Measuring Sprawl:

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Measuring Sprawl

• An Empirical Investigation of North American
  Urban Land Areas 1950 1990
• IL Econ. Assc. Conference
• October 18, 2003
• Daniel T. McGrath

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Introduction

• Within the body of urban economic literature,
  general view on urban sprawl is
• Urbanization is determined by systematic economic
  factors.
• If urban sprawl exists, it is driven by market
  failures specifically errors in agents
  internalizing externalities.

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Introduction

• Interesting quote by Brueckner
• When crafting policies to address sprawl,
  policymakers must recognize that the potential
  market failures involved in urban expansion are
  of secondary importance compared with the
  powerful fundamental forces that underlie this
  expansion. The bulk of the substantial spatial
  growth that has occurred across the United States
  cannot be ascribed to such a cause.

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Introduction

• If there have been market failures resulting in
  urbanization totals greater than social optimum,
  it would important to scale this contribution to
  urban spatial growth .
• This research seeks to provide an empirical
  measurement to urbanization attributable to
  market failures, controlling for standard
  economic factors.

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Origins of this Research

• Began as coastal urbanization forecast for 2025
  for Sea Grant.
• Obtained population and urban land area totals
  for 25 coastal metro. regions from decennial
  census data.
• OLS estimation of equation
• Ln(Area) B1Ln(Pop) B2(Time)

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Economics of Structure of Urban Land Area

• Monocentric Urban Model Alonso (1964) Mills
  (1967) Muth(1969)
• The well-known equilibrium conditions

Population must fit into the urban area
(1)
Land Rents at the urban fringe equal agricultural
rents
(2)
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Economic Theory contd.

• Together, conditions (1) and (2) determine
  equilibrium values for u and?x conditional on n,
  y, t, and ra.
• Wheaton (1974) first presented

(3)
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Empirical Work

• Only one empirical investigation of equation (3)
  Brueckner Fansler (1987) Economics of Urban
  Sprawl
• Does not address sprawl per se.
• Dataset includes 40 small metro. regions (inside
  one county) in 1970 census.

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Brueckner Fansler

• Estimated Equation
• ULA -41.07 .00041? n .0062? y
• - .2444 ? t - .0303 ? ra
• N 40?, R2 .798, signf. At 5
• Transportation variable, t, is defined as the
  percentage of commuters using public
  transportation.
• Elasticities (eval at means) of ULA wrt
• n 1.095 ra -0.234, y 1.497

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Brueckner Fansler

• Interesting concluding remark
• The results of this paper justify a
  dispassionate view of urban sprawl. By showing
  that urban spatial area is related to population,
  income, and agricultural rent in the manner
  predicted by the model, the empirical results
  suggest that sprawl is the result of an orderly
  market process rather than a symptom of an
  economic system out of control.

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Market failures and Sprawl

• 3 identified market failures (Brueckner, 2002,
  Brookings-Wharton Paper Urban Sprawl Lessons
  from Urban Economics)
• 1. Failure to account for social value of open
  space.
• 2. Failure to account for social costs of road
  congestion
• 3. Failure to fully account for the
  infrastructure costs of new development.

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1. Failure to account for social value of open
space

• Social value of open space around city includes
  value as agricultural land plus the open space
  benefits it generates.
• Condition determining social optimal allocation
  of land to urban use

Aggregate social value of undeveloped land
accruing to all residents
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Open Space contd.

• Integral represents the social value of an acre
  of open space. This equals the m.r.s. between
  open space, s, and the numeraire consumption
  good, c.
• If intangible open space benefits are not
  internalized as part of the income earned in
  agricultural use, then
• ?xS lt ?x

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Failure to account for social cost of congestion

• In presence of congestion, travel costs increase
  to t P(x), R(x)
• R(x) is the road/land ratio at x
• P(x) is number people outside x
• An added commuter at x raises P(x) by 1 and
  imposes extra congestion costs of PP(x), R(x)
  on other commuters.

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Congestion Contd.

• Summing across commuters, the total congestion
  damage done by the extra commuter at x is
• P(x)PP(x), R(x)
• Analysis of urban equilibria with congestion
  difficult because commuting costs the spatial
  distribution of population is jointly determined.
  (Wheaton, 1998)

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Congestion contd.

• Bottom Line With no congestion toll to
  internalize externality, transportation costs
  appear lower to the individual commuter and the
  equilibrium urban spatial size is greater than
  optimum so
• ?xCT lt ?x
• Wheaton (1998) shows the imposition of congestion
  tolls would reduce?x by 10 in a simulated city,
  suggesting significant spatial over-expansion.

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3. Failure to fully account for new
infrastructure costs.

• Requires explicitly dynamic model.
• Value differential theory Land is optimally
  converted to urban use at time, t, when the
  annualized net benefit from from urban use is
  greater than agricultural rent.

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Infrastructure contd.

• Under current decentralized institutional system,
  each landowner in jurisdiction equally pays for
  the existing stock of infrastructure.
• Bottom line municipal authorities do not
  calculate marginal infrastructure costs, but
  rather an average infrastructure cost under the
  equal payment regime.

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Infrastructure, contd.

• So land is converted when
• Land conversion costs appear artificially cheap.
  This lowers the value differential required for
  land conversion, or infrastructure is provided
  for a larger population than is required at time
  t so
• ?xI lt ?x

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The Model

• If these market failures ( others) are in
  operation in North American metropolitan regions,
  there should be a systematic increase in urban
  land areas over time

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Functional Form
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The Data

• Dataset includes metropolitan region data from
  decennial censuses 1950 1990 for 34 metro
  regions
• regional urban land area totals (in sq. miles)
• regional population totals, n
• metropolitan real per capita personal income, y
• Metropolitan regional summary tables available in
  hard copy in UIC Library

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Data contd.

• t is represented by personal transportation
  consumer price index (PTCPI) for all regions (for
  most decades 17 missing obs.) available online
  from Economagic, www.economagic.com
• ra is represented by Nominal Agricultural Land
  Values per acre by state (converted to real 2001
  dollars) available online from the USDA Economics
  Statistics system, http//usda.mannlib.cornell.e
  du

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Data contd.

• The agricultural land values for the following
  were averaged
• New York avg of CT, NJ
• Philadelphia avg of PA, NJ, DE
• Pittsburgh avg of PA, OH, WV
• DC avg of VA, MD

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Summary of Variables

• MSAULA MSA Urban Land Area in sq. miles. XBAR
  sqrt(ULA/?)
• MSAPOP Metro region population total in
  thousands.
• RPINC Real per capita personal income for
  metropolitan region in 2001.
• PTCPI Personal transportation consumer price
  index
• RAGVAL Real average agricultural land value for
  state of metro region in 2001.
• DECADE 11950,,51990.

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Estimation Results

• Model 1 Ln(XBAR) K ?1?Ln(MSAPOP)
  ?2?RPINC ?3?PTCPI ?4?RAGVAL
  ?3?DECADE

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Estimation Results contd.

• Testing for fixed effects Including dummy
  variable for each of 34 metropolitan regions.

.1469 implies 15.8 (? 2 mi.) per decade Or
1.47 (.18 mi.) per year.
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Tentative Conclusions

• In contrast to Brueckner Fansler, no
  significant effect of Agricultural Land Values
  counters evidence that higher quality farmland
  more resistant to development.
• Elasticity of XBAR wrt Population
• BF ? 0.55
• We calculate 0.36
• In contrast to BF, significant impact of
  transportation cost variable Implies that
  congestion tolls might be best strategy to
  utilize market mechanism to combat sprawl.
  Elasticity -.14 implies that an 11 increase in
  transportation costs will achieve a 1.5
  reduction in?x.

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Tentative Conclusions

• Evidence supports position that on average North
  American metropolitan regions are systematically
  greater in spatial size than what may be socially
  optimal (possibly due to market failure) between
  26 32 per decade or about 2.6 3.1 per
  year on average. Is that too much?

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Thank You
dmcgrath_at_uic.edu