FRBSF Economic Letter
98-27; September 11, 1998
Cities and Growth
The study of economic growth is an important part of economics. Traditionally,
economists have attempted to understand the process of growth at the level
of the aggregate economy, focusing, for example, on concepts such as the
economy-wide levels of saving or of education. More recently, they have
turned to the study of a smaller unit: the city. This Letter
describes some of the motivation behind the focus on cities and also what
the study of cities has taught us about the process of growth so far.
A basic growth model
Robert Solow's (1956) neoclassical model of economic growth has become
a workhorse for economists engaged in the study of growth. In this model,
output growth depends upon the growth of two factors of production --
capital and labor-- and upon exogenous changes in technology. The model
has been quite useful in describing the growth experience of the U.S.
and other industrialized nations. It also has been used to study the enormous
disparities in growth rates and income levels among countries. In this
role it has helped economists rule out some popular misconceptions about
the causes of sustained disparities in growth rates, such as differences
in tax codes and trade barriers.
Yet, cross-country data on growth provide a fundamental challenge to
a key prediction of the Solow model: the model predicts that incomes should
converge, but the data show convergence only among some subsets of countries.
More generally, the problem is that the persistence and magnitude of differences
in growth rates across nations are difficult to account for in the traditional
growth model framework.
Lucas (1988) suggests a further elaboration of the role of technology
as a solution: "This [technology] seems to me to be the one factor
isolated by the neoclassical model that has the potential to account for
wide differences in income levels and growth rates" (p. 15). If by
the term "technology" we mean society's stock of knowledge,
its level and growth rate should not vary dramatically across countries;
human knowledge is for the most part not proprietary to nations, but universal.
Instead Lucas suggests that in addition to the general knowledge already
included in the Solow growth model we should also consider the knowledge
and skills of particular people.
A role for human capital
It is not hard to see why the skills of the labor force might matter.
For instance, more highly skilled workers are likely to learn new technologies
faster than less skilled workers. Consequently, an economy with a more
skilled labor force is likely to grow faster than an economy with a less
skilled labor force. Thus, the performance of an economy depends not only
upon the size and growth of its labor pool, but also upon the level of
skills possessed by the members of this labor pool. This level of skills
can be thought of as the stock of human capital, much like the stock of
physical capital in the economy.
So far, the role we have envisaged for human capital is straightforward:
replacing a less skilled worker with a more skilled worker will raise
the level of output, much as replacing a typewriter with a computer will.
According to Lucas, however, the level of human capital matters for another
reason as well: the productivity of a worker with a given amount of human
capital depends upon the human capital of the workers that she interacts
with. It is reasonable to think workers' skills are augmented through
learning, and that workers learn from those around them. Thus, moving
a worker from a "group" where the average level of human capital
is low to one where the average level is high will raise her productivity.
What is the appropriate empirical counterpart of the "group"?
Its defining feature is the level and kind of interaction that occurs
among a variety of its members. Clearly, interaction will not be uniform
across space (for instance, across the nation), but will be concentrated
at certain nodes. Lucas suggests that cities are a particularly important
kind of node: "It seems to me that the 'force' we need to postulate
to account for the central role of cities in economic life is of exactly
the same character as the 'external human capital' I have postulated as
a force to account for certain features of aggregative development"
(p. 38).
Concentrations of activity ranging from Silicon Valley to the garment
district in New York suggest that dense agglomerations of economic activity
can be beneficial. The diversity of activity in New York City also suggests
that these gains from agglomeration are not limited to people engaged
in the same kind of activity. Glaeser (1998) points out that cities provide
increased opportunities for interaction, and to the extent that learning
is facilitated by interaction, cities will accelerate the learning process
for urban workers. Geographic proximity allows ideas to travel more rapidly,
and therefore cities reduce the cost of moving ideas. These knowledge
spillovers can lead to increased human capital accumulation through learning
and ultimately to higher productivity levels.
In fact, in the absence of such external effects or spillovers, it can
be hard to explain the existence of cities. Traditional theory would suggest
that rather than clustering together in cities, industries would disperse
as competition for space (cheaper rents) and labor (lower wages) would
drive firms away from urban areas. According to Glaeser, the fact that
firms still choose to locate in cities and pay the higher wages means
that workers in cities are more productive: "...if workers weren't
more productive firms would leave cities altogether and hire elsewhere.
Since the urban wage premium appears to be a centuries-old phenomenon,
we must assume that over the long run, firms are quite willing to pay
these higher wages" (p.142).
This explanation is compelling even in the face of more traditional
explanations for the existence of cities. Traditional explanations focus
on the role of cities in reducing transportation costs, and in providing
firms with easy access to numerous consumers and intermediate suppliers.
There is some evidence to suggest that such factors may be becoming less
important over time. For one thing, transport costs as a share of GDP
are falling (reflecting the decreasing significance of transport as a
factor in the production process). Manufacturing has been in decline relative
to the burgeoning service sector. Particularly notable is the fact (pointed
out by Glaeser) that manufacturing has moved out of cities faster than
it has moved out of the U.S. as a whole.
At the same time, we are aware of no evidence that suggests that cities
are becoming less important over time. The implication is that cities
have advantages beyond the traditional ones related to transportation
cost and market size. These additional advantages appear related to knowledge
and learning, and accrue due to human interaction. As Lucas asks, "What
can people be paying Manhattan or downtown Chicago rents for,
if not for being near other people?" (pp. 38-39). We now turn to
the formal evidence that economists have found in support of the hypothesis
that cities lead to higher productivity.
Some empirical evidence
Sveikauskas (1975) provides some early evidence on the correlation between
productivity and city size. Using a sample consisting of data on 14 industries
and (up to) 212 metropolitan areas, Sveikauskas estimates the relationship
between a measure of productivity (value added per worker) and the population
of the region. Based on the results of this estimation, he concludes that
a doubling of city size is associated with a close to 6% increase in labor
productivity. He goes on to show that this difference in labor productivity
does not reflect the fact that capital investment in cities exceeds investment
outside cities. Similarly, he finds that a doubling in city size leads
to a nearly 5% increase in wages, even after allowing for the influence
of some other factors such as education. Sveikauskas's results show that
large cities tend to be more productive, but as he points out, a significant
question remains --- that of causation. He is unable to answer whether
city size causes productivity gains or whether already productive cities
grow large.
Rauch (1993) uses data from the 1980 population census to estimate productivity
gains due to human capital externalities (or spillovers) in U.S. cities.
He points out that such a study is better suited for this purpose than
a study based on country level data. Countries with high human capital
will tend to be more developed; for instance, they will tend to have a
"...large and technologically current stock of physical capital."
This means that it will be hard to determine the reason for any observed
differences in productivity across countries; such differences could be
due to human capital or to some of the other factors that go with high
levels of development. These considerations are not likely to be as important
for a study that looks at cities within a country.
Rauch defines human capital to contain both education and work experience
components. He estimates a series of wage and rent equations to show that
there are spillovers associated with the level of average human capital.
Further, he finds that the spillover effects associated with education
exceed those associated with experience. These results hold even when
Rauch controls for the effects of other factors such as R&D investment
policies that favor cities, as well as university concentration in urban
areas. Further, his estimates of these externalities are similar to Lucas's
and imply a significant social return to education. Specifically, he finds
that the social return to education is 1.7 times that of private returns,
in line with Lucas's estimate of an external human capital effect of 1.6.
Raising the average education level of a metropolitan area by one year
raises total factor productivity by 2.8%, in line with Lucas's estimate
of 3.2%.
Ciccone and Hall (1996) note large discrepancies in productivity levels
across U.S. states: a worker in the most productive state is two-thirds
more productive than a worker in the least productive state. They use
data at the county level to see if variations in population density can
explain some of these differences. In their analysis, Ciccone and Hall
go to substantial lengths to prevent their results from being contaminated
by "reverse causation," that is, they try to ensure that the
correlation between density and productivity that they find is not the
result of productive regions growing faster than less productive ones.
They find that doubling employment density increases labor productivity
by 6% and that local gains due to employment density can explain more
than half of the labor productivity variation across states. They also
show that the differences in productivity do not reflect other factors,
such as the level of public capital, and that they persist even after
the level of education is taken into account. Finally, they also show
that the positive relationship between density and productivity does not
reflect the influence of market size (since an alternative hypothesis
could be that access to large markets leads to faster growth).
Conclusion
While the results of these studies differ in some ways -- such as the
relative importance of education -- they all find significant spillovers
associated with cities. More specifically, the productivity of workers
in cities is higher than can be explained by the kind of neoclassical
production function used by Solow (where output depends upon labor, capital,
and an exogenous productivity term) or even a neoclassical production
function that has been augmented to allow for direct effects of human
capital. These results provide support for Lucas's statement that such
spillovers are an important part of economic growth.
Kelly Ragan
Research Associate
Bharat Trehan
Research Officer
Reference
Ciccone, A., and R. Hall. 1996. "Productivity and the Density of
Economic Activity." American Economic Review (March) pp.
54-70.
Glaeser, Edward L. 1998. "Are Cities Dying?" Journal of
Economic Perspectives (Spring) pp. 139-160.
Lucas, Robert E. 1988. "On the Mechanics of Economic Development."
Journal of Monetary Economics (Vol. 22) pp. 3-42.
Rauch, James E. 1993. "Productivity Gains from Geographic Concentration
of Human Capital: Evidence from the Cities." Journal of Urban
Economics (November) pp. 380-400.
Solow, Robert M. 1956. "A Contribution to the Theory of Economic
Growth." Quarterly Journal of Economics (February) pp. 65-94.
Sveikauskas, Leo. 1975. "The Productivity of Cities." Quarterly
Journal of Economics (August) pp. 393-411.
Opinions expressed in this newsletter do not necessarily reflect
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or of the Board of Governors of the Federal Reserve System. Editorial
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