Urban and Regional Economics

1. Urban and Regional Economics Weeks 8 and 9 Evaluating Predictions of Standard Urban Location Model and Empirical Evidence

2. Declining Population Density • There is substantial evidence here. • McDonald (1989, Journal of Urban Economics) has a lengthy review article on this evidence. • Suggests downward sloping population density, although there is significant variation between cities. • Older cities appear to have steeper density gradients. • Cities with larger populations have flatter density gradients.

3. Overview of McDonald Article • Paper is extensive • Overview of research • Single-area function issues • Econometric Issues • Findings • Multiple area issues • findings • Let’s focus primarily on Single-Area issues

4. Dates to early 1950’s Economists recognized empirical regularities in density D(u) = D0e-tu where D(u) = population per square mile, u=distance, D0=density extrapolated to city center. in log form: lnD(u) = lnDo-tu D Origins of Literature u

5. How is density measured? • Can look at: • Gross density which includes all land • Net density which includes only land in residential use • Question: Which would generate higher lower density estimates? • Gross land more easily assembled

6. Research in 1950’s and 1960’s • During 1950’s: • Studies expanded evidence to support negative exponential form • During 1960’s: • Urban economists developed SUM • Theoretical consistency with net-density functions, not gross density functions • Some economists questioned negative exponential model • Latham and Yeates, Newling

7. a>0, b<0 Effect of Urban Growth D(u) D(u) u u CBD CBD Alternative form: QuadraticD(u) = D0eau+b*u*uin log form: lnD(u)=lnD0+au+bu2

8. Net Density • Throughout 1970’s, • Negative exponential model remained dominant when considering net density • Some attempts to: • Address some econometric issues • Expand list of determinants (ie., are there other factors besides distance, u, to consider?)

9. Empirical Approach • Econometric • Get data, and fit curve to data • Will summarize issues briefly • Analytic approach developed by Ed Mills • Get data on population and land area of central city, and entire urban area • Analytically derive t. • More later

10. Econometric issues - briefly • Problem with use of Census tract data • Areas have roughly constant population • Areas w/ low densities under-represented since they get lumped in w/ areas w/ greater population. Address w/ WLS • Problem with extrapolation of D0 from log function • E(eln(Do)) not D0, since the log-transformation is nonlinear, and OLS is a linear estimator • A correction exists for this problem

11. Econometric issues - briefly • What is correct functional form? • Shouldn’t just assume negative exponential • Can use Box-Cox flexible form D(u)d-1/d=D0-tu where d=1 implies linear, d=0 implies log • What is correct set of determinants? • Control for differences over time and across cities (if multiple areas considered)

12. Findings • Some support for negative exponential • Some suggest more complex forms are possible. • For example: • Spline regressions allow function to be estimated in sections. Cubic functions can be used between knots in spline regression • Some evidence of peak to right of CBD (up to 4 miles in large cities) • Secondary peak as suburbs approached. • Can account for structural change • Find other factors important • eg., introduction of rail systems, highways, income, racial mix, etc. More later. • Trend surface analysis • Allows for density to evolve in nonsymmetric fashion.

13. Mills Two-Point Method • Analytically derive shape, assuming D(u) = D0e-tu • Inputs are minimal • Population and land area of central city • Population and land area of urban area • Radius of central city • Radius of urban area • There is internal consistency between D(u) and Population • Mathematically integrate: • Density function from zero to the edge of CC to get CC population • Density function from zero to infinity to get entire population • Iteratively determine t as the value that gives total population of central city and of urban area.

14. Factors determining t • Techniques: • Can estimate D(u) and see how t varies across cities with different characteristics • Can include other determinants and see what impact inclusion of these has on estimate of t. • Findings: • Income: Negative influences density (why?) • HH size: Negative influence on density (why?) • Amenities: Increase density (why?) • Pop of city: Flattens density (why?) • Age of city: Older cities have steeper functions (why?) • Time: Have flattened over time (why?)

15. Conclusions • Strong evidence to support SUM predictions • Suggests more research needed for net-density functions • All info. has been gleaned from gross functions • Need to include other determinants • Investigate more policy implications

16. Does Accessibility Matter? • Jackson article suggest that the answer is yes. • However, Bruce Hamilton published an influential article in 1982 (JPE) that cast doubt on the predictability of the SUM. • Measured wasteful commuting, by looking at pop. and employment density functions for cities. • He found that there was 8 times more commuting taking place than could be explained by SUM. • Critics of Hamilton suggest he looked at a simplified model, and omitted important influences

17. Expanding the SUM to Incorporate other Factors • Add in time cost of commuting • Now t depends on income (i.e., t(w)) • Why? • More later. • Add in multiple destinations. • Accessibility to workplace is no longer the only important determinant. • May flatten or steepen. Why? • Add in two earner households • Accessibility of second worker now also important. • May flatten or steepen. Why?

18. Factors that influence H • Demographics (eg., # children) • Since PH/u= -t/H, then anything that increases H, will flatten the gradient • Take second derivative 2PH/uH=t/H2 >0 • Income growth • Since t(w) and H(w), numerator and denominator change. • Take second derivative of housing price gradient with respect to income, w. 2PH/uw=[-H*t/w - (-t*H/w)]/H2

19. Income and housing price gradient • Look at sign of second derivative • If higher income flattens the bid-housing price function, then the second derivative is positive. 2PH/uw=[-H*t/w + (t*H/w)]/H2>0? • This depends on numerator. • Multiply numerator by (w/t*H) which gives: • (t*H/w -H*t/w)*w/t*H • (H/w*w/H -t/w*w/t) • Interpretation?

20. Wheaton Findings

21. Adding in other influences • Amenities and disamenities influence the locational equilibrium. • Can show mathematically that: PH/u= -t/H + V/A* A/u) • The first term is the accessibility factor. • The second term is the monetized value (why?) of the marginal utility of additional amenities, A as location changes. • Better amenities should enhance PH.

22. Adding in Fiscal Factors • Since Tiebout’s seminal article in 1956, it has been know that residents vote with their feet for the fiscal bundle. • Does a more desirable fiscal bundle lead to higher property prices? • Mathematically, this can be shown to be similar to amenity influence. • Would need to introduce tax prices.

23. Let’s play around with some data from Fresno • Dependent variable is real price of housing • Include structural characteristics as controls • Include accessibility measure • Include neighborhood measures • Amenities, disamenities, other factors • Include fiscal measures • Income time dummies, other locational dummies • Examine findings

24. Updated Structure: Multicentric Cities • Monocentric cities are no longer prevalent. • Look at Milwaukee MSA as an example • How do these influence SUM? • Households now choose location based on more than one employment center. • This implies the formula for the slope of bid rent function now changes.

25. Introduce Wage Gradient • Wages now vary with distance. • Reason: Workers must be indifferent between centralized and decentralized jobs. • Question: • How do wages vary with distance? • What determines tradeoff?

26. Modification of Bid Rent • Look at the profit function  = PBB - C - w*L - t*B*u - R*T • Competition for space drives out all profits.  = PBB - C - w(u)*L - t*B*u - R(u)*T=0 • Solve for R= (PBB - C - w*L- t*B*u)/T • Derive slope: R/u= - w/u*L/T - tB/T MB and MC comparison: R/u*T + w/u*L = tB • Interpretation: • What draws firm to suburbs? • What draws firm to central location? • Do high labor users have steeper or flatter bid rent? • Rents would have to fall faster to make them indifferent.

27. R May have multiple rent peaks throughout city Individual firm’s functions vary with t, T, L, B Later, we will look at how some of these factors change with time. Influence of DBD’s on Land Rent Functions u

28. Bid Housing Price Function also changes Modifications complex, but insights similar We will stay with simple model

29. Look at Bender and Hwang article Jean will present this paper

30. Using the SUM to Explain Suburbanization • Suburbanization of households and employment has been dramatic. • Can SUM explain suburbanization of households and employment? • What assumptions re: rent gradients must have occurred? • Alternatively, multiple centers must have evolved.

31. Suppose intracity transportation improves for manufacturers. (i.e., t falls) Recall: R/u= -tB/T The slope will decline: 2R/ut =-B/T<0 Interpretation: As t increases, slope steepens Eventually, price of good also falls since costs fall. Thus, intercept falls also. Effect of declining t on Bid Rent R Bid-Rent shifts from A to B to C (PBB-C)/T (PB’B-C)/T B C A u

32. Transportation innovations such as truck (inter and intra) and interstate highway system, automobile (lowers t). Beltways become important access points. Location of suburban airports (lowers t). Peaks not concentric More land intensive plants (increases T). Use of lighter weight materials (lowers B) Beltway Influence Flattening of Manufacturers Bid Rent R u CBD Beltway

33. Flattening of Retailer’s Bid Rent • Profit function depends on proximity to population their markets. • As population decentralizes, so does retail activity. • Look at growing importance of suburban shopping malls for suburban locations. • Role of parking • Parking space plentiful in suburban locations (land costs lower) • Parking more expensive in central city locations, which disadvantages urban locations.

34. Flattening of Office Firms Bid Rent • Agglomeration economies grow in suburbs (localization and urbanization). • These factors increase productivity in suburbs and reduce need for face-to-face contact in CBD. • Communication improvements lower t. • Teleconferencing, e-mail, data transfer allows decoupling of activities.

35. Influence of Income on Household Suburbanization • Although Wheaton suggested that income growth does not determine slope of bid-rent curve, he does not control for amenities and disamenities. • Next time: We look at Margo paper

36. Original Blight-Flight ProcessBradford and Kelegian - 1973 JPE • Suppose that there is an equilibrium distribution of population between central city and suburbs. • Suppose some high income central city neighborhood becomes middle income neighborhood due to suburbanization. • Tax burden on remaining households increases. • Increases incentive for others to leave. • Services decrease, tax burden increases, leads to ever worsening cycle.

37. Sources of Central City Blight • Growing crime • Declining environmental conditions • Declining public services • Educational system • Increased tax burden as tax base erodes • Racial frictions • Lower employment opportunities (more in next section) • Worsening housing conditions (more in next section)

38. Outcome of Blight-Flight Cycle • Can lead to de-population of the tax base. • According to SUM, what would stem outflow? • Next time: Look at a couple of articles: • Test of theory of Blight-Flight (Adams et.al.) • Are suburbs immune from ills of city? (Voith) • Evaluate regentrification phenomenon (Berry article)

39. Urban and Regional Economics Prof. Clark Week #10

40. Flight from Blight and Metropolitan Suburbanization Revisited” 1996, Charles Adams, Howard B. Fleeter, Yul Kim, Mark Freeman, and Imgon Cho, Urban Affairs Review, Vol. 31, pp. 529-543. Presentation by

41. Richard Voith “Do Suburbs Need Cities?” • Insights from Adams et. al. suggest that increases in central city decline can reduce intracity inmigration to the suburbs. • However, no strong evidence to suggest that there is a movement from city to suburbs as Bradford and Kelegian suggest.

42. Do Suburbs Need Cities • Early blight-flight theory suggested suburbs may actually benefit from city decline • More recent theory suggests causal link between city and suburbs • Why? • Positive externalities from city • Blomquist, Berger and Hoehn (1988) suggest positive inter-jurisdictional spillovers • Examples: Cultural areas, waterfront parks, etc.

43. Need to rigorously test • Adams et.al., attempted this • Voith suggests that a model tied to economic theory is required. • Recognize simultaneous relationship between city and suburban economies • Built around insights of Charles Tiebout (1956) • Residents reveal preference for local public goods by “voting with their feet”.

44. Distinguishing SR and LR Effects • SR: City decline negatively impacts city amenities and fiscal goods and initially leads to suburban growth • LR: Reduction in positive externalities negatively impacts entire community • Suburbs and city both decline • Suburbs have bigger share of shrinking pie

45. Simple Descriptive Picture • Look at Tables 1-3 • Table 1: Avg. growth rates for cities, suburbs and metropolitan areas • In general, suburbs outperformed cities • Table 2: Looks at county level observations • CWMCC (counties with main central city) and NOMCC (counties with no MCC) • Same general patterns • Table 3: Raw Correlations • Income, population and housing values • Growing importance of correlations over time (70’s and 80’s) • May reflect more difficulty in suburbanizing over time

46. More Rigorous Modeling • Four equation system Incomec,it=f(Incs,it, Xs,it, Xcit, dit,e1,it) Incomes,it=f(Incc,it, Incc,it*Size, Xs,it, Xcit, dit,e2,it) Pops,it=f(Incc,it, Incc,it*Size, Xs,it, Xcit, dit,e3,it) Hvals,it=f(Incc,it, Incc,it*Size, Xs,it, Xcit, dit,e3,it) • What are critical coefficients? • For spillover? • For size related impacts?

47. Econometric issues • Simultaneous Equation Systems • Identification of endogenous variables • Excluded variables • Need variables that vary on RHS that vary independent of the error term in the equation • e.g., annexation explanation • Covariance restrictions • Make assumptions about absence of cross-equation correlations

48. Findings • Two different estimation methods • Continuous city size impacts • City size interaction term • Discrete city size effects • Separate equations for small, medium and large cities

49. Continuous Specification • Look at Table 5 • Look at Suburban equations • What is interpretation of city income growth? • What is interpretation of growth interacted with city size? • Elasticities significant for income and real house value appreciation, and impact grows with city size • Small impact for pop, and size interaction insignif.

50. Alternative Specification • Table 6: • Raw correlations imply significant correlation for all size groups for city and suburban income growth. • Table 7: • Model estimates give different conclusion • Income model only significant for large cities • Housing price model significant and much larger coefficient