Public Choice through Mobility
© Allen C. Goodman, 2015
Issues with Optimal Amount
• Optimal literature on choosing the amount
of public goods was pretty pessimistic.
• If you ask people how much they want,
and you tell them they will be taxed, they
will “lowball” their responses.
• If they don’t think it will be related to taxes,
they will “highball” their responses.
• Tiebout wrote a “response” in 1956.
Tiebout Model
• You have a bunch
of municipalities.
• Each one offers
different amounts of
public goods.
• Consumers can’t
adjust at the margin
like with private
goods, but ...
Utica
Clinton
Tw’ship
Sterling
Hts
Eastpointe
St. Clair
Shores
Tiebout Model
• They vote with their
feet.
• If they don’t like
what’s being
provided in one
community, they
move to another.
occurs when people stop moving!
Tiebout Eq’m
Model
• Assumptions
– Jurisdictional Choice –
Households shop for what local
governments provide.
– Information and Mobility –
Households have perfect
information, and are perfectly
mobile.
– No Jurisdictional Spillovers What
is produced in Southfield doesn’t
affect people in Oak Park.
– Community size – City manager
seeks to reach average minimum
cost of producing goods.
– Head Taxes – Pay for things with a
tax per person.
• We get an equilibrium.
People’s preferences are
satisfied.
What happens if people keep moving
From Community 1 to Community 2?
Note on returns to scale
• If public goods can be produced with
constant returns to scale  exact
satisfying of preferences.
• This assumption kind of assumes away
part of what’s public about public goods!
Is Tiebout’s hypothesis sensible?
In 1950s and 1960s, approx 20% of the
population moved each year
In 2008, 35.2 million people (1 year and older)
changed residences w/in the past year
Decrease of 3.5 million from 2007, and smallest
number since 1962
Rate fell from 13.2% to 11.9%
Why do you think this happened?
http://www.census.gov/newsroom/releases/archives/mobility_of_the_population/cb09-62.html
https://www.census.gov/hhes/migration/data/cps/historical.html
https://www.census.gov/hhes/migration/data/cps/historical.html
More about mobility
Local moves tend to be for housing-related
reasons.
Renters move more often than homeowners.
Tiebout Model
• Critique
– People aren’t perfectly informed.
– There may not be enough jurisdictions to
meet everyone’s preferences.
– Income matters. Someone from Detroit
cannot move to Bloomfield Hills to take
advantage of public goods in Bloomfield
Hills.
– Where you work matters.
– It’s probably a better model for suburbs
than for central cities.
– Very few places have a “head tax.”
Lots of Tiebout Literature
• We have to make things more realistic.
• We’re going to do a model that is a little
more sophisticated than what Fisher does.
• In most places local public goods are
financed by property taxes.
• Property taxes are a constant percentage
of the value of the property.
Rent and Value
y is the annual value of housing services (the
amount of rent you would pay. r is interest
rate.
How is this converted into the price P of a
house?
P = y/(1+r) + y/(1+r)2 + … y/(1+r)n
Why?
Rent and Value
P = y/(1+r) + y/(1+r)2 + …+ y/(1+r)n-1 + y/(1+r)n (1)
multiply both sides by (1+r)
(1+r)P = y + y/(1+r) + … + y/(1+r)n-1
(2)
Subtract (2) – (1)
rP = y - y/(1+r)n
(3)
As n gets infinite, we lose the second term.
rP = y
 P = y/r
(3′)
Rent and Value
So, with y as the annual value of housing services.
P = y/r.
We can rewrite this as P = Dy, where D = 1/r
If r is 0.05 (5%), then D = 20,
and P = 20y.
Houses don’t
last infinitely,
So D < 20.
If Asset is taxed at Rate t
Price = Stream of Returns – Stream of Tax
Liabilities
P = Dy – D(tP), where tP = tax liabilities
P(1 + Dt) = Dy
 P = Dy / (1 + Dt)
Price falls because the asset is taxed, but
If the taxes buy X, then
Higher y, X  increased price!
P = Dy + DX – D(tP)
Higher taxes  decreased price!
 P = D(y + X)/(1 + Dt)
PV of Housing
Services
Equations
Pni = Dyn + D (Xi – tiPni)
Value of House
PV of Fiscal
Surplus (Deficit)
Bi = S Pni/n
Tax Base per house (type n
in municipality i)
Xi = ti Bi
$ worth of public good/house
in municipality i.
Example
Think of the tax
rate as a “tax
price” - in %.
Suppose we had a community ONLY of small
houses worth $150,000 each.
If the community wanted Xi = $5,000 worth of public
goods (schools, police, fire, etc.) they would have
to tax themselves.
How much?
Xi = ti Bi
5,000 = ti * 150,000  ti = 5,000/150,000 = 0.033
Why?
Tax rate of 3.33%
Value of the House
What happens to the value of the house?
It stays at $150,000.
Why? Because you are paying $5,000 in taxes for
something worth $5,000 to you.
In a sense buying the public good is no different
than buying groceries.
Example
Think of the tax
rate as a “tax
price” - in %.
Suppose we had a second community ONLY of big
houses worth $300,000 each.
If Community 2 wanted Xi = $5,000 worth of public
goods (schools, police, fire, etc.) they would have
to tax themselves.
How much?
Xi = ti Bi
5,000 = ti * 300,000  ti = 5,000/300,000 = 0.0167
Why?
Tax rate of
1.67%, or
HALF the tax rate of the other
community.
Example
Suppose that someone who can only afford a small
house, would like to pay lower taxes, like 1.67%
rather than 3.33%, to get $5,000 worth of public
goods.
Builds a house in the community of larger houses.
It would seem that by building in the community of
larger houses, he/she would get a fiscal surplus.
It looks like he/she is getting $5,000 worth of
services, while only paying 0.0167 * 150,000, or
$2,500. This generates a fiscal surplus.
BUT, a couple of things happen
Pni = Dyn + D (Xi – tiPni)
Value of House
1. The fiscal surplus is an asset. Anyone else
would love to get hold of this fiscal surplus.
Price will be bid up until someone buying a small
house will be no better off in the community of
large houses, than they were in the community
of small houses. [Paying less for services BUT
more for housing]
2. The tax base in the community of large houses
has fallen. Why? Because the “average house”
is now slightly smaller.
A bunch of things happen
Property tax rate in community of “big
houses” rises (slightly).
Value of other houses in “big” community
falls.
Land values for small houses in big
community rise.
Is this stable?
No.
y
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
Dy
30
45
60
75
90
105
120
135
150
165
180
195
210
225
240
255
Another Example
P
Orig LV
68.7931
6
78.62069
9
88.44828
12
98.27586
15
108.1034
18
117.931
21
127.7586
24
137.5862
27
147.4138
30
157.2414
33
167.069
36
176.8966
39
186.7241
42
196.5517
45
206.3793
48
216.2069
51
New LV
44.79
42.62
40.45
38.28
36.10
33.93
31.76
29.59
27.41
25.24
23.07
20.90
18.72
16.55
14.38
12.21
Tiebout-Hamilton Capitalization (X=5)
Housing and Land Values
Assume
D = 15
What
Will
Happen???
300
Dy
250
P
Orig LV
200
New LV
150
100
50
0
0
2
4
6
8
10
12
14
16
Units of Housing
Base = 9.5
W/ no capitalization Land Value/unit = 3 for all parcels
W/ capitalization Land Value/unit is LARGEST for smallest parcels
18
So, what then …
• Does this explain “large lot zoning?”
• Is this the way that developers develop?
• Are there enough different communities for
this to occur.
• We’ll look at some empirical stuff next
time.