Post on 14-Jan-2016
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.