Public Finance, 2nd Edition

studies are mixed, and the technique fell out of favor as economists began to

realize that no clear pattern of capitalization was ever likely to emerge.

With imperfect Tiebout sorting, there is no reason to expect any one

pattern of coeYcients on the public sector variables, either expenditures or

taxes. They could be positive, negative, or zero, depending on people's prefer-

ences for expenditure±tax bundles relative to the bundles actually provided. If,

for example, most communities in a given area are providing low service

bundles, whereas most people prefer high service bundles, one would expect

to Wnd a positive correlation between property values and public services. If

the situation were reversed, the regression coeYcient would be negative.

Worse yet, suppose most towns are oVering either high or low levels of public

services, whereas most people prefer a medium level of service. If the distribu-

tion of public services were symmetric across communities, a regression of

property values on public services would yield a zero coeYcient. Yet theory

would suggest that rental values in the medium service communities would

capitalize the excess demand for these services. Thus, even if capitalization is

occurring, regression analysis may fail to discover it.

10

Finally, if Tiebout sorting were perfect such that all households lived in

communities with exactly the public service bundle they desired, then the

hedonic price estimates on the public sector variables would again yield zero

coeYcients.

11

In short, economists realized that testing for capitalization with

the hedonic price techniques was unlikely to generate useful information.

ANYTHING IS POSSIBLE

Theoretical models of Wscal federalism have shown that the sorting of people

can lead to almost any outcome. We conclude this section with a simple

model by Stiglitz that can produce a wide range of outcomes, from an eYcient

equilibrium to an ineYcient equilibrium, multiple equilibria, or an equilib-

rium that can be improved upon by grants-in-aid from high-income to low-

income communities.

12

10

This particular example is due to Pauly, although Bruce Hamilton has made essentially

the same point. See M. Pauly, ``A Model of Local Government Expenditure and Tax Capitaliza-

tion,'' Journal of Public Economics, October 1976; B. Hamilton, ``The EVects of Property Taxes

and Local Public Spending on Property Values: A Theoretical Comment,'' Journal of Political

Economy, June 1976.

11

This point was made, and tested, by Matthew Edel and Elliot Sclar in ``Taxes, Spending,

and Property Values: Supply Adjustment in a Tiebout±Oates Model,'' Journal of Political

Economy, September/October 1974.

12

J. Stiglitz, ``The Theory of Local Public Goods,'' in M. Feldstein and R. Inman (Eds.),

The Economics of Public Services: Proceedings of a Conference Held by the International Economic

Association at Turin, Italy, Macmillan, New York, 1977. Reproduced in abridged form in

A. Aktinson and J. Stiglitz, Lectures on Public Economics, McGraw-Hill, New York, 1980,

chap. 17.

30. OPTIMAL FEDERALISM: THE SORTING OF PEOPLE WITHIN THE FISCAL HIERARCHY 873

The Stiglitz Model

Stiglitz' model is a variation of the McGuire model. Stiglitz posits a Wxed

number of communities, but with suYcient undeveloped land available in

each community that expansion or contraction of the town has no eVect on

land prices. Thus he does not include a housing market. The main diVerence

from the McGuire model is that income is generated by production in the

communities, with each person supplying one unit of labor. There are no

other factors of production. The output from production can take the form

of a private good, X, and a Samuelsonian nonexclusive good G. A second

diVerence from the McGuire model is that G is not subject to congestion. Its

services are equally available to everyone in the town. Finally, mobility from

community to community is costless, so that horizontal equityÐequal treat-

ment of equalsÐis the sorting equilibrium condition. Since the people are

assumed to be identical, everyone must have the same utility in equilibrium.

Production

Let:

Y  fN,f

0

> 0 and f

00

< 0 (30:32)

deWne the total income or output generated by the N people in the community

according to the production function f(N). Also,

fNNX  G (30:33)

where X is the amount of the private good received by each person.

Preferences

The identical individuals have utility functions deWned over X and G:

U  UX,G (30:34)

Also, Eq. (30.33) implies that the budget constraint for each individual is

fN/N  X  G/N (30:35)

The Wrst task is to describe the optimal levels of G and N.

The Optimal G

To determine the optimal amount of G for a given N, the individuals

solve the following problem:

max

X; G

UX,G

s:t: fN/N  X  G/N

with the corresponding Lagrangian:

874 ANYTHING IS POSSIBLE