Explaining transit expenses in US urbanised areas: Urban scale, spatial form and fiscal capacity

Abstract

This research seeks to explain patterns of capital investment and operating expenses for urban transit systems in the United States. We isolate supply factors including urban scales, urban spatial form and financial capacity. Individual and group transit demands are accounted for by social and demographic characteristics including education level, immigrant populations, poverty levels, senior population and race. The results demonstrate that transit investments are super-linear to population, directly contradicting predictions of Bettencourt’s popular urban scale theory. Transit expenses are explained primarily by urban scales, urban spatial form and financial capacity, but demand forces such as poverty, car usage and political ideology have strong effects as well.

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Urban Studies
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Explaining transit expenses in US
urbanised areas: Urban scale, spatial
form and fiscal capacity
Jerry Zhirong Zhao
University of Minnesota, USA
Shengnan Lou
University of Minnesota, USA
Camila Fonseca
University of Minnesota, USA
Richard Feiock
Florida State University, USA
Ruowen Shen
Wichita State University, USA
Abstract
This research seeks to explain patterns of capital investment and operating expenses for urban
transit systems in the United States. We isolate supply factors including urban scales, urban spatial
form and financial capacity. Individual and group transit demands are accounted for by social and
demographic characteristics including education level, immigrant populations, poverty levels,
senior population and race. The results demonstrate that transit investments are super-linear to
population, directly contradicting predictions of Bettencourt’s popular urban scale theory. Transit
expenses are explained primarily by urban scales, urban spatial form and financial capacity, but
demand forces such as poverty, car usage and political ideology have strong effects as well.
Keywords
financial capacity, political market, spatial form, transit expenses, urban transit
Corresponding author:
Jerry Zhirong Zhao, University of Minnesota, Humphrey
School of Public Affairs, 301, 19th Avenue South,
Minneapolis, MN, 55455, USA.
Email: zrzhao@umn.edu

Received September 2018; accepted November 2019
Introduction
Investment in urban transit systems is a press-
ing issue for urban areas around the world,
including the United States. How to invest
sufficiently in urban transit is a practical chal-
lenge for current and future cities in their
efforts to ensure social-economic activities
and address social inequities. Urban infra-
structure is treated as a local public good
because urban infrastructure sectors are sub-
ject to market failures, such as monopoly,
externalities and free-rider problems. In public
choice, the median-voter theorem captures the
impact of these factors on public demand at
the city level (Fisher, 2007). Tiebout (1956)
added to these conventional economic factors
the idea that individuals’ residential location
decisions in an urban area reveal citizen pre-
ferences for public goods. Governmental sup-
ply also shapes the provision of public services
(Mikesell, 2003). Conventional economic fac-
tors, such as service prices, household income,
urban population size, etc., have been found
to have a significant impact on the provision
of public goods or services. Within this tradi-
tion, decision-makers pursue their individual
interests in the supply of public goods by
structuring taxation and public service provi-
sions to maximise revenues (Brennan and
Buchanan, 1980; Niskanen, 1971).
Along with economic and political incen-
tives, fiscal capacity and managerial capabil-
ity, from local to federal governments, can
influence decisions to invest in urban infra-
structure (Gramlich, 1994; Oates, 1999). A
local government with greater managerial
and political capabilities may manage to
pass an earmarked local tax for infrastruc-
ture investment (Hannay and Wachs, 2007)
or adopt innovative financial tools, such as
public–private partnership, to fund infra-
structure projects (Koppenjan and Enserink,
2009; Rybeck, 2004; Wang and Zhao, 2014).
More recent work based on the mathe-
matical theory of urban scaling views trans-
portation investments in urban areas as
fundamentally determined by population
growth. This approach views aggregate
human social behaviour as following univer-
sal laws of urban scaling (Bettencourt, 2013;
Bettencourt et al., 2007). Bettencourt and
his colleagues found evidence that urban
infrastructure scales with the population in
a sub-linear pattern following a general
model. Nevertheless, the approach remains
controversial.
Although extant theories address the driv-
ers of public goods and services and goods
provisions, very limited empirical research
focuses on the capital investment in urban
infrastructure to test hypotheses derived
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2Urban Studies 00(0)

from these theories, particularly with regard
to transit infrastructure. To fill this lacuna,
we draw from public finance, political mar-
ket and urban scaling theories to explain the
patterns of capital investment and operating
expenses for urban transit systems in the US.
This study undertakes the first systematic
effort to apply the political market approach
(Feiock, 2013; Lubell et al., 2005) in the
transportation context. The purpose is to
provide insight into how governmental sup-
ply and public demand shape patterns of
transit investment. We aim to test the
Bettencourt urban scale theory which posits
that infrastructure investments are sub-linear
to population. To do so, we isolate supply
factors including urban spatial form and
financial capacity. We also account for vari-
ables related to individual and group
demands for transit.
The remainder of this article is organised
as follows. The second section explains the
research context, including Census-defined
urbanised areas (UZAs), urban transit provi-
ders (UTPs) and the relationship between
the two. The third section briefly reviews the
political market framework of public services
and then applies it to the provision of urban
transit. We develop five hypotheses on both
the supply side and the demand side. The
fourth section describes the data and the
model. In the fifth section we present regres-
sion models to explain transit capital and
operating expenses. The final section con-
cludes with some discussion of the implica-
tions of our findings.
Urbanised areas and the provision
of public transit
Metropolitan regions are the primary drivers
of economic growth and infrastructure
investment (Feiock and Coutts, 2013).
Transit systems are central to both the eco-
nomic development and sustainability of
urban regions. Urban regions in the US vary
in scale, form and economic resources; local
governments within urban regions vary in
their demographic, political, economic and
fiscal capacities. Through the lens of the
political market framework (Feiock, 2013;
Lubell et al., 2005, 2009), these factors are
seen as shaping capital investments and the
operating expenses of urban transit systems.
The 1973 Federal-Aid Highway Act
defined an urbanised area (UZA) as an area
with more than 50,000 people, and man-
dated their inclusion in a metropolitan plan-
ning organization (MPO). MPOs are
responsible for developing long-range trans-
portation plans, which set priorities for a
region’s transportation network over the life
of a 20-year period. MPOs channel funds to
projects that buttress regional goals and pol-
icies. As of 2016, there are 500 designated
urban areas in the US within the boundaries
of 405 MPOs. An urbanised area typically
covers one or multiple municipalities, and
can go beyond city and county boundaries.
Inside UZAs, the transit systems are oper-
ated by Urban Transit Providers (UTPs).
UZAs and UTPs are interconnected with
each other. On one hand, one UZA may be
served by multiple UTPs. On the other
hand, one UTP may serve multiple UZAs,
one of which is designated as its primary
UZA. Until recent years, national data of
urban transit systems in the US have been
reported and compiled only at the UTP
level. In this article, we developed a unique
method to allocate UTP-level data to UZAs.
This method enables a study of transit
finance across a large sample of UZAs,
which was not feasible before.
Urban transit provision through
the lens of the political market
framework
The political market framework of public ser-
vices conceptualises urban policy as the result
of a dynamic contracting process between
Zhao et al. 3

governmental policy supplies and the policy
demander in a society (Alston et al., 1996).
Property rights theories argue that changes
emerge in response to scarcity and relative
prices (Libecap, 1989; North, 1990). Thus
policy outcomes reflect the relative strength
of demands, and the ability or willingness of
government authorities to supply policy
(Alston et al., 1996). Demands for public ser-
vices are driven by localised economic factors
such as land scarcity and group interests that
seek to secure favourable outcomes in the
political arena (Eggertsson, 1990). This is
mirrored in the context of urban transit,
where policy debates are often about the
capacity of a metropolitan area to respond to
demands for extensive transit services given
its scale, geographic conditions, urban forms
and fiscal capacity. Thus, we pay special
attention to several supply-side factors while
controlling for demand-side factors.
Governmental supply
According to the subsidiarity principle of fis-
cal federalism as advanced by Oates (1999,
2005), local governments know better than
the federal government what public goods
and services local residents and businesses
need, and thus they are responsible for the
provision of local public services. This prin-
ciple is thought to ensure efficient allocation
of public resources (Alm, 2015; Bahl and
Bird, 2014). Regarding urban transit infra-
structure, local governments are generally
responsible for planning, financing, con-
structing, owning, operating, and maintain-
ing this infrastructure. Facing these fiscal
responsibilities, local governments can be
the major funders of urban infrastructure or
the facilitators of urban infrastructure proj-
ects, while federal or state governments can
use intergovernmental transfers to increase
the investment in infrastructure sectors that
have significant spillover effects (Alm, 2015;
Bahl and Bird, 2014). Fiscal federalism
theories address how fiscal responsibility is
allocated in the federal systems, but do not
fully account for the impact of supply forces
on public service provision. Economic fac-
tors that shape policy supply include popu-
lation size, location, scale, urban form and
fiscal capacity (Fisher, 2007). Political fac-
tors, including policy decision-maker prefer-
ences, shape public resource allocation as
governmental actors seek to expand reven-
ues and responsibilities (Brennan and
Buchanan, 1980).
The theory of urban scaling has generated
interest and enthusiasm in recent years based
on its prediction that urban development
conforms to universal laws of scaling. The
work of theoretical physicist Luis
Bettencourt and his associates has captured
attention within multiple disciplines by
advancing simple mathematical models based
on city size that predict city development pat-
terns and concluding that GDP growth is
super-linear to population growth but infra-
structure is sub-linear to population growth,
that is, that infrastructure growth is slower
than population growth. They argue further
that deviation from the norm defined by
these scaling laws is sub-optimal (Bettencourt
and West, 2010; Bettencourt et al., 2007).
Recent work casts doubt on the robustness
of scaling law predictions when applied to
variation across place and time within a
single country (Cebrat and Sobczyn
´ski,
2016). We believe that there are several
potential problems with the application of
this theory to explain patterns of urban infra-
structure, and with its prediction of sub-
linear growth of infrastructure relative to
population. First, the scaling literature
largely relies on bivariate correlation, but the
observed patterns between urban scale and
infrastructure are likely to be affected by
other variables. Second, the public finance
literature has established that various public
services or infrastructure will demand differ-
ent levels of economies of scale (Estache and
4Urban Studies 00(0)

Sinha, 1999). We seek to explain the devia-
tion from the scaling prediction. Keeping in
mind that in social science studies the norm
(i.e. sub-linear scaling) is not necessarily the
goal, we not only pay attention to the aver-
age pattern but also to deviation.
Several urban system parameters, such as
economic development, energy and material
use and innovation, have been tested in pre-
vious studies (Bettencourt et al., 2007;
Ramaswami et al., 2016), but the scaling
effect of transit investment has not yet been
tested. We hypothesise that urban transit
systems may be super-linear to population
scale – that is, with higher per capita transit
expenses in areas with a bigger population –
in the United States, where most urbanised
areas are so small in population that they
may not reach the economy of scale to jus-
tify an extensive system of public transit.
H1: Transit expenses are super-linear to
population.
Characteristics of urban form such as the
density and geographic compactness of cities
can be particularly important in the supply
of public transit, which includes a network
of facilities and services overlaying upon cer-
tain geographic space. As a crucial economic
and social feature of an urban area, popula-
tion density has long been a preoccupation
of urban economics (McDonald, 1989). It
may affect the provision of public transit in
multiple ways. The literature shows that
population density is positively associated
with transit network and ridership (Ederer
et al., 2019; Guerra and Cervero, 2011; Shyr
et al., 2017; Taylor et al., 2009). It may be
more feasible to provide public transit services
in higher density areas (Ladd, 1992), where
the governments may elect to allocate a higher
percentage of their budgets to public transit in
response to lower service costs. Furthermore,
recent findings indicate that the investment in
transportation infrastructure is subject to
‘congestion’, which means that the investment
amount increases in cities with higher popula-
tion density (Fisher and Wassmer, 2015). We
hypothesise that, in the US, transit expenses
are positively associated with urban density.
Many urbanised areas are so sparsely popu-
lated that extensive transit services are neither
necessary nor feasible.
H2: Urban areas with higher population den-
sity spend more on public transit.
Another aspect of urban form is its com-
pactness, which has attracted additional
attention in recent years. Compactness may
be measured in many different ways, but the
concept typically concerns the two-
dimensional expansion pattern of an urba-
nised area, which is considered to be more
compact if the pattern is more clustered
towards a centre, and with less sprawl, leap-
frogging or branching (Mubareka et al.,
2011). Urban compactness is considered the
opposite of urban sprawl (Tsai, 2005), which
is associated with high social costs in urban
planning (Squires, 2002). Recent studies
show that urban forms affect patterns of
urban commuting (Song et al., 2017). Urban
compactness along with high urban density
are believed to be beneficial to public transit
(Kotharkar et al., 2014). In this article, we
hypothesise that compact cities are more
efficient at providing public transit and thus
require smaller amounts of transit expenses,
all else being equal.
H3: Urban compactness will be negatively
associated with transit expenses.
Urban transit systems are expensive to
build and to operate. Urbanised areas are
constrained by their fiscal capacity to supply
transit infrastructure and service. Fiscal
capacity can be measured at the individual
level or the governmental level. First, the
capacity to support urban infrastructure is
Zhao et al. 5

linked to personal income levels within the
community. Fisher (2007) found that public
service and public goods are produced at
higher levels in wealthier communities, but
several studies demonstrate mixed results
regarding the relationship between the
investment level and household income
(Bates and Santerre, 2014; Fisher and
Wassmer, 2015; Kwon, 2006). Second, gov-
ernment fiscal capacity can be measured by
the per capita operating expenses of local
governments within an urbanised area. We
hypothesise that urban transit systems are
better developed in urbanised areas with
higher personal income and higher govern-
ment operating expenses, after controlling
for political orientation in the urbanised
area (we expect Democrat-leaning areas to
be more prone to higher public spending,
including on transit).
H4: Areas with higher personal income tend
to spend more on public transit.
H5: Government fiscal capacity will be posi-
tively associated with transit expenses.
Policy demand
Accounts of policy demands in a local politi-
cal market are drawn from public choice
theories and what Barry Weingast and his
colleagues describe as second-generation fis-
cal federalism (Oates, 2005; Weingast, 1995).
Demands are generated both by potential
efficiency gains and by distributive gains to
politically mobilised constituencies.
In a democratic society, the median voters
signal a voting majority, thus elected officials
seek to represent the median voters’ prefer-
ences for public services. This means that
demands for public services and goods can
be reflected by the demands of median vot-
ers. In empirical studies, features of median
voters such as income, demographics, educa-
tion status and political ideology indicate
public demand for public goods and services
in a community or city. This model has been
applied in empirical studies on state and
local capital investment. Bates and Santerre
(2014) find that, in Connecticut cities, the
demand for urban infrastructure investment
is sensitive to the tax rate but not to house-
hold income. Fisher and Wassmer (2015)
link local demand, indicated by household
income, tax price, population size, previous
capital stock and residential preference, to
state–local capital investment in transporta-
tion using the median-voter model. Both
studies have found that community eco-
nomic and political features significantly
influence investment.
At the local level, demands for policy
changes like transit investments come from
diverse interest groups, including individuals
and businesses, development and environ-
mental interest groups and neighbourhood
and homeowner interests, each with their
own demand function. Since additional sup-
port beyond that necessary to achieve the
supply of the desired policy is of less value,
there is a decreasing marginal willingness to
pay for the local government officials’ policy
support. Demanders can offer political
resources and support in exchange for pol-
icy, but this type of political exchange is
characterised by high uncertainty and thus
transaction cost problems. Commitment
problems result from the uncertainty of
long-term benefit flows from policy deci-
sions since future officials can amend or
repeal a policy (Horn, 1995). Agency trans-
action costs arise if administrators do not
comply with the policy intent in the imple-
mentation process.
Demographic differences in the population
typically align with preferences for public
goods and predict spending on public goods
and services (Peterson, 1981). Willingness to
support public transit is anticipated to be
positively related to education levels in the
community because higher-educated groups
care more about environmental sustainability
6Urban Studies 00(0)

(Krause et al., 2014; Lubell et al., 2005). We
expect that the demand for public transit may
be positively associated with the share of
immigrants in the population, the share of
non-white residents, the share of seniors and
the poverty level because these population
groups have less individual mobility and thus
may rely more on public transit. These are
considered as key factors in local sustainabil-
ity, development and public service provision.
Data and method
UTPs are required by the Federal Transit
Administration (FTA) to submit annual
reports to the National Transit Database
(NTD) that include their revenues, expenses
and service indicators. Since NTD data are
at the UTP level, they do not provide the
spatial and geographical context. Finding
the appropriate method of data allocation,
however, can be challenging, due to the
multiple-to-multiple relationship between
agencies and UZAs. Figure 1 illustrates the
relationship between UZAs and UTPs
around New York City. The area includes
six UZAs, among which New York-Newark
alone is served by 46 transit providers, some
of which also serve other UZAs. A previous
approach was to allocate the data of a UTP
to its primary UZA, as if all activities of the
UTP were incurred within its primary UZA
(Fan, 2015). At the national level, the aggre-
gate picture is accurate because all UTP data
are used without double-counting. At the
individual UZA level, however, the allocated
results are unreliable. For example, the
Waterbury area in Figure 1 is served by four
urban transit providers, but the allocation
would assign it only the data for one UTP
(A11). This previous allocation method will
likely over-estimate transit operations in
major metropolitan areas, such as the New
York-Newark area, and under-estimate
them in small urbanised areas.
In this article, we developed a new
method of data allocation based upon the
Federal Funding Allocation (FFA) form,
which only became available after 2014.
According to the National Transit Database
(2014), the FTA requires UTPs to use the
FFA form to report service and operating
Figure 1. Urbanised areas and urban transit providers around New York City.
Zhao et al. 7

expenses for each served area. This informa-
tion allows us to directly allocate operating
expenses and service indicators of each UTP
to different UZAs. With this method of data
allocation, for instance, data for the
Waterbury area in Figure 1 will include dif-
ferent proportions of service and operating
expenses from each of the four UTPs that
serve the area (A1, A11, A10 and A13),
instead of all service and operating expenses
from A11 alone. The allocated annual oper-
ating expenses of the UZAs are shown in
Figure 2. A handful of them – for example,
metropolitan areas around New York,
Chicago and Los Angeles – have extensive
urban transit systems with a billion-dollar
operation, but the majority of UZAs have
very small transit systems. The FFA file,
however, does not provide information
about the share of capital expenses to differ-
ent UZAs. We allocate capital expenses of
UTPs to different UZAs assuming that capi-
tal expenses incurred in a particular UZA
are proportional to operating expenses.
Note that the allocated data about capital
expenses are less accurate on an annual basis
since the capital expenses of urban transit
systems tend to fluctuate substantively over
a year. The NTD includes finance and ser-
vice data for different transit modes, which
we categorised as rail and non-rail transits,
and for which we prepared data about capi-
tal and operating expenses, respectively. The
high correlation between ridership and oper-
ating and capital expenses (0.99 and 0.94
respectively) indicates that transit invest-
ments are accurate indicators of the level of
urban transit developments in metropolitan
areas. This correlation is consistent with pre-
vious findings (Boisjoly et al., 2018).
The supply-side economic and demo-
graphic factors shaping transit production
include population scale, urban form and fis-
cal capacity. Population data of the UZAs
come from the 2014 American Community
Survey 5-Year Estimates. For the urban
transit form, we adopted two measurements:
population density and urban compactness.
The population density data of urbanised
areas is calculated based on the 2014 popula-
tion data and the area of each UZA obtained
directly from the NTD. Our measure of
urban compactness is derived from the frac-
tal dimension index (FDI). Mandelbrot
(1968, 1982) introduced the concept of the
fractal, a geometric form that exhibits
Figure 2. UZA transit operating expenses (2014).
8Urban Studies 00(0)

structure at different spatial scales, and pro-
posed a perimeter-area method to calculate
the fractal dimension of natural planar shapes.
In landscape ecological research, for instance,
the degree of complexity (plane-filling) of a
polygon is often characterised by the fractal
dimension (D), such that the perimeter (P) of
a patch is related to the area (A) of the same
patch by P ’OAD (i.e. log P ½D log A). The
formula can be rearranged as:
D=23Ln PðÞ
Ln A
ðÞ ð1Þ
where P is the perimeter of an object and A
is its area. The fractal dimension index, D,
measures the overall spatial complexity of a
two-dimensional geographic object; its value
ranges from 1 to 2.
When the shape of a polygon is close to a
narrow line, the fractal dimension index is
equal to 2 (D ’2). As the polygon becomes
more complex, the perimeter becomes
increasingly plane-filling, and D gets close to
1. With respect to urban forms, sprawling
cities with many narrow branches or leap-
frogs tend to have smaller D values than
compact cities that are filling and tightly
clustered. For the sake of easier interpreta-
tion, we take the reverse of FDI as the urban
compactness index:
Compactness =Ln AðÞ
23Ln PðÞ ð2Þ
This value ranges from 0.5 to 1, where a
larger value indicates a more compact urban
form. A full circle, which is the most compact
form, will have a compactness equal to 1. We
calculated the compactness index for all UZAs
usingArcGISbasedonthe2010TIGERsha-
pefile from the Census Bureau. Figure 3 illus-
trates the variation of the compactness index
with examples from nine UZAs.
Figure 3. Urban Compactness Index: Examples with Selected UZA (2010).
Zhao et al. 9

At the individual level, fiscal capacity is
measured as the median household income
of an urbanised area in 2014; the data are
collected from the American Community
Survey 5-Year Estimates for urban areas. At
the governmental level, fiscal capacity is
measured by the annual government operat-
ing expenditure per capita in the central city
of each UZA. The data come from the
Census of Government Finance (annual
data available until 2012).
In addition, we include a range of
demand-side factors as control variables, as
they capture specific preferences within the
community. They include population change
in the previous decade, the percentage of the
people over 18 years old with more than a
high school degree, the percentage of white
population, the percentage of people moving
from abroad to the UZA and the percentage
of people over 60 years of age. These data
come from the 2014 American Community
Survey 5-Year Estimates for urban areas.
Lastly, we include a measurement of the
political orientation of the UZA. The mea-
sure corresponds to the percentage of votes
for the Republican party in the presidential
elections of 2012. The data come from the
US General Service Administration and are
available at the county level. We allocate
this to the UZA level using the county that
contains most of the population of the
UZA. Summary statistics of all variables are
reported in Table 1.
We conduct our analysis at the UZA level
in two steps. First, we examine the bivariate
scaling relationship between transit expenses
and population scale, following the
Bettencourt (2013) approach. Second, we use
OLS and robust regressions to examine how
urban scale, spatial form and fiscal capacity
are related to transit expenses, controlling for
some demand-side variables. Robust regres-
sion, which is a form of weighted least squares
regressions, gives the advantage of using the
information on the whole sample while being
less sensitive to outliers and high leverage
points (Li, 1985). Additional robustness
checks include the removal of outliers identi-
fied through the Interquartile Range (IQR)
following Rousseeuw and Croux (2012).
Estimation results
Before conducting our regression analysis,
we transform the data by applying natural
logarithms to our dependent variables (oper-
ating and capital expenses). We perform the
Box–Cox transformation specification test
to verify the pertinence of the transforma-
tion (Box and Cox, 1964). The results show
that the log specification is closer to the
point estimate of the Box–Cox coefficient
compared with the linear specification or
multiplicative inverse transformation (which
are strongly rejected). Hence, we follow
Sheather (2009) and Lindsey and Sheather
(2010) in adopting the closest interpretable
log specification to the Box–Cox results.
This also allows us to directly contrast our
findings with Bettencourt’s popular urban
scale theory.
Estimation results for transit operating
and capital expenses using robust regression
are shown in Table 2. For each dependent
variable, we report estimation results from
three models. Model 1 presents the urban
scaling effect through the bivariate relation-
ship between the log of population and tran-
sit infrastructure capital and operating
expenses allocated to UZAs. This provides a
direct test of the Bettencourt urban scale
prediction advanced in Hypothesis 1. In
Model 2, we add in the other structural
supply-side factors including two measures
for urban spatial form and two measures for
fiscal capacity, to test Hypotheses 2 to 5.
The third model then adds community
demand factors. There are fewer observa-
tions in the estimates for capital expenses, as
some UZAs did no incur them in 2014.
10 Urban Studies 00(0)

All the models fit reasonably well, and we
find that the population scale alone can
explain a majority of the variation, as
indicated by R-squared values. This result
echoes the significance of urban scaling the-
ory. However, we find that the urban scaling
Table 1. Summary statistics.
Variable Definition Mean St. Dev. Min Max Obs.
Dependent variables
OpEXp Transit operating expenses
allocated to the urbanised
area in 2014
88 M 688 M 2479 14,000 M 471
CapExp Transit capital expenses
allocated to the urbanised
area in 2014
35.9 M 234 M – 4290 M 471
Independent variables
Pop Urbanised area population in
2014
474,933 1,324,195 49,512 18,600,000 471
PopChange Population change in the
urbanised area from 2000 to
2010
0.20 0.25 (0.21) 2.12 467
Density Population density in the
urbanised area in 2014
2162 894 804 7127 471
Compactness Spatial compactness of the
urbanised area
0.772 0.017 0.722 0.837 466
ExpendPerCap Annual government
operating expenditure per
capita in the central city of
an urbanised area in 2012
2.45 1.72 0.40 19.44 460
HHIncome Median household income of
an urbanised area in 2014
50,998 12,723 30,163 109,533 471
AboveHighSchool Percentage of people with a
degree higher than High
School in an urbanised area
in 2014 (%)
87.12 5.70 54.76 98.11 471
Republican Percentage of votes for the
GOP in the presidential
elections of 2012 (%)
87.12 5.70 54.76 98.11 471
Migration Percentage of people moved
from abroad to the
urbanised area in 2014 (%)
0.63 0.58 – 5.10 471
White Percentage of white people
in the urbanised area in 2014
(%)
76.59 13.12 15.99 96.07 471
Poverty Percentage of people under
poverty line in the urbanised
area in 2014 (%)
17.38 5.54 5.52 36.83 471
Senior Percentage of people over 60
years old in the urbanised
area in 2014 (%)
19.22 5.31 7.30 66.90 471
Car Percentage of workers
commuting by cars in the
urbanised area in 2014 (%)
49.97 12.95 14.05 88.26 471
Zhao et al. 11

effect is about 1.36 for operating expenses,
and about 1.59 for capital expenses, sup-
porting Hypothesis 1 and directly contra-
dicting predictions from Bettencourt’s
popular urban scale theory. The super-linear
relationship between transit expenses can be
further revealed in Figure 4, which also dis-
tinguishes rail transit and non-rail transit.
Regarding transit operating expenses, for
non-rail transit such as regular bus systems
the scaling coefficient is 1.31, and for rail
transit such as subway or light-rail systems
the scaling coefficient is 1.15. Regarding
transit capital expenses, the two scaling coef-
ficients are 1.40 and 1.59, respectively. The
graphs clearly show that a higher population
in UZAs is associated with higher transit
expenses, and this is even more so for capital
expenses than for operating expenses.
In Models 2 and 3, all those urban scaling
coefficients remain higher than 1 even after
we incorporate additional explanatory
Table 2. Estimation of operating and capital expenses.
Dependent variable Operating expenses (log) Capital expenses (log)
Model 1 Model 2 Model 3 Model 1 Model 2 Model 3
Pop (log) 1.357
***
(0.0332)
1.193
***
(0.0337)
1.222
***
(0.0283)
1.592
***
(0.0673)
1.298
***
(0.0750)
1.345
***
(0.0738)
PopChange –1.012
***
(0.129)
–0.746
***
(0.105)
–0.787
***
(0.288)
–0.567
**
(0.276)
Density (log) 1.075
***
(0.114)
0.499
***
(0.110)
1.691
***
(0.255)
0.678
**
(0.289)
Compactness –7.963
***
(2.129)
–3.241
*
(1.802)
–9.526
**
(4.843)
–2.053
(4.776)
ExpendPerCap (log) 0.210
***
(0.0616)
0.0549
(0.0490)
0.321
**
(0.139)
0.140
(0.130)
HHIncome (log) 0.158
(0.163)
–0.0397
(0.296)
0.576
(0.368)
2.299
***
(0.782)
Republican –0.0150
***
(0.00238)
–0.0169
***
(0.00627)
AboveHighSchool 0.00869
(0.00567)
–0.000879
(0.0149)
Migration –0.204
***
(0.0557)
–0.535
***
(0.152)
White 0.00571
**
(0.00241)
0.0102
(0.00636)
Poverty 0.0111
(0.0116)
0.0853
***
(0.0307)
Senior –0.00220
(0.00617)
0.00550
(0.0160)
Car –0.0593
***
(0.00763)
–0.0751
***
(0.0199)
Constant –0.551
(0.404)
–2.283
(2.040)
5.155
(3.914)
–5.155
***
(0.823)
–13.41
***
(4.625)
–24.94
**
(10.33)
Observations 471 459 459 444 435 435
R-squared 0.781 0.851 0.909 0.559 0.627 0.685
Notes: Standard errors in parentheses.
***p\0.01, **p\0.05, *p\0.1.
12 Urban Studies 00(0)

variables. The super-linear relationship indi-
cates that larger metropolitan areas tend to
invest much higher amounts in urban transit
systems, in contrast to the Bettencourt
hypothesis that infrastructure spending
tends to grow at a lower rate than urban
population growth. The unique scaling fea-
ture of urban transit systems may stem from
the needs in major metropolitan areas as
they deal with aggravated congestion, but it
may also be due to the barrier to entry asso-
ciated with a ‘natural monopoly’ (Fisher,
2007). Urban transit systems, especially rail
systems, may only be feasible or justifiable
after urbanised areas grow to a certain pop-
ulation size so as to provide the economy of
scale. The growth of population since the
previous decade is negatively associated with
transit expenses. This probably means that,
in fast-growing metropolitan areas, the
development of transit systems has failed to
catch up with population growth.
Population density has positive and signifi-
cant coefficients in Models 2 and 3, for both
operating and capital expenses. The finding
supports Hypothesis 2, and echoes a typical
pattern in literature and common observa-
tion. As predicted by Hypothesis 3, the
urban compactness index is negatively asso-
ciated with transit expenses across all mod-
els, likely because it is more cost effective to
develop a network of transit services in more
compact urbanised areas. Its coefficient
drops out of significance in Model 3 for cap-
ital expenses.
The hypothesis about fiscal capacity also
receives support when taking capital
expenses as the dependent variable. In
Model 3, after controlling for demand-side
factors, the household income is positive
and significant. Even though urbanised
areas with higher income levels tend to have
automobile-based transportation, they are
also more prone to invest in transit infra-
structure. Regarding fiscal capacity at the
governmental level (measured by the
central-city per capita operating budget), we
find weak support. In Model 2 of both oper-
ating and capital expenses we find a positive
and significant relation, but when control-
ling for demand-side factors the level of sig-
nificance drops.
Similarly, we find that urbanised areas
with a lower percentage of white population
tend to invest less in the operating expenses
of public transit. This finding may raise
social concerns because the non-white popu-
lation group tends to rely more on the transit
system. The results also suggest that urba-
nised areas with higher poverty levels tend to
invest more in transit infrastructure. We find
that migration and car usage are negatively
associated with both operating and capital
expenses, while the percentage of poverty
population is positively associated with capi-
tal expenses. Lastly, as expected, we find that
Figure 4. The scaling relationship between transit
expenses and population (2014).
Zhao et al. 13

a higher share of Democrats implies higher
operating and capital expenses in an urban
area.
We compared results from these robust
regressions with two alternative approaches.
With simple OLS regression, the results pro-
vide the same point estimates for the coeffi-
cients and do not vary in significance for any
of the variables. We also tried models with
the Box–Cox transformation. The coeffi-
cients are different in magnitude, but pro-
vide the same direction and significance for
all variables.
Conclusion and discussions
The empirical results provide support for our
explanations of transit finance derived from
the political market framework. We report a
positive effect of population size on transit
expenses and a super-linear scaling pattern
between population and transit expenses. The
positive effect of population is even greater
for transit capital expenses. Controlling for
the current population, population growth in
the past decade exerts a negative influence on
transit expenses. We could also infer from the
negative effect that infrastructure develop-
ment, particularly transit development, does
not catch up with the population growth.
Urban form is another important factor in
shaping transit operating costs. Population
density has a positive effect, while compact-
ness leads to lower operating expenses. All
else being equal, an area with a sprawling
urban form would have to spend more on its
transit system since the transit services would
be scattered over the area and thus would
cost more to build and maintain. Both com-
munity and governmental fiscal capacity have
significant positive coefficient estimates as
well. The positive relationship between fiscal
capacity and transit expenses indicates that
transit services can be regarded as a ‘superior
good’. Only when the residents or the govern-
ment of an area have a certain level of
financial capacity can they afford a good
transit system.
This research is a first large-N study seek-
ing to explain urban transit expenses in the
United States. It has significant contribu-
tions to literature and practice. The first con-
tribution regards the urban scaling of
infrastructure. In its strongest form, urban
scaling theory states that essential properties
of cities, including their infrastructure and
socio-economics, are functions of their pop-
ulation size, and the relationships are com-
mon to all urban systems and over time. Our
results, however, indicate that the scaling
relationship between infrastructure and pop-
ulation size may be sector specific. As urban
systems grow larger in population, the aver-
age cost of roadway development may go
down (Bettencourt, 2013), but public transit
expenses actually increase on a per capita
basis. The finding suggests that urban scal-
ing theory has overlooked the heterogeneous
character of the infrastructure sectors, each
reflecting a different way of interaction
between physical and social systems. In prac-
tice, the fact that infrastructure sectors vary
in their scaling relationships with the urban
population has a significant implication. It
means that cities ought to make strategic
decisions about the structure of their infra-
structure investment, and change priorities
at different stages of urban population
growth. As cities grow substantively larger in
population, they should invest more in mass
transit (which is super-linear to scale) than in
roadway systems (which are sub-linear to
scale). Second, regarding the spatial form of
urban development, our study shows that
urban sprawl can be measured in two differ-
ent dimensions – population density and
urban compactness – and each has a differ-
ent impact on urban transit expenses. The
urban compactness index nicely captures the
spatial pattern of sprawl, leapfrogging or
branching in urban development. The find-
ings show the extent to which more compact
14 Urban Studies 00(0)

urban areas take less money for urban tran-
sit development. The insight has significant
implications for transit development and
urban land use planning. Lastly, our findings
regarding fiscal capacity indicate that urban
transit capital expenses are significantly con-
strained by household income levels and in
some way by governmental fiscal revenues.
For cities and planning agencies, this is of
particular relevance given the high and posi-
tive correlation between transit investments
(operating and capital) and ridership. Our
results speak to the importance of inter-
governmental grants and regional collabora-
tions, which should be devised to help
urbanised areas with less fiscal capacity and
a changing urban population.
With the large-N data about urban tran-
sit systems, many important research ques-
tions are waiting to be answered in future
studies. In this article, we include demo-
graphic data as control variables and find
that urban transit expenses are positively
associated with Democrat-leaning areas, the
level of poverty and the share of white popu-
lation. More studies should be conducted to
examine these links and to examine the cau-
sal mechanisms; in particular, how demo-
graphic conditions are translated into
political decision-making, and how the
development of urban transit systems may
alter demographic characteristics in urba-
nised areas. In addition, more should be
explored about the role of Metropolitan
Planning Organizations (MPOs) in transit
decision-making, not only regarding total
transit expenditures but also transit revenue
structures. For example, the organization of
the MPO structure and activities may have a
significant impact on the acquisition of fed-
eral grants, the securing of state budgetary
revenues for transit or the coordination of
local efforts within metropolitan areas.
Lastly, it is important to connect urban
transit finance data to the performance of
urban transit services and, ultimately, to the
economic, social and sustainable outcomes
of urban transit development.
Declaration of conflicting interests
The author(s) declared no potential conflicts of
interest with respect to the research, authorship,
and/or publication of this article.
Funding
The author(s) disclosed receipt of the following
financial support for the research, authorship,
and/or publication of this article: This work was
supported by NSF SRN: Integrated Urban
Infrastructure Solutions for Environmentally
Sustainable, Healthy and Livable Cities, Award
Number: 1444745.
ORCID iD
Zhirong Zhao https://orcid.org/0000-0002-
6758-5723
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