Quantifying the Impact
of New Freeway Segments
Final Report 613
May 2013
Arizona Department of Transportation
Research Center
Quantifying the Impact of New
Freeway Segments
Final Report 613
May 2013
Prepared by:
Jeffrey W. McLellan
4065 East Weldon Avenue
Phoenix, AZ 85018
Prepared for:
Arizona Department of Transportation
206 South 17th Avenue
Phoenix, Arizona 85007
in cooperation with
U.S. Department of Transportation
Federal Highway Administration
This report was funded in part through grants from the Federal Highway Administration,
U.S. Department of Transportation. The contents of this report reflect the views of the
authors, who are responsible for the facts and the accuracy of the data, and for the use or
adaptation of previously published material, presented herein. The contents do not
necessarily reflect the official views or policies of the Arizona Department of Transportation
or the Federal Highway Administration, U.S. Department of Transportation. This report does
not constitute a standard, specification, or regulation. Trade or manufacturers’ names that
may appear herein are cited only because they are considered essential to the objectives of
the report. The U.S. government and the State of Arizona do not endorse products or
manufacturers.
Technical Report Documentation Page
1. Report No.
FHWA-AZ-13-613
2. Government Accession No.
3. Recipient’s Catalog No.
4. Title and Subtitle
Quantifying the Impact of New Freeway Segments
5. Report Date
May 2013
6. Performing Organization Code
7. Authors
Jeffrey W. McLellan
8. Performing Organization Report No.
9. Performing Organization Name and Address
Jeffrey W. McLellan
4065 E. Weldon Avenue
Phoenix, AZ 85018
10. Work Unit No.
11. Contract or Grant No.
SPR-PL-1-(67) 613
12. Sponsoring Agency Name and Address
Arizona Department of Transportation
206 S. 17th Avenue
Phoenix, Arizona 85007
13.Type of Report & Period Covered
FINAL
14. Sponsoring Agency Code
15. Supplementary Notes
Prepared in cooperation with the U.S. Department of Transportation, Federal Highway Administration
16. Abstract
Many freeway users complain that new freeway segments immediately fill up with traffic after they are constructed. This
diminishes the advantages of reduced costs and reduced driving time that would make freeways theoretically superior to
arterial streets. According to previous literature, however, this phenomenon is to be expected and is not an indicator of the
efficiency or inefficiency of having new freeways. Due to Downs’s Law of Peak-hour Traffic Congestion, we expect freeways
to immediately fill upon construction, simply because they do offer superior benefits to roadway users compared to the
alternative arterial streets. Rational drivers choose to enjoy these benefits. Another phenomenon cited in the literature review
is that of induced travel, which states that with the reduction in travel time posed by using freeway segments, it can also be
expected that more commuters will choose to travel on them than otherwise would.
When Downs’s Law works synergistically with the phenomenon of induced travel, more vehicles can be accommodated in a
given geographical area, thus increasing the total number of trips taken. This adds to the overall value of our transportation
system, since after all, the value of that system is predicated on its ability to facilitate increased volume of travel.
This report is based on data acquired from the State of Arizona, the City of Phoenix and Maricopa County, Arizona, and other
sources. Through our analysis of Maricopa County traffic count data we are able to show a significant increase in traffic
volume resulting from adding new freeways. This increase in traffic volume accounts for a net benefit of over $18 million
dollars per year for a given mile-long stretch of roadway. Over a freeway design-life of 20 years this is far in excess of the
average of $72 million needed to construct that mile of freeway.
Ultimately, any evaluation of the freeway system must take into consideration the explicit and implicit benefits of the system.
We know that congestion is going to be present whether new freeways are constructed or not. Before freeway segments are
constructed, the existing arterial streets are congested. After the completion of freeway segments, some drivers shift from
arterial streets to the new freeway. This lessens traffic on the arterials, leading to more drivers taking trips they previously
avoided (i.e. induced travel). Even though congestion is an inevitable condition, even on freeway segments post-construction,
freeways still offer a clear net benefit.
17. Key Words
Freeway, Traffic, Cost/Benefit
18. Distribution statement
Document is available to the U.S.
public through the National Technical
Information Service, Springfield,
Virginia, 22161
23. Registrant’s Seal
19. Security Classification
Unclassified
20. Security Classification
Unclassified
21. No. of Pages
40
22. Price
SI* (MODERN METRIC) CONVERSION FACTORS
APPROXIMATE CONVERSIONS TO SI UNITS APPROXIMATE CONVERSIONS FROM SI UNITS
Symbol When You Know Multiply By To Find Symbol Symbol When You Know Multiply By To Find Symbol
LENGTH
LENGTH
in inches 25.4 millimeters mm mm millimeters 0.039 inches in
ft feet 0.305 meters m m meters 3.28 feet ft
yd yards 0.914 meters m m meters 1.09 yards yd
mi miles 1.61 kilometers km km kilometers 0.621 miles mi
AREA
AREA
in2
square inches 645.2 square millimeters mm2
mm2
square millimeters 0.0016 square inches in2
ft2
square feet 0.093 square meters m2
m2
square meters 10.764 square feet ft2
yd2 square yards 0.836 square meters m2 m2
square meters 1.195 square yards yd2
ac acres 0.405 hectares ha ha hectares 2.47 acres ac
mi2
square miles 2.59 square kilometers km2
km2 square kilometers 0.386 square miles mi2
VOLUME VOLUME
fl oz fluid ounces 29.57 milliliters mL mL milliliters 0.034 fluid ounces fl oz
gal gallons 3.785 liters L L liters 0.264 gallons gal
ft3
cubic feet 0.028 cubic meters m3
m3
cubic meters 35.315 cubic feet ft3
yd3
cubic yards 0.765 cubic meters m3 m3
cubic meters 1.308 cubic yards yd3
NOTE: Volumes greater than 1000L shall be shown in m3.
MASS MASS
oz ounces 28.35 grams g g grams 0.035 ounces oz
lb pounds 0.454 kilograms kg kg kilograms 2.205 pounds lb
T short tons (2000lb) 0.907 megagrams
(or “metric ton”)
mg
(or “t”)
mg
(or “t”)
megagrams
(or “metric ton”)
1.102 short tons (2000lb) T
TEMPERATURE (exact) TEMPERATURE (exact)
ºF Fahrenheit
temperature
5(F-32)/9
or (F-32)/1.8
Celsius temperature ºC ºC Celsius temperature 1.8C + 32 Fahrenheit
temperature
ºF
ILLUMINATION ILLUMINATION
fc foot-candles 10.76 lux lx lx lux 0.0929 foot-candles fc
fl foot-Lamberts 3.426 candela/m2 cd/m2 cd/m2 candela/m2 0.2919 foot-Lamberts fl
FORCE AND PRESSURE OR STRESS FORCE AND PRESSURE OR STRESS
lbf poundforce 4.45 newtons N N newtons 0.225 poundforce lbf
lbf/in2 poundforce per
square inch
6.89 kilopascals kPa kPa kilopascals 0.145 poundforce per
square inch
lbf/in2
v
Contents
Executive Summary ........................................................................................................................ 1
Introduction .................................................................................................................................... 3
Literature Review........................................................................................................................... 5
Model Framework ........................................................................................................................... 9
The Model ...............................................................................................................................12
Case 1. Isolation of Population Change; Single Parallel Street. ................................................... 18
Case 2. Multiple Parallel Streets and Freeway. .............................................................. 19
Case 3. Multiple Parallel Streets Only. .......................................................................... 19
Data and Estimation. ...............................................................................................................21
Estimating the Model. .............................................................................................................24
Estimate 1. Induced-Travel Model. ................................................................................ 24
Estimate 2. Induced-Travel Model with Inclusion of Freeway Count. .......................... 25
Estimate 3. Induced-Travel Model with Addition of Freeway Segment. ....................... 26
Valuation ...................................................................................................................................... 29
Conclusion ................................................................................................................................... 31
References .................................................................................................................................... 33
vi
List of Figures
Figure 1. Greater Phoenix Population Trend ................................................................................ 10
Figure 2. Typical Scatter Plot of Traffic Volume vs. Population with Approximate Best-
Fit Line. 13
Figure 3. Best-Fit optimal X (Population-Adjusted Y ) for Sample Data of Equation 11 ................... 16
Figure 4. Greater Phoenix Traffic Volumes per Freeway Segment vs. Population. ..................... 18
Figure 5. Average Arterial vs. Average Freeway Counts (in Thousands). ................................... 22
Figure 6. Example of Daily Traffic Counts (in Thousands) along Bands of Arterial Streets
Parallel to an Urban Freeway. ....................................................................................... 23
Figure 7. Predicted Traffic Volumes – Induced Travel (1). ......................................................... 25
Figure 8. Predicted Traffic Volumes – Induced Travel (2). ......................................................... 27
List of Tables
Table 1. Segments Sampled by Year. ........................................................................................... 22
Table 2. Induced Travel (1). ......................................................................................................... 24
Table 3. Induced Travel (2). ......................................................................................................... 26
Table 4. Downs’s Law (3) ............................................................................................................ 27
vii
List of Abbreviations, Acronyms, and Symbols
‘ (primed) Symbol for matrix transposition
1 Symbol for matrix inversion
ADOA Arizona Department of Administration
AFTER An instance of x ; binary 1 if freeway is present or 0 otherwise
b Independent variable, or covariate, in a regression equation of k terms
k -row-by-one-column vector of k b for all covariates k under consideration
e Base of the natural logarithm, approximately equal to 2.718
Error in fit of line through a particular data observation n
n -row-by-one-column vector of n for all data observations n
F-Value Significance measurement for determined values of b
FHWA Federal Highway Administration
HOV High-Occupancy Vehicle
k Subscript to distinguish a particular b and to distinguish x belonging to that b
ln Natural logarithm (to the base e )
MAG Maricopa Association of Governments
MILES An instance of x ; miles between freeway and street
n Subscript to distinguish y and x belonging to a particular data observation
POP An instance of x ; population
R2 Fit-closeness measurement for all best-fit lines considered in regression
RARF Regional Area Road Fund
Regression Determination of b by matrix solution of n simultaneous best-fit-line equations
t Value Confidence measurement for determined values of b
TOTART An instance of y ; sum of multiple-arterial traffic volumes
TOTARTFWY An instance of y ; sum of freeway and multiple-arterial traffic volumes
TOTRAF An instance of y ; sum of freeway and one-arterial traffic volumes
TOTMILES An instance of x ; total freeway stock in miles
U.S. United States
USDOT United States Department of Transportation
x Independent variable of the equation of a best-fit line through a particular data observation n
X n -row-by- k -column matrix of n k x , for all data observations n and covariates k
y Dependent variable of the equation of a best-fit line through a particular data observation n
Y n -row-by-one-column vector of n y for all data observations n
viii
1
Executive Summary
Some freeway users complain that new freeway segments fill up with traffic during peak hours
immediately after construction. Because of this concern, the debate about the costs and benefits
of freeways often centers on relieving congestion. The literature states that the long-term relief of
congestion is an elusive goal. While congestion is a pervasive feature of freeways, it does not
mean that constructing them is useless. This study helps to demonstrate that the great benefit of
freeways is to facilitate travel rather than reduce peak-hour congestion. The study finds that the
facilitated travel far outweighs the cost of freeway construction. Even if new freeway capacity
becomes congested during peak travel hours, there is still great benefit in the increased travel
mobility that can be accommodated.
2
3
Introduction
For regular commuters as well as other drivers of motor vehicles, driving on urban freeways has
some inherent advantages to driving on arterial streets. The first benefit that many people may
think of is the time they save going to a particular destination at a higher posted speed than that
typically posted on arterial streets. When driving on urban freeways, drivers can travel safely at
posted speed limits of 65 mph, where the design and operational considerations accommodate
such speed, whereas most arterial streets have posted speed limits of 45 mph, or even less, in
residential areas or school zones. Besides having higher posted speed limits, urban freeways also
lack, absent rush-hour traffic or incidents, the constant cycle of stop and go that drivers
experience at the intersections of busy arterial streets, where the flow of traffic is regulated by
the constant use of traffic lights or stop signs. Additionally, and possibly a lesser known fact to
the transportation-using public, urban freeways have also been shown to be statistically much
safer than arterial streets. The Federal Highway Administration (FHWA) has shown that the
fatality rate on urban freeways is much lower than the fatality rate on urban arterial streets.
(FHWA 2005, Table FI-20) These types of clear and significant benefits should undoubtedly
motivate drivers to choose urban freeways as substitutes for parallel streets whenever and
wherever possible. It is reasonable to assume that discerning drivers, when confronted with two
possible routes of travel from one point to another, should be expected to take the faster and
more predictable route, which could be arterial streets if the trip is only a few miles.
Because urban freeways pose such advantages over arterial streets, where substantial distances
must be traveled, governments commit considerable time, planning, and resources to building
more of them. As segments of these new freeways are finished, drivers should be expected to
start using them immediately over the alternative mode of nearby arterial surface streets. While
this substitution behavior should tend to increase traffic on the newly opened freeway segments,
it should also consequently reduce congestion on parallel arterials, thus increasing space and
mobility there. Along with the reduction in surface-street congestion, travel time to destinations
that would involve the use of these parallel streets is shortened. For drivers choosing to use the
arterial streets, this should reduce the cost of traveling to such destinations, thereby motivating
more drivers to travel. Moreover, as freeways have lower fatality rates than those on arterial
streets, (FHWA 2005, Tables VM-2 and FI-20) there are additional public benefits to
transferring traffic away from parallel streets.
Despite all of the anticipated benefits of urban freeway use over arterial streets, many drivers on
new freeway segments complain that the new segments fill up with new drivers, become
congested, and thus increase average driving times. This is understandable, as congestion can be
thought of as a “time tax”—a tax that is paid by individual drivers with the extra time they spend
in the car. Increased congestion and driving time will naturally diminish some of the benefits of
using new freeway segments in the first place. Hypothetically, a point could be reached where
congestion and increased driving times on new freeways get so bad that there is no longer a
significant advantage to a driver of using the freeways over arterial streets. If it is manifest that
new freeway segments simply “fill up” with drivers during peak hours to the point where their
advantages over arterial streets become nullified, what is the value of building more of them?
The purpose of this research project is to investigate and try to quantify the benefits that are
derived from the construction of these new urban freeway segments.
4
5
Literature Review
As pointed out in the introduction, freeways offer a great series of benefits to roadway travelers.
They allow people to save time, and drivers can travel safely at higher posted speeds than those
on arterial streets. This is corroborated by Lin and Niemeier (2003), who find that actual average
speeds at various levels of service (LOS) are higher on urban freeways than on arterial streets.
Additionally, urban freeways are safer than arterial streets. According to the Federal Highway
Administration, (FHWA 2005, Tables VM-2 and FI-20) the national urban freeway fatality rate
is 0.63 persons per 100 million vehicle miles traveled compared with a rate of 1.07 persons per
100 million vehicle miles traveled on urban arterial streets. In Arizona, the 2004 urban freeway
fatality rate was 57 fatalities on interstate highways, 36 on non-interstate highways, and 446 on
other streets. Thus, avoidance of fatalities adds a bonus benefit to the time saved.
These significant benefits of freeways are diluted by peak-hour congestion. The obvious intent of
building a freeway is to move traffic. Yet, as soon as they are built, urban freeways seem to
become congested with peak-hour traffic. While little has been written, theoretically or
empirically, about this behavior, there have been some attempts to provide a framework for
analyzing the behavior of drivers concerning urban freeways. As early as 1962, economist
Anthony Downs (1962) observed that the construction of new urban freeway segments doesn't
seem to reduce peak-hour traffic congestion on these freeways. Downs coined the phrase
“Downs's Law of Peak-hour Traffic Congestion” to describe the phenomenon.
Downs's Law states that any expressway that does not require a toll and has capacity made
available by trip-reduction programs will soon be utilized by new trips, as people formerly
discouraged from driving on the freeways are attracted to them (Gordon and Richardson 1993).
Cervero and Hansen (2002) and Parry (2002) named this new-trip generation phenomenon
“latent demand,” and other authors have also called it “induced demand” (Noland 2001) and
“underlying demand” (Noland and Lem 2002). This has led many people to believe that building
new urban freeway segments does not alleviate congestion effectively. Downs notes that this fact
seems to frustrate the average commuter and may convey the impression of poor highway
planning. He argues, though, that the failure of new urban freeway segments to reduce
congestion is not a function of poor planning, but rather is due to the nature of traffic
equilibrium.
Downs begins with a few assumptions about commuters. His first assumption is that they attempt
to minimize their travel time and are limited by current technology and income when doing so.
Secondly, he assumes that a commuter won't change his means of transportation or route unless
there is some alteration in his environment. In other words, his preferences exhibit habit
persistence.
Downs also describes how travel times on certain routes tend to equalize. For example, if there
are two routes, A and B, from the same origin to the same destination, where travel times on both
routes are equal (assuming away other differences that may influence behavior such as scenery,
etc.), then there is a balance between the two routes. If there is a change in the environment that
results in a reduction in travel time for commuters who choose route A, then the change will
result in the traffic from these roads being unbalanced. Once drivers on route B become aware
that route A provides a shorter travel time, they will begin to switch from route B to route A,
6
thus increasing congestion on route A, and reducing congestion on route B. This continues until
travel time on the two routes equalizes. Due to commuters' habit persistence, their route
preference will tend to stay the same unless there is some event that alters the travel time on one
route or the other (Downs 1962).
The extension of the above example to the construction of new urban freeway segments is
straightforward. The freeway segment offers a faster route to relevant destinations, and therefore
commuters will shift to that route until they gain no benefit from switching. Due to habit
persistence, those who gain no additional benefit will feel most comfortable staying with their
original route. Following this logic, if the addition of an urban freeway segment adds to the
overall capacity between the origin and destination, then traffic will begin to shift away from
surface streets to the freeway. This shift will reduce travel time on surface streets. With the
reduced travel time, it can also be expected that more commuters will choose to travel than
otherwise would, which results in a higher flow of traffic between the origin and destination.
This increase in traffic flow is known as induced travel. Downs's concepts of Downs's Law and
induced travel appear extensively in the literature (Arnott, de Palma, and Lindsey 1993; Small
1982; Calfee and Winston 1998).
DeCorla-Souza and Cohen (1999) demonstrate how induced travel can be estimated for
incorporation into the evaluation process for highway expansion projects. Their approach is
particularly useful when it is difficult to forecast how many additional commuters will travel due
to the construction of new freeways. They apply this methodology in order to study the benefits
resulting from the hypothetical construction of a new urban freeway segment. Their analysis
suggests that the increase in travel induced by highway expansion not only depends on initial
congestion levels prior to expansion, but is greatly compounded when the congestion is heavy.
This makes sense. If a particular roadway is heavily congested, and drive times on it are
relatively long, then it is clearly a route that is heavily demanded by drivers. Since this road is in
high demand, more drivers will tend to use it when congestion is relieved by an urban freeway
segment than they would a roadway that was relatively less congested to begin with. DeCorla-
Souza and Cohen demonstrate that, even when initial high-level congestion is worsened by the
resulting induced travel, the new segment still makes a large positive impact on congestion relief.
This empirically supports Downs's traffic equilibrium hypothesis and further illustrates the
benefits of the construction of new urban freeway segments.
Even if induced travel does coincide with the construction of new urban freeway segments, it
does not necessarily lead to a conclusion that the benefits of those new segments are offset. The
Thoreau Institute (2006) used a straightforward statistical analysis of Texas Transportation
Institute data from 68 different urban areas from 1982 to 1999 to show that freeway construction
shifts driving from ordinary streets to freeways. Since freeway driving is statistically safer than
driving on arterial or surface streets, shifting more drivers onto the freeways provides a clear
benefit. Thoreau also showed that increases in traffic are not correlated with utilization of public
transit, and therefore spending should be focused on the form of transportation that does get used
more with more congestion, i.e., freeways. Admittedly, Thoreau claimed to have found that,
while freeway per-capita driving increases, arterial- and surface-street driving decreases, causing
total per-capita driving to not necessarily increase. This conclusion differs from that of this
paper, which uses a different data set and methodology.
7
While congestion is virtually inevitable, it can be somewhat alleviated, as is illustrated by Downs
(1992). Downs states that, due to rapid growth, demand-side policies for reducing congestion can
be overwhelmed, thus motivating the application of supply-side remedies. He argues that, while
the intensity of congestion during the zenith of peak periods may not be reduced by adding to
urban freeway capacity, which is explicitly stated in Downs's Law, the additional capacity may
shorten the overall length of the peak period itself. This alone, however, is not a panacea.
Assuming that there is continued rapid growth, as more people move to a metropolitan area, the
peak period will again lengthen in the absence of a corresponding increase in roadway capacity.
Downs (1992) continues on to suggest that it is important to properly manage the efficiency of
traffic flows using such techniques as roving repair vehicles, proper maintenance of roadways,
and electronically controlled signs to inform drivers about conditions ahead. He cites several
studies that show how these techniques, as well as ramp controls, high-occupancy vehicle (HOV)
lanes, and park-and-ride lots, have had a noticeable impact on reducing congestion in Seattle. In
particular, HOV lanes encourage drivers to carpool or ride the bus, in part because the additional
commute time that is generally associated with traveling in such a manner is mitigated by
transferring car pool vehicles or buses from slow-moving congested lanes to faster-moving HOV
lanes. Additionally, commuting via ride-sharing or buses costs less per commuter than driving
alone. Such cost savings, compounded with the time savings, motivate drivers to ride-share or
take buses and, therefore, contribute to reducing congestion. While congestion cannot be
completely eliminated, its negative effects can be reduced by such supply-side remedies.
These remedies are needed all the more as it is certainly clear that there is no end in sight to the
ever-increasing rate of growth in vehicle miles traveled in the United States. Between 1980 and
2005, urban road mileage increased 62 percent, while vehicle miles traveled in urban areas have
increased by 130 percent. (FHWA [1981?], Tables VM-1 and HM-10; FHWA 2006, Tables VM-
1 and HM-10) This is also supported by Parry (2002), who notes that increases in vehicle miles
traveled are exceeding increases in urban freeway capacity. While this established trend lends
support to the need for increased urban freeway capacity, Parry aims to formalize this fact by
analyzing how commuters perceive the tradeoff between urban freeways and other modes of
transportation. He develops a model in which he characterizes this tradeoff by finding the
various points at which the cost to commuters of driving on the freeway during peak periods is
equal to the cost of utilizing various alternative modes of transportation. This resulting set of
tradeoffs is known as the commuters' “marginal rate of substitution.” Ultimately, the driver is
indifferent between driving on the freeway and traveling via all other substitutes.
Drivers, however, fail to consider many of the costs of driving that don't fully affect them. In
particular, individuals fail to consider the costs that their additional vehicles bring about by
increasing the total volume of traffic. Parry (2002) calls these costs “marginal external costs.”
When drivers fail to consider marginal external costs, driving on urban freeways during peak
periods appears less costly to the commuter than it actually is to society. Consequently, this leads
to an inordinately high number of drivers choosing urban freeways as their mode of
transportation during peak periods, which leads to congestion.
Parry (2002) numerically analyzes this phenomenon. After making some simple assumptions
about drivers' preferences, he derives the equilibrium conditions described above. Using previous
literature and relevant data sources, he is able to run his model simulation. Following this
8
framework, Parry simulates the addition of various policies and taxes and judges their impacts on
overall efficiency. His numerical findings support the notion that urban freeways are over-utilized
when drivers are not forced to account for marginal external costs.
Winston and Shirley (1998) come to a similar conclusion. They use a model to estimate the
probability that commuters will choose one form of transportation over another. As expected, the
authors find that higher out-of-pocket costs on a given mode of transportation discourage
passengers from traveling on that mode. They also find that the longer the commute, the less of
an impact costs have on the mode of transportation, and the more drivers tend to dislike
carpooling. Additionally, they are able to use the total travel time per mile and cost per mile to
estimate commuters' value of travel time. They find that the value of travel increases with
distance traveled for all but the longest commutes. This type of framework could easily be
applied to modeling the choice between driving on urban freeways and driving on arterial streets.
While Parry (2002) and Winston and Shirley (1998) focus on the individual driver's assessment
of the costs and benefits of varying modes of travel, another study (Carey, Mansour, and
Semmens 2000) concentrates on the overall value of a single mode of travel within Maricopa
County, Arizona. They accomplish this by means of a corporate-style financial analysis that
evaluates the Maricopa County Regional Area Road Fund (RARF) highway system by its overall
profitability. This style of analysis differs from the traditional government style. In the
government style, all sources of revenue are taken into account, including those sources that
come in the form of subsidies from other branches of government and non-highway users. Not
surprisingly, when the authors analyze the RARF highway system using a corporate-style
analysis, which excludes revenue from subsidies and non-highway users, they find that the
system is not profitable and actually operates at a net loss. They interpret this loss as an indicator
that the revenue generated directly from highway users by current taxes is not sufficient to cover
the cost of the system.
Modern accounting is not the only proposed means of assessing the overall value of a freeway
system. Following Rowell, Buonincontri, and Semmens (1999), Carey, Mansour, and Semmens
(2000) use the cost of owning and operating a vehicle as a proxy for highway value. They
estimate that highway users' willingness to pay is higher than the current user-tax cost per mile
that they actually do pay, which leads them to conclude that highways tend to be undervalued.
Roadways are nearly useless without vehicles to be driven on them, and vehicles are nearly
useless without roadways. Any two goods with this type of relationship are known as
complements. Since roadways and vehicles are nearly perfect complements, the implication of
this is that users value highways more than they are currently paying. If the current highway
system is undervalued, then the public should be willing and able to pay for further expansion of
the urban freeway system.
9
Model Framework
Much of the work cited in the literature review provides a foundation of theories that can be used
to form hypotheses regarding the true impact of adding new freeway segments to an already
existing urban street system. Any such hypotheses must be tested within the framework of a
robust and accurate model that can be estimated using realistic assumptions and adequate data
that is not overly difficult to obtain.
One of the primary and most important assertions in the literature is that freeways reduce the
overall cost of travel. This cost of travel can be thought of as being broken into many constituent
components. One component is the cost of fuel, which increases the longer a vehicle is stuck in
traffic. Another component is the wear and tear exacted on a vehicle as the result of constant
stop-and-go traffic. One of the more subtle costs, while at the same time one of the most
important from an economic perspective, is the opportunity cost to a driver of spending longer
amounts of time in traffic. In other words, each minute spent behind the wheel is one less minute
that a driver could be using towards another desired activity. Simply put, the more time the
driver spends in traffic, the more other opportunities he forfeits, hence the term opportunity cost.
For example, the Greater Phoenix area is one of the nation’s major metropolitan areas. It is
relatively unique in that its low density demands that often great distances must be traveled in
order to take advantage of what the region has to offer. This implies that the opportunity cost of a
lower-capacity road system is higher than would otherwise be the case in a denser urban area.
All of these different forms of cost can be lumped together to form an overall composite cost,
which, conveniently defined for the purposes of this paper, increases or decreases, based on the
time a vehicle spends in traffic on a route between two given points, A and B. The more time
spent in the vehicle, the higher the cost and vice versa. Consequently, in this paper, when we
speak of the cost of travel, it is this overall or composite cost that is being referred to, i.e. a total
cost that can be reduced by shortening the amount of time it takes for a driver to travel from A to
B. What has been found in the literature is that a reduction in the cost of travel brings about a
corresponding increase in per-capita traffic. If it is assumed that roadways and freeways obey the
law of demand, or more specifically, if it is a safe assumption that people will use these modes of
travel more when the cost of doing so decreases, then it also follows that any observed increase
in overall traffic volume can be regarded as an indicator that the cost of taking a trip during peak
hours is lower once a new freeway segment is opened. In the literature, this phenomenon is given
the name of induced travel and, fortunately, it is something that can be empirically tested with
proper data analysis. A question to be answered by any prospective model could then be the
following: did the overall traffic within an urban geographic vicinity increase, with the addition
of a new freeway segment, after accounting for increases in traffic due to other factors?
One such factor that can be identified beforehand is population growth. If it’s assumed that an
increase in population leads to an increase in the number of drivers within a particular
geographic area, then it could be assumed that traffic increases as well; hence the assumption
that population numbers and traffic volumes are positively correlated variables. If this is so, then
any significant changes in population must be incorporated into a specified model. This theorem
could be especially significant in a metropolitan area such as Greater Phoenix, where population
growth has been positive and constant over the last several decades. Using data obtained from
the Arizona Department of Administration, (ADOA 1970-2010) the steady growth in the Greater
Phoenix area is depicted in Figure 1.
10
Figure 1. Greater Phoenix Population Trend
While it may be safe and reasonable to simply assume that a population increase certainly results
in a higher number of drivers on the roads and freeways, an effective model should be able to
quantify the actual degree of increased traffic that can be attributed to an increase in population.
Once this effect is measured, it can be stripped out of the model’s results to isolate the net
increase in traffic due to induced travel from the construction of new urban freeway segments.
A concept related to induced travel, which is also introduced in the literature, is that of Downs’s
Law of Peak-hour Traffic Congestion, which states that any freeway capacity made available by
trip-reduction programs or extra freeway space will soon be utilized by new trips. This results
from latent demand, as people formerly discouraged from driving are attracted to the freeways
given the new, lower cost of driving. The effect of induced travel causes the new capacity of
freeways to be filled up with yet more drivers and vehicles until the cost of driving is about the
same as it was before the addition of the new freeway. The only net difference is that more
drivers are on the freeways and surface streets than before. In other words, the addition of new
urban freeway segments does not significantly reduce congestion over time, but there is a higher
overall traffic volume. In practice, new urban freeway segments do confer this benefit, and,
instead of viewing the reoccurrence of high-volume congestion after the completion of new
urban freeway segments as a negative condition that was supposed to have been eliminated, it
should rather be viewed as an expected result of the new benefit of lower driving cost on urban
freeways, thus fulfilling Downs’s Law.
In summary, then:
A driver typically has a latent demand to drive around more if his, or her, opportunity cost
could be lowered by an uncongested street or freeway.
Opening a new freeway segment lowers this person’s cost and thus induces him, or her, to
travel.
Many such drivers fill up the new freeway segment, according to Downs’s Law, until they
balance against a restored cost.
11
Given these interrelated concepts, there are several key questions that can be answered by a
properly specified model:
1. Does the permanence of long-term congestion in general mean that new urban freeway
segments have little or no benefit?
2. Are there other effects conferred by the building of new urban freeway segments besides
congestion?
3. What is the effect on arterial street traffic volume in the wake of building new urban
freeway segments?
As with the process of building any model, we have formulated several hypotheses as to what the
effects of adding new freeway segments might be. These are as follows:
1. Building new urban freeway segments has benefits outside of simply alleviating
congestion, as we expect total traffic volume to increase due to induced travel, which, in
and of itself, is a benefit to the public.
2. Total volume of arterial street traffic during peak hours will either remain constant as
latent-demand driving fills the void left by drivers drawn to the new freeway or actually
decrease if the added freeway capacity exceeds the latent demand.
In order to test these hypotheses, an experimental design was constructed according to the
following assumptions and specifications:
1. If the theory of induced travel turns out to be true, then, when a new urban freeway
segment is completed, we should see more total traffic within a defined geographical band
than before the segment was built.
2. If we see that freeway traffic increases for every unit increase in arterial street traffic
volume, we can show that not only are people substituting freeway driving for arterial-street
driving, but also marginal drivers are now motivated to take an arterial-street trip that
they wouldn’t have otherwise taken. Such a result would simultaneously exemplify the
theories of Downs’s Law and induced travel.
To numerically analyze this experimental design, we will employ an analysis technique
commonly used in economic analysis known as regression analysis. The next section describes
this technique and how it is applied in this paper to develop and then estimate models of urban
traffic.
12
The Model
Regression analysis is a common statistical technique used to determine the relationship between
a set of variables and some response. It is widely used in econometrics to determine the
relationship among variables; in the economy, in labor markets, in financial markets, etc. It is
used in this paper to help determine if a relationship exists between the addition of new freeway
segments and traffic volumes. This section will explain the concept of regression analysis and
then illustrate its use by explaining how it was applied to construct and estimate the induced-travel
model.
The goal of the analysis is to determine whether the construction of a freeway segment has an
impact on total traffic volumes in the Greater Phoenix area. The hard part, however, is that we
want to know, all else being equal, the relationship between total traffic and a new freeway
segment. In order to do this, we need to control for potential confounding factors. Thus, we need
to ask the question: what other factors could affect total traffic volumes in an area? One potential
factor is the local population.
Figure 2 shows a scatter plot with the natural logarithm of total traffic depicted on the vertical
axis and the natural logarithm of the population of the Greater Phoenix area along the horizontal
axis.1 The plot has two sets of points: one set representing traffic volumes at each population
level where there are freeways present and one set where freeways are not present. The goal here
is to estimate what the difference in total traffic is between areas that have freeway segments and
areas that don’t have freeway segments, controlling for changes in population. We do this by
calculating a “line of best fit” through the data points, as suggested in the figure. This line may
be written in the familiar slope-intercept form as
1 0 y b xb
where:
y is the natural logarithm of total traffic.
x is the natural logarithm of population.
1 b is the line’s slope, which is the change in y divided by the change in x.
0 b is the value of y where the line intercepts the vertical axis at the hypothetical
place (off the graph) where the natural logarithm of population is zero.
To determine 1 b and 0 b with mathematical rigor, we may start by drawing the line that goes
through the first traffic-volume measurement 1 y at a time of known population 1 x with a
presently unknown slope and intercept. To account for the error between the known 1 y and its
yet-undetermined equivalent calculated by 1 0 b x b , we introduce an error term , which, with
rearrangement of the order of addition, leads to:
1 0 1 1 1 y b b x
1 Strictly, the quantities, of which these natural logarithms are taken, are scaled so as to make the numbers smaller
than the raw quantities, but this does not affect our analysis, as we shall see.
(Eq. 1)
(Eq. 2)
13
Figure 2. Typical Scatter Plot of Traffic Volume vs. Population with Approximate
Best-Fit Line.
Then we may draw another line that goes through another measurement 2 y at the time of known
population 2 x , which would have the equation:
2 0 1 2 2 y b b x
After drawing as many of these lines as there are traffic-volume measurements available, we
may solve for their best-fit coefficients 1 b and 0 b so as to minimize the error terms taken as a
group. We use a matrix equation of the form:
4
3
2
1
1
0
4
3
2
1
4
3
2
1
1
1
1
1
b
b
x
x
x
x
y
y
y
y
or
Y X
where:
Y is the response variable, a vector (one-column, or n1 matrix) of the natural
(Eq. 3)
(Eq. 5)
(Eq. 4)
14
logarithms of all the observed traffic volumes, where n (here, 4) is the number of
observations.
X is an n k matrix, where k (here, 2) is the number of independent variables
in below. Its columns, for the case of Equation 4 are, respectively, unity multipliers for
0 b and the populations applicable to each observation. Such variables are often called
covariates. They are also called confounding factors, if they represent changing conditions
that might obscure desired results over a period of interest.
is the vector containing our 0 b and 1 b , the coefficients, where 0 b is the
intercept of the line of best fit, and 1 b is the slope of the line of best fit. These coefficients
determine the effects that the independent variables in X have on the dependent variables
in Y .
is the error vector containing the residuals, which are the predicted
observations minus the actual dependent observations.
Going back to the form of Equation 2, we may express y and x as the traffic and population
quantities they represent, namely
ln( ) ln( ) 0 1 TOTRAF b b POP
where:
TOTRAF is the sum of traffic volumes on an arterial street parallel to the freeway
plus the traffic volume on that freeway segment if it exists. TOTRAF is
exemplified by the vertical axis of the graph of Figure 2.
POP is the population pertinent to a TOTRAF observation, exemplified by the
horizontal axis of the graph of Figure 2.
Our analysis, however, has more independent variables than just population. Fundamental to this
study is the presence or absence of a freeway, which is a binary switch variable, with values of 0
or 1. Other variables may be the distance from the point of measurement to the freeway and the
total stock of freeway mileage available in an area. All the variables cannot be shown
simultaneously as in Figure 2, which is limited to only the two dimensions of traffic volume and
population, but they may be mathematically accounted for in determining the coefficients of the
best-fit conceptual line that would course through such a multi-dimensional graph. We may
expand Equation 6 to include these other independent variables:
ln( ) ln( ) ln( ) ln( ) 0 1 2 3 4 TOTRAF b b AFTER b POP b MILES b TOTMILES
where the new variables are:
AFTER , a binary switch variable (0 or1) to denote that the freeway is not present
or present.
MILES , the distance, in miles, from the freeway segment to the arterial street.
TOTMILES , the total stock, in miles, of urban freeway in a given year.
k b , coefficients as before, with some arbitrary renumbering of the subscripts.
(Eq. 6)
(Eq. 7)
15
Despite the fact that Equation 7 has four independent variables compared to the one in Equation
6, the system of simultaneous equations of this form may still be written in the form of Equation
5, namely
Y X
except that X will now have five columns instead of the two columns in Equation 4, and will
be a five-deep vector instead of two.
This is our model of the forces that result in the data of Figure 2, and it is the vehicle by which to
obtain the vector that describes the best-fit line that minimizes the distances between points
on the line2 and their respective actual data points. The specific structure of Equation 7, with its
particular choice of covariates, is called a specification.
We obtain the best-fit by using matrix calculus to minimize the sum of the squares of in
Equation 5; that is, we minimize
'
Where ' is the transpose of . But because
Y X
We can substitute Y X for in Equation 8 to get:
(Y X )Y X
Then, using calculus, we find the coefficients k b that minimize this expression. It can be shown
that the solution vector is:
X X X Y optimal 1
where the -1 exponent means the matrix inversion of X X .
A numerical example may be useful here. Leaving the last two covariates out of Equation 7,
casting it in the matrix form of Equation 5, and assigning some test values to it, we have:
Y X
4
3
2
1
2
1
0
1 1 2.3
1 1 2.71
1 0 2.6
1 0 2.5
2.73
2.94
1.25
2.56
b
b
b
x
Here the Y matrix contains the natural logs of four observations of total traffic in its four rows;
and the columns of the X matrix are, respectively, the intercept multiplier (unity), a binary
indicator variable, where 1 indicates the presence of a freeway and 0 indicates otherwise, and the
2 It is understood that the “line” is no longer readily visualizable in a single graph because it now
courses through five dimensions instead of the two dimensions of Figure 2.
(Eq. 5)
(Eq. 5)
(Eq. 11)
(Eq. 8)
(Eq. 9)
(Eq. 5a)
(Eq. 10)
16
natural log of population. The vector, which is now three deep to accommodate the three
covariates in X , contains, from the top, the intercept, the freeway-or-not slope parameter, and
the population slope parameter. Substituting into Equation 10 to find the optimal values for :
2.73
2.94
1.25
2.56
2.5 2.6 2.71 2.3
0 0 1 1
1 1 1 1
1 1 2.3
1 1 2.71
1 0 2.6
1 0 2.5
2.5 2.6 2.71 2.3
0 0 1 1
1 1 1 1
1
optimal
0.265
0.923
2.557
23.896
5.670
9.480
28.668 0.506 11.242
1.790 1.023 0.506
73.603 1.790 28.668
That is,
Associated Covariate Symbol Value
Unity (Intercept) 0 b 2.557
AFTER 1 b 0.923
ln(POP) 2 b -0.265
Now we obtain our best-fit optimal X , which will be our four raw observations in Y
( ln(TOTRAF) ) adjusted for population:
2.871
2.762
1.868
1.895
0.265
0.923
2.557
1 1 2.3
1 1 2.71
1 0 2.6
1 0 2.5
optimal X
We may plot this result in Figure 3, also showing our original Y for comparison:
Figure 3. Best-Fit optimal X (Population-Adjusted Y ) for Sample Data of Equation 11.
(Eq. 12)
17
It can be seen in the figure that a freeway (represented by the third and fourth observations) is
associated with higher amounts of traffic. The increase in the natural log of total traffic, with
population held constant, may be estimated by taking the difference between the means of the
latter pair of observations and the first pair. That is,
0.935
2
1.895 1.868
2
2.762 2.871
ln( )
TOTRAF
2.547 0.935 e
TOTRAF
TOTRAF
BEFORE
AFTER
This means that TOTRAF , after the freeway opening, increases by an estimated factor of 1.547,
or 155 percent, with population held constant.
However, it is unnecessary to draw Figure 3 and evaluate Equations 13 and 14 to reach this
conclusion. When the covariates in Y are log-transformed as they are for n TOTRAF in Equation
7, and some binary covariates in X are untransformed as they are for n AFTER , then it can be
shown that the change in TOTRAF caused by the change in AFTER from 0 to 1, with other
covariates held constant, is obtained by simply applying exponentiation to 1 b . That is,
2.517 0.923 e
TOTRAF
TOTRAF
BEFORE
AFTER
This means that TOTRAF after the freeway opening increases by a factor of 1.517, or 155
percent, with population held constant. This is the rigorously correct result, differing from our
coarse estimate of Equation 14 by a relative 2 percent.
The ultimate goal of the model of Equation 7 is to describe and quantify the effects of new,
urban freeway segments on overall traffic, specifically within the Greater Phoenix metropolitan
area. As mentioned, there are two expected consequences from the development of new urban
freeway segments:
1. A reduction in the cost of traveling, thus increasing the overall number of trips
taken within the area—induced travel.
2. Preference for driving on freeways over driving on arterial streets—Downs’s Law
of Peak-hour Traffic Congestion.
By confirming the theory of induced travel on the Greater Phoenix-area arterial streets and urban
freeways, using Equations 11 through 15 with real observed data, we are halfway toward
showing the existence of Downs’s Law. When a new urban freeway segment is added, we expect
some of the traffic on paralleling arterial streets to shift to the new segment, decreasing traffic
volumes on these arterial streets. This reduction will motivate motorists who were previously on
the margin to take a trip they wouldn’t have otherwise taken if the freeway hadn’t been built. The
theory of induced travel, however, predicts that the decreased traffic on arterial streets reduces
the cost of driving on those streets, causing induced travel because of the latent demand, and thus
increasing the total amount of traffic in the area. By studying traffic volumes before and after a
(Eq. 13)
(Eq. 14)
(Eq. 15)
18
new freeway segment is constructed, we can determine if there is an overall increase in traffic. If
so, induced travel is present.
As mentioned earlier, the model of Equation 7 (whose matrix form is that of Equation 5)
estimates the effects of urban freeways while controlling for other factors that could potentially
influence total traffic volumes. Its appropriateness and fit will be analyzed in the following
section.
Utilizing this model framework, which is designed to use factors such as the existence of urban
freeway segments, as well as other factors, to predict total traffic volumes, we can analyze the
effect of new urban freeway segments on total traffic in an area immediately surrounding the
segment. We can show the induced travel effect by demonstrating that total traffic has increased
as captured by the binary variable AFTER. If the coefficient of AFTER, β1, is positive, then that
is statistical evidence that total traffic increases after the completion of a new freeway segment,
leading us to confirm the theory of induced travel. Additionally, given our specification of
Equation 7 to estimate total traffic volume, with both the dependent variable and the non-binary
covariates expressed as natural logarithms, we can interpret the coefficients β as percentage
changes rather than absolute changes.
Case 1. Isolation of Population Change; Single Parallel Street
As we can see in Figure 4, by plotting yearly average total traffic per freeway segment in our
sample on the same graph as yearly population, we see a strong correlation.
Figure 4. Greater Phoenix Traffic Volumes per Freeway Segment vs. Population.
19
Though the variables do not track perfectly, it is clear that population is a strong contributor to
increases in traffic volumes within a given geographic band. By evaluating the model of
Equation 7 with the ln(MILES) and ln(TOTMILES) covariates omitted, we can isolate the
effects on traffic of a new freeway segment from changes in population, exactly as we did for the
sample data of Equation 11. Restoring these covariates will also isolate the traffic effects from
distance-to-freeway and freeway mileage stock, leading to determining how much they, too,
have affected the traffic volumes. Using varying number of covariates will change the sizes of
the resulting matrices but not the analysis method.
Case 2. Multiple Parallel Streets and Freeway
Case 1 measured the effects of a freeway segment on total traffic, relative to a single substitute
arterial street in each observation. We can expand this analysis to a collection of nearby arterial
street segments that run parallel to a freeway segment and are located within 3 miles of the
freeway. For example, for a given segment of freeway that runs, say, east to west, we can look at
the corresponding parallel arterial street segments that run 1 mile north, 2 miles north, and 3
miles north, respectively, of the freeway segment. We would then look at the three parallel
arterial street segments that run, respectively, 1, 2, and 3 miles south of the freeway segment.
The given freeway segment and all six of the corresponding parallel arterial street segments can
be looked at as one composite traffic band that spans approximately 6 miles (3 miles on either
side of the freeway segment). To show that total traffic volumes increase in the entire 6-mile
band, we can create a new, total-traffic, dependent variable that sums across these parallel
arterial streets in addition to the urban freeway, if available. To use this stratagem, we modify the
specification of Equation 7 to become
ln( ) ln( ) ln( ) 0 1 2 3 TOTARTFWY b b AFTER b POP b TOTMILES
where:
TOTARTFWY is the sum of traffic volumes on multiple arterial streets parallel to the
alignment of the freeway plus the traffic volume on that freeway segment, if it exists.
0 b is the value of lnTOTARTFWY where the line graphed as in Figure 2 intercepts
the vertical axis at the hypothetical place where the other covariates or their natural
logarithms, where applicable, are zero.
1 b through 4 b are the line’s slope with respect to the associated covariate or its
natural logarithm, where applicable.
All other variables and constants are the same as in Equation 7.
Similarly, as in Case 1, we may perform regressions without ln(POP) and/or ln(TOTMILES) to
check how much they affected the other results.
Case 3. Multiple Parallel Streets Only
As just discussed, the concept of induced travel and its resultant Downs’s Law of Peak-hour
Traffic Congestion predict that a reduction in cost of traveling associated with the construction of
a new freeway segment motivates more people to travel. They predict further that freeways are a
(Eq. 16)
20
more attractive alternative and hence should fill to capacity faster than arterial streets. If we are
able to confirm the hypothesis of induced travel in Equation 7, then, to show that Downs’s Law
holds, we need to show that drivers are forsaking travel on surface streets for travel on freeway
segments. If Downs’s Law holds and total traffic increases, the bulk of that increase should be
due to drivers shifting toward the freeway. As a result, if parallel arterial street traffic either
decreases or remains constant while total traffic increases, and we adjust for potential covariates
such as population growth, then we can be assured that the increase in traffic was due primarily
to the construction of the new freeway segment. In order to prove this hypothesis, we again
modify the specification of Equation 7 to become
ln( ) ln( ) ln( ) 0 1 2 3 TOTART b b AFTER b POP b TOTMILES
where:
TOTART is the sum of traffic volumes on multiple arterial streets parallel to the
alignment of the freeway, not including the traffic volume on that freeway, even if it
exists
0 b is the value of lnTOTART where the line graphed as in Figure 2 intercepts the
vertical axis at the hypothetical place where the other covariates or their natural
logarithms, where applicable, are zero.
1 b through 4 b are the same as in Equation 16, and all other variables and constants
are the same as in Equation 7.
If 1 b is negative or zero, then the increase in total traffic must be primarily due to drivers’
preference for driving on the freeway; thus Downs’s Law would hold.
It is important to note that, due to the nature of traffic volume data, the origins and destinations
of individual drivers are unknown. Because of this fact, a person could originate from anywhere
in the region and travel to anywhere in the region. Thus a region-wide population variable is a
reasonable proxy to represent potential freeway demand.
(Eq. 17)
21
Data and Estimation
As described earlier in the paper, hypotheses are useful only insofar as there are realistic and
workable models that can be formed to test them. Although such a model was proposed in the
preceding section, the process of building any model is inherently limited by the amount and
quality of data that may be used in a model’s estimation.
For use in our proposed model, such data was obtained using a series of traffic count maps over
an interval of time and by compiling data related to population to isolate the effects of population
growth. Nine traffic-count maps were obtained from the Maricopa Association of Governments
(MAG), each of which indicated the average number of vehicles that utilized a given segment of
arterial street or freeway. According to MAG, the traffic volumes shown on the maps are average
weekday traffic, developed from 24-hour counts for each year. Traffic counts were seasonally
adjusted in order to account for the effects of traffic count variation among different times of the
year. The maps included the years 1980, 1984, 1986, 1988, 1990, 1993, 1998, 2002, and 2003.
For the purposes of this research, each map was divided into traffic bands based around existing
or future freeway segments. Traffic counts on arterial streets were used on parallel streets aligned
3 miles or less from an existing or future freeway segment. A distance of 3 miles was chosen
primarily due to the fact that data were consistently available for most freeway segments in the
geographical band. Secondly, according to Downs (1992), due to the nature of habit persistence,
drivers do not tend to shift their typical driving behavior to great degrees. Thus, it is only
necessary to include those alternative parallel streets that would be likely substitutes for a new
freeway segment.
In the maps, each unique segment of arterial street or freeway has been labeled with the actual
traffic count number observed for that year. The segments on the maps were divided more or less
according to the Phoenix grid network of streets, where one segment begins with one
perpendicular street and ends with the next major perpendicular street. With the segments
delineated in this manner, each arterial street and freeway segment has an average length of
approximately 1 mile.
A dataset was compiled where each segment was given a name based on the perpendicular
streets that defined each end of the segment. The only arterial street segments that were used for
analysis were those that had a traffic count assigned to them and that were located within 3 miles
of, and ran parallel to, an existing segment of freeway, or a segment of road or space that
eventually became a segment of freeway.
Of all the segments used in the final analysis, Table 1 depicts the map year from which each
segment was drawn, the total number of segments used from that map, and the population of the
Greater Phoenix valley in each map’s year. The segments in each year were randomly chosen
from the new segments built in that year.
For a visual representation of the annual trends of arterial street and freeway traffic volumes,
Figure 5 shows each count plotted over time. While the average daily traffic on arterial streets
has stayed more or less constant, the average daily traffic on freeways used in the analysis has
increased dramatically over time.
22
Table 1. Segments Sampled by Year.
Map Year # Sampled Segments Population
1980 63 1,509,175
1984 209 1,736,952
1986 159 1,905,504
1988 63 2,048,441
1990 138 2,122,101
1993 183 2,359,883
1998 367 2,909,040
2002 215 3,293,606
2003 98 3,388,768
Figure 5. Average Arterial vs. Average Freeway Counts (in Thousands).
Figure 6, below, gives a more detailed representation of how traffic counts are marked between
major perpendicular streets in the maps. This is true for freeway segments as well as arterial
streets. In situations where a parallel street did not have a count, that portion of the street was
omitted from the analysis for the years for which that count was missing. To calculate total
traffic in a band, we add the counts of parallel streets between two perpendicular streets. For
example, in the diagram below, the total daily arterial street traffic (TOTART ) (in thousands)
between the first perpendicular streets and within 3 miles of the freeway would be 35 + 49 + 52
+ 50 + 40 + 39 = 265. The total traffic counts (TOTRAF ) are the daily traffic count on the
freeway plus the count on a substitute arterial street. In the diagram below, the first three streets
above the freeway would have daily counts of 52 + 80 = 132, 49 + 80 = 129 and 35 + 80 = 115,
respectively. In areas before the construction of the freeway, the total traffic is equal to the
arterial street traffic.
23
Figure 6. Example of Daily Traffic Counts (in Thousands) along Bands of Arterial Streets
Parallel to an Urban Freeway.
24
Estimating the Model
The results of the estimates resulting from the approach of the previous section as applied to
Equations 7, 16, and 17 are presented in this section. The models are estimated using ordinary
least squares. First we present the estimates of various specifications of both the induced travel
model and the Downs’s Law model, which were previously discussed. Finally, we analyze and
interpret the results. The t-value is listed as a measure of the confidence with which the estimate
can be taken. It is each coefficient’s estimate divided by its standard error. The larger the
absolute value of t, the less likely that the actual value of the k b could be zero. The F value,
which is the ratio of the mean regression sum of squares divided by the mean error sum of
squares, tests the overall significance of the regression model by testing whether all of the k b are
equal to zero. This tests the full model against a model with no variables and with the estimate of
the dependent variable being the mean of the values of the dependent variable. Its value will
range from zero, showing that the independent variables are random with respect to the
dependent variable, to an arbitrarily large number.
Estimate 1. Induced-Travel Model
Table 2. Induced Travel (1).
Induced Travel (1) Dependent Var: ln(TOTRAF)
Specification
0 b
(Intercept)
1 b
(AFTER)
2 b
ln(POP)
3 b
ln(MILES)
4 b
ln(TOTMILES) F-Value3 R24
1
Estimate 2.88* 1.01* N/A N/A N/A
183.46* 0.18
t Value5 60.49 13.54 N/A N/A N/A
2
Estimate -2.08* 0.89* 1.74* N/A -0.11
107.82* 0.28
t Value -4.01 12.40 3.91 N/A -0.46
3
Estimate -1.69* 0.87* 1.53* -0.12* N/A
103.66* 0.28
t Value -3.64 11.99 10.32 -3.34 N/A
4
Estimate -1.96* 0.89* 1.55* N/A N/A
161.77* 0.28
t Value -4.33 12.50 10.73 N/A N/A
*Denotes estimate significant at the 95% confidence level.
3 A nonlinear regression and curve fitting website (Sherrod 2008) defines the F-value as the ratio of the mean
regression sum of squares divided by the mean error sum of squares. It tests the overall significance of the full
regression model by testing whether all of the k b are equal to zero, thus comparing the model to a model with no
variables and with the estimate of the dependent variable being the mean of the values of the dependent variable. Its
value will range from zero, showing that the independent variables are random with respect to the dependent
variable, to an arbitrarily large number.
4 A note about R2: In the quintessential graduate econometrics textbook, William Greene states, "In terms of the
values one normally encounters in cross sections, an R2 of 0.5 is relatively high. Coefficients of determination
(which is an R2) in cross sections of individual data as high as 0.2 are sometimes noteworthy. The point of this
discussion is that whether a regression line provides a good fit to a body of data depends on the setting." (Greene
2002)
5 A nonlinear regression and curve fitting website (Sherrod 2008) defines the t-value as a measure of the confidence
with which the estimate can be taken. It is the slope coefficient's estimate divided by its standard error. The larger
the absolute value of t, the less likely that the actual value of the k b could be zero.
25
All variations on the general model used to test the hypothesis of induced travel present robust
results with regard to the primary variable of interest, 1 b . In the first variation, 1 b is highly
significant with a positive value. This supports the hypothesis of induced travel. Subsequent
regressions with different combinations of covariates (specifications), shown in rows 2 through 4
of Table 2, are done to confirm this, and all yield consistent results: The addition of an urban
freeway segment can be shown to increase overall travel rather than simply shifting traffic from
the arterial streets to nearby parallel freeways.
By adding the additional covariates representing potential confounding effects in rows 2 through
4 of Table 2, we attempted to discern the robustness of the effect of a new freeway segment on
overall traffic. These covariates were the population ( POP ), the distance from the freeway
segment to the arterial street (MILES ), and the total miles in the freeway network
(TOTMILES ). The potential effect of population is discussed above and is included in the
remaining model variations. In each model, the effect of AFTER on 1 b is significant, positive,
and relatively stable, ranging from 0.87 to 1.01. This indicates that, even after we control for
population growth, total freeway miles, and distance from the arterial street to the freeway, the
addition of an urban freeway segment has a significant, positive effect on traffic volumes, which
can be seen in all variations of the model. These results indicate that the construction of a new
urban freeway segment results in a 138 percent to 175 percent increase in total traffic. This
represents a large increase in regional mobility and is depicted in Figure 7.
Figure 7. Predicted Traffic Volumes – Induced Travel (1).
Estimate 2. Induced-Travel Model with Inclusion of Freeway Count
To attempt to estimate the network effects of urban freeways, the variable TOTMILES was
included. This variable measures the total stock, in miles, of urban freeway in a given year. If
network effects are present, the effect of TOTMILES should be positive — the more miles of
26
urban freeway, the higher the total traffic volume we would expect. However, as seen in Table 3,
the effect of the covariateTOTMILES is insignificant. This is likely due to the fact that total
freeway miles and population are correlated to the extent that their individual effects can’t be
separated by regression analysis.
Table 3. Induced Travel (2).
Induced Travel (2) Dependent Var: ln(TOTARTFWY)
Specification
0 b
(Intercept)
1 b
(AFTER)
2 b
ln(POP)
3 b
ln(TOTMILES) F-Value R2
1
Estimate 4.35* 0.89* N/A N/A
43.75* 0.20
t Value 60.35 6.61 N/A N/A
2
Estimate 1.59* 0.61* N/A 0.64*
42.13* 0.32
t Value 3.26 4.54 N/A 5.72
3
Estimate 0.91 0.62* 0.69 0.31
28.34* 0.32
t Value 1.03 4.61 0.92 0.81
4
Estimate 0.46 0.64* 1.26* N/A
42.27* 0.32
t Value 0.68 4.88 5.75 N/A
*Denotes estimate significant at the 95% confidence level.
To confirm that total traffic has, in fact, increased, we estimate Equation 16. This is similar to
Equation 7, except that the dependent variable lnTOTARTFWY includes freeway traffic counts,
when available, rather than solely arterial street traffic counts. As evinced in Table 3, Equation
16 corroborates the estimations of Equation 7. In all four regressions, 1 b is significant and
positive. When AFTER is the only covariate considered, the change in TOTARTFWY indicated
by 1 b of the first specification in Table 3 is found in the manner of Equation 15, namely,
2.44 0.89 e
TOTARTFWY
TOTARTFWY
BEFORE
AFTER
This means that TOTARTFWY after the freeway opening increases by a factor of 1.44, or 144
percent, with population not held constant, across a 6-mile parallel band. When population is
accounted for, as in the fourth specification, the construction of a new freeway still represents a
90 percent increase in total traffic volume. This result is depicted in Figure 8.
Estimate 3. Induced-Travel Model with Addition of Freeway Segment
As discussed above, in order to show Downs’s Law, we need to show that the addition of
freeway segments either have no effect or a negative effect on arterial street traffic volumes. In
all four specifications presented in Table 4, the addition of a freeway segment has no impact on
the sum of substitute arterial street traffic counts, as evidenced by the near-zero values of 1 b . In
all of these outcomes, the results are clear: the addition of a freeway segment does not result in
an increase in arterial street traffic volume, thus confirming Downs’s Law of Peak-hour Traffic
Congestion.
(Eq. 18)
27
Figure 8. Predicted Traffic Volumes – Induced Travel (2).
Table 4. Downs’s Law (3)
Downs’s Law (3) Dependent Var: ln(TOTART)
Specification
0 b
(Intercept)
1 b
(AFTER)
2 b
ln(POP)
3 b
ln(TOTMILES) F-Value R2
1
Estimate 4.30* 0.16 N/A N/A
1.25 0.01
t Value 55.14 1.12 N/A N/A
2
Estimate 1.50* -0.12 N/A 0.65*
14.77* 0.14
t Value 2.82 -0.85 N/A 5.30
3
Estimate 2.06* -0.13 -0.58 0.93*
9.99* 0.14
t Value 2.15 -0.92 -0.71 2.24
4
Estimate 0.70 -0.07 1.17* N/A
12.21* 0.12
t Value 0.93 -0.47 4.80 N/A
*Denotes estimate significant at the 95% confidence level.
28
29
Valuation
The cost per vehicle-mile of trips taken is less than or equal to the value the drivers place on
making the trip. Conversely, the cost per vehicle-mile of trips not taken is greater than the
perceived value. If a number of vehicles per year do not make the trip because a freeway is not
present, and if we know the overall cost per vehicle-mile that the drivers consequently do not
spend, then this cost is at least just greater than the value that these drivers placed on taking the
trip. In other words, this cost is the minimum possible value of the value that these drivers placed
on taking the trip.
We can start to obtain this value by using the second model and Equation 16 to predict the total
amount of traffic flowing in a given area with and without freeways. We do this by taking the
traffic load as it is today, with the freeways that we have today, and then using the model to
predict what the traffic would be today without freeways, but adjusted for the increase in
population and other confounds. We then use the difference between the two traffic volumes to
get an idea of what the value of today's freeways are, using the published statistics for the value
of a trip.
As seen in the fourth specification in Table 3 and its associated discussion, estimation of
Equation 16 predicts a 90 percent increase in traffic flow over bands of arterial streets when a
freeway is placed as a central band (as in Figure 6). Thus, if we were to never have built the
freeway in a typical 1- by 6-mile area in Figure 6, the population-adjusted average daily traffic
flow, as predicted by our model, would not have reached the present-day 254,435 daily vehicles,
but would have stayed at 134,162, representing 120,273 vehicles per day or 43,899,753 vehicles
per year that would not have made the trip.
Using U.S. Department of Transportation (USDOT) statistics on personal consumption
expenditures (USDOT 2010) and the Federal Highway Administration’s Highway Statistics
(FHWA 2008), we find that the estimated 2006 cost per vehicle-mile for automobiles was about
37 cents.6 At the time of this research, data for trucking, which was no more recent than 2001
(USDOT 2003), gives the estimated cost for trucks as $2.25.7 Additionally, the same source
shows that approximately 92.5 percent of traffic consists of autos and the remainder for trucks.
Thus, the minimum value to these drivers of their trips, which is to say the annual benefit of a
mile of freeway, can be calculated as:
Benefit =
$22,432,774
$2.25
0.075 43,899,753
$0.37
0.925 43,899,753
yr veh mi
veh
yr veh mi
veh per mi per yr
According to MAG, the average cost per lane-mile of a freeway segment is $12,000,000
(Loudon, Connors, and Herzog 2004).8 On an average six-lane freeway, this amounts to
6 $1,028 billion in expenditures divided by 2,784 billion vehicle-miles of travel.
7 $467 billion in expenditures divided by 208 billion vehicle-miles of travel.
8 This paper estimated a cost of $3.7 billion for adding 490 lane-miles to the Phoenix urban freeway system in 2003.
Given a 50 percent increase in highway construction costs since then, a cost of $12 million per lane-mile is
estimated.
30
$72,000,000. With a design life of 20 years, we have an average yearly cost of $3.6 million. This
amount is clearly far less than the economic benefit of over $22.4 million. Thus, the annual
mobility benefit of constructing a new freeway segment is approximately six times larger than
the cost.
31
Conclusion
As stated at the beginning of this paper, many freeway users complain that new freeway
segments fill up with traffic immediately after they are constructed. This phenomenon would
seem to diminish the advantages of reduced costs and reduced driving time that would make
freeways theoretically superior to arterial streets. According to previous literature, however, this
phenomenon is to be expected and is not an indicator of the efficiency or inefficiency of having
new freeways. Due to Downs’s Law of Peak-hour Traffic Congestion, we expect newly
completed freeways to experience peak-hour congestion simply because they do offer superior
benefits to roadway users compared to the alternative arterial streets. Discerning drivers choose
to enjoy these benefits. Another phenomenon cited in the literature review is that of induced
travel, which states that, with the reduction in travel time gained by using freeway segments,
more commuters can be expected to choose to travel on them than otherwise would. This, of
course, will result in a higher flow of traffic between a given origin and a given destination.
When Downs’s Law works synergistically with the phenomenon of induced travel, more
vehicles can be accommodated in a given geographical area, thus increasing the total number of
trips taken. This result adds to the overall value of our transportation system, since, after all, the
value of that system is predicated on its ability to facilitate increased volumes of travel.
The process of valuating a freeway by an economic analysis is nicely validated by a section of
the Federal Highway Administration’s (FHWA) Procedural Guidelines for Highway Feasibility
Studies, which is based, in turn, on guidance from the Office of Management and Budget. The
Guidelines state, “Economic justification is typically a baseline consideration and the most
important element in a feasibility study.” The document proceeds to name a “benefit-cost
analysis” and, particularly, “non-monetary but quantifiable considerations” as two “most
important points to keep in mind during the study of economic justification” of a facility or
strategy. It is this last item that this paper has sought to fulfill.
This paper is clearly founded on the conditions that drivers in an area of interest have unmet
demand for mobility, are free to choose whether to drive or not and by what routes, and do not
already have reasonably convenient, alternative roadways near the newly opened freeway. Surely
these conditions affect the applicability of the principles of latent demand and induced travel
and, accordingly, affect the monetary valuation that the methods of this paper would ascribe to
each mile of new freeway, based on the cost to the driver of trips not taken because of freeways
that were not constructed. Through our analysis of Maricopa County traffic count data, we have
shown that Downs’s Law, latent demand, and induced travel, previously validated in the
references, are indeed present on Greater Phoenix freeways. Even when we account for changes
in the local population, we are able to show a significant increase in traffic volume. At the
margin, this increase in traffic volume accounts for a net benefit of over $18 million per year for
a given mile-long stretch of roadway. Over any reasonable design-life, this benefit will far
exceed the $72 million needed to construct that mile of freeway.
Of course, the reader is always free to temper the valuation of a particular new local freeway
according to his estimation of the parameters governing the particular drivers who may proceed
to congest it. The paper at least succeeds in providing a basis for the valuation. It also points the
way to further study that could include testing the effects of further confounding factors on our
32
regression model, considering hourly variations in traffic, estimating the model at various stages
of long-term traffic equilibration, and comparing estimates of the model with real-world traffic
data in various locations.
Ultimately, any evaluation of the freeway system must take into consideration the explicit and
implicit benefits of the system. We know that congestion is going to be present whether new
freeways are constructed or not. Before freeway segments are constructed, the existing arterial
streets are congested. After the completion of freeway segments, some drivers shift from arterial
streets to the new freeway. This relief lessens traffic on the arterials, leading to more drivers
taking trips they previously avoided (i.e. induced travel). Even though congestion is an inevitable
condition, even on newly constructed freeway segments, freeways still offer a clear net benefit.
The debate over building freeways to alleviate congestion is trumped by the overwhelming truth
that, after freeways are constructed, more of the population can travel. If mobility is valued, the
net benefit of new freeways suggests that they should be built where it is reasonably feasible to
do so.
33
References
Arizona Department of Administration (ADOA) Office of Employment and Population Statistics
spreadsheets at http://www.workforce.az.gov/population-estimates.aspx.
Arnott, Richard, André de Palma, and Robin Lindsey. 1993. “A Structural Model of Peak-period
Congestion: A Traffic Bottleneck with Elastic Demand.” The American Economic Review, 83
(1): 161-179.
Calfee, John, and Clifford Winston. 1998. “The Value of Automobile Travel Time: Implications
for Congestion Policy.” Journal of Public Economics, 69 (1): 83-102.
Carey, Jason, Nadia Mansour, and John Semmens. 2000. “The Value of the RARF Freeway
System: A Corporate-style Financial Analysis.” FHWA-AZ-00-475(2). Phoenix: Arizona
Department of Transportation.
Cervero, Robert, and Mark Hansen. 2002. “Induced Travel Demand and Induced Road
Investment: A Simultaneous Equation Analysis.” Journal of Transport Economics and Policy
36: 469-490.
DeCorla-Souza, Patrick, and Harry Cohen. 1999. “Estimating Induced Travel for Evaluation of
Metropolitan Highway Expansion.” Transportation 26: 249-262.
Downs, Anthony. 1962. “The Law of Peak-hour Expressway Congestion.” Traffic Quarterly 16:
393-409.
Downs, Anthony. 1992. Stuck in Traffic. Washington, DC: Brookings Institute.
Federal Highway Administration (FHWA). [1981?] Highway Statistics 1980, Tables VM-1 and
HM-10. Washington, DC: Federal Highway Administration.
——— 2005. Highway Statistics 2004, Tables VM-2 and FI-20. Washington, DC: Federal
Highway Administration.
——— 2006. Highway Statistics 2005, Tables VM-1 and HM-10. Washington, DC: Federal
Highway Administration.
——— 2008. Highway Statistics 2006, Table VM-1: Annual Vehicle Distance Traveled in Miles
and Related Data. Washington, DC: Federal Highway Administration.
Gordon, Peter, and Harry W. Richardson. 1993. The Facts about Gridlock in Southern
California. Policy Study 165. Los Angeles: Reason Foundation.
http://www.reason.org/ps165.html
Greene, William H. 2002. Econometric Analysis. 5th edition. New York City: Macmillan
Publishing Company.
34
Lin, Jie, and D.A. Niemeier. 2003. “Regional Driving Characteristics, Regional Driving Cycles.”
Transportation Research Part D 8 (5): 361-381.
Loudon, William R., Michael Connors, and Roger Herzog. 2004. “Preparation of a Phoenix
Metropolitan Area Regional Transportation Plan Using Performance-based Planning.” Accessed
May 2013. http://www.dksassociates.com/wp-content/
files_mf/1334880931LoudonITEDistrict62004Paper.pdf.
Noland, Robert B., and Lewison L. Lem. 2002 “A Review of the Evidence for Induced Travel
and Changes in Transportation and Environmental Policy in the US and the UK.” Transportation
Research Part D, 7 (1): 1-26.
Noland, Robert B. 2001. “Relationships between Highway Capacity and Induced Vehicle
Travel.” Transportation Research Part A, 35A (1): 47-72.
Parry, I.W.H. 2002. “Comparing the Efficiency of Alternative Policies for Reducing Traffic
Congestion.” Journal of Public Economics 85 (3): 333-362.
Rowell, Matt, Rick Buonincontri, and John Semmens. 1999. Analysis of Bonding vs. Pay-As-
You-Go Financing. FHWA-AZ-98-470. Phoenix: Arizona Department of Transportation.
Sherrod, Phillip H. 2008. Nonlinear Regression and Curve Fitting (website): “Understanding the
Results of an Analysis.” Accessed March 14, 2008. http://www.nlreg.com/results.htm
Small, Kenneth A. 1982 “The Scheduling of Consumer Activities: Work Trips.” The American
Economic Review, 72 (3): 467-479.
Thoreau Institute. 2006. Vanishing Automobile Update #14: Do More Highways Cause
Congestion? E-mail updates ceased December 2006. Camp Sherman, OR: Thoreau Institute.
Accessed May 2013. http://www.ti.org/vaupdate14.html
U.S. Department of Transportation (USDOT). 2003. Bureau of Transportation
Statistics/National Transportation Statistics. Table 3-7: Passenger and Freight Transportation
Expenditures (Current $ millions), see column 2001. Accessed April 8, 2013.
http://www.rita.dot.gov/bts/sites/rita.dot.gov.bts/files/publications/national_transportation_statist
ics/2003/html/table_03_07.html
——— 2010. Bureau of Transportation Statistics/National Transportation Statistics. Table 3-13:
Personal Consumption Expenditures on Transportation by Subcategory, see column 2006.
Accessed April 8, 2013.
http://www.rita.dot.gov/bts/sites/rita.dot.gov.bts/files/publications/national_transportation_statist
ics/2010/html/table_03_13.html
Winston, Clifford, and Chad Shirley. 1998. Alternate Route: Toward Efficient Urban
Transportation. Washington, DC: Brookings Institute.