Alternative Measures of Urban Form in U.S. Metropolitan Areas

1. Alternative Measures of Urban Form in U.S. Metropolitan Areas Stephen Malpezzi Wen-Kai Guo University of Wisconsin-Madison

2. What is sprawl? • Most writers and activists fail to define sprawl. Some elements of a definition might include: • Low density • Discontiguous (“leapfrog”) development • Lack of public open space • Other outcomes that may or may not be associated with sprawl include: • High auto use, low transit use • Differences in the cost of public services • Excessive loss of farmland

3. Overall Plan for Malpezzi and Guo • Estimate a number of candidate measures of urban form • MSA specific indexes, based on Census tract data • Which incorporate the ‘most information’ about form? • Regress each index against other indexes, examine fit and t-statistics • Which are reasonably related to determinants? • Regress each index against a reasonable set of determinants • Link to second paper: take the best index, and run with it.

4. Candidate Indexes • Average MSA density • Sort tracts by their density. Pick density of tract containing the “median person.” • Many variations on this theme. • Estimate exponential density models • Univariate: intercept as well as delta, compare to flexible forms. Incorporate measures of fit. • Measures of dispersion • Gini, Theil indexes • Weighted average distances • to center; to all tracts • Gravity measures • Spatial autocorrelation

5. Selected Previous Research • A number of ‘sprawl’ papers examine average metropolitan density (Brueckner and Fansler, Peiser) • Many papers examine population density gradients, and related measures (Mills, Muth, etc., see McDonald review) • Compare and evaluate alternative measures • A fair number evaluate, e.g., power terms, test SUE model against a flexible alternative (e.g. Kau and Lee) • Only a few examine a fair range of alternatives (e.g. Song)

6. Sprawl, Related Issues • Bertaud and Malpezzi demonstrate that, in fact, cities like Paris and Los Angeles have much more efficient form than Seoul or Moscow, or Johannesburg. • What are the specific costs of sprawl which give rise to this concern? Are there benefits to “sprawl?” What are the most efficient policy responses? • E. Mills and B. Song, Urbanization and Urban Problems. Harvard, 1979. • G. Ingram, Land in Perspective. In Cullen and Woolrey, World Congress on Land Policy, DC Heath, 1982 • A. Bertaud and S. Malpezzi, The Spatial Distribution of Population in 35 World Cities

7. Measuring Sprawl • Since sprawl is hard to define, it’s not surprising few papers have tried to measure it. • Many papers rely on average population density in the metro area. • Our usual density gradients • including power terms, R-squared • Moments of tract density • Gini coefficients, Theil information measures • Distance/gravity measures • Techniques of measuring spatial autocorrelation • Data reduction (principal components?)

8. Measuring Sprawl • Our initial measure will rely on tract densities within MSAs. • Sort each MSA’s census tracts by density, lowest to highest. Use the density of the tract containing the 10th percentile of MSA population, when tracts are so ordered. • Can use other percentiles (median, quartiles, etc.) • A better measure of density at the fringe. • Pros and cons? • Under development: average lot size for a “new” single family house, from AHS

9. Example of a measure based on order statistics: the average density of the tract containing the median of the MA population, when tracts are ranked by density. Our MA has 7 tracts, total pop. is 100. Where is person 50?

10. The measure we focus on today. • The average density of the tract containing the 10th percentile of the metropolitan area’s population, when tracts are ranked by density. Say it 10 times, fast. • Pros: • Distinguishes between MAs with a lot of open space, and those without. • Gets at density on “the margin” without a particular assumption about monocentricity. • Cons: • There’s no guarantee that this “fringe” tract is really on the fringe. • The usual issues with using “gross” tract densities.

11. Costs and Benefits of Sprawl: The “Pure Cost” View $ Costs per housing unit fall with density Maximum feasible density, under current rules and practices Density of Development Figure 1

12. Costs and Benefits of Sprawl: The Cost-Benefit View $ Costs fall with density Willingness-to-pay first rises, then falls, with density Maximum feasible density Density of Development Maximize Benefit-Cost Figure 2

13. Costs and Benefits of Sprawl: The Cost-Benefit View, with Externalities Social costs (= private costs + external cost) $ Private costs Willingness-to-pay Maximum feasible density Density of Development Maximize Private Benefit-Cost Maximize Social Benefit-Cost Figure 3

14. Figure 1-A

15. Figure 1-B

16. Figure 2

17. Figure 3

18. Figure 4

19. Figure 4

20. Figure 5

21. Figure 6

22. Figure 8

23. Figure 9

24. Figure 10

25. Figure 11

26. Figure 12

27. Figure 13

28. Figure 14 (Preliminary)

29. Figure 15

30. Figure 16

36. Figure 6

37. Figure 7

38. Nine Causes of Sprawl (Richard K. Green) • Rent gradient • Demographics • Growing affluence • Transportation changes • Government service differentials • Racial discrimination and segregation • Plattage and plottage • Tax policy • Land use regulation

39. More causes of sprawl • Economic structure • The degree of monocentricity • Opportunity cost of land in rural uses

40. Some Opinions • American Farmland Trust, Farming on the Edge • Bank of America et al., Beyond Sprawl • Al Gore, several recent speeches • Peter Gordon and Harry Richardson, “Are Compact Cities a Desirable Planning Goal?” • Reid Ewing, “Is Los Angeles Style Sprawl Desirable?” • John Norquist, The Wealth of Cities • Richard Moe, Growing Smarter • Many more, type “sprawl” into your browser and stand back.

41. Some Literature • Real Estate Research Corporation, The Costs of Sprawl (1974) • Critiques of RERC by Altshuler (1977) and Windsor (1979) • Downs, New Visions for a Metropolitan America • Helen Ladd, “Population Growth, Density, and the Costs of Providing Public Services” (1992) • David Mills (1981) • Richard Peiser (1989) • Brueckner and Fansler (1983) • Burchell and Listokin, others at Rutgers, on “fiscal impact analysis” (various), The Costs of Sprawl Revisited (1998)

42. Highly Tentative Conclusions • Transit infrastructure has little effect on density per se. • More mass transit is associated with longer commutes. • Higher densities lower commutes, ceteris paribus. • Will these results hold up to further work?

43. Some Next Steps • Alternative sprawl measures (e.g. AHS new housing density) • Better measures of transit infrastructure • Model other outcomes that reflect potential costs and benefits of sprawl • environmental outcomes • public service costs • racial and economic segregation • Endogeneity, endogeneity, endogeneity

44. Percent of Metro Population and Employment in Central Cities Source: O’Sullivan, Kain, Census

45. Why Do We Observe Decentralization? • Standard Urban Economics (SUE) model: rising incomes, falling transport costs • “Blight Flight” or Amenities/disamenities models • Public policies • Change in technology, shift to service economy, incubator processes?

46. The U.S. is Well-Endowed with Land • The U.S. has 7% of the world’s land area. • But 13% of the world’s cropland is in the U.S. • The U.S. has roughly 10 acres of land for every inhabitant.

47. Population Density, Selected Countries

48. U.S. Population if settled at other countries’ densities

49. How U.S. Urban Land is Used, 1980 Source: Vesterby and Heimlich, 1991

50. U.S. Land Use • Urban land is 3 percent of U.S. land by area, but the majority of land by value. • With about 4 hectares of land per person (gross), the U.S. is far from typical in density. • However, even very dense countries, like Korea, have small percentages of land in urban uses (see below).