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16 March2009
Frank Cowell: EC426 Public Economics
MSc Public Economics
2008/9
http://darp.lse.ac.uk/ec426
Fiscal Governance: Local Public Goods
Frank Cowell: EC426 Public Economics
Fiscal governance
Overview...
Introduction
The basic
intuition
Clubs
Local public
goods
Equilibrium
Mode of
provision
Frank Cowell: EC426 Public Economics
Public goods and the public sector

Public and semi-public goods provide a challenge




There are some standard answers



how to ensure efficient allocation
how to reveal willingness to pay
should they be provided in private or public sector?
only work for small communities?
special mechanisms
Here examine an alternative approach



redefine the problem
focus on the way people make choices…
what kind of fiscal environment do they want?
Frank Cowell: EC426 Public Economics
Tiebout’s intuition

Up to now the economy as a whole has been fixed



Introduce the possibility of multiple jurisdictions




no question of governance
nor of “jurisdiction” of the fiscal system
affects basket of goods provided
zone in which it is possible to determine taxes
crucial point: relationship amongst jurisdictions
Tiebout (1956) virtually invented our topic




changed context of the public-goods argument
a new role for consumer choice: voting with your feet
made an analogy with a private market place
modern evidence that this choice mechanism works (Banzhaf
and Walsh 2008)
Frank Cowell: EC426 Public Economics
Tiebout: questions

What type of equilibrium?


How are communities determined?



Equilibrium concepts that take into account the endogenous
structure of communities
How does the economy work out of equilibrium?


Depends upon the exact specification of the mechanism that
is supposed to be operating
Tiebout suggested a migration mechanism
Will there be an efficient outcome from the Tiebout
process?
Is this more than just a demand-revealing mechanism?
Frank Cowell: EC426 Public Economics
Fiscal governance
Overview...
Introduction
An extension of
the public goods
idea
Clubs
Local public
goods
Equilibrium
Mode of
provision
Frank Cowell: EC426 Public Economics
Endogenous structure





The endogeneity of the community gives a nice clue
Think of each community as privately determined
The public good issues remain within each community
But free choice between communities
This suggests an analogy with the theory of clubs



Originally developed by Buchanan (1965)
Combines public and private elements
See also Cornes and Sandler (1996)
Frank Cowell: EC426 Public Economics
Clubs: excludability and rivalness


The good is like a public good within the club
Excludability: club good is restricted to its members




people can be excluded from membership
can charge a membership fee
membership entitles you to full consumption of the good
without further charge
Rivalness: could we assume that club good is non-rival?



for realism, allow for the possibility of congestion
cost of providing the club good may rise with the membership
same may also be true of the marginal cost
Frank Cowell: EC426 Public Economics
Clubs: model of production

A two good economy


Notation:





x – amount of private good,
z – amount of club good,
s – size of the of club
C(z, s) – cost of producing the club good
Standard assumptions about cost:




measure values in terms of private good
Cz(z, s) > 0 – MC of club good is positive
Czz(z, s)  0 – MC of club good is nondecreasing in z
Cs(z, s)  0 – possibility of congestion
Examine this in an economy with fixed total output

equivalent to assuming a given amount of income y
Frank Cowell: EC426 Public Economics
Clubs: production possibilities
Club good versus total private good
production frontier
sx
marginal rate of transformation
 xs + C(z, s) = sy
 curvature comes from
increasing marginal cost of z

z
d (sx)
– ——— = Cz(z, s)
dz
Frank Cowell: EC426 Public Economics
Clubs: individual optimisation



Use this in a model of individual choice
Each individual has the utility function U(x, z)
Assume that club costs are divided equally: C(z, s) / s



So the problem becomes: maximise


U(y  C(z, s) / s , z)
Differentiate with respect to z:


so the budget constraint is:
x + C(z, s) / s ≤ y
1
 — Cz(z, s) Ux(x, z) + Uz(x, z) = 0
s
Differentiate with respect to s:

1
— [C(z, s)  s Cs(z, s)] Ux(x, z) = 0
s2
Frank Cowell: EC426 Public Economics
Club model: individual’s equilibrium
boundary of individual feasible set
individual IC
x
equilibrium
 x + C(z, s) / s = y
U(x, z) = const
 curvature from increasing MC
 comes from Czz > 0

A
 Cz(z, s) / s = Uz(x, z) / Ux(x, z)
z
Frank Cowell: EC426 Public Economics
Clubs: basic results

Optimal amount of club good must satisfy:




Cz(z, s) =
s
Uz(x, z)
────
Ux(x, z)
MRT= S MRS
just as for public goods
The optimal membership must satisfy:


Cs(z, s) = C(z, s) / s
MC of providing services = Access cost
Frank Cowell: EC426 Public Economics
Clubs: summary



Model is a simple extension of classic public goods
Novelty is to introduce a type of partial exclusion
mechanism
In the standard case we get two easily interpreted
marginalist rules:


On the level of provision of the club good
On the access conditions to the club
Frank Cowell: EC426 Public Economics
Fiscal governance
Overview...
Introduction
Using the club
approach to
model local
jurisdictions
Clubs
Local public
goods
Equilibrium
Mode of
provision
Frank Cowell: EC426 Public Economics
Modelling local public goods

Focus on a collection of communities



Affinity with the club model






an excludable non-rival good
no exclusion within the jurisdiction
local public good and private good may / may not be perfect substitutes
there may or may not be congestion
may also need to consider overall size of the “economy”
People choose jurisdiction in the same way they choose a club



think of them as tax jurisdictions
each jurisdiction works a bit like a club
have preferences over private, public goods
migration mechanism: vote with their feet
What would the outcome look like?
Frank Cowell: EC426 Public Economics
Stiglitz model of a community

Assume simple linear technology




Assume production depends on the size of the community:





Community subject to diminishing returns in population
Q = f (s)
f is an increasing concave function
Take tradeoff in (public,private)-space
For a given size of community this is linear



no congestion costs
MRT in community is set at 1
total output is given by Q = xs + z
All public: (f (s), 0)
All private: (0, f (s) / s )
Consider the optimum for a given community size
Frank Cowell: EC426 Public Economics
Stiglitz model: single s
max amount available of private good
max amount available of local public
good
x
linear tradeoff between two types of goods
solution for given s
 note that this solution is
conditional on a given s
f(s)/s

U(x, z) = const

A

f(s)
z
Frank Cowell: EC426 Public Economics
Stiglitz model: solution





Previous diagram is a “short-run” model
Optimum determined in usual way
 MRS = 1 / s
 MRT = S MRS =1
However we ought to consider the possibility of
multiple jurisdictions
Each one may differ in size
Overall production possibility determined as an
envelope
Frank Cowell: EC426 Public Economics
Stiglitz model: multiple s
linear tradeoff for low s
linear tradeoff for medium s
linear tradeoff for high s
x
the envelope for s  {low, middle, high}
the envelope for s  [0, ∞)
feasible set
U(x, z) = const
solution
 possibilities with just 3 sizes
of jurisdiction
 possibilities with arbitrarily

A
many sizes of jurisdiction
 note the fundamental
z
nonconvexity of the problem
Frank Cowell: EC426 Public Economics
x
Stiglitz model: types of solution
x
interior solution
solution – no public good

A
solution – no private goods
multiple solutions

A
z
x
x


A
z
A

B
Frank Cowell: EC426 Public Economics
Stiglitz model: questions

Why the nonconvexity?





Homogenous consumers?




Follows from relationship between size and provision of
goods
An artefact of special assumptions?
What if we used a conventional club-good model?
Introduce rising marginal cost again
Suppose people differ in their taste for public goods
Will the demand-revelation mechanism work?
Will an equilibrium always exist?
Deal with each of these in turn…
Frank Cowell: EC426 Public Economics
Modified model: multiple s
nonlinear tradeoff for low s
nonlinear tradeoff for medium s
x
nonlinear tradeoff for high s
the envelope for s  {low, middle, high}
 shape is the same as for the
club model
 clearly attainable set could be
nonconvex, even with Czz > 0
z
Frank Cowell: EC426 Public Economics
Heterogeneous citizens

A simple example to illustrate the point:



Preferences are given by



group i specialises in public good type i
If the two are together:



citizen type 1: U(x, z1 + kz3) where 0 < κ < 1
citizen type 2: U(x, z2 + kz3)
If the two types are separated:


three types of public goods
two types of citizen
may be economies of scale in the production of good 3
particularly important if κ is close to 1
So free allocation via migration may not be efficient

analogous to the market failure of pure private goods where there is
increasing returns
Frank Cowell: EC426 Public Economics
Equilibrium: the core

Core: set of unblocked allocations




Core of an economy with public goods



existence theorem does not necessarily apply
equilibrium mechanisms different
The core may be empty unless




a fundamental solution concept for equilibrium
for private goods core is non-empty
any competitive equilibrium must lie in the core
equal sharing is enforced (Pauly 1970 )
all clubs are of uniform size (Pauly 1970 )
if individuals have the same tastes (Stiglitz 1977)
Need to examine nature of Tiebout equilibrium more closely
Frank Cowell: EC426 Public Economics
Fiscal governance
Overview...
Introduction
Using the club
approach to
model local
jurisdictions
Clubs
Local public
goods
Equilibrium
and Optimality
Mode of
provision
Frank Cowell: EC426 Public Economics
Basic questions on equilibrium

What type of choice?





What type of mechanism?



Fixed number of jurisdictions?
Freely set up jurisdictions (prairie model)?
Fixed overall population
Single type of public good
usually assume simple migration
people follow the money
Will equilibrium be efficient?
Frank Cowell: EC426 Public Economics
Local public goods: fixed number
of communities

Assume that there are just two communities





Allow for free choice between communities
Two possibilities of equilibrium
(1) Where only one community is settled:


Overall size is given at N
s1 + s2 = N
u(N)  0
(2) Where both communities are settled:

u(s1) = u(s2)
Frank Cowell: EC426 Public Economics
A model of social welfare

Assume Benthamite objective function:





For an interior welfare maximum the optimal size where:



∂W
—— = 0
∂ s1
which implies s1u'(s1) + u(s1) – [N – s1] u'(N – s1) – u(N – s1) = 0
But two complications



Per-person utility is same for everyone in a given community of size s: u(s)
Welfare is weighted sum of per-person utility in each community
W = s1u(s1) + s2u(s2)
= s1u(s1) + [N – s1] u(N – s1)
we also have to take account of corners
interior maximum may not be unique
Need to derive utility-possibility set from equilibrium conditions
Frank Cowell: EC426 Public Economics
2-jurisdiction U-possibility (1)
utility in community 1
s2u2
utility in community 2
equality ray
utility possibility set
welfare contours

 unique interior welfare
maximum
 two communities settled
s1u1
Frank Cowell: EC426 Public Economics
2-jurisdiction U-possibility (2)
utility possibility set
s2u2
welfare contours

 two extreme welfare maxima
 only one community settled
s1u1

Frank Cowell: EC426 Public Economics
2-jurisdiction U-possibility (3)
utility possibility set
s2u2
welfare contours

 two interior welfare maxima
 two communities settled

s1u1
Frank Cowell: EC426 Public Economics
Migration mechanism

Will migration “work”?





First case involves substantial economies of scale




Get multiple equilibria
Only extreme cases are stable
Only extreme cases are efficient
Second case also involves economies of scale



yields stable equilibria?
yields efficient equilibria?
examine four cases
combined diagram facilitates interpretation
Only extreme cases are stable
Only interior case is efficient
Other cases show that multiple equilibria do not necessarily
involve extremes
Frank Cowell: EC426 Public Economics
Pareto-efficient: extreme equilibria
u1
u2
u(s2)
u(s1)
stable
stable
unstable
s1 rising
s1 falling
s1
Frank Cowell: EC426 Public Economics
3 Equilibria: inefficient extremes
u1
u2
u(s2)
u(s1)
unstable
stable
stable
s1 rising
s1 falling
s1
Frank Cowell: EC426 Public Economics
3 interior eqa: efficient equality
u1
u2
u(s2)
u(s1)
unstable
stable
stable
s1 rising
s1 falling
s1
Frank Cowell: EC426 Public Economics
5 Equilibria: inefficient equality
u1
u2
stable
stable
unstable
unstable
stable
u(s2)
s1 rising
u(s1)
s1 falling
s1
Frank Cowell: EC426 Public Economics
Equilibria

May be multiple equilibria




An equilibrium is bound to exist if





alternation between stable and unstable equilibria
two-community and single community equilibria may coexist
stable equilibria may be inefficient
if land values play no role
everyone is identical
the υ(·) functions are continuous
Where individuals differ, will equilibrium exist?
Need to examine specific models…
Frank Cowell: EC426 Public Economics
Fiscal governance
Overview...
Introduction
Coercion or
voluntarism?
Clubs
Local public
goods
Equilibrium
Mode of
provision
Frank Cowell: EC426 Public Economics
Role of the state



Should the provision of public goods be based on voluntarism,
or coercion?
Local public goods models suggest more than one paradigm
With heterogeneous individuals there is a conflict of interests



Involuntary contributions:



can overcome the free-rider problem
do not resolve the conflict-of-interest problem
Voluntarism



Individuals will not agree on appropriate output and contributions:
They may be compelled to contribute at tax rates that seem to be unfair
avoids “unfairness” from compulsion
may not be consistent with the absence of free riding
Given the Tiebout adjustment mechanism, will one of these be
eliminated?
Frank Cowell: EC426 Public Economics
An illustrative model

To address “public or private?” question




Utility of individual i




u(xi, z) = [xi1–s + z1–s] / [1 – s ]
private good xi public good z
s is nonnegative elasticity of substitution
Production




construct a model of public good production
model two provision modes
allow Tiebout style choice between two modes
private incomes yi are exogenous
public goods produced from “contributions” of private good ci= yi – xi
MRT = 1, so amount of public good is: z = Si ci
Provision modes treated as two different models of a
community…
Frank Cowell: EC426 Public Economics
Two provision modes

Coercive provision: public good provided by taxation





tax based on community aggregate income Y := Si yi
so i has to contribute ci = tY
tax rate t is selected by voting
chosen tax rate: t = [1 + [ymedian/Y]b]1, b := [1 – s]/s
Voluntary provision: based on individual contributions



Like “conformity model” in tax compliance (Bergstrom et al
1986)
optimal contribution decision depends on income
ci = max {yi – Y / n*, 0}, n* := 1 + #{cj > 0}
Frank Cowell: EC426 Public Economics
Provision: endogenous choice

Suppose two communities exist simultaneously



Three possible types of equilibrium:




people can “choose” public or private
use Tiebout model to address choice between communities
all individuals migrate to the voluntary-provision community
all individuals migrate to the coercive-provision community
‘interior’ equilibria: collections of individuals in both communities
The relevant type depends on



degree of substitution (parameter s)
income distribution
 see Glomm and Lagunoff (1998)
Frank Cowell: EC426 Public Economics
Which mode of provision?


Results for three types
Type 1: voluntary provision only


Type 2: coercive provision only



equilibrium always exists
sometimes exists
need conditions on preferences and income distribution
Type-3: interior (mixed-mode) equilibria:



exists if income is sufficiently polarised
richer individuals migrate to the community with voluntary
provision
poorer individuals reside in the public provision
community
Frank Cowell: EC426 Public Economics
Mode of provision – extension

Extend the Glomm and Lagunoff (1998) analysis





Individuals make repeated sequential decisions




a dynamic economy
congestion costs
wealth accumulation
Glomm and Lagunoff (1999)
which community to inhabit?
coercive community?
voluntarist community?
The essence of the static model persists:




maybe voluntary provision exists as a within-period Nash equilibrium
outcome
but if there is convergence of the wealth distribution…
…then coercive mechanism is selected in the perfect equilibrium
result may not hold if there is no wealth convergence in the long run
Frank Cowell: EC426 Public Economics
A fundamental trade-off?

Consider trade-off between fundamental effects of taxation and
spending policies



Analyse using a two-community economy:



Tiebout mechanism interpreted as unrestricted migration between
jurisdictions
Kessler and Lülfesmann (2005)
Individuals differ



provision of public goods
redistributive objectives
in their incomes
in their tastes for a local public good
In each jurisdiction


amount of public services determined by inhabitants (majority vote)
local spending financed by linear income tax specific to the jurisdiction
Frank Cowell: EC426 Public Economics
A fundamental trade-off

Individuals make a selection from this trade-off



Kessler and Lülfesmann (2005) show that Tiebout-like
sorting equilibria exist




by choice of jurisdiction through migration
by the voting mechanism
if the spread in tastes is very large almost perfect sorting by
preferences
otherwise, a partial sorting prevails…
…stratification into rich, poor communities is more
pronounced
Existence of sorting equilibria is robust

independent of whether individuals can relocate after voting
Frank Cowell: EC426 Public Economics
Decentralisation?

Is decentralisation a good idea?



1 Tiebout argument



positive case for decentralisation
revealed preference for public goods
2 Tax competition




at the heart of fiscal governance debate
contrast two types of model
negative case against decentralisation
intergovernmental competition relies on distortionary tax
inefficient outcome?
Main question




in an economy with mobile, heterogeneous consumers…
…where public goods financed by distortionary tax on mobile capital
is decentralization desirable?
 see Brueckner (2004 )
Frank Cowell: EC426 Public Economics
Decentralisation: recommendations

1 Tiebout argument for decentralisation



2 Tax competition against decentralisation





allow sorting by migration
(but will this lead to efficient equilibrium?)
if governments agree common tax rate on capital can get efficient publicgood level
remove fiscal autonomy of subnational governments
a uniform tax on capital to provide a common public good
national capital tax effectively lump sum: eliminate distortion
Which dominates?




Brueckner (2004 ) uses numerical simulation
given dispersion of preferences…
gains from Tiebout sorting are likely to outweigh the loss from the
capital-tax distortions
otherwise decentralization may be undesirable
Frank Cowell: EC426 Public Economics
References











Banzhaf, H. S. and Walsh, R. P. (2008) “Do People Vote with Their Feet? An
Empirical Test of Tiebout’s Mechanism,” American Economic Review, 98, 843-863
Bergstrom, T., L. Blume, and H. Varian (1986) “On the private provision of public
goods,” Journal of Public Economics 29, 25-49.
Brueckner, J. (2004 ) “Fiscal Decentralization with Distortionary Taxation: Tiebout
vs. Tax Competition,” International Tax and Public Finance, 11, 133-153}
Buchanan, J. M. (1965) “An economic theory of clubs.” Economica, 32, 1-14.
Cornes, R. and T. Sandler (1996). The Theory of Externalities, Public Goods and Club
Goods (second ed.). Cambridge University Press.
Glomm, G. and R. Lagunoff (1998) “A Tiebout theory of public vs private provision
of collective goods,” Journal of Public Economics, 68 , 91-112.
Glomm, G. and R. Lagunoff (1999) “A dynamic Tiebout theory of voluntary vs
involuntary provision of public goods,” Review of Economic Studies, 66, 659-677.
Kessler, A. S. and C. Lülfesmann (2005) “Tiebout and redistribution in a model of
residential and political choice,” Journal of Public Economics, 89, 501.528.
Pauly, M. V. (1970) “Optimality, .public. goods and local governments: A general
theoretical analysis,” Journal of Political Economy, 78, 572-585.
Stiglitz, J. E. (1977) “The theory of local public goods, “in M. S. Feldstein and R. P.
Inman (Eds.), The Economics of Public Services. London, UK: Macmillan.
Tiebout, C. M. (1956) “A pure theory of local expenditures,” Journal of Political
Economy, 64, 416-424.