the entire population, whereas columns 2 and 3 show the impact on each income type. It should be noted that in this simulation, high and low income types were
defined as those who earned more or less than the average wage respectively. In addition, as shown by the confidence intervals there is a statistically significant difference in cost reduction between the two income types, with low income drivers receiving a larger reduction in costs. This is demonstrated by the fact that the two confidence intervals are not overlapping, resulting in a significant difference at the 95% level. This means that not only will HOT lane implementation be beneficial for all, but it appears the concerns posed by many in regards to the income effects are unfounded.
6 Conclusion
Within the scope of this thesis it was my aim to demonstrate not only the necessity of highway regulation in the GTA but to also compare and contrast a variety of the proposed mechanisms as well as their impact on consumers. While it was clear that highways in the GTA cannot remain in the current regulatory state, it was far less clear what impact each of the proposed mechanisms may have. Due to the economic significance not only on a local level but also internationally as a result of its impact on trade corridors, indicators such as congestion and average welfare levels must be carefully monitored to fully understand the impacts posed to each from different regulatory regimes. Through theoretical analysis as well as simulation I have shown the potential positive impact of progressing to HOT lane regulation in the GTA, benefiting not only the population as a whole but also providing substantial evidence against the notion that this regulatory scheme is tailored for the upper class. Where this study falls short is the lack of evidence from a real world setting. While the analysis in this paper provides a basis for informed debate there will need to be further investigation ideally in a live trial on an existing roadway. Although this would represent a sizeable commitment to this regulatory mechanism I believe that this paper has provided the basis required to progress towards this direction. From my investigation it is my opinion that the positive economic impact of HOT lane introduction warrants further analysis from the Canadian Government.
7 Appendix
7.1 Derivation of Elasticity
As defined by Berry (1994) Logit Utility for person i in regards to product j is: p uij= δj+ εij= βxj− α j+ ξj+ εij The share of product j relative to all k products is: sj= eδj ∑N k=0e δk Normalizing the mean utility of the outside good to 0 gives us the share of outside good: δ0= 0 eδ0= 1 s0= 1 1+ ∑N k=1e δk Rewrite the share of product j: sj= eδj 1+ ∑N k=1e δk= s e0 δj Solve for OwnPrice Elasticity: (a b b ) ηj= δp s j j δs pj j = s j pj δ δpj(
s e0 δj)
= sj pj δ δpj 1 1+ ∑N k=1e δk(
e βx −αp +ξj j j)
= sj pj δ δpj(a) (b) = sj pj ′ + a ′ Where a’ is: e s δ δpj 1 1+ ∑N k=1e δk = αeδj 1+(
∑N k=1e δk)
2 = α δj 2 0 Where b’ is: − e − e δ δpj(
eβx −αp +ξj j j)
= α βx −αp +ξj j j= α δj Therefor OwnPrice Elasticity is: − p (1 ) ηj= s j pj αe s e αe(
δj 2 0 δj− s0 δj)
= sj αpj s(
j2− sj)
= α j − sj7.2 Explanation of Simulation Values
7.2.1 Hourly Income Mean and SD
Average hourly income of Canadian population is $25.55 (Statistics Canada, 2016) Minimum hourly wage in Canada is $11.25 (Ontario Ministry of Labour, 2016) Since 99.7% of observations will be within 3 standard deviations in a normal distribution and I am bound by the minimum wage, I chose a standard deviation of $4.507.2.2 Average Commute Distance
Statistics Canada states an average commute of 9.4km for residents of Toronto (Statistics Canada, 2009)7.2.3 Coordination Time Mean and SD
When considering how long it would take for two people to meet at a set location and then the possibility of having to finish at two separate locations I decided a range from 0 minutes (if they live and work together) to 90 minutes (if they live and work in very different locations) would be reasonable. Therefor I set the mean value to be 45 minutes and the standard deviation to be 15 minutes. When dividing this time cost over 9.4km of average commute it results in a mean value of 0.0766 hours and a standard deviation of 0.025 hours per kilometer of travel. While this may appear to be extreme, keep in mind that empirically very few commuters choose to carpool. These values for coordination time resulted in levels of HOV carpooling similar to that which are exhibited in Toronto (Statistics Canada, 2015A).7.2.4 Critical Traffic Level and Marginal Cost of Congestion
Information on how many vehicles could safely fit in 1km of road travelling at 100km/h was derived from a vehicle stopping distance calculator (CSG Network, 2016). This was then used to see how many vehicles could safely fit in the same space at a variety of lower speeds to calculate the slope and intercept for the cost of time as a function of traffic volume.7.2.5 Gas Consumption
As I was unable to find a statistic on the average gas consumption of a Canadian vehicle I decided on a value of 9L/100km as a fair estimate. At the time of this paper gasoline prices were approximately $1.20/L in the GTA, resulting in a cost per km of $0.108.7.2.6 Individuals Value for Driving
When choosing to drive instead of taking transit you will save the cost of a transit fare as well as benefit from any time savings as a result of taking the faster mode of transportation. Dividing the current fare for the Toronto Transit Commission, $3.25(Toronto Transit Commission, 2016), over the average 9.4km commute gives a savings of $0.35/km. In addition, Statistics Canada reports a 29 minute average commute by car and a 49 minute average commute by transit for the Toronto population(Statistics Canada, 2015). This results in a savings of 20 minutes over the course of the journey, or 0.0355 hours/km of commute. The combination of these two savings define the value for driving for individual i as follows: .35 .0355V VDriving, i= 0 + 0 i7.2.7 Random Value Generation
Within the simulation there are a couple of instances where values must be generated to create the population of drivers and their preferences. Specifically this was implemented to independently generate a distribution of incomes as well as coordination times. For the generation of these values I made use of a command in Stata that would generate a sample of values that were normally distributed with a specified mean and standard deviation.7.3 Stata Code
***************** capture log close ********** **Thesis** ********** clear version 13.0 set more off //SECTION 1 DRIVER CHARACTERISTICS AND DESCRIPTIVE VARIABLES //Define number of drivers in each simulation loc Drivers=300 set obs `Drivers' //Create descriptive variables for analysis gen Average_HOV=. gen Average_HOT=. gen Revenue_From_Toll=. gen The_Final_Toll=. gen Traffic_HOV_Normal=. gen Traffic_HOV_Carpool=. gen Traffic_HOT_Normal=. gen Traffic_HOT_Carpool=. gen Traffic_HOT_Toll=. gen Average_Cost_HOV_High=. gen Average_Cost_HOV_Low=. gen Average_Cost_HOT_High=. gen Average_Cost_HOT_Low=. //This loop will test the performance of HOT against HOV //Each iteration of the loop will generate a unique set of drivers with the characteristics below //Each iteration of the loop will record the values for the above descriptive variables //Loop is set for 300 iterations loc a= 1 while `a'<=300 { *DRIVER GENERATOR loc Drivers=300 //Number of drivers generated loc Mean_Value "25.55" loc SD_Value "4.5"loc Mean_Coordination_Time "0.0766" loc SD_Coordination_Time "0.025" loc Crit_Traffic "12.26" //Cars that can fit safely in 1km loc Switching_Likelihood "0.85" //Likelihood any driver will switch lanes in a following trip if they observe a potential gain loc Gas_Cost "0.108" loc Congestion_Slope "0.0004149" //Marginal congestion for each additional driver gen Value=rnormal(`Mean_Value',`SD_Value') //Value in dollars gen Coordination_Time=rnormal(`Mean_Coordination_Time',`SD_Coordination_Time') //Cost in hours gen Coordination_Cost=Coordination_Time*Value //Cost in dollars gen High_Value=0 replace High_Value=1 if Value>`Mean_Value' //Define "highvalue" and "topvalue" drivers gen Top_Value=0 replace Top_Value=1 if Value>(`Mean_Value'+`SD_Value') ******************************************************************************** //SECTION 2 HOV gen High_Cost=0 replace High_Cost=1 if Coordination_Time>`Mean_Coordination_Time' //0Carpool 1Normal gen Choice_Normal=1 //Initially put High Cost people in carpool lane to promote initial lane changing replace Choice_Normal=0 if High_Cost==1 //This loop will organise drivers amongst lanes in a natural progression until at least 70% of drivers cannot improve from a lane switch loc i = 1 gen Total_Switch_Left_`i'=`Drivers' while Total_Switch_Left_`i'>`Drivers'*(0.3) { drop Total_Switch_Left_`i' if `i'>1{ drop Normal_Count HOV_Count } count if Choice_Normal==1 scalar Normal=r(N) gen Normal_Count=Normal count if Choice_Normal==0 scalar HOV=(r(N))*(1/2) gen HOV_Count=HOV //Calculate Cost and alternate Cost (if driver switched lanes) gen Congestion_HOV_`i'=0 //Cost in hours replace Congestion_HOV_`i'= 0.0048463 + `Congestion_Slope'*Normal if Choice_Normal==1 & Normal>`Crit_Traffic' replace Congestion_HOV_`i'= 0.0048463 + `Congestion_Slope'*HOV if Choice_Normal==0 & HOV>`Crit_Traffic' gen Congestion_Cost_HOV_`i'=Value*Congestion_HOV_`i' //Cost in dollars
gen Alt_Congestion_HOV_`i'=0 //Cost in hours replace Alt_Congestion_HOV_`i'= 0.0048463 + `Congestion_Slope'*(HOV+(1/2)) if Choice_Normal==1 & (HOV+(1/2))>`Crit_Traffic' replace Alt_Congestion_HOV_`i'= 0.0048463 + `Congestion_Slope'*(Normal+1) if Choice_Normal==0 & (Normal+1)>`Crit_Traffic' gen Alt_Congestion_Cost_HOV_`i'=Value*Alt_Congestion_HOV_`i' //Cost in dollars gen Cost_HOV_`i'=(0.35+0.0355*Value) Congestion_Cost_HOV_`i' `Gas_Cost' replace Cost_HOV_`i'=(0.35+0.0355*Value) Congestion_Cost_HOV_`i' Coordination_Cost (1/2)*`Gas_Cost' if Choice_Normal==0 replace Cost_HOV_`i'=(1)*Cost_HOV_`i' gen Alt_Cost_HOV_`i'=(0.35+0.0355*Value) Alt_Congestion_Cost_HOV_`i' `Gas_Cost' replace Alt_Cost_HOV_`i'=(0.35+0.0355*Value) Alt_Congestion_Cost_HOV_`i' Coordination_Cost (1/2)*`Gas_Cost' if Choice_Normal==1 replace Alt_Cost_HOV_`i'=(1)*Alt_Cost_HOV_`i' //Calculate average cost overall as well as average cost for each income group egen Avg_Cost_HOV_`i'=mean(Cost_HOV_`i') su Cost_HOV_`i' if High_Value==1 replace Average_Cost_HOV_High=r(mean) in `a' su Cost_HOV_`i' if High_Value==0 replace Average_Cost_HOV_Low=r(mean) in `a' //Switching mechanism to determine if a driver would be better off switching lanes in a subsequent round //Note: To avoid overswitching, drivers will switch lanes if they observe lower possible Cost at a probability < 1 gen Should_Still_Switch=. replace Should_Still_Switch=1 if Alt_Cost_HOV_`i'>Cost_HOV_`i' gen Switching_Chance=runiform() gen Switched_Already=0 replace Switched_Already=1 if Choice_Normal==1 & Alt_Cost_HOV_`i'<Cost_HOV_`i' & Switching_Chance<=`Switching_Likelihood' replace Choice_Normal=0 if Choice_Normal==1 & Alt_Cost_HOV_`i'<Cost_HOV_`i' & Switching_Chance<=`Switching_Likelihood' replace Choice_Normal=1 if Choice_Normal==0 & Alt_Cost_HOV_`i'<Cost_HOV_`i' & Switched_Already==0 & Switching_Chance<=`Switching_Likelihood' loc j=`i' 1 if `i'>2 { drop Avg_Cost_HOV_`j' } loc i = `i' + 1 replace Should_Still_Switch=0 if Switched_Already==1 count if Should_Still_Switch==1 gen Total_Switch_Left_`i'= r(N) drop Switching_Chance Switched_Already Should* Alt* Cong* Cost* scalar drop _all } local i = `i' 1 //Store final observations gen Final_Avg_Cost_HOV_`i'=Avg_Cost_HOV_`i' drop Avg* Total* replace Traffic_HOV_Carpool=HOV_Count in `a' replace Traffic_HOV_Normal=Normal_Count in `a' replace Average_HOV=Final_Avg_Cost_HOV_`i' in `a' drop Normal_Count HOV_Count
******************************************************************************** //SECTION 3 HOT //Define lane choice variables //0regular lane 1toll 2carpool gen Choice=0 replace Choice=2 if High_Value==1 replace Choice=1 if Top_Value==1 //This loop will organise drivers amongst lanes in a natural progression until at least 70% of drivers cannot improve from a lane switch loc r=1 gen Toll1=0.6 gen Toll2=0.6 gen Total_Switch_Left_`r'=`Drivers'/2 while Total_Switch_Left_`r'>`Drivers'*(0.3) { drop Total_Switch_Left_`r' //Create variables to indicate observed traffic levels in each lane //sj represesnts traffic in same lane //s0 represents traffic in outside option gen sj_`r'=. gen s0_`r'=. count if Choice==0 scalar Traffic_`r'Normal=r(N) replace s0_`r'=r(N) replace sj_`r'=r(N) if Choice==0 count if Choice==1 scalar Traffic_Toll=r(N) replace sj_`r'=r(N) if Choice==1 count if Choice==2 scalar Traffic_Carpool=r(N)*(1/2) replace sj_`r'=r(N)*(1/2) if Choice==2 scalar Traffic_`r'HOT=Traffic_Toll+Traffic_Carpool //Create descriptive variable to measure total revenue from toll vehicles gen Toll_Revenue`r'=Traffic_Toll*Toll`r' //Calculate cost for drivers under current toll price gen Congestion_HOT_`r'=0 //Cost in hours replace Congestion_HOT_`r'= 0.0048463 + `Congestion_Slope'*Traffic_`r'Normal if Choice==0 & Traffic_`r'Normal>`Crit_Traffic' replace Congestion_HOT_`r'= 0.0048463 + `Congestion_Slope'*Traffic_`r'HOT if Choice==1 & Traffic_`r'HOT>`Crit_Traffic' replace Congestion_HOT_`r'= 0.0048463 + `Congestion_Slope'*Traffic_`r'HOT if Choice==2 & Traffic_`r'HOT>`Crit_Traffic' gen Congestion_Cost_HOT_`r'=Value*Congestion_HOT_`r' //Cost in dollars gen Cost_HOT_`r'=(0.35+0.0355*Value) Congestion_Cost_HOT_`r' `Gas_Cost' replace Cost_HOT_`r'=(0.35+0.0355*Value) Congestion_Cost_HOT_`r' `Gas_Cost' Toll`r' if Choice==1 replace Cost_HOT_`r'=(0.35+0.0355*Value) Congestion_Cost_HOT_`r' Coordination_Cost (1/2)*`Gas_Cost' if Choice==2 replace Cost_HOT_`r'=(1)*Cost_HOT_`r' gen Observable_`r'=`Gas_Cost'+ Congestion_HOT_`r'
replace Observable_`r'=(1/2)*`Gas_Cost' + Congestion_HOT_`r' if Choice==2 //This loop updates toll for subsequent round based on observed traffic levels and current toll price loc m = 1 if `r' > `m' { loc t = `r' + 1 loc n = `r' 1 gen y_`r'=ln(sj_`r'/s0_`r') reg y_`r' Observable_`r' Toll`r', noconst scalar Alpha_OLS_`r'=_b[Toll`r'] scalar Beta_OLS_`r'=_b[Observable_`r'] //Calculate Price Elasticity information and update toll based on targeted traffic distribution gen Own_Price_Elasticity_`r'=Alpha_OLS_`r'*Toll`r'*(1sj_`r') su Own_Price_Elasticity_`r' if Choice==1 scalar OPE_`r' = r(mean) scalar Toll_Change_`r'=(((1/30)*Traffic_`r'NormalTraffic_CarpoolTraffic_Toll)*Toll`r')/(OPE_`r'*(Traffic_Toll+Traffic_Carpool)) scalar New_Toll = Toll`r' Toll_Change_`r' //If current iteration of loop has no toll payers, elasticity function fails. //This section of code insures the program does not crash by applying a slightly smaller toll on subsequent iteration if this is the case gen Toll`t'= (Toll`r')*(4/5) replace Toll`t'= (Toll`r' Toll_Change_`r') if New_Toll>0 & Traffic_Toll !=0 & OPE_`r' !=0 drop y* Own* } //Calculate cost for drivers if they switched behavior in subsequent round gen Alt_Congestion_Cost_0=Congestion_Cost_HOT_`r' gen Alt_Congestion_Cost_1=Congestion_Cost_HOT_`r' gen Alt_Congestion_Cost_2=Congestion_Cost_HOT_`r' replace Alt_Congestion_Cost_0= Value*(0.0048463 + `Congestion_Slope'*(Traffic_`r'Normal+1)) if Choice!=0 & (Traffic_`r'Normal+1)>`Crit_Traffic' replace Alt_Congestion_Cost_1= Value*(0.0048463 + `Congestion_Slope'*(Traffic_`r'HOT+1)) if Choice!=1 & (Traffic_`r'HOT+1)>`Crit_Traffic' replace Alt_Congestion_Cost_2= Value*(0.0048463 + `Congestion_Slope'*(Traffic_`r'HOT+(1/2))) if Choice!=2 & (Traffic_`r'HOT+(1/2))>`Crit_Traffic' gen Cost_if_0=(1)*((0.35+0.0355*Value) Alt_Congestion_Cost_0 `Gas_Cost') gen Cost_if_1=(1)*((0.35+0.0355*Value) Alt_Congestion_Cost_1 `Gas_Cost' Toll`r') gen Cost_if_2=(1)*((0.35+0.0355*Value) Alt_Congestion_Cost_2 Coordination_Cost (1/2)*`Gas_Cost') //Switch drivers to the lane that would provide the best cost with new toll information //Note: To avoid overswitching, drivers will switch lanes if they observe lower possible cost at a probability < 1 gen Switching_Chance=runiform() gen Wants_Switch=0 replace Wants_Switch=1 if Cost_if_0<Cost_if_1 & Cost_if_0<Cost_if_2 & Choice!=0 & Switching_Chance<=`Switching_Likelihood' replace Choice=0 if Cost_if_0<Cost_if_1 & Cost_if_0<Cost_if_2 & Choice!=0 & Switching_Chance<=`Switching_Likelihood' replace Wants_Switch=1 if Cost_if_1<Cost_if_0 & Cost_if_1<Cost_if_2 & Choice!=1 & Switching_Chance<=`Switching_Likelihood' replace Choice=1 if Cost_if_1<Cost_if_0 & Cost_if_1<Cost_if_2 & Choice!=1 & Switching_Chance<=`Switching_Likelihood' replace Wants_Switch=1 if Cost_if_2<Cost_if_0 & Cost_if_2<Cost_if_1 & Choice!=2 & Switching_Chance<=`Switching_Likelihood' replace Choice=2 if Cost_if_2<Cost_if_0 & Cost_if_2<Cost_if_1 & Choice!=2 & Switching_Chance<=`Switching_Likelihood'
local s = `r' + 1 count if Wants_Switch==1 gen Total_Switch_Left_`s'=r(N) //Store final observations egen Avg_Cost_HOT_`r'=mean(Cost_HOT_`r') loc b = `r'1 if `b'>0 { drop Avg_Cost_HOT_`b' Toll`b' Toll_Revenue`b' } su Cost_HOT_`r' if High_Value==1 replace Average_Cost_HOT_High=r(mean) in `a' su Cost_HOT_`r' if High_Value==0 replace Average_Cost_HOT_Low=r(mean) in `a' drop sj* s0* Cost* Switching_Chance Wants_Switch Congestion_HOT* Alt_Congestion* Congestion_Cost* Cost_if* Observable_* loc r = `r' + 1 if `r'>100 { if Total_Switch_Left_`r'>`Drivers'*(0.35){ replace Total_Switch_Left_`r'=0 } } } local c=`r'1 //Store final observations replace Traffic_HOT_Normal=Traffic_`c'Normal in `a' replace Traffic_HOT_Toll=Traffic_Toll in `a' replace Traffic_HOT_Carpool=Traffic_Carpool in `a' replace Average_HOT=Avg_Cost_HOT_`c' in `a' replace Revenue_From_Toll=Toll_Revenue`c' in `a' replace The_Final_Toll=Toll`c' in `a' drop Value* Coordination* High* Top* Toll* Choice* Final* Total* Avg* loc a= `a'+1 } gen round= _n //Calculate difference in average cost from addition of HOT lanes gen difference=Average_HOTAverage_HOV //Display average traffic levels for each lane in each experiment su Traffic_HOV_Normal display r(mean) su Traffic_HOV_Carpool display r(mean) su Traffic_HOT_Normal display r(mean) su Traffic_HOT_Toll display r(mean) su Traffic_HOT_Carpool display r(mean) //Display Toll Information su The_Final_Toll display r(mean)
su Revenue_From_Toll display r(mean) //Regress average costs to show if there is an overall improvement from new regulation //Regress average Costs to show if there is an improvement to each income type rename Average_HOV Relative_Cost rename Average_Cost_HOV_High High_Type rename Average_Cost_HOV_Low Low_Type eststo: reg Average_HOT Relative_Cost, noconst eststo: reg Average_Cost_HOT_High High_Type, noconst eststo: reg Average_Cost_HOT_Low Low_Type, noconst esttab, ci noabbrev /// title("Table 2: Impact Of HOT Overall & On Different Income Types") /// mlabels("Overall" "High Income" "Low Income") /// legend collabels(none) eststo clear //Note: the use of the word costs instead of payoffs within the code is purely a technicality and captures the same information as described in the theoretical model. In this context cost = (1)*payoff (with payoff being that which is described in the formulas)
