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Measuring Sprawl:

Measuring Sprawl:. An Empirical Investigation of North American Urban Land Areas 1950 – 1990 IL Econ. Assc. Conference October 18, 2003 Daniel T. McGrath. Introduction. Within the body of urban economic literature, general view on urban sprawl is :

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Measuring Sprawl:

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  1. Measuring Sprawl: An Empirical Investigation of North American Urban Land Areas 1950 – 1990 IL Econ. Assc. Conference October 18, 2003 Daniel T. McGrath

  2. 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.

  3. 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.”

  4. 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.

  5. 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) = B1*Ln(Pop) + B2(Time)

  6. 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)

  7. Economic Theory cont’d. • Together, conditions (1) and (2) determine equilibrium values for u andx conditional on n, y, t, and ra. • Wheaton (1974) first presented: (3)

  8. 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.

  9. 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

  10. 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.”

  11. 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.

  12. 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

  13. Open Space cont’d. • 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: x*S < x

  14. Failure to account for social cost of congestion • In presence of congestion, travel costs increase to t + ƒ[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 ƒP[P(x), R(x)] on other commuters.

  15. Congestion Cont’d. • Summing across commuters, the total congestion damage done by the extra commuter at x is: P(x)ƒP[P(x), R(x)] • Analysis of urban equilibria with congestion difficult because commuting costs & the spatial distribution of population is jointly determined. (Wheaton, 1998)

  16. Congestion cont’d. • 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: x*CT < x • Wheaton (1998) shows the imposition of congestion tolls would reducexby 10% in a simulated city, suggesting significant spatial over-expansion.

  17. 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.

  18. Infrastructure cont’d. • 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.

  19. Infrastructure, cont’d. • 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: x*I < x

  20. 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

  21. Functional Form

  22. 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

  23. Data cont’d. • 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.edu

  24. Data cont’d. • 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

  25. 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 – 1=1950,…,5=1990.

  26. Estimation Results • Model 1: Ln(XBAR) = K + 1Ln(MSAPOP) + 2RPINC + 3PTCPI + 4RAGVAL + 3DECADE

  27. Estimation Results cont’d. • 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.

  28. 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: • B&F  0.55 • We calculate 0.36 • In contrast to B&F, 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.

  29. 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?

  30. Thank You dmcgrath@uic.edu

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