Transcript Urban and Regional Economics

Urban and Regional
Economics
Weeks 8 and 9
Evaluating Predictions of Standard
Urban Location Model and Empirical
Evidence
Declining Population Density
There is substantial evidence here.
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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
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Overview of research
Single-area function issues
 Econometric Issues
 Findings
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Multiple area issues
 findings
Let’s focus primarily on Single-Area issues
Origins of Literature
Dates to early 1950’s
Economists recognized
empirical regularities in
density
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D
D(u) = D0e-tu
 where D(u) = population
per square mile,
u=distance, D0=density
extrapolated to city
center.
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in log form:
lnD(u) = lnDo-tu
u
How is density measured?
Can look at:
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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:
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Studies expanded evidence to support negative
exponential form
During 1960’s:
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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: Quadratic
D(u) = D0eau+b*u*u
in log form: lnD(u)=lnD0+au+bu2
a>0, b<0
Effect of Urban Growth
D(u)
CBD
D(u)
u
CBD
u
Net Density
Throughout 1970’s,
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Negative exponential model remained
dominant when considering net density
Some attempts to:
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Address some econometric issues
Expand list of determinants (ie., are there
other factors besides distance, u, to
consider?)
Empirical Approach
Econometric
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Get data, and fit curve to data
Will summarize issues briefly
Analytic approach developed by Ed Mills
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Get data on population and land area of
central city, and entire urban area
 Analytically derive t.
 More later
Econometric issues - briefly
Problem with use of Census tract data
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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
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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?
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Shouldn’t just assume negative exponential
Can use Box-Cox flexible form
D(u)d-1/d=D0-tu
d=0 implies log
where d=1 implies linear,
What is correct set of determinants?

Control for differences over time and
across cities (if multiple areas considered)
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
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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
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Find other factors important
 eg., introduction of rail systems, highways, income,
racial mix, etc. More later.
 Trend surface analysis
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Allows for density to evolve in nonsymmetric fashion.
Mills Two-Point Method
Analytically derive shape, assuming D(u) = D0e-tu
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Inputs are minimal
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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
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Iteratively determine t as the value that gives total
population of central city and of urban area.
Factors determining t
Techniques:
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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:
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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
predictions
Suggests more research needed for
net-density functions
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All info. has been gleaned from gross
functions
Need to include other determinants
Investigate more policy implications
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.
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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 Factors
Add in time cost of commuting
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Now t depends on income (i.e., t(w))
 Why?
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More later.
Add in multiple destinations.
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Accessibility to workplace is no longer the only
important determinant.
May flatten or steepen. Why?
Add in two earner households
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Accessibility of second worker now also
important.
May flatten or steepen. Why?
Factors that influence H
Demographics (eg., # children)
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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
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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
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.
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2PH/uw=[-H*t/w +
(t*H/w)]/H2>0?
This depends on numerator.
Multiply numerator by (w/t*H) which gives:
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(t*H/w -H*t/w)*w/t*H
(H/w*w/H -t/w*w/t)
Interpretation?
Wheaton Findings
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.
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.
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Would need to introduce tax prices.
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
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Amenities, disamenities, other factors
Include fiscal measures
Income time dummies, other locational dummies
Examine findings
Updated Structure: Multicentric
Cities
Monocentric cities are no longer
prevalent.
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Look at Milwaukee MSA as an example
How do these influence SUM?
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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.
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Reason: Workers must be indifferent
between centralized and decentralized
jobs.
Question:
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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/T
MB and MC comparison: R/u*T + w/u*L = tB
Interpretation:
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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
May have multiple
rent peaks
throughout city
Individual firm’s
functions vary with
t, T, L, B
R
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u
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
Suburbanization
Suburbanization of households and
employment has been dramatic.
Can SUM explain suburbanization of
households and employment?
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What assumptions re: rent gradients must
have occurred?
 Alternatively, multiple centers must have
evolved.
Effect 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/ut =-B/T<0
Interpretation:
R
Bid-Rent shifts
from A to B to C
(PBB-C)/T
(PB’B-C)/T
As t increases, slope
steepens
Eventually, price of good
also falls since costs fall.
 Thus, intercept falls
also.
A
B
C
u
Flattening of Manufacturers
Bid Rent
Transportation
innovations such as
truck (inter and intra)
and interstate highway
system, automobile
(lowers t).
Beltway Influence
R
 Beltways become
important access points.
Location of suburban
airports (lowers t).
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Peaks not concentric
More land intensive
plants (increases T).
Use of lighter weight
materials (lowers B)
CBD
Belt
way
u
Flattening of Retailer’s Bid Rent
Profit function depends on proximity to
population their markets.
As population decentralizes, so does retail
activity.
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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 Rent
Agglomeration economies grow in
suburbs (localization and urbanization).
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These factors increase productivity in
suburbs and reduce need for face-to-face
contact in CBD.
Communication improvements lower t.
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Teleconferencing, e-mail, data transfer
allows decoupling of activities.
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 Process
Bradford 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.
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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 crime
Declining environmental conditions
Declining public services
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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)
Outcome of Blight-Flight Cycle
Can lead to de-population of the tax base.
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According to SUM, what would stem outflow?
Next time: Look at a couple of articles:
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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. Clark
Week #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 decline
More recent theory suggests causal link
between city and suburbs
Why?
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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 this
Voith suggests that a model tied to
economic theory is required.
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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 growth
LR: Reduction in positive externalities
negatively impacts entire community
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Suburbs and city both decline
Suburbs have bigger share of shrinking pie
Simple Descriptive Picture
Look at Tables 1-3
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Table 1: Avg. growth rates for cities, suburbs and
metropolitan areas
 In general, suburbs outperformed cities
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Table 2: Looks at county level observations
 CWMCC (counties with main central city) and NOMCC
(counties with no MCC)
 Same general patterns
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Table 3: Raw Correlations
 Income, population and housing values
 Growing importance of correlations over time (70’s and
80’s)
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May reflect more difficulty in suburbanizing over time
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?
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For spillover?
For size related impacts?
Econometric issues
Simultaneous Equation Systems
Identification of endogenous variables
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Excluded variables
 Need variables that vary on RHS that vary
independent of the error term in the equation
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e.g., annexation explanation
Covariance restrictions
 Make assumptions about absence of cross-
equation correlations
Findings
Two different estimation methods
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Continuous city size impacts
 City size interaction term
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Discrete city size effects
 Separate equations for small, medium and
large cities
Continuous Specification
Look at Table 5
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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:
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Raw correlations imply significant
correlation for all size groups for city and
suburban income growth.
Table 7:
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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
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Causal link established
Externality effects are not universal across
city size
Policy implications
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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”
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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
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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 overview
You are responsible for all the material in
Chapter 11.
Up to this point, we have assumed no
restrictions on land use.
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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.
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“...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.
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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
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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.
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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)
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Purpose is to promote public health, safety,
and welfare.
Substantive due process
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Requires legitimate public purpose.
Equal protection (i.e., nondiscrimatory)
Just compensation (i.e., no violation of 5th
Amendment).
Goals of Land Use Regulations
Population control/reduce
sprawl
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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
ROffice
Service
limit
Rag.
Rresidential
u
General Equilibrium Effects
Funnel resident demand
into smaller areas
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Bid Rent shifts up
Reduce size of office
district
Makes central core less
attractive as costs of land
increase
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lowers Office Bid Rent
Reduces employment
density
R
ROffice
Service
limit
Rag.
Rresidential
u
Your book looks at other
examples of these effects
You are responsible for these
How big a problem is sprawl?
Look at debate
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Anthony Downs
Gordon and Richardson
Types of Land Use Zoning
Nuisance Zoning
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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
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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.
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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.
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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.
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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.
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Agricultural land, parks, etc.
The Houston Example
Until recently, Houston had no land use
controls.
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Now there are limited controls.
Consequences
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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
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Without a court challenge, they are unlikely to go
away.
They have both desirable and undesirable
consequences.
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Discriminatory consequences most troublesome.
They may not be necessary to achieve the
stated goals of the controls.