Lecture on Household Sorting
and municipal differentiation
Based on Chapters 13 and 20 in Urban Economics by
Arthur O’Sullivan, 5th edition and Chapter 14 of The
Economics of Zoning Laws by William Fischel
Adapted and summarized by Austin Troy,
University of Vermont
Urban differentiation and mobility
• We looked at two ways of allocating resources
voter rule and benefits taxation; first results in
inefficient allocation and second is unrealistic
• An alternate way of allocating is to let
households form new municipalities based on
their preferences
• In this model, preferences are homogeneous
within jurisdiction so MSB=MPB, so privately
determined allocation decisions are efficient
How big should park be?
Cost/
acre
Marginal social benefit=
MB1+MB2+MB3
MC
$60
MB curves
for three
citizens
MB1
MB2
Marginal
private cost
MB3
Q1
Q2
Q* acres
Q3
Urban differentiation and mobility
If all people in jurisdiction have
same preferences….
MCsocial
MBsocial
MCPrivate
MBPrivate
Q*
Note: mistake in book
Voting with feet:
Interjurisdictional mobility
• Charles Tiebout model (1956) explains how
differences in pricing and provision of services
define jurisdictions, and residents “shop” for
those bundles.
• Tiebout model suggests that interjurisdictional
mobility might prevent median voter
inefficiencies
• Increases efficiency in allocation of public
services, but not equity of distribution
Voting with feet:
Interjurisdictional mobility
• In the model, households sort themselves
according to housing consumption and public
goods consumption into homogeneous
communities
• Hence residents go to where their preferences
are, rather than imposing their preferences on
those who don’t want them
• Essentially provides market for public services
Simplified Tiebout model
assumptions
• Households choose municipality providing
ideal level of public goods, meaning there are
enough jurisdictions from which to choose
• There is perfect information and costless
mobility
• There are no interjurisdictional spillovers
• City pays for public goods with head tax
Tiebout and the park example
• Households move so as to maximize utility
given income, preferences, taxes, and prices of
private goods (land, housing)
• Mobility plus more jurisdictions will increase
intra-city homogeneity
• Park lovers all go to one city with big parks,
and those who value other uses for their money
over parks sort themselves in a different city
• Park size will be efficient within each city
• In this case, the median voter is irrelevant
Tiebout model and sorting
• Each household moves to the jurisdiction with the
service quantities for which they are willing to pay
• Because public goods are “normal goods” high
income households have higher marginal benefit
• The tradeoff for more services is higher tax burden
• At a low quantity of public good, benefits> tax
burden for all households, but as increase amount, tax
burden>benefits for lower income households
• Hence low income households outbid high income
people in low public good areas and vice versa.
Tiebout model and sorting
• Because public goods are income elastic,
high income households will have larger
MB from consuming public goods than low
income, therefore steeper BR functions and
will outbid where level of PG is high
• Hence when HH’s sort themselves based on
public goods will sort based on income—
this is because income determines MB
Tiebout model and sorting
Bid rent: high income HH
Bid rent: low income HH
Low inc zone
high inc zone
Where tax outweigh
benefits of public
goods for rich
Where tax outweigh
benefits of public
goods for poor
Q of local public good
Tiebout mode—empirical evidence
• Metro areas with one municipality have wide variety of
demanders for public services (Gramlich and Rubinfeld
1982)
• The greater the number of municipalities, the more
homogeneous each is with respect to demand for public
services, and hence clustering of residents with similar
preferences occurs (G and R 1982, Heikkila 1996).
• There are more and smaller municipalities on average in
metro areas with heterogeneous demand for public
services (Fisher and Wassmer 1998).
Jurisdictions in NYC area
Jurisdictions in Boston Area
Jurisdictions in LA Area
Jurisdictions in SF BayArea
Tiebout model with qualifications
from Fischel
• Because most of these goods are actually partial rather
than pure, they are impacted by crowding; Av cost
curve goes down, then up with size
• At N0 , newcomers start imposing a congestion cost on
others(becomes semi-rivalrous), however, until cost
minimizing point (N1), impact of crowding is made up
for by contribution of new users to average cost, hence
they are welcomed until then.
• Towns use zoning to get towards N1
Fischel Amendment to the
Tiebout model While AC
$ per
capita
MC
Additional users
are welcome until
congestion costs
(MC)>AC, at N1
AC
Congestion
point: here
additional
people start
imposing cost
on others
declines
(<N1), it is
pure public
good
According to Tiebout, this is
the optimal size, because it
minimizes average cost of
services (AC)
N0
N1
Community size
Fischel Amendment to the
Tiebout model
• Hence, communities that are smaller will
encourage development and communities that
are bigger, or nearing that size will use
exclusionary zoning to limit supply.
• This is why rural communities will have
highly permissive zoning and established
suburbs will not.
Fischel Amendment to the
Tiebout model
• In some cases, N1(min point for AC), is not most efficient
point
• Assume town does not have monopoly zoning power (does
not affect prices in metro area) and that residents do not
share cost equally (don’t all pay AC; assumes non-uniform
assessment of property ). Then efficient level is now N2,
where MC intersects MR/AR, which is horizontal because
their decisions have no effect on regional supply and they
are price takers.
• Means last household to move in is WTP exactly amount
that costs community in additional provision services
Fischel Amendment to the
Tiebout model
If N1’, town is too small
because costs BD imposed on
community, but perceived
benefit by prospective
residents in AD. As long as
new residents pay at least BD,
town is no worse off
MC
$ per
capita
AC
A
A
MR=AR
B
C
D
N0
N1 N1’ N2
Community size
N3
N2= Optimal size without
monopoly zoning power
Optimal community size without
MZ
• A population less than N2 is inefficient
because more net benefits could be gained
by addition of more residents since
marginal benefit (AD) is still greater than
the marginal cost (BD). Only when they are
equal (exhausted) have all potential gains
been used up. Hence Pareto improvements
to moving from N1’ to N2.
Optimal community size without
MZ
• The key point here is the order in which people
came. If all residents shared costs equally
(uniform assessments), then N1 would be optimal
for them, since at N1’ new residents pay the AC
but they impose a larger MC (BD, rather than
CD). This forms a subsidy to the new
development at expense of previous homeowners
• Without controls, new residents would make
decisions based on AC, and hence they would
continue arriving until N3
Fischel: size without controls
MC
$ per
capita
AC
A
MR=AR
That’s bad for the
community, because
MC> MR after N2; from
there until N3 it benefits
newcomers, but at the
expense of previous
residents
N0
New residents will arrive
until size= N3
N1
N2
Community size
N3
Hamilton addition: Tiebout model
and property tax
• The Tiebout model assumes a simple head tax
as the entry price.
• Under this scenario, residents sort only on the
basis of public good preference, not on the
basis of home value because the amount paid
is independent of home value
• With property tax, sorting now occurs on two
dimensions: goods preference and home value
• This will result in more jurisdictions
Hamilton addition: Tiebout model
and property tax
• If lower income family moves to town and
sets up house worth less than average, they
pay less tax, but still get same amount of
service (e.g. schooling)
• This constitutes a transfer, so incentive for
existing residents to zone them out.
• Illegal to zone by home value, but lot size can
proxy that often.
Hamilton addition: Tiebout model
and property tax
• What about lower income residents who are
willing to pay that amount in taxes for that
level of service, but can’t afford the house
• In theory, there will be enough jurisdictions
such that one out there will have high tax
rates on small, low value houses, coupled
with high expenditure on the service.
• Are there this many? In reality, D for housing
and services is highly correlated.
Tiebout model and property tax
• Example:
• Head tax: all pay equal amount; property tax:
those with expensive houses pay more
• Assume 50% houses big (300k) and 50% small
($100k)
• City must raise average of $3k/ HH
• To do this they have 1.5% rate, resulting in
$4.5k in tax for big HH and $1.5k for small
How does Property Tax Affect
Location Choice?
• Big households now pay $4,500 but only get
$3,000 in services
• They could set up own municipality with only
expensive houses so that they can lower the tax
rate and all households pay for the level of
services they get
• They will do this if gains to doing so are large
relative to transaction costs
• They will enforce this in new town through use of
large lot zoning, keeps property values high
• This leaves small house town with high tax rate
Effects of Property Tax
• Increases the number of jurisdictions because leads
to more sorting
• Now sorting based not just on desired level of
public goods, but on housing consumption
• Under head tax only sort based on local public good
preferences
• I.E. There would be high public good/small lot
town, high public good/large lot town, etc.
• When households sort based on housing
consumption, they also sort based on income
because housing is a “normal good”
Tiebout model with property tax and
variable local public goods
• Assume single public good-parks
• Half of households are wealthy and have $100k
homes; half are low income and have $50k homes
• Half of households in each income group want large
park budget ($2k) and half small budget ($500).
• Households can establish new municipalities using
large lot zoning to set house values.
• Use of the property tax and zoning can actually help
municipalities obtain their optimal size.
Tiebout model with property tax and
variable local public goods
• Households sort based on park demand and property value
to form four municipalities (wealthy+big PB,
wealthy+small PB, LI+big PB, LI+small PB).
• High PB communities will have higher tax rate, as will
poorer communities, hence
W-LB
W-SB
LI-LB
LI-SB
House val
100k
100k
50k
50k
Park Budg
2k
500
2k
500
Tax rate
2%
.2%
4%
.4%
Tiebout model with property tax and
variable local public goods
• If communities are totally homogeneous, property
tax is like a user fee; you pay $X in fee and get $X
worth of park
• That’s why poor municipality with big PB pays
higher tax rate than wealthy municipality with big
PB—because the amount is the same, just like with
any fee; hence you get what you pay for
Problems with the Tiebout model
• Perfect homogeneity of communities is impossible; there
will never be enough municipalities to allow citizens to sort
themselves into perfectly homogeneous communities,
especially when considering all the factors that people
could sort on (think of some)
• This is especially true in larger, denser central cities where
there is simply to much heterogeneity within a small area.
• Hence, usually suburban municipalities are much more
likely to display Tiebout properties than urban ones
• However, research in LA (Heikkila 1996) found that
communities do form demographic clusters with relative
homogeneity
Problems with the Tiebout model
• Assumes no transaction costs to moving around or to
forming new jurisdictions, which is clearly inaccurate;
moving is expensive
• Assumes no cost to forming a new jurisdiction, hence there
won’t be unlimited combinations of service and tax levels.
– Nevertheless, Fisher and Wassmer(1998) find that in highly diverse
MSAs there will be more municipalities than in more homogeneous
ones
• Also assumes no spillovers, which is clearly unrealistic
– But many similar towns with similar LU patterns tend to aggregate
• Clearly information about cities in imperfect. Moreover,
they are changing over time.
Racial Sorting
• Facts: 2/3 blacks live in central cities and 1/3
in suburbs; reversed for whites.
• Dissimilarity index: to achieve same racial
composition within a neighborhood as within
metro area, what percentage of the people
would have to move?
• The average for the US is 69%
• The larger the metro area, the more
segregation there is
Causes of Racial Sorting
• Empirical studies find blacks prefer to live in
more integrated neighborhoods than whites
on average
• Income sorting generally leads to racial
sorting because of correlation
– Nevertheless, a black HH with same
income/characteristics as white suburban HH is
still less likely to live in suburbs, disparity must
be explained by something else (Rosenthal 1989,
Kain 1985). What??
Real Estate Practices and Racial
Sorting
• Racial Steering: Real estate agents “steers” minority
homebuyers towards certain neighborhoods(Ondrich
1998)
• Often minority housing is of lower quality relative to
price compared to housing in white neighborhoods
(Milgram 1988, Krivo 1995)
• Minorities often given poorer levels of service in
information and financing (Yinger 1998)
• “Fair housing audits” now increasingly common