Lecture on Household Sorting and municipal differentiation

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?Marginal social benefit= MB1+MB2+MB3

MB1

MB2

MB3

MC

Q* acres

$60

Cost/acre

MB curves for three citizens

Marginal private cost

Q1Q2 Q3

Urban differentiation and mobility

MBPrivate

MBsocial

Note: mistake in book

MCsocial

MCPrivate

Q*

If all people in jurisdiction have same preferences….

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

Community size

$ per capita

N1N0

MC

AC

Additional users are welcome until congestion costs (MC)>AC, at N1

Congestion point: here additional people start imposing cost on others

According to Tiebout, this is the optimal size, because it minimizes average cost of services (AC)

While AC declines (<N1), it is pure public good


• 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.


• 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


Community size

$ per capita

N1 N2N0

MC

MR=AR

AC

N2= Optimal size without monopoly zoning power

A

C

B

A

D

N1’

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

N3

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

Community size

$ per capita

N1 N2N0

MC

MR=AR

AC

New residents will arrive until size= N3

A

N3

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

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


• 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.


• 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.


• 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

House val Park Budg Tax rate

W-LB 100k 2k 2%

W-SB 100k 500 .2%

LI-LB 50k 2k 4%

LI-SB 50k 500 .4%


• 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

Documents

Lecture on Household Sorting and municipal differentiation