Urban and Regional Economics

Weeks 8 and 9 Evaluating Predictions of Standard

Urban Location Model and Empirical Evidence

Declining Population Declining Population DensityDensityDeclining Population Declining Population DensityDensity

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.

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

Origins of LiteratureDates to early 1950’sEconomists recognized empirical regularities in density

D(u) = D0e-u where D(u) =

population per square mile, u=distance, D0=density extrapolated to city center.

in log form: lnD(u) = lnDo-u

D

u

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

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

Alternative form: QuadraticD(u) = D0eau+b*u*u

in log form: lnD(u)=lnD0+au+bu2

a>0, b<0

Effect of Urban Growth

D(u)

uCBD

D(u)

uCBD

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?)

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 . More later

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

Econometric issues - briefly

What is correct functional form? Shouldn’t just assume negative

exponential Can use Box-Cox flexible form

D(u)-1/=D0-u where =1 implies linear, =0 implies log

What is correct set of determinants? Control for differences over time and

across cities (if multiple areas considered)

Findings

Some support for negative exponentialSome 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.

Mills Two-Point Method

Analytically derive shape, assuming D(u) = D0e-u

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 as the value that gives total

population of central city and of urban area.

Factors determining Techniques: Can estimate D(u) and see how varies across cities

with different characteristics Can include other determinants and see what impact

inclusion of these has on estimate of .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?)

Conclusions

Strong evidence to support SUM predictionsSuggests more research needed for net-density functions All info. has been gleaned from gross

functions Need to include other determinants Investigate more policy implications

Does Accessibility Matter?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

Expanding the SUM to Incorporate other FactorsExpanding 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?

Factors that influence H 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/uH=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/uw=[-H*t/w - (-t*H/w)]/H2

Income and housing price gradientIncome and housing price gradient

Look at sign of second derivativeIf higher income flattens the bid-housing price function, then the second derivative is positive.2PH/uw=[-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?

Wheaton FindingsWheaton Findings

Adding in other influencesAdding 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.

Adding in Fiscal FactorsAdding 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.

Let’s play around with some data from FresnoLet’s play around with some data from Fresno

Dependent variable is real price of housingInclude structural characteristics as controlsInclude accessibility measureInclude neighborhood measures Amenities, disamenities, other factors

Include fiscal measuresIncome time dummies, other locational dummiesExamine findings

Updated Structure: Multicentric CitiesUpdated 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.

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?

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/TMB 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.

Influence of DBD’s on Land Rent Functions

R

u

May have multiple rent peaks throughout cityIndividual firm’s functions vary with t, T, L, B Later, we will look

at how some of these factors change with time.

Bid Housing Price Function also changes

Modifications complex, but insights similar

We will stay with simple model

Look at Bender and Hwang article

Jean will present this paper

Using the SUM to Explain SuburbanizationUsing 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.

Effect of declining t on Bid RentEffect of declining t on Bid Rent

Suppose intracity transportation improves for manufacturers. (i.e., t falls)

Recall: R/u= -tB/T

The slope will decline:2R/ut =-B/T<0

Interpretation:As t increases, slope steepens

Eventually, price of good also falls since costs fall. Thus, intercept falls

also.

R

u

(PBB-C)/T

B

AC

Bid-Rent shifts from A to B to C

(PB’B-C)/T

Flattening of Manufacturers Bid Rent Flattening of Manufacturers Bid Rent

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 InfluenceR

uCBD Beltway

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.

Flattening of Office Firms Bid Flattening of Office Firms Bid RentRentFlattening of Office Firms Bid Flattening of Office Firms Bid RentRent

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.

Influence of Income on Household Suburbanization

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

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.

Sources of Central City Blight

Growing crimeDeclining environmental conditionsDeclining public services Educational system

Increased tax burden as tax base erodesRacial frictionsLower employment opportunities (more in next section)Worsening housing conditions (more in next section)

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)

Urban and Regional Economics

Prof. ClarkWeek #10

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

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.

Do Suburbs Need Cities

Early blight-flight theory suggested suburbs may actually benefit from city declineMore recent theory suggests causal link between city and suburbsWhy? Positive externalities from city

Blomquist, Berger and Hoehn (1988) suggest positive inter-jurisdictional spillovers

Examples: Cultural areas, waterfront parks, etc.

Need to rigorously test

Adams et.al., attempted thisVoith 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”.

Distinguishing SR and LR Effects

SR: City decline negatively impacts city amenities and fiscal goods and initially leads to suburban growthLR: Reduction in positive externalities negatively impacts entire community Suburbs and city both decline Suburbs have bigger share of shrinking pie

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

More Rigorous Modeling

Four equation systemIncomec,it=f(Incs,it, Xs,it, Xcit, dit,1,it)

Incomes,it=f(Incc,it, Incc,it*Size, Xs,it, Xcit, dit,2,it)

Pops,it=f(Incc,it, Incc,it*Size, Xs,it, Xcit, dit,3,it)

Hvals,it=f(Incc,it, Incc,it*Size, Xs,it, Xcit, dit,3,it)

What are critical coefficients? For spillover? For size related impacts?

Econometric issues

Simultaneous Equation SystemsIdentification 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

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

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.

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

Implications of different raw correlation and model results

Implies simultaneous equation system approach works

Can disentangle simultaneity

Conclusions

Findings suggest suburbs do need cities Causal link established Externality effects are not universal

across city size

Policy implications Suggests suburbs may think they don’t

suffer Not a zero-sum game

Why?

Regentrification

During late 1970’s and early 1980’s, some cities experienced “regentrification” Upper income households moved into former

“dilapidated” neighborhoods. Brought back hope of a “back to city”

movement.

Berry article “Islands of Renewal in a Sea of Decay” evaluates this phenomenon Presented by:

Questions: Is Blight-Flight Model Really Alternative to SUM?

Look at factors which led to flight? Can these be modeled in context of SUM?

Urban Land-Use Controls and Zoning

Brief overviewYou are responsible for all the material in Chapter 11.Up to this point, we have assumed no restrictions on land use. Land always went to the highest and best

use. However, in the real world, most cities have

regulations which place restrictions on the use of land. Houston exception

Historical Perspective

Early cases of government land use controls tended to focus on taking issue in Fifth Amendment to U.S. Constitution. “...nor shall private property be taken for

public use without just compensation” Frequently sided with land owner.

Courts have also concluded that the right to property does not imply the right to use property to the detriment of others.

Early Land Use Controls

First zoning policies were established as a way to keep minority Chinese households out of specific neighborhoods in San Francisco. More blatant laws had been struck down. A zoning law arguing that laundries were a

conflicting land use, and thus could not be permitted in specific neighborhoods, was deemed constitutional.

Supreme Court ruling opened door for massive zoning Village of Euclid vs. Ambler Realty Co., 1926.

Growth of Zoning Regulations

In 1915, there were 5 U.S. cities with zoning ordinances.Euclid set off explosion of zoning ordinances. By end of 1930’s, nearly all large

cities and many small towns and suburbs had zoning laws.

Today: Very few communities without zoning.

Legal Premises

Zoning laws typically follow Standard State Zoning Enabling Act (Dept. of Commerce) Purpose is to promote public health,

safety, and welfare.

Substantive due process Requires legitimate public purpose.

Equal protection (i.e., nondiscrimatory)Just compensation (i.e., no violation of 5th Amendment).

Goals of Land Use RegulationsPopulation control/reduce sprawl

If communities concerned with population growth, they may establish zoning regulations which effectively limit growth.

Restrict service boundary of city. Keeps growth within city.

Limit number of building permits issued.

R

u

ROffice

Rresidential

Rag.

Service limit

General Equilibrium EffectsFunnel resident demand into smaller areas

Bid Rent shifts up Reduce size of office

district

Makes central core less attractive as costs of land increase

lowers Office Bid Rent Reduces employment

density

R

u

ROffice

Rresidential

Rag.

Service limit

Your book looks at other examples of these effects

You are responsible for these

How big a problem is sprawl?

Look at debate Anthony Downs Gordon and Richardson

Types of Land Use ZoningNuisance Zoning This keeps certain types of “incompatable” land uses

separate. Industrial nuisances are separated residential land uses to

reduce exposure to externalities associated with industrial uses although your book notes that effluent fees may be preferable.

Retail nuisances include congestion, traffic, noise, pollution, etc. Residential nuisances include mixing high density with low

density uses.

Performance Zoning Sets limits on activities (e.g., noise, pollution, etc.). If this can be achieved, then allow the mixing of

activities.

Fiscal Zoning

Designed to reduce free riding on fiscal bundle. If property tax is the primary revenue source for a

community, then smaller houses pay smaller portion of property tax burden. Higher the density of housing, the more free riding. May use large lot zoning techniques These often exclusionary

Question: Is the ride really free?If neighborhood generates disproportional service requirements.

Fringe neighborhoods often need more costly services. May try to institute impact or development fees.

Fiscal Zoning: Continued

Commercial and industrial development often requires that infrastructure be constructed to support activity. City may restrict land available for these

activities, or restrict building height. City may also impose impact fees to try

and recoup some of these expenses.

Design Zoning

Permits activity which is consistent with the infrastructure in place. e.g., streets may not accommodate commercial

activity, or waste disposal may be inadequate for some types of industrial uses.

On residential side, there may be Historic Preservation Districts which limit development.Open-space zoning may establish green space. Agricultural land, parks, etc.

The Houston Example

Until recently, Houston had no land use controls. Now there are limited controls.

Consequences More multifamily housing. Smaller lot sizes in some areas. Industrial and commercial activities separated. More strip malls. Neighborhood covenants used

Coase Theorem at work!

Conclusions

Land use controls are pervasive Without a court challenge, they are unlikely

to go away.

They have both desirable and undesirable consequences. Discriminatory consequences most

troublesome.

They may not be necessary to achieve the stated goals of the controls.