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Federal Reserve Bank of Philadelphia

NOVEMBER • DECEMBER 1987




Productivity In Cities:
Does City Size Matter?
Gerald A. Carlino

Commuter Rail Ridershi
The Long and the Short H
Richard Voith

W id g ets

NOVEMBER/DECEMBER 1987

PRODUCTIVITY IN CITIES:
DOES CITY SIZE MATTER?
Gerald A. Carlino
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While we sometimes hear gloomy reports
of the decline of American cities, econo­
mists have found that big cities can enhance
the productivity of the firms located there.
In some cases, firms benefit from being
near similar firms, in order to dip into the
city's pool of specialized workers or spe­
cialized products. In other cases, firms
benefit from the great variety of workers
and services a big city offers. Firms will
exploit these advantages through the “in­
visible hand" of the market place. But local
policymakers have a role in “lending a
hand" to minimize the costs of growth,
such as congestion, high rents, and high
wages.

COMMUTER RAIL RIDERSHIP:
THE LONG AND THE SHORT HAUL
Richard Voith
Riders on commuter rail lines, from New
York to California, know too well the cycle
of service reductions, rising fares, and
declining ridership observed in many sec­
tors of the public transportation industry.
The dilemma for transit authorities and
state and local policymakers centers on the
consumers, who are the ultimate judges
of public transit policies. In particular,
although disgruntled consumers may not
be able to react quickly when fares rise or
service declines, in the long run they can
take to the highway, or even change their
homes or workplaces, to avoid depending
on public transportation.

Productivity in Cities:
Does City Size Matter?
Gerald A. Carlino*
INTRODUCTION
Economists have long recognized that a firm's
size can affect its productivity. As a firm increases
its size, it can sometimes increase productivity
by having its workers specialize in particular
tasks, or by using its capital equipment more
efficiently. In these situations a firm is said to
enjoy internal economies of scale.
Another important source of a firm's produc­
tivity that is often overlooked is a type of
*Gerald A. Carlino is a Senior Economist and Research
Advisor in the Urban and Regional Section of the Research
Department at the Federal Reserve Bank of Philadelphia.




economies of scale that is external to the firm.
These external econom ies of scale are also
referred to as agglomeration economies. Increases
in productivity due to agglomeration economies
depend not upon the size of the firm itself, as in
the case of internal economies of scale, but either
upon the size of a firm's industry in a particular
city or upon the size of the city itself.
To a large extent, market forces will encourage
private firms to seek out and take advantage of
agglomeration economies as they attempt to
become more productive. But city planners also
have a crucial role to play in accommodating
such growth. If planners fail to address and
3

BUSINESS REVIEW

resolve the problems of congestion that arise as
a city grows, firms will find their costs of doing
business in that city increasing. The productivity
gains from city size may not be fully tapped if the
city cannot accom m odate the growth which
agglomeration econom ies spur. This means
investing in public infrastructure, such as roads,
bridges, sew ers, and public transportation
systems.
In addition to enabling firms to take advantage
of agglomeration econom ies by investing in
public infrastructure, local governments accom­
modate economic activity by making an invest­
ment in the people who live there. It is through
education and training, which is primarily the
responsibility of local authorities, that worker
productivity is increased and that advances in
technology are introduced to the labor force.
Economists have not only developed theories
about why firms may be more productive in
cities, but they have also attempted to measure
how much agglomeration economies matter,
and how much public infrastructure as well as
education and training may influence produc­
tivity. Without exception, the effects of each of
these factors on productivity have been found to
be significant.
BIGGER IS OFTEN BETTER:
WHY AGGLOMERATION ECONOMIES
MEAN GREATER PRODUCTIVITY
Economists describe the advantages and dis­
advantages of a firm's expanding in terms of
"returns to scale." Suppose a firm doubles all of
its inputs in production, using twice as much
raw material, twice as many workers, and twice
as much capital equipment. If it more than
doubles its original level of output, the firm is
said to be enjoying increasing returns to scale, or
internal economies of scale. In this case, bigger is
better. If the firm doubles all of its inputs and
produces exactly twice as much output as origi­
nally, economists refer to this as constant returns
to scale. When a firm doubles all of its inputs and
finds that its output is less than twice the original
level, it has reached the point of decreasing

4


NOVEMBER/DECEMBER 19B7

returns to scale (diseconomies of scale). This
typically occurs as the scale of a firm expands
beyond a certain point, because management
becomes less efficient in very large-scale opera­
tions. In this case, bigger is not necessarily better
(see ECONOMIES OF SCALE FOR THE INDI­
VIDUAL FIRM).
Just as internal economies of scale lead to
increased productivity as a firm grows up to a
point, external econom ies of scale may also
increase a firm's productivity up to some point
as well. Economists have identified two such
types of external economies of scale, or agglom­
eration economies. The first type, localization
economies, depends not upon the size of any one
firm in an industry, but upon the size of the
firm's industry in a given city. That is, as more
and more firms in a given industry locate in a
city, each firm's productivity increases. The
second type, urbanization economies, does not
depend upon the size of any one firm in the city,
or upon the size of its industry in that city, but
upon the overall size of the city itself. That is, as
more and more firms of any sort locate in a city,
the productivity of each firm increases.1
Just as in the case of the growth of an individ­
ual firm, growth of an industry in a given city or
growth of the city itself increases firms' produc­
tivity only up to some point. Growth brings not
only greater efficiency, but also problems, such
as congestion, that may eventually balance or
outweigh the efficiency gains from size. When
size becomes a hindrance rather than a help,
firms in a city experience what is called "dis­
economies of scale."
The Size of a Firm 's Industry in a City
M atters. . . The origin of an industry in a particu­
lar city could be the result of natural resources or

^The expressions "city," "urban," "urban areas," "m etro­
politan area," and their adjectives are being used to desig­
nate a metropolitan statistical area (M SA). In general, MSAs
are statistical constructs used to represent integrated labor
market areas. They typically are geographic areas combining
a large population nucleus with adjacent communities that
have a high degree of economic integration with the nucleus.

FEDERAL RESERVE BANK OF PHILADELPHIA

Productivity In Cities: Does City Size Matter?

Gerald A. Carlino

Economies of Scale for the Individual Firm
Average Cost
Per Widget

The notion of economies of scale for a firm is easily illustrated by looking at the long-run average cost
curve (LACW for a hypothetical firm, Original Widgets. The long-run average cost curve shows how a
)
firm's cost of production changes as it varies all inputs, including its plant size, or scale of operation.
Economies of scale enable the firm to produce large outputs at lower average cost than small outputs. For
example, a large financial outlay is usually required to commence production at all. The larger the
output, the less is this fixed outlay per unit of product. In theory, a firm's long-run average cost curve is
“U-shaped;" as output increases, average cost decreases up to some point and then increases.
To produce 10 widgets a day, Original Widgets' cost per widget is $60. By producing twice as many
widgets per day, Original Widgets cuts its average cost to $50 per widget. If Original Widgets again
increases production, to 30 widgets per day, its average cost again declines, though not by as much, to
$45 per widget.
Up to this point, Original Widgets has enjoyed increasing returns to scale. At 30 widgets per day, the
minimum point of its average cost curve, Original Widgets is producing at the point of constant returns
to scale. Expansion of widget production beyond 30 units per day results in an increase in Original
Widgets' average cost. The average cost of producing 40 widgets per day goes back up to $50, the same as
the cost of producing only 20 widgets per day. In other words, Original Widgets is operating with
decreasing returns to scale. Decreasing returns may happen when Original Widgets grows so large that
it becomes hard to manage effectively. Original Widgets actually does best when it achieves constant
returns to scale, or 30 widgets per day at an average cost of $45 per widget.




5

BUSINESS REVIEW

simply a historical accident. But once an industry
develops in a geographic location, individual
firms in that industry often reap special benefits
by also locating there. Consider for example,
California's Silicon Valley, Route 128 near Boston,
North Carolina's Research Triangle, and Route
202 in the Philadelphia suburbs, four areas where
the computer industry has concentrated. Com­
puter manufacturing firms occasionally require
highly sp ecialized w o rk ers w h o m aintain an d

repair computer manufacturing instruments. A
computer firm located far from one of the indus­
trial clusters would need to employ full-time
computer repair specialists, or else spend con­
siderable time and money bringing them from a
distance when they are needed. But when firms
cluster together, their combined needs for the
repair of their instruments can support at least
one firm that specializes in instrument repair.
Thus, those services becom e available at lower
cost from a local firm. All the computer firms in
the cluster can enjoy a lower average cost of
production by contracting for these specialized
services only when they are needed.
Of course, computer manufacturing firms that
cluster together conceivably share a number of
other inputs. For example, these industrial con­
centrations tend to contain common pools of
specialized workers that any one firm in the
industry can draw upon when it wants to expand
its work force. They also typically contain sup­
pliers of component parts, such as computer
chips, and other intermediate inputs that are
used by many firms in the industry.
Localization economies undoubtedly played
a significant role in the concentration of the
motion picture industry in Los Angeles, the auto
industry in the Detroit area, and the steel industry
in the Pittsburgh region. While a localized input
such as ore deposits, or a large body of water,
may have been important in getting these indus­
tries started, localization economies have been a
factor in maintaining these concentrations. In
1985 over half the steel production in the U.S.
was concentrated in three states, Pennsylvania,
O hio, and Indiana, and in 1986 M ichigan
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NOVEMBER/DECEMBER 1987

accounted for about 44 percent of total employ­
ment in the auto industry.
. . . And So Does the Size of the City Itself. Just as
some kinds of business, such as the repair of
computer instruments, are found only where
specific industries concentrate, other activities,
such as financial and business services, are
generally found only in urban areas. In some
cases, only a large urban setting can provide a
sufficient client base for these specialized firms
to flourish. Access to these types of specialized
services in a city gives rise to the economies of
scale that are external to any one firm and to its
industry—urbanization economies. Urbanization
economies involve the more general cost savings
that a firm in any industry may receive by locating
in a metropolitan area. For example, urban areas
provide wholesaling facilities that reduce the
level of inventories any one firm needs on hand.
Urban areas also provide access to large and
varied labor pools, and to accounting, data pro­
cessing, legal, and other specialized business
services. A Wall Street Journal story (July 7,1987,
p. 1) reports an interesting example. A bicycle
manufacturer in suburban Boston was "too small
to have a full-time chief financial officer, but big
enough to have some of the same problems that
confront far larger companies." However, it was
able to find a local firm that provides financial
managers who spend part of each week "doing
what CFOs are supposed to do: prepare budgets,
project sales, negotiate with banks, and figure
out how to cope with the sagging dollar."
The degree of urbanization econom ies de­
pends upon the number of firms in a city, regard­
less of what industry they represent. Some of
the advantages that a firm gets by locating in one
of the nation's largest cities, such as New York
City, Los Angeles, or Chicago, could not be real­
ized by locating instead in much smaller cities
such as Akron, Ohio, or York, Pennsylvania.
New York City not only has many banks, invest­
ment houses, advertising agencies, and law firms,
but it is large enough to maintain highly special­
ized varieties of these types of firms. In addition,
New York City's labor market is so large that it
FEDERAL RESERVE BANK OF PHILADELPHIA

Productivity In Cities: Does City Size Matter?

offers not only a large number of placement
firms, but also a large number of agencies that
specialize in particular kinds of personnel.
HOW MUCH DIFFERENCE
DOES SIZE MAKE?
Econom ists have measured agglomeration
economies by applying the notion of a produc­
tion function to metropolitan areas. A production
function shows the relationship between the
inputs of production (labor, land, capital, and so
on) and output. The production function for an
individual firm will show whether proportionate
changes in all its inputs lead to a proportionate
increase in output (constant returns), a more
than proportionate increase (increasing returns),
or a less than proportionate increase (decreas­
ing returns). If increasing returns to scale or
agglomeration econom ies exist in a city, we
would expect to find that a proportionate change
in all inputs in a city would result in a more
than proportionate increase in output (see
AGGLOM ERATION ECON OM IES LOWER
THE AVERAGE COST OF PRODUCTION, p. 8).
Empirical analysis of agglomeration econo­
mies has had to deal with two data problems.
First, data on the stock of capital at the metro­
politan area level are simply not available.2
Fortunately, a production function technique
has been developed that permits the estimation

2Some researchers have put together estimates of capital
stocks. However, their results are not strictly comparable to
those reported here, though the general direction of the
results is the same. See David Segal, "Are There Returns to
Scale in City Size?" Review of Economics and Statistics 58
(1976) pp. 339-350. Segal analyses the change in urban
productivity with city size but does not focus on agglom­
eration economies, which is one component of city pro­
ductivity. He finds that on average cities with over 2 million
people are 8 percent more productive than cities with under
2 million people. See also Patricia Beeson, "Total Factor
Productivity Growth and Agglom eration Econom ies in
Manufacturing, 1959-73," The Journal of Regional Science 27
(1987) pp. 183-190. Since Beeson uses state level data her
findings are hard to compare with those reported here.
Beeson uses a capital stock series developed in Lynne Brown,
Peter Mieszkowski, and Richard Syron, "Regional Invest­
ment Patterns," New England Economic Review, (July/August
1980) pp. 5-23.




Gerald A. Carlino

of economies of scale without the need for data
on the capital stock.3 Second, data on industries
other than manufacturing are sparse. Therefore,
research has had to focus almost exclusively on
manufacturing industries in the past 15 years to
determine whether agglomeration economies
are a fact of economic life for U.S. cities.
Two studies from the 1970s focusing at the
industry level take som ew hat different ap­
proaches to estim ate the degree to which
agglomeration economies exist for manufactur­
ing in U.S. cities. Daniel Shefer looks at 20
industries in a cross section of cities (ranging
from 26 cities in the leather industry to 62 cities
in the printing and publishing industry) in the
years 1958 and 1963.4 He finds evidence of
econom ies of scale for urban manufacturing
industries in both years. For example, for the
primary metal industry in 1963, he estimates
that, on average, a 1.0 percent increase in all
inputs used by this industry in a city would
result in a 1.12 percent increase in output. One
limitation of the Shefer study is that we do not
know to what extent his estimates reflect internal
or external economies of scale.
In a more recent study, Gerald Carlino extends
the analysis of agglomeration economies. He
estimates economies of scale for 19 industries in
each of 68 metropolitan areas over the period
1957-1972.5 He derives a single measure of
overall returns to scale in each industry in each
city over that period. He then analyzes these
industry-specific measures across cities to deter­
mine the extent to which overall economies of
scale are related to internal economies of scale,
localization economies, and urbanization econo3The technique involves estimating a wage equation. It is
assumed that, since workers are paid according to their
productivity (that is, there is perfect competition in local
labor markets), wages and the demand for labor reflect the
advantages of agglomeration economies.
^Daniel Shefer, "Localization Economies in SMSAs: A
Production Function Approach," Journal of Regional Science
13 (1973) pp. 55-64.
5G erald A. Carlino, "Increasing Returns to Scale in
Metropolitan Manufacturing," Journal of Regional Science 19
(1979) pp. 343-351.

7

BUSINESS REVIEW

NOVEMBER/DECEMBER 1987

Agglomeration Economies Lower the Average Cost of Production
Letting the Specialists Produce the Zidgets . . .
Average Cost
Per Zidget

. . . Lowers the Overall Cost of Producing Widgets
Average Cost
Per Widget
70

To see how agglomeration economies can lower a firm's long-run average cost, we can return to
Original Widgets and assume that a crucial part of making a widget involves a fitting called a zidget (in
reality, this crucial factor may be repair services, accounting, financial and legal services, computer
programmers, and so forth). The top panel shows the long-run average cost of making zidgets, which
involves substantial economies of scale. At 30 zidgets per day the cost is $15 per zidget, but when 90
zidgets are produced, the cost per zidget drops to $10.
Original Widgets cannot take full advantage of the economies of scale of zidget-making internally,
because it only needs 30 per day for its widget production. But, suppose the local widget industry
expands, say to three widget firms producing a total of 90 widgets per day. Now a separate firm, Acme
Zidgets, can take advantage of the economies of scale of zidget production and supply them to all three
widget manufacturers in the area. The result is shown in the second panel, where Original Widgets (as
well as the other two widget firms) enjoys the cost-savings due to agglomeration economies because its
average cost of producing 30 widgets per day could drop by as much as $5 (from $45 to $40).

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FEDERAL RESERVE BANK OF PHILADELPHIA

Productivity In Cities: Does City Size Matter?

mies by industry. The results strongly suggest
the importance of external economies of scale
for urban manufacturing firms. He finds that
urbanization economies are the more general
source of external economies, since they are
indicated for 12 of the 19 industries studied.67
For five of the remaining industries, localization
economies are an important source of external
economies of scale. Of the two remaining indus­
tries, internal scale economies are indicated in one
case, and no significant source of economies of
scale were found in one industry (see SOURCES
OF ECONOM IES OF SCALE IN SELECTED
INDUSTRIES, p. 10).
Using the same techniques with which they
m easured agglom eration econom ies at the
industry level, Shefer and Carlino also estimate
the degree to which agglomeration economies
exist for manufacturing in general in U.S. cities.
This provides another measure of urbanization
economies. In the same study covering 67 cities
in 1963, Shefer finds that a 1.0 percent increase
in inputs used in urban manufacturing results in
about a 1.2 percent increase in urban manufac­
turing output, on average. Carlino obtains an
estimate of urbanization economies in manu­
facturing city by city. His study includes 82
metropolitan places during the period 1957 to
191 7 ? He finds that agglomeration economies

^Two other studies using a somewhat different technique
from the one discussed here have found that localization
economies are dominant in urban manufacturing. See, J.
Vernon H enderson, "Efficiency of Resource Usage and City
Size," Journal of Urban Economics 19 (1986) pp. 47-70, and
Ronald Moomaw, "Agglomeration Econom ies: Urbanization
or Localization?" unpublished manuscript (1987). These
findings may follow from the fact that they use only industry
level data.
7Gerald Carlino, "Manufacturing Agglomeration Econo­
mies as Returns to Scale," Papers of the Regional Science
Association 50 (1982) pp. 95-108. A number of studies since
the m id -1970s have shown that productivity in general
increases with the size of a city at least over the observed
range of city sizes. These studies have found that a 3 to 6
percent increase in city productivity is associated with every
doubling of city size. For a survey of this literature, see
Ronald Moomaw, "Spatial Productivity Variations in Man­
ufacturing: A Critical Survey of Cross-Sectional Analyses,"
International Regional Science Review 8 (1983) pp. 1-22.




Gerald A. Carlino

also tend to increase with city size, up to some
point. For example, a 1.0 percent increase in all
inputs resulted in a 1.9 percent increase in out­
put in Peoria, a 1.4 percent increase in output in
Cincinnati, a 1.3 percent increase in output in
both Kansas City and St. Louis, and a 1.2 percent
increase in Boston's output. But estimates for
Philadelphia, the fourth largest metropolitan
area in the U.S. in 1980, indicate only about a 1.0
percent increase in output (that is, constant
returns).
Why would a large metropolitan area such as
Philadelphia, which contained approximately
4.7 million people in 1980, offer constant returns
to its manufacturing firms on average while, say,
Peoria, which contained less than 400,000 people
in 1980, offers substantial returns to scale on
average? The answer lies in the costs to both
firms and households that result from increased
urban size.
FACING THE COSTS OF GROWTH
The positive effects of agglomeration econo­
mies make up one side of the urban size ledger.
The negative effects of congestion on households
and firms brought on by city growth (agglom­
eration diseconomies) make up the other. The
growth of cities is influenced by both forces,
with agglomeration econom ies encouraging
growth, and agglomeration diseconomies dis­
couraging it.
Higher Transportation Costs . . . After some
point, further increases in the number of people
and firms residing in a metropolitan area tend to
clog its roads and transportation network and
increase the average time and cost of transport­
ing goods and commuting either to work or to
leisure activities. In addition, as a metropolitan
area grows, its boundaries may spread out, which
increases both the time and distance of the
average commute. As a result, households will
have to spend more annually for gasoline and
auto maintenance, and they may even need to
purchase a second car.
. . . Higher R ents. . . Most commuting to work
involves trips to and from a metropolitan area's
9

BUSINESS REVIEW

NOVEMBER/DECEMBER 1987

Sources of Economies of Scale
in Selected Industries
These 19 industrial groupings represent the two-digit Standard Industrial Classifications as defined
by the U.S. Office of Management and Budget. Each consists of a fairly broad aggregate of establishments,
each of which may derive different benefits from localization economies and urbanization economies.
For example, the classification Electrical Machinery includes establishments engaged in manufacturing
equipment for the generation, storage, transmission, and transformation of electrical power, establish­
ments manufacturing computers and related products, and firms manufacturing household appliances.
Thus, the finding that a particular two-digit industry does or does not depend upon a particular kind of
agglomeration economy may not apply to all of its component establishments. The data used in this
study are averaged over the period 1957-1972.
Industry

Internal

External
Localization

Food Products
Textiles
Apparel
Wood
Furniture
Paper
Printing and Publishing
Chemical
Petroleum and Coal
Rubber and Plastics
Leather
Stone, Clay and Glass
Primary Metal
Fabricated Metal
Nonelectrical Machinery
Electrical Machinery
Transportation Equipment
Instruments
Others

Yes
No
No
No
No
No
No
No
No
Yes
No
No
Yes
No
No
No
No
No
No

Urbanization

No
No
No
No
No
Yes
No
No
No
No
No
Yes
No
No
Yes
Yes
No
Yes
No

Yes
Yes
Yes
Yes
Yes
Yes
Yes
No
Yes
Yes
Yes
No
Yes
Yes
No
No
No
No
Yes

SOURCE: Compiled from G.A. Carlino, "Increasing Returns to Scale in Metropolitan Manufacturing", Journal of
Regional Science 19 (1979) Table 2.

downtown, or its central business district. Many
firms seek these central locations, in part, because
they offer agglomeration economies. This com­
petition will increase business rents. As house­
holds attempt to locate near these large centers
of economic activity to avoid long commutes,
they bid up residential rents as well. As a result,
rents in a metropolitan area tend to reflect the
proximity of a parcel of land to its central busi­
ness district. Moreover, rents in an entire metro­
politan area tend to be driven up by the growth
of households and firms in that area.
. . . And Higher Wages. Workers in large cities
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will demand higher wages in order to offset
these increases in transportation costs and
rents.8*As a result, wages tend to increase with
metropolitan size. Firms are able to pay these
higher wages to w orkers to the extent that
agglomeration economies have made workers

8For a fuller discussion that includes analysis of the effects
of local amenities and disamenities on wages, see Sherwin
Rosen, "Wage-Based Indexes of Urban Quality of Life," in
Current Issues in Urban Economics, Peter Mieszkowski and
Mahlon Straszheim, eds., (Baltimore: The Johns Hopkins
University Press, 1979).

FEDERAL RESERVE BANK OF PHILADELPHIA

Productivity In Cities: Does City Size Matter?

more productive. But there is a limit to a firm's
ability to compensate its workers for these higher
living costs.
Finding the Balance: Is There An Optimal
City Size? The agglom eration diseconom ies
reflected in higher transportation costs, higher
rents, and higher wages serve to increase the
unit cost of production for firms. As long as
these additional costs are offset by increased
productivity, firms will be willing to pay them,
and a city will continue to grow. When the unit
cost-saving from the agglomeration of people
and firms is just offset by the increased cost due
to agglom eration d iseconom ies, a city has
reached what economists call its optimal size. At
the optimal size, the average cost of production
is minimized.
While the notion of an optimal city size has
been addressed in a number of studies, it has
proven hard to identify precisely for any city.
Part of the reason is that a city's optimal size will
depend on its mix of industries, its proximity to
other cities, its rate of technical change and the
level of its infrastructure. Since the cost of labor
and land and the advantages of agglomeration
economies vary with city size, firms' decision
about locating in cities of particular sizes will
depend on how much they use labor and land,
and how much they would gain by taking advan­
tage of agglomeration economies. The estimation
of the optimal size for individual cities has not
been attempted because the size of the popula­
tion in most cities has not varied substantially
during the period for which data are available.9
HOW CAN POLICYMAKERS
ENHANCE PRODUCTIVITY?
Individual firms that have incentives to exploit
agglom eration econom ies are guided by the

^Economists have, however, estimated an optimal size for
an average city based on economies of scale in manufacturing
using cross-sectional data. See, for example, Gerald A.
Carlino, "Manufacturing Agglomeration Economies as Re­
turns to Scale," Papers of the Regional Science Association 50
(1982) pp. 95-108 who finds the optimal size to be around
3.5 million people.




Gerald A. Carlino

"invisible hand" of the marketplace to locate
near other firms in the same industry or in areas
where there is a general concentration of eco­
nomic activity. Local policymakers have a major
role in "lending a hand" to accommodate ag­
glomeration econom ies by providing public
infrastructure. In this sense public infrastructure
and private capital are complementary inputs to
local production. Local policymakers have an
additional role to play in enhancing the produc­
tivity of firms by investing in the education of
the city's workers.10 This sort of investment in
education can result in what economists call
increased "human capital."
Investment In Public Infrastructure. When a
city is growing rapidly because it offers net
agglomeration economies to firms in a number
of industries, local planners need to make sure
that the city's public infrastructure keeps in step
with private growth. If local infrastructure is not
growing fast enough, the area could become
congested more rapidly, leading to a more rapid
increase in wages, rents, and transportation
costs. Such a situation could halt the growth of
an area. After some point, additional public
infrastructure is necessary for future growth to
occur.
In a recent study, Randall Eberts measured
the level of public infrastructure for 38 metro­
politan places for the time period 1958-1981.11

productivity. They include the characteristics of a city's work
force other than educational and skill attainment, local
policies and regulations, research and development spend­
ing, unionization rates, and environmental considerations.
While these factors may determ ine differences in city
productivity, little, if any, research has been conducted on
these issues.
11 Randall Eberts, "Estimating the Contribution of Urban
Public Infrastructure to Regional Growth," Working Paper
8610, Federal Reserve Bank of Cleveland (1986). Eberts
estimates the level of public infrastructure by summing up
the past investments made to the stock of infrastructure in
each of these metropolitan places, after adjusting these
stocks for depreciation and discard. He uses a pooled crosssection of time-series approach to derive an average estimate
of the effect of infrastructure on productivity across these 38
metropolitan places.

11

BUSINESS REVIEW

As with the studies that examine the effect of
agglom eration econ om ies on productivity,
Eberts considers public infrastructure an input,
together with labor and private capital, in a
citywide manufacturing production function.
While his method of estimation gives no par­
ticulars about specific cities, Eberts finds that a
doubling of public infrastructure would lead to a
4 percent increase in manufacturing output on
average in his sample of 38 metropolitan places.
Investment In Education. Besides determining
the quality of local infrastructure, local policy­
makers in the U.S. have a great deal of influence
on the skill level of the work force because they
control the public education system. These in­
vestments in human capital lead to increased
city productivity not only because education
makes a city's work force more employable but
also because education introduces a city's work­
ers to new techniques and skills. For example,
many high schools throughout the country have
developed programs in computer literacy.
John Mullen and Martin Williams consider
these issues in manufacturing for a sample of 29
metropolitan places during the 1958-1978 time
period.12 They compute the portion of a city's
12John Mullen and Martin Williams, "Technical Progress
in Urban Manufacturing," Journal of Urban Economics (forth­
coming). One problem with this approach to measuring
technical progress is that it fails to account for the growth in
output that is due to agglomeration economies. As a result,
some of the increase in productivity that is attributed to
technical progress may be due to agglomeration economies.


12


NOVEMBER/DECEMBER 1987

growth of manufacturing output that can be
accounted for by that city's increases in the
number of workers and capital that took place
during the period. The growth of a city's output
beyond that explained by the increases in capital
and labor they attribute to technical progress.
They then decompose this measure of technical
progress into that which is due to better workers
(embodied in labor) and that which is due to
better capital (embodied in capital). They find
that across metropolitan places, technical pro­
gress embodied in the labor force was a more
important source of productivity growth than
technical progress embodied in private capital.
This study suggests that local policies that
increase the educational attainment and skill
levels of its work force are highly worth pursuing.
Where Best to Put the Effort? Much has been
written about the decline of large American cities
— the urban blight, the crime, the many negative
but very tangible and visible features of American
urban life. But large cities have existed and will
continue to exist at least in part because they
tend to make workers and other factors of pro­
duction more productive, as various studies
have shown. Local planners need to recognize
the fact that city size matters, for if they allow
infrastructure and schools either to remain as
they are or to decay, they will fail to exploit to the
fullest the growth that agglomeration economies
provide.

FEDERAL RESERVE BANK OF PHILADELPHIA

Commuter Rail Ridership:
The Long and the Short Haul
Richard Voith*
INTRODUCTION
Many American cities have commuter rail
systems which, in addition to serving their riders,
are intended to benefit the region as a whole by
reducing congestion and air pollution, enhancing
economic development, and providing trans­
portation services to the poor. The degree to
which these potential benefits are realized
depends upon the number of riders the system
can attract. A commuter rail system with little

^Richard Voith is an Economist in the Urban and Regional
Section of the Research Department of the Federal Reserve
Bank of Philadelphia.




patronage cannot contribute much to congestion
relief or air pollution abatement.
Demand for commuter rail transportation,
like the demand for any service, depends upon
its price, the price of alternatives, and the quality
of the service. Unlike most other services, how­
ever, prices or fares in the regional public trans­
portation industry are determined not in the
marketplace but by a public authority. Most
public transportation systems, including com­
muter rail systems, depend on state and local
governments for subsidies, as fares cover only a
portion of the operating cost. Fares, the quality
of service, and ultimately the level of ridership,
13

BUSINESS REVIEW

will depend on the level of subsidy available for
public transportation and on how that subsidy is
allocated throughout the service area. When
state and local governments decide how much
subsidy to provide, they walk a fine line between
allocating enough funds to reap the benefits of
public transportation and keeping enough
budgetary pressure on the transit authority to
provide the service in a cost-effective manner.
If lower subsidies induce the transit authority
to produce transportation services more effi­
ciently, that is clearly beneficial. Transit authori­
ties, however, often respond to budgetary short­
falls by increasing fares, reducing service, or
both. While such actions balance the budget in
the current year, they can lead to problems in
the future. In the short run, increases in price
and reductions in service have a relatively small
impact on ridership. But, in the long run, con­
sumers can exercise more options among their
commuting alternatives; therefore, ridership
may decline after the initial impact of the price
increase or service reduction, leaving the system
with lower and lower farebox revenues. The
difference in commuters' short-run and longrun responses to changes in price and service
levels may help explain the familiar cycle of
service reductions, increasing fares, and falling
ridership often observed in the public trans­
portation industry.
THE EVOLUTION
OF COMMUTER RAIL DEMAND
Consumers are the ultimate judges of public
transportation policies, and they evaluate public
transportation relative to the price and quality of
other alternatives. Important elements in the
quality of commuter rail transportation are fre­
quency of service, speed, reliability, and factors
affecting comfort, such as crowding and cleanli­
ness. Changes in the price or characteristics of the
rail system (or of competing means of transporta­
tion) will affect the choices of some consumers
immediately, while others will be affected only
after some lag as they make long-term decisions.
In the short run, a consumer faces a fairly

14


NOVEMBER/DECEMBER 1987

narrow set of alternative types of transportation
and will choose the most attractive among them
to get from place to place. For example, he can
choose to drive if he owns a car, or take the train
or a bus from home to his place of work. In the
short run, the consumer's transportation alter­
natives themselves and the origins and destina­
tions of trips cannot readily be changed.
Over the longer term, however, a consumer
can change his transportation alternatives by
making investments, such as purchasing a car or
perhaps a second car. He might be able to join a
car or van pool to reduce the cost of private
transportation. He can even change the origin
and destination of his commuting trips by mov­
ing or changing employment. Transportation is
often a major consideration in such a change.
Thus, in the long run a consumer has consid­
erably more options in responding to changes in
the relative prices and qualities of various
transportation alternatives.
It is not just current price and quality that
affect these long-run decisions but future con­
siderations as well. If there is a great deal of
uncertainty about the price or the existence of
the commuter rail service in the future, the
potential benefits of that system are discounted
in the consumer's long-term decision.
Taken together, the short-run and long-run
decisions of consum ers in the entire region
determine the evolution of ridership over time.
If the price and quality of train service make it an
attractive alternative, people and firms are likely
to make long-term location and investment
decisions that will lead to high levels of ridership
in the future. Areas well served by the system
will grow and develop. Individuals who work
along the train lines will sort themselves into
residential locations that have train service. For
instance, most systems have a hub in the center
of the city so that people who work there will be
more likely to live in areas with train service,
which will probably raise property values there.
On the other hand, people who work where train
service is not available will choose to live in areas
that are not near train stations to avoid paying
FEDERAL RESERVE BANK OF PHILADELPHIA

Commuter Rail Ridership

higher housing prices. Locations well served by
the train, therefore, will have a disproportion­
ately large number of people who routinely
travel by train. Hence, ridership will be high.
On the other hand, if the quality of service is
poor, or too expensive, or if future subsidies are
uncertain, individuals and firms will not weigh
the possibility of future train service heavily in
their investment and location decisions. People
will invest more in automobiles, making it less
likely that they would choose to ride the train in
the near future, even if the price and quality of
the train service were improved. People may
choose to live in areas not served by the train
even if their job location has train service.
Employers may choose locations not served by
the train. As a result, where people live and
work would not be consistent with high future
ridership.
Setting the Public Transportation Budget.
Since the transit authority and state and local
governments together choose the prices and
service levels, they influence the evolution of
demand. The transit authority actually sets the
fares and service levels within the framework of
a balanced budget. Its operating expenses cannot
exceed its revenues, which include both proceeds
from the farebox and government subsidies. But
the authority can only go so far in balancing the
budget by cutting operating expenses or in­
creasing fares. Operating expenses cannot be
reduced if they result in service levels that are
inadequate to sustain consumer demand. And
the amount of revenue available from the farebox is limited because riders can opt for other
means of transportation if fares are too high.
The other source of revenue for balancing the
budget, namely the amount of subsidy available,
is a matter of public policy. W hen state and local
governments choose the level of subsidy for
public transportation, they weigh a myriad of
economic and political considerations.1 In addi-

^For a discussion of the role of public investment and
productivity, see Gerald A. Carlino, "Productivity in Cities:
Does City Size M atter?" this issue of the Business Review.




Richard Voith

tion, they often use legislative review of the
subsidy and budgetary restraint to induce the
transit authority to minimize waste.2 The share
of expenditures covered by the farebox, or
operating ratio, is a common measure of the
performance of public transportation authorities.
Achieving a high operating ratio, however, may
not necessarily coincide with achieving the low­
est subsidy cost per passenger. It is possible, for
example, for a transit authority to attain a very
large share of revenue from the farebox by
charging high fares, while having relatively low
ridership. In this case the subsidy would benefit
few riders, and the benefits in terms of traffic
congestion relief would be small. Forcing high
fares through low subsidies may result in high
subsidy costs on a per rider basis. Since the
public benefits of the system depend on the
level of ridership, a better goal for policymakers
may be to choose the subsidy that minimizes
subsidy cost per rider.
The "C a tch -2 2 " of Public Transportation.
There is a trade-off between the reduced waste
induced by budgetary restraint and the adverse
long-run impacts of higher prices and lower
service which may result from a low level of
subsidy. In the short run, ridership may not
change much in response to changes in price
and service levels. Thus, service cuts and fare
increases may balance the budget in the current
period. But, because of the effect of fares and
service levels on people's long-run decisions,
the loss in ridership and corresponding decline
in farebox revenue resulting from changes in
prices and service may be much greater in the
long run. In economic terminology, demand is
more elastic in the long run than in the short run.
(See SHORT-RUN AND LONG-RUN ELASTI­
CITIES, p. 16.)

2Several studies have noted a correlation between higher
levels of government transit subsidies and higher transit
worker wages and lower productivity. See J. Gomez-Ibanez,
"The Federal Role in Urban Transportation," in American
Domestic Priorities: An Economic Appraisal, John M. Quigley
and Daniel L. Rubinfeld, eds. (Berkeley: University of
California Press, 1985) pp. 183-223.

15

NOVEMBER/DECEMBER 1987

BUSINESS REVIEW

Short-Run and Long-Run Elasticities
Economists often express the change in demand for a product in response to a change in its price or some
other factor in terms of "elasticities"— the percentage change in one thing divided by the percentage
change in another. Consider, for example, the price elasticity of train ridership:
Percent Change in Ridership
Elasticity = -----------------------------------------Percent Change in Price
If this ratio is more than 1 (ridership, in percentage terms, changes more than price in percentage terms),
then price demand is "elastic." If the ratio is less than 1 (ridership, in percentage terms, changes less than
price in percentage terms), then price demand is said to be "inelastic."
It is a general economic proposition that demand is more elastic in the long run than in the short run.
Thus, in some cases, price increases may produce more revenue in the short run, but in the long run
during which people have more time to exercise other options, price increases may lead to declines in
total revenue.
The graphs below compare examples of elastic and inelastic demand curves to illustrate their effects
on total revenues. In both cases, when the railway fare is, say, $1.00 per ticket, the quantity demanded is
200, and total revenue is $200. But, if the fare goes up to, say, $1.50 per ticket, the effect on total revenue
is very different depending on the elasticity of demand. Where demand is inelastic, total revenues
increase from $200 to $270 even though ridership declines somewhat, from 200 to 180. But where
demand is elastic, ridership falls so much—from 200 to 3 0 —that revenues are only a small fraction of
what they originally were, falling from $200 to $45.
Inelastic Demand

Price

Price

30

100

180 200

Elastic Demand

300

Ridership


16


FEDERAL RESERVE BANK OF PHILADELPHIA

Commuter Rail Ridership

If long-run demand is significantly more
elastic than short-run demand, then price hikes
and service cuts are likely to result in higher
long-term subsidy costs per passenger. Because
high fares or poor quality service lead people to
look for alternatives to the train, revenue from
the farebox falls but the large fixed costs of the
rail system remain unchanged; thus the govern­
ments' cost per rider increases. Since transpor­
tation policies are an important factor shaping
the development of a region, the long-run and
short-run effects of changes in fares and quality
of service should be important considerations of
both the transit authority and its state and local
subsidizers. A prerequisite for formulating
rational transportation policy is knowledge of
the short-run and long-run impacts of price and
service changes.
ANALYZING THE DEMAND
FOR COMMUTER RAIL
TRANSPORTATION
From a planning perspective, transit authori­
ties need to know how much the demand for rail
transportation is affected by changes in price,
quantity, and quality of service. Measuring the
total effects of these changes is difficult because
the level of ridership depends not only on the
price and attributes of train service but also on a
number of other factors, such as the number of
potential customers, their transportation prefer­
ences, their investments in private transporta­
tion, and the price and quality of alternatives to
the train, such as buses and van pools. The size
and makeup of the potential pool of riders play
important roles in the level of ridership at any
particular location.
Most studies have focused only on the shortrun impacts of price and service characteristics
on demand, assuming that the choices com­
muters have now are the only ones available. By
observing the choices of many individuals, each
facing different circumstances in terms of the
prices and attributes of the alternative modes of
transportation, the short-run impact of changes
in prices and service on their transportation



Richard Voith

choices can be measured.3
Since these short-run analyses do not take
into account the transportation system's impact
on individuals' long-term choices, and hence its
impact on the potential pool of riders, they
underestimate the total impacts of price and
service changes. To predict the total impact of
changes in the price and service levels of the
train system on ridership, one must take into
account the effects which may not occur instan­
taneously, but rather gradually as such changes
affect the locational distribution of the regional
population and the investment decisions of that
population.4
By examining the evolution of ridership at
particular locations in a region over a period of
several years, one can estimate both the longrun and short-run impacts of price and service
changes.5 Fortunately, data are available for
this type of analysis from the Southeastern
Pennsylvania Transportation Authority (SEPTA)
rail system in the Philadelphia area (see the
Appendix, pp. 22-23, for technical details of the
study). From 1978 to 1986 changes in ridership,
prices, and service have varied considerably
from station to station in the SEPTA system
(see TRENDS IN SEPTA COMMUTER RAIL
RIDERSHIP, pp. 18-19).

3The theory and methods of empirical analysis of indi­
vidual choice of travel mode in the short run are based on the
pioneering work of Daniel McFadden, "Conditional Logit
Analysis of Quantal Choice Behavior," in Frontiers of Econo­
metrics, Paul Zarembka, ed. (NY: Academic Press, 1974)
pp. 105-142.
4Mateen Thobani, "A Nested Logit Model of Travel Mode
to Work and Auto O w nership," Journal of Urban Economics,
15 (1984) pp. 2 8 7 -3 0 1 , analyzes the joint decision of
purchasing a car and choice of travel mode as functions of
the price and attributes of the public transit system. Alex
Anas, "Estim ation of Multinomial Logit Models of Joint
Location and Travel Modal Choice from Aggregated Data,"
Journal of Regional Science, 21 (1981) pp. 223-242, examines
the transit system's impact on residential location.
5A complete discussion of this methodology is discussed
in Richard Voith, "Determinants of Comm uter Rail Rider­
ship: The Long and Short Haul," Federal Reserve Bank of
Philadelphia Working Paper (forthcoming). A more com ­
plete discussion of the data is contained there as well.

17

NOVEMBER/DECEMBER 1987

BUSINESS REVIEW

Richard Voith

Commuter Rail Ridership

Trends in SEPTA Commtifei* Rail Ridership 1978-1986
The Zone-By-Zone Trend

The Overall Trend
Ridership Per Station Per Day
500

Percent Change, 1978-1986
Zone Ridership Price
450

Number
of Trains

5

25.7

- 6.0

126.0

12.1

- 6.5

128.0

2.9

2

-32.2

176.5

-19.7

1

• Norristown

97.3

3
• Chestnut Hill

5.7

4

• Trenton

-41.0

151.7

-14.6

• Center City
• Angora

• Paoli

200

79

80

81

82

83

84

85

86

87

From 1978 to 1980, ridership rose slightly to its peak, but in the next two years declined rapidly as fares
increased and service levels fell. In 1983, SEPTA took over operation of the system from Conrail and, in
an effort to reduce costs, endured a strike that lasted over three months. The gap in the data is a result of
the strike; fall 1982 was the last pre-strike observation and spring 1984 was the first post-strike
observation. By spring 1984, ridership had fallen dramatically to its all time low. Since 1984, ridership
has rebounded to about 80 percent of its 1980 peak.

18


FEDERAL RESERVE BANK OF PHILADELPHIA

The aggregate figures mask significant differences over time when the data are broken down by fare
zone. Zones 1 and 2, which are the closest to the center of the city, have had dramatic declines in
ridership, while ridership fell slightly in zones 3 and 4 and increased in zone 5. The dramatic fall in
ridership in the interior zones was accompanied by significant reductions in the total number of trains
and large price increases. On the other hand, in zone 5 where ridership increased, the total number of
trains increased by 25 percent and the price increase was much smaller.
While some of the ridership loss in the close-in zones, especially zone 1, may have been caused by
population declines in the city of Philadelphia (unrelated to the changes in the transportation system),
these declines are very small relative to the magnitude of the decrease in ridership. It appears that much
of the ridership loss is a result of the price increases and service reductions. One might expect these areas
to be especially sensitive to price, because alternative forms of public transportation—buses and
subways—are available. Also there has been significant improvement in the quality of the bus and
subway system over this period. In the more distant zones, population growth should have provided
natural growth in ridership for the commuter rail system. However, with employment booming in these
outlying areas, many people now both live and work there. The increase in ridership in the most distant
zone indicates that the increase in service and more modest price increases had a positive effect on
ridership.

19

NOVEMBER/DECEMBER 1987

BUSINESS REVIEW

Short-Run and Long-Run Demand Elasticity
on the SEPTA Rail System. Econometric analysis
of the SEPTA data reveals that the long-run
responses of ridership to changes in prices and
service attributes are considerably larger than
the short-run responses (see Table 1). Short-run
responses— those which occur at the time of
the change— all proved to be inelastic; that is,
the percentage change in ridership is less than
the percentage change in price, number of peak
or off-peak trains, or speed of the train. As pre­
dicted, the estimated total impacts of changes in
prices and service attributes are much larger
than the short-run impacts—more than twice as
large. The analysis further suggests that about
half of the total impact occurs within the first
year.
In the case of price, the short-run elasticity is
about -0.68, meaning that a 10 percent increase
in price generates a 6.8 percent decrease in
ridership. This estim ate is sim ilar to other
measurements of the short-term price elasticity
of other com m uter system s.6 The long-run
elasticity is almost three times as great, at -1.84.
To illustrate how these price elasticities could
affect revenues (holding everything else con­

6See Clifford Winston, "Conceptual Developments in the
Economics of Transportation: An Interpretive Survey,"
Journal of Economic Literature, 23 (1985) pp. 5 7 -9 4 , for
estimates of the price elasticity of ridership on the BART
commuter rail system in San Francisco.

stant), suppose SEPTA, which has about 100,000
riders, increased the average one-way ticket price
by $0.25 or 9.2 percent (Figure 1). Daily revenue
would increase immediately by $8,000 per day.
So, because ridership is inelastic in the short
run, the transit authority could increase revenues
in the short run by increasing fares. But, in the
long run, the revenue picture deteriorates. After
the first half-year, the increase drops to zero; by
the end of the first full year, daily revenue is
reduced by almost $6,500, and after four years,
revenues are below the original levels by over
$19,000. Since these elasticities work in the
opposite way when the fare drops by $0.25,
SEPTA might be able to generate more revenue
by lowering prices, provided it can handle the
extra passengers.
The budgetary implications of elastic versus
inelastic demand are less conclusive in the case
of service attributes, since the financial effects of
changing the service attributes depend not only
on the change in ridership but also on the costs
of changing the quality of service. The short-run
elasticities for the number of peak trains and the
number of off-peak trains are 0.19 and 0.54,
respectively, while the short-run speed elasticity
is about .24. Since the average number of peak
trains in 1986 was 7.6, this implies that an addi­
tion of one peak train (a 13 percent increase)
will increase peak ridership along that line by
2.6 percent. An additional off-peak train (a 5.3
percent increase) would increase off-peak rider-

TABLE 1

Ridership Is More Elastic in the Long Run
Short Run
Average Nominal Price
Peak Number of Trains
Off-peak Number of Trains
Speed

Long Run

-0.68
0.19
0.54
0.24

-1.84
0.52
1.47
0.66

NOTE: Elasticities are evaluated at 1986 levels and are derived from the coefficients in the Appendix. For example,
the short-run price elasticity is: eD= (-41.8 x 5.4)/3 3 3 = -0.68. The long-run price elasticity is: = ( l / ( l - 0 .6 3 ) ) x-0.68
= -1.84.

Digitized 20 FRASER
for


FEDERAL RESERVE BANK OF PHILADELPHIA

Richard Voith

Commuter Rail Ridership

FIGURE 1

The Long-Run Impact
of a $0.25 Fare Increase

Change in Daily Revenue
$ 10,000

NOTE: The future r e v e n u e , < b a n be'calculated as follows: (1) base year farebox revenue is F0 = p0Ro, where p is
price and R is ridership a$d th e subscript denotes the initial period; (2) ridership t periods after the change in price,
Ap, is given by R t = [1+e t* (A p /(p + A p ))] Rq where e t is the t-period price elasticity; (3) the t-period price elasticity
can be calculated using the formula, e t = (e„/(l-A.) )(1-Xt+1), where e0 is the short-run elasticity and A is the lag
.
param eter (0.63) from the Appendix; (4) the farebox revenue in period t is Ft = R* (p + A p ) and the revenue impact
is Ft-F0. Since each period is about eight months long for the available data, the t for a one-year impact is 1.5.

ship by 2.8 percent. Likewise, since the average
speed of the system in 1986 was 22 miles per
hour, increasing average speed by 10 miles per
hour (a 45 percent increase) would result in a
10.8 percent increase in ridership. While not as
striking as the long-run price elasticity, the longrun implications of service changes are signifi­
cant as well. The addition of one peak train
would increase peak ridership by 7 percent;
increasing speed by 10 miles per hour would
increase ridership by 29 percent. An increase in
speed would tend to have even greater impacts
since the authority could operate more trains
with no additional equipment or crews. If the
greater speed allowed the frequency of service
to go up 30 percent, the combined effect on
ridership would be an increase greater than
40 percent.



These estimates indicate that there is consid­
erable scope for SEPTA to increase patronage
by increasing speed and frequency and lowering
price—if the short-run budget constraint could
be loosened and if appropriate investments are
made by the transit authority to improve service
along the dimensions consumers value. Further­
more, price increases and service reductions
may be counterproductive in the long run, even
if they do balance the budget in the short run.
These actions actually may result in a higher
subsidy cost per rider or per passenger mile,
though the total subsidy may be lower. This is
true not only of the SEPTA system, but of any
rail system in which price and service changes
have relatively small effects on ridership in the
short run and relatively large effects in the long
run.
21

BUSINESS REVIEW

NOVEMBER/DECEMBER 1987

THREE IMPLICATIONS
FOR TRANSIT POLICYMAKERS
Three basic policy implications emerge from
long-run price and service elasticities that are
greater than short-run elasticities. First, transit
authorities should closely examine their pricing
and service policies to ensure that they are
consistent with long-term cost-effective service.
This means that the transit authority should
actively pursue strategies that encourage devel­
opment and location decisions that will lead to
future ridership.
Second, those who subsidize public trans­
portation should recognize that price increases,
service reductions, and uncertainty about the
level of future service may have counterpro­
ductive effects in the long run. In order to obtain
reasonable costs per rider, the subsidy level will
have to be large enough to provide service that
will induce people to make location and invest­
ment decisions that are consistent with public
transportation usage. If people are uncertain
about the future levels of service, they will insure
themselves by becom ing less dependent on

public transportation, which will lead to lower
future ridership.
Because ridership is more responsive to price
and service changes in the long run than in the
short run, balancing a transit authority's budget
through price increases and service reductions
may result in future financial difficulties. The
findings based on the analysis of data on one
commuter rail system (SEPTA) suggest that the
long-term impacts may be sufficiently large that
further price increases and reduction in the
frequency of trains will not improve a transit
authority's long-term financial performance.
Finally, because the consequences of price
and service changes are not completely mani­
fest in a single budget year, state and local
governments should consider alternatives such
as multiyear appropriations. In that case, transit
authorities could balance their budgets over a
longer period rather than in each budget year. A
longer planning liorizon would allow transit
authorities to aVoidrnaking short-run decisions
which, in the long run-,^an lower ridership and
increase subsidy costs j$er rider.

Appendix
The estimates of elasticities for the SEPTA system reported in this article are derived from a dynamic
fixed-effects model. The basic model of ridership from any location consists of two equations:

= Mpg, P i Ag, A i; D
i>)
D > = f(pM-l, pi-'-’, A)-''1 Ai*'1; »'->)
>
,
i
where:

=

1, 2, . . . ,

00

Rjf is ridership from location j in period t.
p|J

is the price of a trip on the train from j in period t.

p^

is the price of a trip in the car from j in period t.

Ao is the vector of service attributes of the train from j in t.
A f is the vector of service attributes of the car from j in t.
D)1 is a distribution of the characteristics of the population in location j at time t which
includes the number of people, their destinations, their investments in transportation
alternatives, their income, and preferences.
Z)4 is a vector of factors unrelated to transportation affecting D.


22


FEDERAL RESERVE BANK OF PHILADELPHIA

Richard Voith

Commuter Rail Ridership

Substituting for D in the first equation, ridership simply becomes a function of current and lagged price
and service attributes and a vector of factors unrelated to previous price and service levels which affect
ridership only through demographics.
Several assumptions are made to estimate this dynamic model. These are:
(1)
(2)
(3)
(4)

The effects of lagged variables decline geometrically over time.
The decay rate is the same for each explanatory variable.
Attributes of car travel, except for price, are unchanged during the sample period.
Demographic differences across locations (which may be the result of differing prior levels and
price of transportation) which give rise to different mean ridership levels across locations can be
adequately represented by "fixed effects," meaning that we can use dummy variables for each
location.
(5) Z)1 is uncorrelated with the transportation variables and so can be disregarded when estimating
the impacts of price and service changes.

Given these assumptions, the following equation can be estimated:

Ri4 = XRi't_1 + cqpi,4 + a2p^ + a3A£ + 8D + e
where X is the geometric lag parameter and D is a vector of dummy variables for location. In the actual
regression, dummy variables for years 1984 and 1985 which immediately followed a 3-month strike by
SEPTA workers are included as well. The a's give the short-run impact of the variable, while the term a /
(1-X) gives the total impact. The mean lag is X/(l-X ). The model has been estimated with an asymptotic
equivalent of maximum likelihood.
The data set consists of data on 129 of the 165 stations served by SEPTA for twelve observation periods
between 1978 and 1986. In addition, the cost of operating, owning and parking a car have been added to
the SEPTA data.
The estimation results are presented below. The prices used in the estimation are nominal. The results
all conform to what is expected theoretically, and generally the estimated coefficients are highly
significant, including those on the lag parameter. The "truncation parameter" is a necessary artifact of the
maximum likelihood estimation used here.

Estimation Results: Full Sample, Nominal Prices
Independent Variable

Coefficient

Standard Error

0.63
5.8
3.1
-41.8
3.7
48.8
12.9
-81.8
-32.5
65.8

0.04
1.6
0.6
5.3

Lagged Ridership
Peak Number of Trains
Off-peak Number of Trains
Price
Speed
Variable Cost of Auto Trip
Fixed Cost of Auto Ownership
1984
1985
Truncation Parameter
Number of Observations
Mean Square Error
Mean Lag

1.0
7.9
6.3
8.7
9.0
14.0

1986 Mean
287.2
7.6
18.9
5.4
22.0
8.1
7.1
0.083
0.083

1548
7945.2
1.7

NOTE: The average time period is eight months, so the mean lag of 1.7 can be converted to 13.6 months. The
dependent variable is ridership per station; its mean for the whole sample is 349. The mean for 1986 was 333.




23

Business Review Index 1987
January/February
Paul Calem, "Interstate Bank Mergers and Competition in Banking"
Loretta J. Mester, "Efficient Production of Financial Services: Scale and Scope Economies"

March/April
Theodore Crone, "Housing Costs After Tax Reform"
Edwin S. Mills, "Dividing Up the Investment Pie: Have We Overinvested in Housing?"

May/June
Brian R. Horrigan, "The CPI Futures Market: The Inflation Hedge That Won't Grow"
Robert H. DeFitia, "Explaining Long-Term Unemployment: A New Piece to an Old Puzzle"

July/August
Mitchell Berlin, "Bank Loans and Marketable Securities: How Do Financial Contracts Control
Borrowing Firms?"
Janice M. Moulton, "New Guidelines for Bank Capital: An Attempt to Reflect Risk"
Edward G. Boehne, "Is There Consistency in Monetary Policy?"

September/October
Joel F. Houston, "The Underground Economy: A Troubling Issue for Policymakers"
John J. Merrick, Jr., "Fact and Fantasy about Stock Index Futures Program Trading"

November/December
Gerald A. Carlino, "Productivity in Cities: Does City Size Matter?"
Richard Voith, "Commuter Rail Ridership: The Long and the Short Haul"

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RESERVE BANK OF
PHILADELPHIA
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