The impact of metropolitan consolidation on fiscally induced migration

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The impact of metropolitan consolidation on fiscally induced migration an econometric simulation approach
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Thesis--University of Florida.
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Includes bibliographical references (leaves 154-159).
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by Richard Wayne Ellson.
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THE IMPACT OF METROPOLITAN CONSOLIDATION ON FISCALLY
INDUCED MIGRATION: AN ECONOMETRIC SIMULATION APPROACH















By

RICHARD WAYNE ELLSON


A DISSERTATION PRESENTED TO THE GRADUATE COUNCIL OF
THE UNIVERSITY OF FLORIDA
IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE
DEGREE OF DOCTOR OF PHILOSOPHY



UNIVERSITY OF FLORIDA


1977



































COPYRIGHT

1977



Richard W. Ellson















ACKNOWLEDGEMENTS


The author wishes to thank his Chairman, Professor Jerome

Milliman, for his wisdom, guidance and friendship throughout the course

of this study. Special thanks is given to Professors Henry Fishkind and

Blaine Roberts, whose conscientiousness and support were invaluable.

The author would also like to express his appreciation to Professors

Fred Goddard.and Gary Lynne for their contributions.

Finally, the author extends his profound gratitude to his wife

for her love, constant personal support and professional editing skills.

The author's parents were also an invaluable source of love and under-

standing.














TABLE OF CONTENTS


Page

Acknowledgements iii

List of Tables vi

List of Figures vii

Abstract viii

Chapter 1 Introduction 1

1.1 Problem Statement 1
1.2 The Issue of Metropolitan Government 4
1.3 Proposed Methodology 8
1.4 Outline of the Study 11

Chapter 2 Review of the Literature 13

2.1 The Tiebout Model 13
2.11 Introduction 13
2.12 The Tiebout Model 14
2.13 Theoretical Revisions 17
2.14 Empirical Studies on the Tiebout Hypothesis 28
2.2 Fiscal Analysis of Metropolitan Areas 45
2.21 Introduction 45
2.22 Single Equation Models 47
2.23 Aggregate Expenditure Functions and
Multiequation Models 53
2.24 Primary Conclusions 59

Chapter 3 A Theoretical Model of Residential Location 61

3.1 Introduction 61
3.2 Discussion of Previous Studies 62
3.3 Individual Utility and Residential Location 66
3.31 A Scenario 66
3.32 The Utility Function 72
3.33 Comparative Static Analysis 76
3.4 Implications of the Model 79











Page


Chapter 4 The Empirical Model and Results


4.1 The Data
4.11 The Sample
4.12 The Calculation of the
4.13 The Calculation of the
4.2 Empirical Results
4.21 The Total Sample
4.22 Declining Areas
4.23 Growing Areas
4.3 Limitations of the Model


Income Classes
Fiscal Variables


Chapter 5 Summary

5.1 Introduction
5.2 Residential Location and the Tiebout
Hypothesis
5.3 The Tiebout Hypothesis, Consolidation and
the Empirical Results
5.4 Final Comments


86
86
88
93
106
106
118
124
130

136

136

137

143
152







List of Tables


Chapter 4

TABLE 4.1

TABLE 4.2

TABLE 4.3

TABLE 4.4

TABLE 4.5

TABLE 4.6

TABLE 4.7

TABLE 4.8

TABLE 4.9

TABLE 4.10


TABLE

TABLE

TABLE



TABLE

TABLE

TABLE


4.11

4.12

4.13



4.14

4.15

4.16


Population

Income Classes

Allocation of Expenditures and Nonlocal Revenues

Per Capita Expenditures and Revenues

Allocation of Local Revenues

Fiscal Ratio

Description of the Variables

Location Equations Total Sample'

Fiscal Equations Total Sample

Simulation Results Comparative Locational

Audices Total Sample

Location Equations Declining Cities

Fiscal Equations Declining Cities

Simulation Results Comparative Locational

Audices Declining Central Cities

Location Equations Growing Cities

Fiscal Equations Growing Cities

Simulation Results Comparative Locational

Audices Growing Central Cities


Page

89

94

97

99

103

107

108

113

114



116

119

120



123

127

128



129






List of Figures


Chapter 3 Page

Figure 1 67

Figure 2 68

Figure 3 69













Abstract of Dissertation Presented to the Graduate Council
of the University of Florida in Partial Fulfillment of the Requirements
for the Degree of Doctor of Philosophy

THE IMPACT OF METROPOLITAN CONSOLIDATION ON FISCALLY
INDUCED MIGRATION: AN ECONOMETRIC SIMULATION APPROACH

By

Richard Wayne Ellson

December 1977

Chairman: Jerome W. Milliman
Major Department: Economics

This study focuses on the degree to which fiscal variations in

a metropolitan area influence residential location. Efforts to explain

this aspect of locational behavior have essentially resulted in the

empirical testing of the Tiebout hypothesis, which states that an indi-

vidual will locate in that community which provides the mix of public

services and taxes best suited to his own tastes and preferences. In

other words, the Tiebout hypothesis seeks to explain the phenomenon of

"voting with one's feet" whereby individuals can gain fiscal advantages

by their choice of residential location.

It is assumed that governmental consolidation will eliminate the

source of metropolitan fiscal variations which result from differing

allocations of revenues and tax burdens. Therefore, if residential is

in part determined by fiscal variations across a metropolitan area, then

the implementation of a consolidated government can be expected to

influence residential choice. Thus, the model developed in this study

is important on both a theoretical and an institutional basis.

The model is primarily concerned with middle class residential

location. It is assumed that this income group represents the primary

viii







component of the urban decentralization trend. Furthermore, it is

hypothesized that this group will react to the Tiebout forces. However,

the determinants of middle class location are used to estimate the

location of upper and lower income groups. In this way, the differing

behavioral patterns of each income group are contrasted.

The theoretical model in this study ties the fiscal sector to the

traditional models of residential location. Within this framework,

both the Tiebout hypothesis and the effects of metropolitan consolidation

are examined. An important conclusion from this analysis is that it is

optimal for upper income households to locate in,the central city under

certain conditions, despite fiscal advantages and greater neighborhood

amenities in the suburbs. The utility function provides an important

link between accessibility models of residential location and the local

government sector.

Significant results can also be drawn from the empirical model.

First, the determinants of residential location were found to vary

substantially by income groups. Second, the Tiebout hypothesis may not

be valid in all metropolitan areas. This finding comes directly from

the subsample regressions, and it further implies that cross-section

models are not sufficient for analyzing a dynamic process such as resi-

dential location.

The goal of the consolidation simulation was to obtain an estimate

of the response of households to the elimination of metropolitan fiscal

variations. The results suggest that consolidation may have substan-

tial effects on household location. This provides support for the

Tiebout hypothesis. However, since the simulation assumed perfect

mobility and instantaneous adjustment, the magnitude of the response

was much too large.























DEDICATION

TO MY WIFE AND PARENTS













CHAPTER 1

INTRODUCTION

1.1 Problem Statement


It has been argued that the flight of households to the suburbs

has been a primary factor in the deterioration of the central city

in some metropolitan areas. With the departure of the middle and

upper income groups, the central city has become'increasingly

populated by the poor, who demand relatively larger public expen-

ditures for social services, but who provide relatively smaller tax

revenues. As the central city attempts to increase its tax revenues

to finance these higher service demands, primarily through wealth

taxes (property and income), there is an increased incentive for

the remaining middle and upper income families to also relocate in

the suburbs. Accordingly, there is an increased discrepancy between

metropolitan core cities and their suburbs in the fiscal capacity

to raise adequate revenue on the other.

One of the major causes of this metropolitan fiscal imbalance

against the central city is the requirements of poverty-related

services. Woo Sik Kee (NTJ, 1968) found that metropolitan areas with

large city expenditures for such services had substantial differentials

in their general revenue requirements and tax effort between the city

and the suburbs. The sample consisted of the 22 largest SMSAs, 13 of

which are located in the north and east. Since these older and






declining central cities have been subject to decentralization trends

for some time, the results found by Woo Sik Kee are not surprising.

This studywill focus on the degree to which fiscal variations

in a metropolitan area influence residential location. Although the

decentralization process in metropolitan areas has been composed of both

firms and households, the location of firms will be treated exogenously

in this study. It is clear that firms also respond to changes in

transportation costs and fiscal advantages. However, these parameters

are assumed to differ between households and firms, and this study will

concentrate on the determinants of household location.

Efforts to explain the impact of fiscal variations on household

location have essentially resulted in the empirical testing of the

Tiebout hypothesis (JPE, 1956). Given the assumptions of perfect mobility

and knowledge, a large number of potential residential communities and

the absence of external economies or diseconomies among communities, the

Tiebout hypothesis states that an individual will locate in that

community which provides the mix of public services and taxes best

suited to his own tastes and preferences. In other words, the Tiebout

hypothesis seeks to explain the phenomenon of "voting with one's feet"

whereby individuals can gain fiscal advantages by their choice of

residential location. It also incorporates location into the individual's

utility maximizing behavior. Thus, it has been offered as a partial

rationale for the suburban flight of the middle and upper income groups.

Given the fiscal dilemma of the central cities and the concurrent

flight to the suburbs, several proposals have been made to mitigate the

situation. Commonly cited solutions include a commuter tax, increased

user charges, the shifting of financial responsibilities for poverty-







related services to higher levels of government and metropolitan govern-

mental consolidation. The issue of metropolitan consolidation is

undergoing widespread debate at present, and to date, consolidated

governments have been instituted in six metropolitan areas: Miami,

Florida; Jacksonville, Florida; Indianapolis, Indiana, Nashville,

Tennessee; Lexington, Kentucky; and Anchorage, Alaska.

It is apparent that if residential location is in part determined

by fiscal variations across a metropolitan area, then the implementation

of a consolidated government can be expected to influence residential

choice. The model developed in this study will analyze this issue,

and it is important for two reasons. First, the study represents a

direct test of the Tiebout hypothesis. Eliminating metropolitan fiscal

disparities through the mechanism of governmental consolidation allows

one to determine the sensitivity of residential location by comparing

actual data with an ex post simulation. Second, it applies to a viable

public Policy issue. Bish and Nourse (1975) point out that over 100

communities have studied the possibility of consolidated government

in varying forms. However, if a metropolitan area chooses to implement

governmental consolidation, it has little a priori knowledge of its

effects on locational choice. This area certainly merits attention,

particularly for its potential to alter the movement of households out

of the central city.

The remainder of this chapter will elaborate upon the following

points. First, the next section will analyze the arguments, both pro

and con, on the issue of consolidation. Second, the empirical model

will be briefly described. Last, an outline of the study will be

presented.







1.2 The Issue of Metropolitan Government

The debate surrounding the issue of urban governmental organiza-

tion has grown with the increasing movement of firms and households out

of the core city and into the suburbs. As the responsibilities of

local governments multiplied, the reform of local governmental struc-

tures became the central forcus for the resolution of the difficulties

associated with both central city deterioration and suburban growth.

The polar positions in this debate can be roughly categorized as those

who favor consolidated governments and those who favor decentralized

local governments. The arguments of each group'can be quite vociferous.

For example, Campbell and Burkhead (1968) state that the fragmentation

of governments in metropolitan areas both mirrors and reinforces

anarchy in urban areas. Alternatively, Warren (JAIP, 1964) argues that

the viability of decentralized governments has been distorted and

greatly underestimated, whereas the expectations of benefits with

respect to consolidated governments exceed what can be predicted on the

basis of evidence. Although considerable information has been received

since these statements were made, present debates mirror these positions,

and the issue remains unresolved.

The proponents of consolidated government base their arguments on

two factors: efficiency and equity. Increases in efficiency are

assumed to be realized from the following source. It is believed that

fragmented and overlapping jurisdictions result in an inefficient

duplication of services. Therefore, a consolidated government would

be able to take advantage of economies of scale in the provision of

publicly provided goods and services, and lower unit costs could be

achieved.









Bish and Ostrom (1973) point out that the efficiency argument

rests on three critical assumptions. First, it assumes that large-

scale public bureaucracies can obtain, process and utilize information

on public needs and can produce and distribute public services more

efficiently than smaller public units. Bish and Ostrom argue that the

potential distortion and loss of information at each level of organization

may preclude any efficiency gains. Second, the realization of scale

economies assumes that consumers' tastes and preferences with respect

to public goods are similar, that all public goods are homogeneous

and that uniform levels of all public goods and services should be pro-

vided throughout the metropolitan area. This is clearly a tenuous

assumption. Third, proponents of consolidation assume that all public

goods and services are sufficiently similar that they can be provided

by the same organization. However, Hirsch (1968) suggests that economies

of scale will vary greatly among different public goods and services.

This latter point is elaborated on by Warren. An advocate of

decentralized local governments, Warren suggests that small governmental

units can realize economies of scale by contracting external producers

for specific public goods. In this situation, a community can negotiate

for a given service level, and it permits the right to withdraw and

utilize other options. Thus, there is a separation of the production

and provision of public goods and services, and a quasi-market is

established.

Unfortunately, however, there is a dearth of empirical information

on the efficiency characteristics of consolidated governments. Although

the efficiency argument is intuitively logical, it rests on some very

restrictive assumptions. It is hoped that in the near future, as the

present consolidated governments become entrenched, an effort will be









made to assess the benefits and co:;ts of consolidation.

The belief that metropolitan consolidation will increase equity

rests on the assumption that the suburbs are somehow exploiting the

central city. This can result from two sources. First, suburban

commuters (workers and shoppers) are viewed as consuming central city

goods and services while avoiding the full burden of taxation for them.

Therefore,the suburban commuters, who are predominantly middle and upper

inco. e groups, are essentially subsidized by the central city. Second,

it is assumed that suburban residents do not pay their equitable portion

of poverty-related services, which are alleged to be metropolitan

in nature. Thus, middle and upper income families who move to the

suburbs are able to avoid this tax burden.

The first point has been analyzed in several studies. Woo Sik

Kee reached the conclusion that commuters only partially offset the

costs that they impose on central cities. He states that central cities

with a large number of commuters must increase both expenditures and

tax effort, which implies a larger degree of exploitation for these

cities. However, these results are in contrast to those of Vincent

(1971). Using a cross-section, recursive econometric model, Vincent's

study suggests that commuters pay more in terms of central city taxes

than they receive in central city services. Vincent's model estimated

the impact of both commuting shoppers and workers on selected central

city expenditures and revenues. He was able to derive the benefits

and costs from the estimated coefficients for the workers and

shoppers, and they indicate that exploitation does not exist in this

respect.

The question of poverty-related exploitation has been much more

difficult to analyze. Neenan (NTJ, 1970; Greene et al., 1974) has








studied this problem in the Detroit and Washington, D.C. metropolitan

areas. Neenan utilizes two concepts to allocate expenditures between

the central city and the suburbs: the cost of service and the willing-

ness to pay. The cost of service method allocates expenditures on a

dollar basis to specific locations. The second method allocates

benefits from government services according to a willingness to pay

index, which is based primarily on the income distribution of the area.

For example, upper income groups in the suburbs are assumed to have a

willingness to pay value in excess of the allocated cost of service.

Although this methodology has received some criticism (Brown, NTJ, 1971),

Neenan found that exploitation does not exist on a cost of service

basis. This result is reversed if the willingness to pay index is used.

Therefore, definitive statements on this issue must be qualified despite

the rigorous examination of specific metropolitan areas.

Given the indeterminancy of the efficiency and equity issues, the

grounds for imposing consolidated governments appear to be questionable.

Nevertheless, consolidation continues to draw considerable interest in

all sections of the nation. For example, in June, 1971, over 125

metropolitan areas in 35 states were studying the issue (ACIR, 1972).

In addition, a basic question is to determine under what conditions

consolidation will take place. Rosenbaum and Henderson (Journal of

Politics, 1972) suggest that since consolidation represents a radical

change in the urban environment, then the basic causes are analogous

to those accompanied by revolutions at the national level. An example

would include a situation of social disequilibriumand an inadequate

governmental policy, which is followed by power deflation and radical

change in the local political structure (e.g. consolidation).

The relevance of this scenario is subject to doubt, but consolidation








is an extreme step. Cowing and Holtmann (Land Econ., 1974),

who studied the distributional impact of consolidating welfare services

in Binghamton-Broome County, New York, state that local consolidation

initiatives depend on the distributionof gainers and losers between

the central city and the suburbs. However, institutional processes

vary from state to state, and consolidated government can also be the

province of state legislatures.

This study will not be concerned with these normative aspects of

the issue of metropolitan consolidation. Each metropolitan area contains

unique characteristics, and it is beyond the state of the art to make

definitive statements regarding the viability of consolidated government

except on a case by case basis. Therefore, the primary goal of this

study is to determine the impact of metropolitan governmental consolidation

on residential location within the metropolitan area. It is hypothesized

that consolidation would eliminate fiscal variations between the central

city and the suburbs, and that household location would be influenced.

This hypothesis is contingent upon two assumptions. First, households

are assumed to derive a fiscal advantage by their choice of location.

Second, this fiscal advantage is assumed to be a significant variable

with respect to residential preferences. It is expected that fiscal

advantages are but one of several determinants of location. Others

include the quality of neighborhoods and job location. The following

section will briefly describe the methodology which is used in this

study.


1.3 Proposed Methodology

The model in this study will focus on middle class residential

location. It is assumed that this income group represents the primary









component of the decentralization Lrend. It is hypothesized that this

group will react to the Tiebout forces, which are discussed in section

2.1. The determinants of middle class location will also be used to

estimate the location of upper and lower income groups. In this way,

the differing behavioral patterns of each income group can be contrasted.

Since consolidation typically takes place between a central city

and its surrounding county, cities which are part of more than one county

will be excluded from the sample. The land area that a central city

occupies within a given county will vary greatly. Therefore, the

endogenous variable for the location equations will be constructed as
MS/PS
an index, which, for the middle class, takes the form of M/P where:
MC/Pc
MS = the number of middle class families in the suburbs

PS = total number of families in the suburbs

MC = the number of middle class families in the city

PC = total number of families in the city

This index will provide insight into the relative density of each income

group. A value greater than one implies that an income group is relatively

more concentrated in the suburbs.

This study utilizes cross-section data, and the sample comprises

50 metropolitan areas. With the exception of fiscal data which is

lagged three years, the data is taken from the 1970 census year. However,

since location is expected to be sensitive to decentralization processes,

a proxy for the movement of firms will be constructed.

The measure of fiscal variation is endogenous within the model, and

the equation system will be estimated with two-stage least squares.

The fiscal variation will be calculated as an identity of the ratio of

per capital expenditures divided by per capital local revenues for the









suburb and city respectively. E.,.i of the components of this measure

will be estimated separately.

Although the residential location equations will be estimated for

the entire sample, considerable insights will be gained by the use of

a stratified sample to capture any variation due to regional factors.

Specifically, central cities with positive growth, which are concentrated

in the south and west, will be contrasted with cities which had negative

population growth, primarily in the north and east. Therefore, it will

be possible to determine if the type of city has a significant influence

on location.

The potential impact of consolidation will be evaluated by a

simulation technique. When consolidation is assumed to take place, the

major influence of fiscal variation will be eliminated from the model.

This implies that services and tax rates will be equalized throughout the

consolidated area. Two assumptions are required. First, movement over

space is assumed to be frictionless. For example, a household that

locates one block away from a fire station will not receive better service

than a household which is located several blocks away. Second, service

quality differentials are assumed to be insignificant after a simulated

consolidation. The effects of space and service quality are clearly not

measurable. These complications do not invalidate the model because

the measure of fiscal variation is developed in purely monetary terms.

The Tiebout hypothesis will be tested within this simulation

framework. It is generally recognized that fiscal advantages have been

partially responsible for the exodus to the suburbs, but this may not

be true for all metropolitan areas. If a consolidated government is









implemented in a metropolitan area, a monetary fiscal advantage would

disappear. Therefore, it is expected that household location would

be determined by accessibility and neighborhood quality following

consolidation. Any simulated movements would bear directly on the

Tiebout hypothesis. It should be noted that this procedure violates

Tiebout's assumption of a number of communities with varying tax-service

mixes. This model assumes a homogeneous suburb which is contrasted with

the central city. Although this assumption is somewhat unrealistic,

it is necessary due to data limitations. Movements between core cities

and the suburbs are assumed to be of more critical importance than

movements between suburban communities.


1.4 Outline of the Study

The next chapter presents a rather lengthy literature review on the

Tiebout hypothesis and the determinants of local government expenditures

and revenues. The Tiebout hypothesis has undergone substantial theoretical

and empirical revisions, and these will be examined in depth. Since

the components of the measure of fiscal variation in this study are

estimated separately, the proper specification of these equations is

essential. The literature on local government expenditures and revenues

therefore becomes quite important.

In Chapter 3, a model will be developed which incorporates fiscal

variables into traditional residential location theory. Using compara-

tive static analysis, it becomes possible to determine the location of

households with different incomes. In addition, the impact of metro-

politan consolidation can be analyzed within this framework.

Chapter 4 will present the empirical model which is composed of





12



nine equations. This model will be estimated for the entire sample,

declining central cities and growing central cities. Considerable

insight will be gained across both income groups and regions. These

results will be summarized in Chapter 5, and they will be placed in

the context of the Tiebout and consolidation literature.













CHAPTER 2

REVIEW OF THE LITERATURE


This chapter will review the literature on the relation of fiscal

variables to residential location. This literature is composed of two

parts. The first section will analyze the Tiebout hypothesis, its

theoretical extensions and related empirical studies. The second section

will examine the literature on revenue and expenditure functions for

metropolitan areas. Both strands of literature are essential for this

study on the impact of metropolitan consolidation on fiscal variables

which may affect residential location.


2.1 The Tiebout Model

2.11 Introduction

The Tiebout model is an important theoretical construct in the field

of urban public finance. Initially published in 1956 in response to

Samuelson's exposition on the theory of public goods (Restat., 1954, 1955),

the Tiebout hypothesis has been the subject of both theoretical revision

and empirical research. Although the model explicitly considers neither

central cities nor metropolitan areas, it is often considered as a point

of departure in the investigation of urban fiscal problems. Mills and

Oates (1975) provide an apt description of the theoretical power of the

model. They state that substantial questions must be resolved with

respect to the degree to which Tiebout forces operate in the local public

sector. Unquestionably,however, the process which Tiebout envisioned

possesses both considerable descriptive power and important but

controversial implications. Thus, Mills and Oates conclude that the







model can be characterized in terms of remarkable theoretical insight-

fulness and unresolved empirical issues.

The analysis of the Tiebout hypothesis will be done in the follow-

ing manner. First, the following section will evaluate the model as it

was originally set forth. In the next section the theoretical revisions

of the model will be discussed. Although the original paper was

published twenty years ago, important clarifications have been formulated

only relatively recently. However, these revisions add insight by

incorporating issues such as residential location theory, and the theory

of public goods and urban fiscal trends which have been developed to a

far greater degree since the time of the original publication. Finally,

the third section will analyze the strengths and weaknesses of the

empirical tests on the Tiebout hypothesis.


2.12 The Tiebout Model

In his pioneering work, Samuelson derived the conditions for the

optimal provision of public goods. More precisely, he demonstrated that

public goods are characterized by jointness in consumption. Therefore,

the total demand for a public good is determined by the vertical summa-

tion of individual demand curves. In contrast, the market demand for

a private good is derived by the horizontal summation of individual

demand curves. Mathematically, the Pareto optimal condition for public

goods is represented by:

au /Dx auB /x DF/3X
+ orZ MRS = MRT where
AU /DX DU B/DX F/DX
r r r

A and B are individuals

X = a public good
P








X = private good numecirire

F = an implicit production function, F(X ,Xr)

Using the same notation, the corresponding Pareto optimal condition for

private goods is:

SUA/Dx ~UB/lx aF/8X
g- = g = where X is also a private good.
A/aX auB/ax a F/aXr g
r r

Thus, the property of jointness implies that price responds to a constant

quantity (which everyone may consume) in the pure public good case,

whereas quantity varies with respect to a given price in terms of private

goods,assuming perfect competition.

The ramifications of Samuelson's work are far-reaching. The joint-

ness property of pure public goods implies that the marginal cost to an

additional consumer is zero. Accordingly, consumers have incentive to

engage in strategic bargaining by understating their true preferences.

Therefore, the individual demand curves are in essence "pseudo" demand

curves, and the lack of revealed preference on the part of consumers

will produce a nonoptimal provision of public goods. In essence,public

goods represent one type of market failure.

Tiebout sought to prove that efficiency conditions could be met in

the local public sector, and he separated himself from Samuelson by

stating that the latter implicitly assumed that public expenditure

decisions are made at the central government level. This represents an

error by Tiebout. The issue with respect to Samuelsonian public goods is

not their provision through public rather than private means, nor is the

inability to exclude consumers either a necessary or sufficient condition

with respect to pure public goods. Thus, Samuelsonian public goods are

a consumption phenomena. Alternatively, Tiebout derived conditions for









the efficient provision of local publicly provided goods, and he mentioned

such examples as police protection and education which are not pure

public goods in the Samuelsonian sense.

Tiebout's model rests on the following assumptions:

1. Consumers are fully mobile, and they will move to the community

which best satisfies their preferences in terms of publicly provided

goods.

2. Consumers have perfect knowledge with respect to the revenues

and expenditures which are set in each community.

3. There are a large number of communities in which to reside.

4. The sole source of income is dividend income. Therefore, the

influences of job location are eliminated.

5. The publicly provided goods are characterized by the absence

of external economies and diseconomies between communities.

6. Optimum city size is defined as the number of residents for

which the bundle of publicly provided goods can be produced at the

minimum average cost.

7. Communities below the optimum size will try to attract

residents, and those above will try to reduce their population. A

community which is at the optimum size can maintain its status by

enacting zoning laws.

Given these assumptions, jurisdictional mobility on the part of

consumers will produce an efficient allocation of resources in the

local public sector. The greater the diversity between communities in

terms of tax-service mix, the more likely the consumer will be able

to locate in an area which closely approximates his tastes and preferences.

Therefore, consumers are forced to reveal their preference by locational

choice, and efficiency results when each community achieves its optimum size.








Tiebout mentions a number otf difficulties with his model. First,

consumers move to the community which best satisfy their preferences.

However, if preferences were to be exactly satisfied, then there could

conceivably be an infinite number of communities. Second, some of the

assumptions are quite unrealistic. For example, moving is not costless,

and perfect knowledge is unlikely.

The assumption that external economies and diseconomies are absent

limits the application of the Tiebout model to Samuelson's theory of

public goods. Tiebout assumes that the joint consumption characteristic

of local public goods is internalized within each community. Since

this is not the case, the Tiebout model is only peripherally related

to Samuelson's work. This point will be developed further in the follow-

ing section.

Although the Tiebout hypothesis does contain several restrictive

assumptions, it is a conceptual solution to the efficient provision of

local publicly provided goods. With respect to policy implications, it

presents a strong challenge to the proponents of metropolitan consolidation,

who generally believe that centralization will produce greater efficiency

in local public goods provision. However, Tiebout efficiency requires

segregation according to the tastes and preferences of consumers. The

determinants and implications of this jurisdictional segregation will

also be discussed in the following section.


2.13 Theoretical Revisions

Three important theoretical revisions will be analyzed in this

section. First, Buchanan and Goetz (Journal of Public Economics, 1972)

argue that the nonappropriability of locally provided public goods,as

well as the locational dimension of both public and private goods,








places severe limits on the efficiency of the Tiebout model. The

second area to be explored is related to the efficiency of the property

tax as a pricing mechanism within the Tiebout framework. Hamilton

(Urban Studies, 1975) and Hirsch and Margolis (1976) present contrasting

results in their analyses. Finally, the distributional implications of

the Tiebout hypothesis will also be discussed. Mills and Oates (1975)

are the primary contributors in this area. Empirical studies related

to these issues will be analyzed in section 2.14.

Buchanan and Goetz

Buchanan and Goetz attempt to prove that inefficiencies are inherent

in the Tiebout model even in this conceptual form. In their view,

Tiebout sought to describe a nonspatial adjustment process which would

achieve a Pareto optimal solution through the formation of voluntary

clubs. In this scenario, locational constraints do not exist. Accordingly,

Buchanan and Goetz argue that if gains from trade can be secured from

either the consumption or production side, then these gains will be

exploited by the participants until the gains are exhausted. Buchanan

and Goetz allude to Tiebout's assumption of dividend income as evidence

of the latter's nonspatial analysis. Within the Tiebout framework,

therefore, migration is neither a necessary nor sufficient condition for

Sie.:aiity, and location by consumers (club members) would be

independent of the allocation of resources in the public sector. Thus,

the model enables the individual to locate in space strictly on the basis

of individual productivity criteria in the private sector. The club

which he chooses is independent of this decision.

However, local governments contain spatial properties in addition

to "membership" dimensions. Furthermore, resources are not ubiquitous









in the private sector across any :iven area. Using the notation of

Buchanan and Goetz, the necessary conditions for Pareto optimality
S i i i
are: MVPi + MVG = MVP + MVG where i refers to individuals, x and
x x y y -
y refers to two communities and MVP and MVG represents the marginal

value product of private and public goods,respectively. To a potential

migrant, the optimality conditions will be expanded to:


MVP' + (B Ti) + -
x x x aN N
x x

i [ 3(CBJ) (~(TJ)
= MVP + (B Ti) + E a
y y y DN 3N
y y

where i, j = 1,2,...,N i # j

N = number of persons in a community

B = benefits received from the public good by the individual

T = taxes paid by the individual

B T = fiscal residuum to the individual.

Given the assumption that both communities produce the same quality of

a Samuelsonian pure public good, the model will produce a Pareto optimal

solution. The joint consumption characteristic implies that:


a(EB) a(B )
x y =o
aN N
x y
The corresponding tax shares are:

T (ETJ) (ET )
,i ix
x DN y aN
x y

Therefore, the optimality condition reduces to MVP = MVP However,
x y
this model is incorrect in the sense that individuals will have no

incentive to reveal their true preferences. Moreover, this is not a model

of mobility-induced efficiency because the marginal cost to an additional

resident is zero.








The most glaring weakness in l he Tiebout model is the assumption

that private returns are equalized across communities. For example,

suppose that fiscally-induced migration can equalize the fiscal residuum

between communities for a given income group. However, if MVPx # MVP ,

then a nonoptimal solution is reached. This is the result of locational

constraints in relation to the private sector, whereby a differential

locational rent is earned across communities. The migration that results

will equalize MVPx and MVPy but there will be an over-concentration of

residents in the more productive community. Therefore, Nx # N is

necessary for MVPx = MVP The ultimate result is that public services

will not be provided at minimum average cost. Tiebout's assumption of

dividend income is overly restrictive and unrealistic.

A similar nonoptimal result is reached if "impure" public goods

are considered. For example, local publicly provided goods are not

equivalent to Samuelson's definition of public goods. Therefore, a

migrant will impose congestion costs (MC # 0) on the community to which

he moves. Mathematically, this is represented as:
J J J
dN = TQ- ) d + B where Q is the quantity of the public good.
dN DQ dN +N

If congestion is present, then it is likely that -- < 0. The total
dB
effect -dN) will be negative if the effect of congestion is greater than

the increased cost-sharing of the tax burden. In other words, dQ/N

will be negative if the price effect due to the increased cost-sharing

is less than the downward shift in the marginal evaluation schedules as

the good becomes more congested. Mobility would be likely to produce

disequilibrium in the public sector.

In summary, Buchanan and Goetz conclude that the Tiebout model is

not a market analogue to the private sector. Essentially, the model is

limited in two respects. First, locational constraints enter into both








the private locationall rents) anl, the public (congestion) sectors.

Second, there is the problem associated with determining the marginal

evaluation by individuals of both pure public goods and local (impure)

public goods. Therefore, the use of the Tiebout hypothesis as an

efficiency benchmark is severely limited.

Hamilton

Hamilton argues that an efficiency mechanism does operate within

the Tiebout model. He suggests that the major failure of Tiebout was

his failure to devise a system of prices which would operate within the

equilibrating mechanism (mobility). Hamilton's model contains two

basic assumptions. First, a proportional property tax is the sole source

of revenue, and the effective rates may vary between communities.

Second, each community has a zoning ordinance which sets a minimum level

of housing consumption for all residents within the community. Given

these assumptions, Hamilton derives the following results. First,

Tiebout efficiency will be maintained in the provision of local public

goods. Second, the property tax becomes an efficient pricing mechanism

which does not impose an excess burden between housing consumption and

other goods. Third, local governments cannot engage in income redistribution.

Finally, it is shown that neither taxes nor public expenditures are

capitalized into property values.

Every household in Hamilton's model has the utility function:

U = U(X1,X2,X3) where

X1 = per family consumption of housing

X2 = per family consumption of local public goods

X3 = per family consumption of composite private commodity bundle

Both X1 and X2 as well as the property tax rate can vary among communities,

but they must be constant within communities. The zoning restriction








requires that each resident in community i must consume at least Xli

of housing. The constraint faced by the consumer is: Y = P X1 +

P2X2 + P3X3, and maximizing utility subject to the constraint yields

the household's optimum commodity bundle (XI, X2, X3). Accordingly,

the household's optimum location will be in that community where X1

equals the zoning restriction Xli. He cannot reside in a community
*
where X1 < X i. Furthermore, if he lives in a community where X1 > Xli,

he can either increase his consumption of X2 or reduce his tax price

by moving to that community where X1 = Xli. Therefore, each community

is characterized by X', X', and a sufficient number of communities

would insure a market analogue in the public sector. The property tax

becomes an efficient pricing mechanism because the tax price is

independent of all goods with the exception of X', and accordingly, it

carries no deadweight loss. For any given tax payment, housing

consumption can be varied without the consumer bearing any capitalization

in terms of Pl. Thus, the property tax is perceived only in terms of

local public goods received, and it essentially becomes a head tax

with no distortion on prices.

Hamilton extends his model to include non-optimal states. First,

if there is an excess demand for housing within a given jurisdiction, the

value of the land will be bid up, and an economic rent will be earned

by landlords. This type of capitalization will be discussed in the

following section. Second, there are difficulties associated with the

joint consumption characteristic of public goods. This was discussed

previously. Third, the production functions for local public goods are

not known. For example, the measurement of public outputs is an

extremely arbitrary task. Therefore, pricing at minimum average cost

represents a purely normative statement. Thus, considerable doubt can








be cast on Tiebout efficiency wit.iin Hamilton's theoretical framework.

Hamilton (1975) tests the efficiency of the property tax in the

following manner. His hypothesis states that central city residents

regard the property tax as a component of the price of housing, whereas

suburbanites do not. In other words,Tiebout efficiency exists in the

suburbs, but not in the central city. The equation to be estimated

takes the form of:


ln(V) = In(C) + B ln(Y) + a ln(F) + Cu ln(U) + CDD

where

V = house value

C = a constant

Y = family income

S= income elasticity of the demand for housing

F = family size

U = distance from CBD

D = dummy variable, 1 = city 0 = suburbs

The model was estimated for fifteen SMSA's using 1960 census data.

Hamilton argues that if the property tax is regarded by suburbanites

as a benefit tax for local public goods and services, then they will

consume more housing. Assuming a price elasticity of demand for housing

equal to negative one, Hamilton calculates a predicted value of

CD = -.135. Four of the SMSA's were eliminated from the sample because

they had three or less school districts. Thus, they were not represen-

tative of a Tiebout framework which allows for sufficient diversity in

the provision of public goods. Of those remaining,ten of the eleven

SMSA's had negative values for CD, and the mean value was -.132.

Therefore, Hamilton viewed his hypothesis as verified.








However, there are several d: 'ficulties with his hedonic price

model. First, the t-statistics for CD are quite low in most cases.

Therefore, the standard error of the coefficients is likely to be

large. Second, (U) is used as a proxy for the price of housing, but

it represents accessibility which is but one component of housing

services. In addition, Cu was generally insignificant. Finally, it

is possible that CD captures amenity and environmental characteristics,

and that these effects are responsible for the result obtained by Hamilton.

Therefore, the efficiency of the property tax is not verified within

this model.

Hirsch and Margolis

Hirsch and Margolis suggest several difficulties inherent in the

Tiebout model. Specifically, they mention the problem of locational

constraints and the variability of expenditures and revenues in a

community, which Tiebout viewed as fixed. However, their primary

concern is to demonstrate that the property tax is an inefficient

pricing mechanism which does impose an excess burden.

Utilizing normal rent-bid curve analysis, they state that parcels

of land will go to the highest bidder. The model includes the following

assumptions. First, employment is located in a CBD. Second, there are

two communities a and b, with a located nearer to the CBD. Third,

there are two builders who construct apartments and housing respectively.

Fourth, the same number of commuters emanate from each area (m).

Commuting costs for a and b are denoted by Ca and Cb respectively.

Therefore, the locational rent that apartment builders will pay for

a is greater than that for house builders because apartment density is

greater than household density (dl > d2). The differential is shown








as d1m (Cb Ca) > d2m (Cb Ca). This result duplicates the usual

rent-bid analysis.

The imposition of a property tax introduces two distortions. First,

the locational tendency described above is reversed in the presence of

a property tax. This result rests on the conclusion that property

value per house is lower in b than a, and that the structure value per

acre is greater for apartments than for single family housing. Both

represent realistic assumptions. Mathematically, the condition for

locational reversal is shown as: dlSl(ta-tb) > d2S2(ta-tb) where

S1 = structure value of apartments

S2 = structure value of houses

t = effective tax rate in a
a

tb = effective tax rate in b

Therefore, since the property tax is not a general tax on capital due

to exemptions and varying rates, a substitution between locations occurs.

The property tax also introduces an additional distortion. Hirsch

and Margolis assume diminishing returns with respect to the provision

of public goods. Assuming increasing costs, if a household that

consumes less than the average housing moves into a community, it

will impose costs on the rest of the residents. This is denoted by:


3C
N > t V. where
aN i

C = cost of government

N = number of residents

t = effective tax rate

th
V. = housing value of i resident
1








This transfer of costs implies tli.:( the property tax redistributes income

from the rich to the poor, and that all new residents should build

housing of lower value than the community average. However, old residents

have three options. First, they can lessen their consumption of housing

by reducing maintenance expenditures. Second, they can move to another

community. Third, they can impose zoning restrictions.

This conclusion has substantial implications with respect to the

deterioration of residential areas. Hirsch and Margolis also demonstrate

that in the absence of zoning regulations (Hamilton), the property tax

is an inefficient pricing mechanism. Therefore, Tiebout efficiency is

further questioned. However, Hirsch and Margolis provide support for

Hamilton's position that redistribution is inefficient at the local

level. Since the rich are mobile, segregation by income classes becomes

a distinct possibility. This point will be discussed below.

Mills and Oates

Mills and Oates (1975) analyze the distributional implications of

the Tiebout model. For example, if the mix of public services within

a community is partially determined by income levels, then the Tiebout

model implies that communities will be segregated by income. This view

is consistent with the results obtained by Hamilton and Hirsch and

Margolis.

It was noted in the previous discussion that there are incentives

for households with low housing consumption to enter wealthier communities.

If the property tax is equivalent to housing consumption, these migrants

will not bear the marginal cost of the local public goods, and consequently,

part of the costs are shifted onto the old residents. This phenomenon

is the rationale for the type of fiscal zoning which was suggested by

Hamilton. However, Mills and Oates suggest that another form of zoning








may also exist, and they refer to it as public goods zoning. In this

situation,old residents try to control the characteristics of in-migrants,

and by doing so, the community achieves a desired level of public goods

output. For an example, consider the case of police protection. Mills

and Oates argue that a low level of crime (the output of police protection)

can be achieved in a community which is populated by upper income residents

rather than the poor. Therefore, public goods zoning represents an

alternative means to obtain revealed preference in the public sector.

Mills and Oates further argue that the Tiebout model applies only

to suburbs and not the central city. Because the poor lack mobility,

they are stranded as a residual in the central city. Thus, the Tiebout

model is consistent with patterns of decentralization in urban areas.

This implies that local redistribution efforts will be unsuccessful,

and exclusionary zoning will enable the rich to gain greater efficiency

in public goods provision. However, Mills and Oates suggest that higher

incomes, cheaper means of transportation and FHA policies are primarily

responsible for exclusionary suburbs. Tiebout processes merely

represent another constraint on housing location, which may produce

greater decentralization. Furthermore, they state that people may live

and work in places other than where they would reside if a metropolitan

government was implemented. This latter point represents the hypothesis

of this study.

The theoretical revisions which have been analyzed in this section

have made important contributions to the understanding of the Tiebout

hypothesis. First, Tiebout efficiency is achieved only under extremely

restrictive conditions (zoning). Buchanan and Goetz point out that the

Tiebout model can be efficient only in a nonspatial context. Second,

it is unlikely that the property tax acts as an efficient pricing








mechanism in the public sector. Hamilton's theoretical model is somewhat

simplistic, and the regression which he estimates to support his theory

contains glaring errors. Third, Tiebout processes are a contributing

factor to the decentralization of urban areas. Therefore, although the

Tiebout model is limited in its usefulness relative to the optimal

provision of local public goods and services, it remains an important

empirical hypothesis to test the effects of fiscal variations on house-

hold location within metropolitan areas. The following section will

analyze some of the empirical models which have dealt with the Tiebout

hypothesis.


2.14 Empirical Studies on the Tiebout Hypothesis

Empirical research on the Tiebout hypothesis has centered on the

degree to which Tiebout forces operate in the local public sector.

Two basic approaches have been pursued. First, Oates (JPE, 1969)

stated that the relative attractiveness of a community with respect to

local public expenditures and taxes will be capitalized in the property

values of a given community. The methodology of Oates was duplicated

by Edel and Sclar (JPE, 1974), who incorporated time-series analysis

into the model. In addition,this methodology was the subject of

considerable criticism by Pollakowski (JPE, 1973), to which Oates

replied (JPE, 1973). This debate will be analyzed in considerable depth.

The second approach is primarily centered on the influence of fiscal

variations within a metropolitan area on the location of residences in

the central city vis-a-vis the suburbs. A fiscal residuum was utilized

as the measure of fiscal variation in studies by Aronson and Schwartz

(NTJ, 1973) and Bradford and Kelejian (JPE, 1973). Haurin and Tolley (1976)

use the concept of a fiscal externality to measure the welfare

losses of nonoptimal residential location. These empirical






studies suggest that the original intent of the Tiebout model has been

all but discarded. Tiebout's response to the Samuelsonian theory of

public goods has been largely ignored. However, empirical research has

transformed the Tiebout hypothesis into a model which seeks to explain

the impact of local fiscal variations on locational choice. Therefore,

the strength.of the model is its theoretical flexibility, and its

insights remain formidable in light of recent urban trends.

Oates and his Critics

Oates' study represents the major paper in terms of the empirical

research on the Tiebout hypothesis. First, Oates assumes that individ-

uals' residential location is at least partially determined by the tax-

expenditure mix across communities. Second, he argues that property

values would be bid up in those communities which have a more attractive

tax-expenditure mix. Therefore, capitalized property values were

viewed by Oates as evidence that Tiebout forces exist. Third, Oates

states that the coefficients of the tax-expenditure variables in his

econometric model would indicate the degree to which the Tiebout

hypothesis operates.

Oates utilizes cross-section data, and his sample consists of fifty-

three municipalities in New Jersey which are located within the New

York City metropolitan area. In addition to tax-expenditure variables,

Oates includes housing quality, income characteristics and accessibility

to New York in order to account for neighborhood quality, population

factors and commuting time, respectively. The specified form of the

model is:


V = f(T,E,M,R,N,Y,P) where








V = median home value in thtiouands of dollars

T = the effective percentage tax rate

E = per pupil expenditures for education

M = linear distance of the community to New York

R = median number of rooms per owner-occupied house

N = percentage of houses built in the previous decade

Y = median family income in thousands of dollars

P = percentage of families with an income of less than $3,000

Each of the right-hand variables were converted into natural logs, and

the equation was estimated by both ordinary least squares and two-

stage least squares. Possible specification errors and other econometric

problems will be evaluated in relation to Pollakowski's analysis.

The results obtained from OLSQ and TSLS did not differ significantly.

Oates' rationale for employing TSLS was to adjust for a possible

simultaneous equation bias between the tax and expenditure variables. The

estimated coefficient for the tax variable was -3.6 in both equations,

whereas the value for the expenditure proxy (education) was 3.2 and 4.9

for the OLSQ and TSLS regressions,respectively. Using these values,

Oates found that the capitalization of education would offset approximately

two-thirds of a capitalized increase in the effective property tax rate

of from two to three percent, assuming a home with a value of $20,000,

an expected life of forty years and a discount rate of five percent.

However, Oates points out that increases in property tax rates unaccom-

panied by increases in public services will cause property values to be

lowered in a given community. Therefore, if individuals do respond to

fiscal variations, then income segregation by community is a distinct

reality. For example, those communities which enforce some type of









fiscal zoning will be able to offer either a given level of public services

at lower tax rates or a higher level of public goods at the same effective

tax rate. One would expect that there would be higher rates of expen-

diture capitalization in such instances.

Hamilton (JPE, 1976) challenges the theoretical basis of the Oates

model. He argues that the correlation between fiscal variables and

property can be attributed to two factors. First, he suggests that

there may be systematic differences in the production functions for

raising revenues and/or providing public services across communities.

Therefore, a household will pay a rent based on the nonreproducible

efficiency of a local government. Second, he argues that capitalization

may occur because of a disequilibrium in which there is a short-run

shortage of "fiscal havens." For example, if the impact of rising incomes

or net migration (such as the poor) causes a relative shortage of a

particular type of community, then property values will rise in the

relatively scarce communities. Therefore, capitalization will occur

for any set of government activities which are in short supply, and it

can include both "fiscal havens" and "fiscal slums." Moreover, Hamilton

suggests that the results that Oates obtained from his sample are not

reproducible using other samples.

The supply disequilibrium aspect of Hamilton's comments were

empirically tested by Edel and Sclar within the framework of Oates'

model. Although Oates' conclusions appear to suggest that individuals

do respond to local fiscal variations, Edel and Sclar argue that he

failed to include supply conditions into his model. Furthermore, they

state that Oates discovered the presence of a Tiebout disequilibrium.

If a competitive equilibrium had been achieved, Edel and Sclar claim








that neither tax nor expenditure ipitalization would have occurred.

Finally, they point out that the Tiebout hypothesis may be valid only

in terms of particular local public goods and services rather than

public expenditures in the aggregate. Therefore, Edel and Sclar seek

to reintroduce the efficiency aspect of the Tiebout model into Oates'

methodology. Declining tax-expenditure capitalization over time would be

evidence that a metropolitan area was approaching a Tiebout equilibrium.

However, one should recall the restrictiveness of Tiebout's assumptions.

The absence of capitalization could result from consumer indifference

between services and taxes, imperfect knowledge of local tax-service

mixes or restricted mobility. These conditions may also be changing

over time.

Edel and Sclar analyze the Boston area, and they estimate a cross-

section equation for each of the census years 1930-70. The equation is

specified as:

V = f(T,D,0,E,H) where

V,T, and E have the same definitions as in Oates' model

D = population per square mile

0 = percent of housing owner-occupied

H = highway maintenance (dollars per square mile)

Two other distinctions should be noted. First, the values of the right-

hand variables were not normalized into log form. Second, Edel and

Sclar do not state whether they employed OLSQ or TSLS.

However, their results suggest that OLSQ may have been utilized.

For example, the coefficient for tax capitalization fluctuates greatly

(from a value of -811 to -43.3), and it is not significant for 1930

and 1960. Moreover, school expenditures are not statistically sig-

nificant in any year with the exception of 1950, and the signs are








negative for 1930 and 1940. In a !
fail a t-test at the .01 level. Finally, the coefficient of determin-

ation is substantially lower in all years relative to Oates' regressions.

In spite of these conflicting results, Edel and Sclar argue that the

smaller rates of capitalization are not evidence of indifference, but

rather they indicate movement toward a Tiebout equilibrium for some

public goods. For example, the estimated coefficient for education

declined from 23.7 in 1950 to 1.99 in 1970. According to Edel and Sclar,

this is illustrative of the effects of the post-war baby boom. Supply

adjustments over time have reduced the capitalization of education to

a point where a Tiebout equilibrium is approximated.

One can disagree with these results. If OLSQ was used to estimate

the equations, then it contains a simultaneous equation bias. Not only

are taxes and expenditures highly correlated, but property values are

certainly a determinant of tax rates. Therefore, the coefficients of

the parameters are both biased and inconsistent, and this can account for

the insignificance of the variables as well as their lack of stability

over time. If these econometric problems do in fact exist, any comparisons

to the results obtained by Oates must be discounted. However, since

Edel and Sclar neglect to discuss their estimation procedure, this line

of reasoning may be inappropriate. Alternatively, one could question

the realism of Tiebout's assumptions.

The contribution of Edel and Sclar rests with their use of cross-

section data over consecutive census years. Unfortunately, the question

of Tiebout efficiency remains unanswered. This is due to either

econometric misspecification or the unrealistic assumptions of the








Tiebout model itself. Therefore, ie must be skeptical of both the

results derived and their interpretation in this model.

Oates was cognizant of the econometric problems which he faced.

He stated that his results should be viewed as an order of magnitude

rather than indicating a precise outcome. In his criticism of Oates,

Pollakowski cites three major difficulties, and each will be analyzed in

turn below. First, Oates' model may be seriously misspecified. Second,

there is the possibility of relevant omitted variables. Third, the

sample may reflect conditions which would increase the likelihood that

the Tiebout hypothesis would be validated.

Pollakowski questions the use of median family income in Gates'

model. Oates states that median family income serves as a proxy for

neighborhood and environmental amenities. However, Pollakowski asserts

that this variable artificially augments the explanatory power of the

regression. For example, two-stage least squares is properly uspd when

the stochastic right hand variables (T and E in this example) are

regressed on exogenous variables which are correlated with T and E

but uncorrelated with the error term. Since the error term most likely

contains the intangible quality characteristics of a community, the use

of median family income as an exogenous variable would add to rather

than eliminate the simultaneous bias in the equation. Moreover, one

could argue that a simultaneous equation system is required to eliminate

the bias of Oates' regressions. For example, the impact of inter-

governmental revenue is ignored in the model. Therefore, the expenditure

and tax variables should be fully specified. This issue will be dealt

with in section 2.2.

Second, Oates utilized per pupil educational expenditures as his

proxy for the level of public services. However, Pollakowski asserts








that this technique neglects otihe: components of the expenditure mix

which may also influence property values. In effect, while Oates

interpreted his results in terms of educational expenditures, he

neglected to specify the relationship between education and other public

expenditures. This specification error (the omission of relevant

variables) will bias the coefficient of the education expenditure

variable. The magnitude and direction of the bias will depend on the

degree of correlation between the specified and omitted variable and the

importance of the omitted variable in the regression. This can be

denoted as: i. = i + a.. B. where


8. = the estimated coefficient of the education variable
1

.i = the estimated coefficient of the education variable with

the omitted variable included in the regression

a.. = the coefficient obtained by regressing the omitted variable

on the education variable

B = the coefficient of the omitted variable

Therefore, Pollakowski states that Oates' interpretation of the results

is valid only if other public services are not capitalized, and if the

output of other public services is unrelated to the provision of

education. Edel and Sclar suggest that the former may be realistic.

However, the latter assumption is certainly not viable.

Finally, Pollakowski argues that Oates' sample produces biases

of its own. For example, the Tiebout hypothesis assumes that mobility

is not restricted in any way. However, although this may be valid for

suburban communities, it is not for the poor residents of the central

city. Therefore, Oates' choice of residential suburbs for his sample

is likely to produce results which would seem to verify the Tiebout









hypothesis. Pollakowski states that this verification is valid only

for the particular sample selected, and it is not applicable in a

general context.

Pollakowski specified a model which incorporated these criticisms

but yet was analogous to Oates' study, and it was tested in the San

Francisco Bay area. His results suggest that extreme caution must be

used in the interpretation of the estimated coefficients. However, this

caveat was also made by Oates in his study. Therefore, although

Pollakowski was able to elucidate some of the deficiencies of the Oates

model, he failed to provide a method to improve it.

Oates' reply to Pollakowski was somewhat superficial. Admitting

that the omission of other public expenditures did produce biased

estimates, Oates reformulated his regression to include a variable for

a composite public goods and services other than education. However,

Oates defended his use of median family income by stating that this

measure is suitable as a proxy for community intangibles, particularly

since Pollakowski failed to provide a more reasonable measure.

This debate misses the point. The determinants of public expen-

ditures, taxes and property values must be specified within the frame-

work of a simultaneous equation system. Since this was not done, Oates

is quite correct in qualifying the results of his model. Although

Tiebout forces may indeed be realistic, the degree to which they operate

cannot be determined on the basis of Oates' results.

It seems clear that testing for the presence of capitalization

represents at best only an indirect means of depicting the movement

of households which is implied by the Tiebout hypothesis. Therefore,

it is more plausible, a priori, to develop a model in which fiscal









variations are more clearly dev-eoped, and in which residential location

is determined by such variations. The following studies are based on

this point.

Aronson and Schwartz

Aronson and Schwartz state that the purpose of their paper is to

prove that a Tiebout equilibrium is dynamically unstable. This results

from two factors. First, they argue that local taxes are based on

income and wealth, and therefore, they do not represent a true benefit

tax. Second, since there is an unequal distribution of income and wealth

across communities, a motive exists for jurisdictional mobility which

may be independent of an individual's tastes and preferences in terms

of local public goods and services. Essentially, this reasoning is

similar to that developed by Hamilton and Hirsch and Margolis, who

found that in the absence of zoning restrictions, there is an incentive

for the poor to migrate to areas with a higher tax base. According to

Aronson and Schwartz, an individual will receive a positive fiscal

residuum (benefits minus costs) in community i if his personal income

is less than the per capital income of community i.

In terms of fiscal variables, the individual will try to maximize

his fiscal residuum. It is assumed that taxes are based on income.

Therefore migration will occur if the following condition holds:


AE > Y At where
x

AE = difference in two communities' per capital expenditures

Yx = personal income of individual x

At = difference in two communities' tax rates

Indifference with respect to location will occur when AE = Y At.
x








Therefore, a boundary line on th~l~i migration is 1/Y with the slope

At
given by -E. This slope approaches zero for those with high incomes

relative to the community average, and these individuals will have

incentive to relocate in any community which has a lower tax rate.

Conversely, this slope will approach infinity for the poor, and they

will relocate (assuming costless moves) in a community with higher per

capital expenditures.

Equilibrium in this model would result when FRxi = FR ... =

FR where FR is the fiscal residuum. This condition can only hold
xz'
when tax rates, expenditures and per capital income are equalized across

all communities. However, since income is not equally distributed,

fiscally induced migration is likely to result in a widening of these

disparities. For example,if a relatively poor migrant enters a community,

then per capital expenditures would fall unless taxes are raised.

Accordingly, the same result would occur if a relatively rich individual

migrated away from the community. Therefore, a stable quasi-equili-

brium can exist when the following restrictive conditions hold:

(1) only the poor are permitted to migrate.

(2) no vacant land exists.

(3) fiscal zoning is prohibited.

In their empirical analysis Aronson and Schwartz divide communities

into potential origins and destinations. A destination community is

defined as one which offers either higher per capital expenditures at an

equivalent tax rate or equivalent per capital expenditures at a lower

tax rate. Therefore, each town is an origin town, and potential

destinations were determined by calculating the effective tax rate, per

capital expenditures and thus the fiscal residuum for all communities.

Their fiscal maps were computed for the census years 1950-70.








If the hypothesis is correct, then, ceteris paribus, the population

of destination towns should increase relative to their origin towns.

The result was determined by comparing the percentage change in the

population of origin communities over a ten year period with that of

destination towns. In the interval 1950-60 approximately sixty-nine

percent of the migration went in the predicted direction. This

increased to eighty-nine percent for the years 1960-70. Therefore,

Aronson and Schwartz conclude that fiscal variations are important in

the determination of residential choice within an urban area.

There are two major weaknesses in this study. First, the fiscal

residuum does not deal with the expenditure mix of a community.

Theoretically, the mix of publicly provided goods could change substantially

without altering an individual's fiscal residuum. Second, this model

ignores all other determinants of locational choice. For example, it

was previously discussed that relatively wealthy communities can provide

a given level of services at lower effective tax rates. It can also be

expected that neighborhood amenities are closely correlated with the

income of a community. Therefore, separating the effects of fiscal

variations and other community characteristics with respect to locational

choice are impossible within the framework of this model.

Bradford and Kelejian

A more sophisticated econometric approach is taken by Bradford

and Kelejian. Since their model seeks to explain the determinants of the

middle class exodus to the suburbs, it is relevant to the Tiebout

hypothesis. Specifically, Bradford and Kelejian found that fiscal

surplus differentials are important in explaining middle class location.

Moreover, their model suggests that a degree of income segregation would









result from this process. The mi ,dJle class will migrate to the suburbs,

and the poor will be locked in a deteriorating central city.

Bradford and Kelejian hypothesize that the movement of middle class

families to the suburbs is a "cumulative flight phenomenon." Therefore,

a cycle is established by the increasing concentration of poor in

the central city, middle class migration and the increased fiscal burden

on those middle class families remaining in the central city. This

implies that the incentives for migration will be increasing over time.

Bradford and Kelejian used cross-section data from the 1960 census

year, and the sample consisted of eighty-seven of the most populated

SMSA's in the country. Furthermore, they define the urban fringe

(suburbs) to be the portion of land within the urbanized area which is

outside of the central city boundary. The specification of the model

is:

MC
i PC20-
S= f(MFI, CONPOP, MFISC, F6MF5, -) where:
MU. POPC
i T-10 T-3


MC.
__ = middle class density in the central city
MU.

MFI = median family income in the urbanized area

CONPOP = population density in the urbanized area lagged
T-10
ten years

MFISC = net fiscal surplus received by middle class families
T-3
in the central city lagged 3 years

F6MF5 = a measure of the relative size of the central city

to the urbanized area from 1950-60

PC20-
= percentage of poor in the central city
POPC









The equation was estimated with Ltw-stage least squares, and MFISC

was endogenous within the system.

Of central importance in this model is the role of the middle class

fiscal residuum. Since this variable was significant and had the

appropriate sign, Bradford and Kelejian are able to conclude that income

redistribution efforts by central cities are self-defeating. Further-

more, they state that reductions in central city poverty could be

expected to lure middle class families back to the central city.

This model is deficient in several respects. First, historical

concentrations are used as a proxy for "natural" geography and the central

city infrastructure. However, Bradford and Kelejian ignore the location

of industry, arguing that the same determinants of residential location

will determine job location. This is rather questionable reasoning.

The decentralization of jobs may be the result of changing production

functions of firms (land intensiveness) or of cost differentials (less

expensive office space). Therefore, job location may represent an

omitted relevant variable. Second, although the model does contain a

variable for the relative size of the central city to the urban area,
MS/POPS
a more reasonable measure of middle class density could be
MC/POPC'
A density index such as this may be more desirable because it would

indicate middle class concentrations in the central city relative to

the suburbs, rather than just a percentage. Moreover, it could better

account for the problems of central city size. Third, the fiscal residuum

(MFISC) is based on questionable assumptions. Implicitly, Bradford

and Kelejian assume a constant marginal utility of government expenditures

across all income classes coupled with a proportional tax for all non-

poor families. However, they assume that a nonpoor family in the city

pays 2.5 times as much taxes than a poor family. Therefore,








MFISC government Expend i res 2.5 (Locally generated revenues)
Total Population poor + 2.5 (# non-poor)

This measure is inadequate for two reasons. First, it is based on

inspection rather than economic theory. Bradford and Kelejian use

Gillespie's (Musgrave, 1965) estimates of tax-expenditure incidence

which is based on 1960 income data. Their multiplicative measure (2.5)

is extremely arbitrary in the sense that it is based on an average

nonpoor family. The failure to differentiate between middle and upper

income groups introduces a bias in terms of the income distribution in a

particular urban area. Second, a more appropriate measure would relate

the fiscal residuum of central city middle class families to that in

the suburbs. It is this differential which is the incentive for

migration, and not the relationship of MFISC and the fiscal residuum

for the poor in the central city only.

A fourth criticism is that Bradford and Kelejian state that race

is not a significant determinant of middle class location. However,

using the same data and sample, Parvin (JPE, 1975) introduced the

percentage of nonwhites as an independent variable, and it.was significant

in the regression. Therefore, Parvin states that the scarcity of

segregated areas in the central city is likely to increase the flight

of the predominantly white middle class.

Despite these criticisms, Bradford and Kelejian do present results

which are consistent with hypotheses previously discussed. First, income

redistribution is an inappropriate task for local governments to engage

in. Second, fiscal variations within a metropolitan area are likely to

produce income segregation. Therefore, this study represents an important

contribution to the verification that Tiebout forces do indeed operate

in urban areas.








Haurin and Tolley

Haurin and Tolley attempted to explore the spatial and welfare

implications of a fiscal externality within a metropolitan area.

They utilize the phrase "fiscal externality" in the context of a

distortion between benefits received and taxes paid with respect to

public services. Their model is based on Hamilton, who argued that

efficiency in the public sector is achieved in the suburbs but not in the

central city. This result rests on the assumption that the property tax

is a head tax in the suburbs, but that it carries an excess burden in the

central city. For this to occur, the income of the residents for the

city and suburbs must be heterogeneous and homogeneous, respectively.

This distortion represents a violation of horizontal equity.

Haurin and Tolley develop a rather sophisticated mathematical

exposition to analyze the welfare costs of the distortion cited above.

First, they specify an individual utility function of housing, public

goods and a composite private good. The budget constraint includes

transportation costs, whichincrease with distance from a CBD. Each

individual consumes the same amount of the public good, but the tax-

price will vary because the public good is financed through the property

tax. Second, a Cobb-Douglas production function (land and capital)

for housing is specified, and a rent-bid function is derived. Next, the

demand for housing is assumed to be a function of income and its price,

and the price contains the capitalization of the fiscal variation

between the central city and the suburbs. With respect to Hamilton's

model, this is equivalent to a minimum zoning requirement that exists

in the suburbs but not in the city. This is also consistent with the

assumption of Bradford and Kelejian that the rich pay more than the

poor for public services in the central city.









Although the mathematics will niot be reproduced here, the format

described above allows Haurin and Tolley to evaluate the distortions in

the housing and public service sectors. Using simple single-equation

OLS techniques, they obtained estimates for the income elasticity of

demand for housing, public services and travel costs. These values are

used to solve the mathematical model, and the following conclusions

were reached:

(1) The distortion in the property tax creates a net loss to

the rich in the city. Therefore, they have incentive to move

to the suburbs.

(2) The distortion in property taxes also results in a dis-

equilibrium in the central city housing market.

(3) The periphery of the urban area is extended excessively.

(4) This welfare loss can be reduced by the creation of a

metropolitan government. In addition, if the central city

is more industrialized than the suburbs, then the welfare

loss will be further reduced.

These results are consistent with those obtained by Hamilton and Bradford

and Kelejian.

The analysis of Haurin and Tolley contains many simplifying

assumptions, such as the CBD, the use of a pure public good and the

property tax as the sole source of revenue. It is apparent that the

key to the model rests on the assumption that all upper class households

should locate in the suburbs. In order to justify this, Haurin and

Tolley specify a rent-bid function where the rich will live in the

suburbs if:

[o + ty] > [0 + t
Y Y Y 1
1 2








where

t0 = fixed transportation costs

ty = marginal time cost of travel (a constant)

Y1 = the poor

Y2 = the rich

61 = income elasticity of demand for housing

Therefore, for 61 > 1, the condition of complete segregation by income

and jurisdiction will hold.

The assumption that ty is constant is not justified because it

makes the rent-bid function linear with respect to transportation costs.

Numerous studies such as Muth (RSA Papers, 1961) prove that the rent-bid

curve is nonlinear with respect to transportation costs. This assumption

is clearly erroneous, and it casts considerable doubts on the resultsof

Haurin and Tolley. In Chapter 3 it will be shown that it is optimal for

the rich to locate in the city under certain conditions. Although

Haurin and Tolley's results are interesting, their model reinforces the

restrictiveness of the conditions required for Tiebout efficiency.


2.2 Fiscal Analysis of Metropolitan Areas

2.21 Introduction

Coinciding with the post-war decentralization of urban areas, one

of the most active areas of research in public finance has been the deter-

minants of local government expenditures and revenues. The literature

can be roughly classified into the following two categories. First, the

bulk of the empirical research has sought to estimate the determinants of

particular publicly provided urban services. Examples would include

police and fire protection, sanitation and highways. The methodology

employed in these studies was primarily single-equation multivariate








models, and per capital expenditure., were used as the endogenous variable

in most cases. Because of the rather simple econometric techniques

employed, most of the debate has centered on the proper specification of

these selected local services, using primarily cross-section data.

Prominent studies in this area would include Brazer (1959), Woo Sik Kee

(NTJ, 1965) and Hirsch (1973), though this list is practically limitless.

In addition,there have been attempts to estimate aggregate expenditure

functions within this single-equation framework. Illustrative of these

efforts is Hansen (Restat, 1965).

The second major category of research is comprised of more complex

simultaneous equation systems. For the most part these studies have attempted

to estimate aggregate expenditure functions. For example, since measures

of locally generated revenues are both determinants of expenditures as

well as partially determined by the level of expenditures, a second

equation for local revenues must be specified to eliminate this simultaneous

equation bias. A model of this nature was developed by Henderson (Restat,

1968). Unfortunately, the addition of a local revenue equation is not

sufficient by itself. The tremendous growth in non-local revenues from

state and federal sources suggests the need of a third equation to complete

the simultaneous system. Since non-local revenues are a component of

local government expenditures, it is likely to be correlated with the

error term in the expenditure equation. Therefore, non-local revenues

should be treated endogenously if the estimated coefficients are to be

unbiased and consistent. Horowitz (SEJ, 1968) has developed a model which

incorporates this method.

A proper estimation procedure for local expenditures and revenues is

crucial to this study. It is hypothesized that residential location

decisions are influenced ceteris paribus by fiscal variations between

central cities and their suburbs. Therefore, the fiscal variables must








be properly specified so that ac:ir te estimates of these Tiebout forces

can be obtained. An example where improper procedures were used was

Oates' model. One should recall from the analysis in section 2.14 that

Oates stressed that his results represented only an estimate of magnitude

rather than a precise outcome. Through the use of a simultaneous equation

approach, it is hoped that the results in this study will be somewhat

more sharply defined.

The format of this section will be as follows. First, there will

be some discussion of single equation methods of estimation. Although

this study will be concerned with aggregate expenditures, many of the

specification problems have been analyzed with respect to selected

local functions. Second, the use of simultaneous equation systems will

be discussed. The emphasis here will be on proper econometric techniques

in a multi-equation system. Finally, potential econometric problems in

this study will be addressed.


2.22 Single Equation Methods

Specific Functions

The analysis of single equation models for specific government

functions will draw heavily from a study by Weicher (NTJ, 1970).

Weicher states that previous studies of determinants of local govern-

ment expenditures can be grouped into four categories:

1. the effects of political fragmentation in a metropolitan area.

2. the possibility of economies of scale in public goods provision.

3. the relationship between local expenditures and nonlocal revenue.

4. the effect of changes in fiscal capacity on local expenditures.

Weicher further points out that these categories are quite interrelated,

and this is readily apparent particularly between the first and second

topics as well as the third and fourth. Finally, Weicher suggests that








these studies are deficient in the sense that they do not consider what

he terms "taste" and "service" conditions. The former refers to

demographic and socioeconomic conditions, while the latter is viewed

as those factors affecting input requirements. Weicher states that

the inclusion of these variables into the equations for police and

fire protection, sewers and sanitation and highways will provide

insights into two major problems of cross-sectional single equation

studies: multicollinearity and interstate differences in local

responsibility.

Hirsch

Rather than discuss each of the studies cited by Weicher, a

pioneering study by Hirsch (Restat, 1959) will be compared to a model

specified by Weicher. The central focus of Hirsch's work was related

to the first and second categories cited above. That is, Hirsch sought

to determine whether or not scale economies exist in the provision of

urban services. This factor has obvious implications for the optimal

size of local governments in terms of pure efficiency considerations.

For police protection Hirsch specified the following equation:

x1 = B + X + 2 + 3X3 + ... + xo
11 0 1X2 2X2 3X3 1010

where

X1 = per capital total costs of police protection

X2 = nighttime population

X3 = total miles of street

X4 = nighttime population density per square mile

X5 = percentage of nonwhite population

X6 = percentage of nighttime population under 25 years of age

X7 = combined receipts of wholesale, retail and service

establishments








X8 = number of wholesale, rtLail and service establishments

X9 = index of scope and quality of police protection

X10 = average per capital assessed valuation of real property

With respect to Weicher's taxonomy, Hirsch's model does not include

independent variables for the degree of political fragmentation or

for nonlocal revenues. However, this is reasonable given that Hirsch

was concerned with downtown areas, and that nonlocal revenues were not

significant at that time.

Using ordinary least squares, Hirsch found that only X5, X6, X9 and

X10 were significant at the .05 level. Since the R2 = .90, this

suggests the presence of multicollinearity, and accordingly, the

coefficients would have large standard errors and low T-statistics.

Furthermore, X7 and X10 not only impact on police costs, but they also

reflect demand considerations in terms of ability to pay. Finally,

Hirsch's scale proxies, X2 and X3, were not significant. Although this

may be attributed to multicollinearity, Hirsch concludes that scale

economies for police protection do not exist.

Weicher

Alternatively, Weicher's equation for police protection contained

a total of twenty-one variables from a sample of 206 SMSA's and included

proxies for each of the six categories. Of the twenty-one, twelve

variables were significant at the .05 level, and they are arranged in

2
their appropriate category below. The R = .73 for the regression,

which is somewhat lower than that for Hirsch. However, city population

was not significant, and Weicher interprets this as support for the

lack of economies of scale in the provision of police protection.









Taste
proportion of foreign stock
proportion of nonwhite
proportion of young persons

Nonlocal Revenue
per capital intergovernmental
revenue


Table 2.1

Service Fiscal Capacity
density income
average size of unemployment
manufacturing retail sales

Political Fragmentation
central city's share of SMSA
manufacturing


Weicher's regression for police protection is illustrative of

several points. First, he points out multicollinearity is an inherent

problem with such models. However, Weicher defends himself in the

following manner. He argues that the use of additional variables,

which are not significant in the regression but correlated with other

studies to become significant. This represents a rather curious method

of econometric modeling. Furthermore, the presence of multicollinearity

precludes any forthright examination of the magnitude of the estimated

coefficients. Second, the excessive number of independent variables

makes any interpretation of them exceedingly precarious. Therefore,

in his extended efforts to expand the determinants of specific local

expenditures to include taste and service conditions, Weicher has

failed to respond to econometric difficulties which are prevalent in

this area of research. Rather, he has reinforced them.



Hansen

Although models of aggregate expenditures within a single equation

framework are relatively rare, one study will be analyzed in this

section. Hansen attempts to specify equations for aggregate








expenditures, social services and hle urban infrastructure. lie designates

these as overhead capital (OC), social overhead capital (SOC) and

economic overhead capital (EOC) respectively. The criticisms which are

cited below will be directed toward improper econometric techniques

in this study. However, his theoretical contributions will receive

only superficial treatment.

Hansen's division of public services is done in terms of the degree

of horizontal and vertical integration. Services classified as SOC

include education, fire and police protection, health and welfare and

various amenities. Therefore, SOC can be viewed as having economies of

scale which are exhausted at relatively low population levels.

Alternatively, EOC is composed of such things as transportation systems

and utilities. These services are primarily oriented to direct productive

activity, and they are viewed as having relatively large economies of

scale. The classification of SOC and EOC has been supported by Hirsch

in the two studies cited previously.

A significant problem which is encountered by Hansen concerns his

use of cross-section data. Since Hansen's endogenous expenditure

variables include capital expenditures, one could argue that time-series

data would be much more meaningful due to the lumpiness of public

investment. Hansen tries to avoid this difficulty by utilizing the

mean values of per capital capital outlays over a five year period as the

endogenous variables. Although this certainly represents an improvement

over one observation period, there is no a priori justification for

this particular time span, and it should be regarded as strictly arbi-

trary. One could expect substantial difficulties to arise with respect

to older, declining urban areas compared to those which are relatively

new and developing.








Hansen hypothesizes that SO'" is determined by static variables such

as absolute population and the density of industrial employment, whereas

EOC is assumed to be sensitive to the growth rates of these variables.

In other words, EOC is the result of population growth which exceeds the

capacity of a service. The following regressions were estimated by

ordinary least squares:

OC = 458 + 28.1(AH/L) 12.3A + 29.7(AB/B)

+ 31.8C + 88.1(AH/H) R2 = .58


SOC = -196 + .08(P/L) + 22.7(AH/L) + 28.0C

+ .58(I/P) R2 = .569


EOC = 699 + 80.4(AP/P) + 20.7(AB/B)

+ 40.1(AH/H) R2 = .267

where OC, SOC and EOC = money outlays,

AH/L = change in housing density during the study period

A = percent of labor force in agriculture

AB/B = percentage change of built-up land

C = accessibility index

AH/H = percentage change in the number of houses

P/L = population density

I/P = industrial employment per 1000 population

AP/P = percentage change in population

The low coefficient of determination suggests that EOC is extremely

sensitive to the lumpiness of capital outlays which was previously

discussed. The argument can be made that EOC is particularly dependent

on a minimum demand threshold. Therefore, heteroskedastic disturbances

may be rather significant. However, Hansen does not appear to test for

heteroskedasticity. In addition, multicollinearity is likely to be








present between the housing and p i ulation variables, but again, Hansen

does not discuss this point.

This analysis suggests that capital expenditures should be deleted

from cross-section studies. Furthermore, it also points out the need

for a simultaneous equation approach to the problem. For example, EOC

and OC are determined by rates of growth and development. However, one

could argue that growth and development are determined by the capital

infrastructure of an urban area, a process generally referred to as

economies of agglomeration. Thus, it is apparent that Hansen's metho-

dology has several weaknesses for the study of public expenditures.


2.23 Aggregate Expenditure Functions and Multiequation Models

Two models will be analyzed in this section. First, Henderson

employed a two-equation model to explain local expenditures. The

strengths and weaknesses of this model will be explored in depth, and it

will be shown that it is inadequate because it treats nonlocal revenues

as an exogenous variable. Second, Horowitz developed a generalized

model for state and local government expenditures. In this model,

nonlocal revenues are treated endogenously within a simultaneous equation

framework, and the objections cited with respect to Henderson are met.

Henderson

Henderson utilizes a social welfare function as the theoretical

foundation for the determinants of local government expenditures.

Although the model which is developed is somewhat simplistic in terms of

the specified predetermined variables, it contains both an expenditure

and a tax equation. Therefore, by the use of two-stage least squares,

Henderson is able to eliminate inconsistent and biased coefficients which

would result from the correlation between the expenditure and tax








variables. It has been argued thlit expenditures and taxes represent a

recursive rather than a simultaneous system (Vincent, 1971). Although

it is possible that available revenues determine the level of expen-

ditures in any one year, the relative elasticities of local expenditures

to local revenues indicate that a simultaneous system is more appropriate.

Henderson's social welfare function, which he describes as a

community's ordinal collective welfare, takes the form of:


(1) W = (a0 + alY + a2R + a3P) In G + X

where

Y = per capital income

R = per capital revenue from federal and state sources

P = population

X = per capital private expenditures

G = per capital government expenditures

The determinants of local revenues are specified as:


(2) T = B(G R)

Therefore, taxes are assumed to be a fixed proportion of the difference

between per capital expenditures and per capital revenues from other

sources (0 < B < 1). Thus, per capital local debt can be estimated as

the residual: D = G-T-R = (1-B)(G-R). If B = 1, then there is no

public debt. By substituting the identity, T = Y-X into (2), the

community's budget constraint can be expressed as:

X + SG = Y + BR

Two assumptions are quite crucial at this point. First, although private

savings does not enter into the model, the assumption that the savings

rate does not vary across communities is a sufficient condition for








the identity, T = Y-X, to hold. second it is assumed that local

representatives maximize G and X within the community.

The Lagrangian expression takes the form of:


(4) L = (aO + alY + a2R + a3P) In G + X

A(X + SG Y BR).

Setting the partial derivatives equal to zero yields:

(a0 + alY + a2R + a P)
aL/aG = AB = 0
G

aL/aX = 1 X = 0

aL/DA = X + SG Y 8R = 0,

and the first order conditions for maximization are:
a a a2 a3
s0 1 "2 "3
(5) G Y + a R + a P


(6) X = Y B(G R)

The Lagrangian multiplier is constrained to unity.

The equations in stochastic form are:

a0 a1 a2 a3
(7) G. =- + Y + + a R. + P. + u.


T. = 8(G. R.) + V.
1 1 1 1

Since Henderson views R as exogenous in the model, the expenditure

equation is estimated with ordinary least squares. However, due to the

inclusion of G in the tax equation, two-stage least squares must be

used. Moreover, the intercept term in the tax equation is constrained

to zero.

Henderson divides his cross-section sample into metropolitan and

nonmetropolitan counties in order to gauge the impact of marginal changes









of the exogenous variables on loc-,l expenditures, private expenditures,

local taxes and local debt. The strengths of his model are twofold.

First, the use of two-stage least squares eliminates the probable

simultaneous bias between the expenditure and tax variables. Second,

his model contains a great deal of insight, particularly with respect

to local debt.

However, there are three particular drawbacks. First, it can be

argued that a social welfare function is an inappropriate tool of

theoretical analysis. This is a point made by Arrow (1963) and

Samuelson (QJE, 1956). Second, the coefficients of determination of

Henderson's regressions were rather low, .65 and .55 for the expenditure

equations and .39 and .38 for the tax equations. This may result from the

aggregation of the demographic (population) and income variables. It

would appear that the disaggregation of these explanatory variables

would increase the explanatory power of the model.

The most important criticism, however, is the use of nonlocal

revenues as an exogenous variable, and misspecification is suggested

by the large coefficients for R. In addition, it seems more plausible,

a priori, that R and G would be jointly determined by other exogenous

variables. For example, counties with higher income are likely to be

located in states with higher income.. This would probably result in

higher state tax collections, and thus, larger per capital R from state

sources. From Henderson's results, the likelihood of misspecification

can be amply supported, and this conclusion can be derived as follows.

From equation (1)








Z dC dX
dW/dY = a In G + d-
1 G dY Y

Z dG dX
dW/dR = a2 In G + d + where


Z = (O0 + alY + a2R + a3P)

From (5), it may be seen that Z = G/B. Therefore, Z/G = 1/B. From

the total differentiation of (5) and (6), it is possible to determine

dG/dY, dX/dY, dG/dR and dX/dR. Substituting the appropriate values in the

above equations yields:

dW/dY = al In G + (1/6)2 al + (1-a1)

dW/dR = a2 In G + (1/8)2 2 + (B-a2)


dW/dY =10.26 metropolitan 1.42 nonmetropolitan

dW/dR = 0.33 metropolitan 6.28 nonmetropolitan

dW/dR
Therefore, dW/d = 7.4 (metropolitan), 4.4 (nonmetropolitan)


This is a rather curious result, given that R is more likely to be

constrained (i.e., categorical aid) relative to Y. With full fungability

one would expect dW/dR to be equal to dW/dY. However, any restrictions

placed on R would seem to indicate that dW/dR should be less than dW/dY.

Thus, R should be viewed as endogenous within Henderson's model, and a

third equation should be added with R as the dependent variable.

Horowitz

A much more satisfactory methodology was developed by Horowitz,

who formulated a simultaneous equation system for the determinants of

both state and local government expenditures. Therefore, it represents

a more generalized model with the stated purpose of analyzing interstate

differences in state and local per capital expenditures. Horowitz

also specifies a model for the number of state and local governmental








employees per 10,000 population. howeverr, this model will be ignored

in the following discussion because the emphasis is on the determinants

of expenditures only.

Although Horowitz developed a number of models for per capital

expenditures, the one which yields the best results is specified as:


E = f(I,T,G,Fi), i = 1,2

T = f(B,M)

G = f(I,M)

Fi = f(I, 1/P, E), i = 1,2.

In reduced form the estimated expenditure equation is:


E = -540.12 + .141 + 2.27T + 624G + 1.01F1 R2 = .86

E = -549.43 + .141 + 2.36T + 600G + 1.26F2 R2 = .86

where

E = per capital expenditures

I = per capital income

T = Oppermann's measure of tax effort

G = distribution of income (Gini coefficient)

B = taxes paid per $1000 of personal income

M = manufacturing employees as a percent of total employees

in the state

1/P = inverse of population

F1 = per capital total revenue from the federal government

F2 = per capital grants-in-aid

Two-stage least squares was utilized to estimate the expenditure

equations, with the endogenous variables of each being replaced by

their first-state estimates. One surprising result of the analysis is

that all of the variables are significant at the .01 level with the







exception of G, the distribution of income. Horowitz justifies this

phenomenon by stating that greater income inequality may result in

a lesser demand for some goods and services, while being associated

with a larger demand for others (poverty-related services). Thus, the

conflicting effects would offset one another. One minor objection to

this study is that the expenditure variable is per capital total

expenditures. This implies that capital outlays are included, and

the discontinuity of investment problem (similar to Hansen's difficulty)

may bias the results. Second, the use of 8 as a determinant of tax

effort may introduce a simultaneous equation bias.

The strength of this model refers to the treatment of federal grants,

which is endogenous in the system. Horowitz points out that federal

matching grants (e.g. highways) are a major component of state and

local expenditures. This would also be true for such intergovernmental

transfers as public welfare which do not require matching funds.

Therefore, it would appear that federal grants and state and local

revenues are mutually determined by other exogenous variables. Thus,

Horowitz supports the conclusion reached in the criticism of Henderson's

model. Within this framework both nonlocal and local sources of revenue

and local expenditures are determined simultaneously, and the estimated

coefficients of the reduced form expenditure equations are unbiased and

consistent. This econometric procedure is clearly superior to those

previously discussed.


2.24 Primary Conclusions

The purpose of this section has been to focus on the major empirical

problems faced in the study of local government fiscal determinants.

First, Weicher's study was illustrative of difficulties encountered with









the specification of local public expenditures and the interpretation

of the independent variables. However, the introduction of taste and

service conditions by Weicher would appear to be particularly relevant

to the determinants of aggregate expenditures which will be focused

upon in this study. On the other hand Weicher did little to rectify

the problem of multicollinearity in such studies. In fact he appeared

to defend improper econometric practices.

Second, it has been clearly demonstrated that a multi-equation

system is required for the determinants of aggregate expenditures.

This is due to the existence of a simultaneous bias between expendi-

tures and revenue. Furthermore, revenues from local and nonlocal

sources must be estimated separately. This results from the growing

trend in intergovernmental revenues.

With respect to this study, a simultaneous equation system will

be developed which corresponds to the needs previously discussed. How-

ever, problems may arise due to the use of cross-section data in this

study. The previous analysis suggests that the discontinuity of public

investment is incompatible with cross-section data. Therefore, capital

outlays will be eliminated from the aggregate expenditure measure.

The separate estimation of city and suburban expenditures and revenues

is not expected to pose a serious difficulty.















CHAPTER 3

A THEORETICAL MODEL OF RESIDENTIAL LOCATION

3.1 Introduction

Prior studies on the determinants of residential location can be

divided into two categories. First, some of the efforts have been

directed to the impact of accessibility on location, with accessibility

being defined in terms of the journey to work. Examples include

Kain (RSA Papers, 1962), Muth (RSA Papers, 1961; 1969) and Fisher and

Fisher (JRS, 1975). The second category has extended these accessibility

models to include the effects of neighborhood quality on residential

location, and they are represented by Harris et al. (Restat, 1968),

Granfield (Applied Econ., 1974), Jackson (1975) and Stegman (JAIP, 1969).

These studies will be briefly discussed in the following section.

In Chapter 2 it was seen that the Tiebout hypothesis has recently

been converted into a theoretical and empirical framework for determining

the impact of fiscal variations on residential location. Therefore, the

purpose of this chapter is two-fold. First, a model will be developed

which will demonstrate the impact of location on individual utility.

It will therefore extend the theory of residential location by incor-

porating fiscal variables, which are assumed to be sensitive to spatial

influences, into the models cited above. Second, this chapter will

analyze the utility maximizing behavior of households. Different

income groups will not respond to the same incentives in a spatial

framework, and this is demonstrated by the existence of a rent-bid

curve which portrays the economic rents that accrue to each location.








This traditionally takes the for:: of a negative exponential curve

which peaks at the core of the city (the node) and falls to zero at the

agricultural land on the periphery. The rent-bid curve represents an

outcome of the competitive bidding for sites, and the effects of accessi-

bility, neighborhood quality and fiscal variations can cause shifts,

subnodes and discontinuities in the rent-bid curve. These effects will

result from the impact of location on individual utility, and they will

be explored in depth.

The following section will briefly discuss prior studies on

residential location. Next, the individual utility function will be

specified and analyzed. This function will incorporate the government

sector into the traditional residential land use models, which are

based primarily on accessibility. The last section will summarize

the major findings from the theoretical model, and these conclusions

will be related to the literature reviewed in Chapter 2.

One additional point should be made. The following model ignores

the incentives which have brought about the decentralization of firms

in metropolitan areas. Clearly, firms respond to similar forces as

households: accessibility to markets and suppliers, and fiscal

advantages. The decentralization of firms and households can be viewed

as mutually supportive, and the rent-bid curve would be affected by the

actions of both. However, the determinants of the location of firms

will not be analyzed in this study.


3.2 Discussion of Previous Studies

Accessibility, an obvious determinant of residential location, can

be defined in terms of the journey to work and the proximity to shopping

and recreation facilities. This factor has received the most attention








in both theoretical and empirical ~rsearch. Increasing accessibility

has a positive effect on utility by reducing commuting costs, ceteris

paribus, in the individual's budget constraint.

Early studies, such as those of Kain and Muth,viewed the journey

to work as the most important determinant of location. However, these

efforts made the restrictive assumption that employment was concentrated

in a CBD. The rent-bid curve thus depended primarily on income and the

substitution of commuting expenses for household expenditures.

More recent efforts have incorporated the decentralization of firms

into the models. Goldberg (JRS, 1970) developed an analytic model to

explain the intraurban location of manufacturing industries. His model

verified a hypothesis stated by Vernon (1960), who argued that the

location of manufacturing plants depends on the relative economies or

diseconomies of central city location. Since larger firms are able to

internalize many central city agglomeration economies, they are relatively

footloose and are more likely to locate outside of the central city.

Conversely, smaller firms are less able to internalize these external

economies and tend to remain in the central city. However, this model

was not empirically tested.

Alternatively, Fisher and Fisher employed econometric techniques

to analyze the decentralization of both firms and households. Using

a simultaneous equation approach, they found that employment and residen-

tial location are jointly determined. This reinforces the view that

the decentralization of firms and households are mutually supportive,

and it breaks away from the restrictiveness of a model which is based

on a CBD.

One of the basic assumptions of the accessibility models is that

the urban area is located on a homogeneous plain. However, this is









clearly not the case, and amenitici can be expected to vary widely from

one location to another. This will, in turn, affect the utility derived

from a specified location.

Harris et al. point out that if amenities were completely divisible

and could be produced at constant costs, then households would choose

location on the basis of commuting costs alone. Accordingly, the price

of amenities would be independent of location. It is unlikely, however,

that the condition of constant costs exists. For example, unique features

may endow locations with characteristics that cannot be easily reproduced.

In their empirical analysis, amenities are found to be a major component

of land value. Furthermore, the income elasticity of demand was in the

range which indicates that amenities are superior goods.

Granfield developed a three equation recursive model of residential

location. First, a budget for housing services is established. Second,

the housing budget as well as amenities and accessibility are used to

determine location in terms of distance from the CBD. Finally, the

budget and distance from the CBD determine housing type. His results

suggest that neighborhood quality rather than accessibility is the

dominant determinant of location.

Jackson (1975) extends the spatial theory of consumer behavior

developed by Muth (1969) to include neighborhood characteristics such

as pollution, racial composition and income status. Using the concept

of housing services, Jackson specifies a household production function

in which housing services are a function of land, structure and

neighborhood attributes. Jackson goes on to construct hedonic price

indices for housing services at different locations in a metropolitan

area (Milwaukee), which are based in part on neighborhood characteristics.








Stegman employs survey methV.,, and his conclusions are in contrast

with those of Kain and Muth. First, his survey suggests that urban

services and activities are no more accessible to inner city residents

than to suburban residents. This results from both decentralization

and the construction of expressways, which effectively reduce transpor-

tation costs. Second, suburban families are very concerned with neighbor-

hood quality. Therefore, he concludes that the tradeoff between

accessibility and neighborhood quality may not be valid. Suburban

households are able to have both according to Stegman's survey.

An obvious extension to the models discussed here is the.inclusion of

a fiscal sector. Just as accessibility and neighborhood quality will

vary with location, fiscal advantages will vary by jurisdiction.

Individual utility based on these characteristics will be developed in

the following section.

One major drawback to the comparative static analysis is that

housing is viewed in terms of a flow of services in one time period, and

housing as an investment good is ignored. For example, the argument can

be made that a home represents the primary asset of many households.

The household can be viewed as a firm which attempts to maximize its

net value over time, such as in Jorgenson's model (AER, 1963).

Accordingly, the household's future expectations with respect to location

will be an important determinant in terms of the city-suburb location

decision. If uncertainty is introduced, a risk-averse household may

be biased toward the selection of the relatively homogeneous jurisdiction.

Thus, a "switching model" between alternative locations would be

appropriate with time-series data. A limited dependent variable of a

similar nature was developed by Trost (1977), who analyzed the rent-

ownership decisions of households. Such a model would be effective








for estimating intertemporal loc;jiion decisions. However, this issue

is beyond the scope of this study.


3.3 Individual Utility and Residential Location

3.31 A Scenario

The purpose of the forthcoming model is to examine why people

reside in certain locations. Before proceeding with the mathematical

model, a graphic representation can clarify the analysis. First,

assume the simplest case where there.is no government, all economic

activity is located at the core and housing and neighborhood quality

are homogeneous. Furthermore, assume that there are only two income

groups. From Figure 1, it can be seen that the upper income group (Y1)

will occupy the most accessible locations, and the lower income group

(Y2) will reside only from a to b. Figure 1 is consistent with the model

developed by Muth.

Next, assume that office buildings and a shopping center are

located in the hinterland. This represents the decentralization of

retail firms and employment. As can be seen in Figure 2, the rent-bid

curves are no longer continuously declining from the core, and a subnode

is established at N. Retaining the previous assumptions, Y1 will reside

from the core to a and from b to c. Accordingly, Y2 would locate from

a to b and from c to d.

Finally, assume that two governments are instituted with a political

boundary at J. From Figure 3, two results predominate. First, the

rent-bid curves exhibit a discontinuity at J. Second, the Y1 income

group is primarily concentrated in the suburbs. This implies that

Y1 receives a fiscal advantage from locating beyond J. The central

question is: what caused the fiscal advantage?




I' /

















0







i~-4
j3
























r.r+



cn




















H
















00
k~Ci




'













































































































- --


























































































- ~- -- -








The initial stimulus to upper income suburban flight may result

from two conditions:

(1) Public services are normal goods.

(2) The rich are myopic.

Since the rich (Y ) were originally located in the central cities as

in Figure 1, the level of public services would be relatively high in

this jurisdiction, particularly with respect to social services, since

the poor are relatively small in number. The rich falsely assumed that

the number of poor would not increase. However, the inmigration of

the poor from the south to the central cities altered this situation.

The poor moved into the central city where inexpensive housing and

unskilled jobs were available, and it became advantageous for the rich

to move out. The burden on the rich was continually increasing in the

city, and a cumulative flight phenomenon was established. Improved

transportation modes, federal housing policies which encourage suburbs

and preferences to locate with one's "class" only reinforced this trend.

Therefore, the rent-bid curve for Y1 in the city would be declining

over time, whereas it would be increasing in the suburbs. The reverse

would be true for the poor (Y2). Although the scenario is rather

simplistic, it does offer some insight into how a residential

distribution such as Figure 3 could result.

It is apparent that the term "location must comprise several

meanings in the following utility function. With respect to accessi-

bility, it implies distance. However, neighborhood quality attaches

neighborhood amenities to specific locations. Finally, the concept

of fiscal variations implies that location can be defined as a specific

jurisdiction.









It is important to recogni.s,, however, that the discussion

deals with the "voting with one's feet" in the tradition of the

Tiebout model. One should recall that this model does not specify

how budgets and the mix of taxes and expenditures are established in

the first place. It seems to assume that budgets do not change, and

that voter-consumers will vote primarily through the mechanism of

mobility. In the real world it is clear that voter preferences for

fiscal considerations can be reflected at the polls and by other

means.

Clearly, a complex model should consider both types of voter-

consumer response, and it should include an explicit consideration

of the relative costs of responding to each. Voting with feet

involves moving costs, and voting at the ballot entails transactions

costs and costs associated with group dynamics. The utility function

developed below will concentrate on the migration aspect of voter-

consumer behavior. It is assumed that this mechanism is the most

efficient response for household to make, particularly for the middle

class. However, this restriction does not appear to be unreasonable

in view of the focus on this study.

Individual utility with respect to residential location will be

defined in terms of housing services a composite of private goods and

public goods. The concept of public goods used in this section does

not refer to Samuelson's definition of public goods; rather, it

encompasses those goods and services that are provided by local

governments.









Utility in this model will !,c subject to both a time and an

income constraint. Nelson (Urban Studies), 1973) suggests that

residential location can be explained, ceteris paribus, by examining

the land rent differences which will produce consumer indifference

among locations with different accessibilities. Traditional analyses

assume that rent differentials essentially compensate for transportation

costs at varoius locations in the urban area. Nelson points our several

difficulties with this method. First, accessibility is usually defined

with respect to one central location, normally the CBD. Second, the

number of trips to the CBD is assumed to be perfectly inelastic in

terms of costs per trip. Third, time costs as a component of travel

costs are ignored.

The latter criticism is an adaptation of a model developed by

Becker (Ec. Journal, 1965). With the addition of an effective time

constraint, the price of any good has two components: a money price

and a time price. Thus, the total price is equal to the money price

plus an opportunity cost which is equal to the loss of income from

not working while consuming the good. Although Johnson (WEH, 1966)

has argued that the time price should be evaluated at less than the

individual's wage rate, wage rates will be used in this model.


3.32 The Utility Function

For static analysis with certainty,a utility function of this

specification would appear as:

(1) U. = U.(X, H, G(k))

subject to:

wk = PXX + P (k, G(k) H + PG(k,H,wi) G(k)
X +H PG(k,H,wk) G








and

T = Z + tR(k) + tXX + tHH + tGG

where

Ui = utility of the individual in the ith income group

H = housing services

G = public goods

X = composite private good (including leisure)

= labor

k = location

w = wage rate

PH = price of housing services

PX = private good numeraire

PG = local tax price of public goods

tR = transportation time

T = total time allocation (24 hours)

tG = time cost of public goods

tX = time cost of private goods

tH = time cost of housing services

It should be noted that housing services refer to land, structure

and neighborhood attributes. To aid in the mathematical analysis,

H does not vary with k. It is assumed that housing services are

reproducible for an appropriate PH, which does vary with k. This

assumption requires that "natural" amenities are ubiquitous, which is

in contrast to the model of Buchanan and Goetz. However, it does not

detract from the goal of analyzing the impact of fiscal variations on

residential location. The ratio of government services to their tax

price is the measure of fiscal variation, and from this point on, it

will be referred to as FV. Finally, the tax price of public services







will vary by location, housing services (property tax) and income.

Substituting the second constraint into the first, and setting

up the Lagrangian expression yields:


(2) L = UiIX,H,G(k)] A{(PX + txw)X + [PH(k,FV) + tHW]


H + [PG(k,H,wk) + tGwlG(k) + wtR(k) wT} = 0.

Differentiating with respect to X, H, k and A gives the first order

conditions:


(3) IL
(3) = U X(P + t w) = 0




(4 L HaP
(4) H = UH- [(PH + tHW) + H -V FV'(H) + PG'(H)G(k)] = 0



(5) = UGG'(k) A[(PH'(k) + jV FV'(k)) + PG'(k)G(k)


+ G'(k)(PG(k) + tGW) + tR'(k)w] = 0



(6) = {(P + txw)X + (PH(k,FV) + tHwJH + IPG(k,H,wk)


+ tCw]G(k) + wtR(k) wT} = 0








Taking the total derivative of the first order conditions yields:


(7) UXdX + UHdH + UXkdk dX(Px*) = Ad(Px*)


(8) URdX + UHHdH + UHkdk dX(a) = Ad(a)


(9) UGXG' (k)dX + UGHG'(k) dh + UGGG'(k) dk


+ UGG"(k) dk dA(b) = Ad(b)


(10) -Px*dX [c]dH [e]dk = d(wT) + Xd(PX*)

+ H d[c] + k d[e]


where:

PX = PX + tXw

3P
a = [(PH + tHW) + H FV'(H) + P '(H)G(k)]

aP
b = [H(PH'(k) +- FV'(k)) + PG'(k)G(k)


+ (PG(k) + tGW) G'(k) + tR'(k)w]


c = [PH(k,FV) + tHW]


e = {[PG(k,H,wk) + tGW] G(k) + tR(k)w}


The second order conditions for utility maximization require that the

bordered Hessian be negative definite. Therefore, for the bordered

Hessian determinant, H =









UXX UXH UXk PX*

UHX UHH UHk -[a]
UGxG'(k) UGHG'(k) UGGG'(k)+ -[b]
UGG"(k)

-PX* -[c] -[e] 0


H2 > 0, and H3 < 0. Assuming that the marginal and cross-partial

arguments are positive, and that the second derivatives are negative,

then these conditions are met unambiguously.


3.33 Comparative Static Analysis

The purpose of this analysis is to determine why different income

groups may reside in different locations (as in Figure 3). The most

appropriate framework under conditions of certainty is to utilize

comparative static analysis. This method allows for an examination

of the income effects on housing services and location by income group.

Equations (7), (8), (9) and (10) in matrix form would appear as:

UXX UXH UXk PX* dX Xd(Px

UHX UHH UHk -[a] dH Ad[a]

UGXG'(k) UGHG'(k) UGGG'(k) -[b] dk Ad[b]
+ UGG"(k)

-PX* -[c] -[e] 0 dA Z


where

Z = -d(wT) + Xd(Px*) + Hd[c] + kd[e]

Using Cramer's Rule, it becomes possible to solve for dH and dK:







U Ad(P *) UXk -P *
xx X Xk X

dH UHX d[a] UHk -[a]
dH =
UGG'(k) Ad[b] UGGG'(k)+ -[b]
UGG" (k)
-PX* Z -[e] 0


D



UXX UXH Xd(P*) -PX*

UHX UHH Ad[a] -[a]
dk =
UGXG'(k) UGHG'(k) Ad[b] -[b]

-Px* -[c] Z 0

D

where D is the determinant of the coefficient matrix. Solving the

numerator by expanding cofactors, simplifying and differentiating by wT

yields the income effects (assuming that all prices are constant)

for housing services and location. These are given below:

-{(-a)[UGXG'(k)UXk-UXX(UGGG'(k)+UGG"(k))]+
(-b)(UXXUHk-UXkUHX) +(-P*)[UHX (UGGG'(k)+
= (GG'G(k)'k
( H U G"(k))-U HkU G'(k)]}
(11) (wT) G Hk GX
D(wT)
D



{ [ (-aG' (k)) (UGXUXH-UXXUGH) ]+[ (-b) (UXXUHH
-UXHUHx)]+[ (-PX*G'(k))(U UGH-UHHUGx)
ak
() (wT)
D
Before analyzing the income effect, it is necessary to examine the

components of [a] and [b]. From the preceding discussion, it can be seen

that land rents at any one location are determined by accessibility,

neighborhood quality and now, fiscal variations. Each of these factors

will be capitalized. With respect to [a], the land rents will include








aP
the term, H FV'(H), which shows the effect of neighborhood quality on
3FV
the fiscal variation that impacts on the price of housing services.

For example, if a low-income housing project was located in an upper

class neighborhood which had a fiscal advantage, then land rents in
aP
that area may be lowered (FV'(H) < 0, F-- > 0). This assumes that some
SFV
of the poverty-related services would be borne locally.

However, [b) has a substantially larger impact on land rents,
aP
and this is represented by H(PH'(k) + FV FV'(k)) + tR'(k)w. This term

includes the capitalized value of location, fiscal advantages and

accessibility. Accordingly, k assumes three dimensions in this context:

(1) Neighborhood attributes

(2) A political jurisdiction

(3) Distance

If upper income groups are assumed to gain a fiscal advantage in

the suburbs,and housing services and location are normal goods, then it

is likely this income group will reside in the suburbs as in Figure 3.
8H
However, if housing services and location are inferior goods ( wT_ < 0,
3k
S< 0), this result is not clear-cut. The effects of transportation
a(wT)
costs to the central city may outweigh other factors.

The argument can be made that after some threshold is reached, the

marginal utility of public services will fall to zero for the rich.

For example, children are sent to private rather than public schools,

private alarm systems are installed as a substitute for police protection,

and poverty services do not provide any direct benefits. Therefore, with
aH
respect to (w-- UG, UGG, G'(k), G"(k) and [a] are likely to be quite

small. Although the first bracket is indeterminate in sign in (11),the

last two brackets are definitely positive. Since the numerator is

multiplied by a negative one, and D is negative, housing services must







be considered as normal good.

This is not necessarily true for the sign of a(wT Assuming

that the poor are concentrated in the central city, it is likely that

G'(k) can be zero or even negative. Alternatively, t '(k)w is likely

to be quite larger because of w, and the numerator is positive

ak
(UXXUHk < 0, UXkUH > 0). Thus, the conditions for (wT) < 0 can be

met. If under certain circumstances location becomes an inferior good

ak
(which in the "weak" case only require that be negative), the
3(wT)
location of residences will vary for members of the same income group.

The implications of this model are far-reaching. The next section

will summarize the conclusions which can be drawn from the model and

will relate them to the rent-bid curves in Section 3.3. In addition,

they will be incorporated into the literature reviewed in Chapter 2.


3.4 Implications of the Model

A Consideration of Locational Attributes

A major conclusion derived from the mathematical model was that

location can become very complex under certain conditions, particularly

for high income groups. This implies that if income increases, less

"location" is demanded. Since location takes on several meanings in this

model, the first requirement is to determine exactly what is meant by

location.

Location in this model was defined in terms of neighborhood

attributes, accessibility and government jurisdictions. With respect

to neighborhood and government, the implications are rather straight-

forward. Demanding less of these goods as income increases suggests that

an individual will sacrifice some neighborhood amenities and fiscal

advantages in the choice of residential location. Assume that the

suburbs are characterized by less crime and pollution and that upper







income households can derive a fiscal advantage by locating there. If

some aspects of location are inferior goods, however, then the upper

income household will demand fewer neighborhood amenities, and the fiscal

advantage will not be appropriate. Accordingly, all other goods must be

superior in the aggregate. Since the introduction of the government

sector restricts residential choice to a city of suburban jurisdiction,

this analysis suggest that the upper income household will reside in

the central city.

Examining location in terms of accessibility presents more of a

problem. In other words, what is the economic interpretation of "less"

accessibility? It was stated previously that accessibility was properly

defined in terms of the journey to work, shopping and recreation. If one

makes the assumption of a CBD, where all economic activity occurs, then

accessibility will decline with distance from the CBD. However, the

advent of suburban shopping centers, industrial parks and office build-

ings invalidates this assumption. According to Stegman, suburban residents

have better access to central city facilities than city residents. It

is likely that improve transportation facilities (highways) and the

increasing decentralization of firms have further increased accessibility

in the suburbs. Therefore the argument can be made that residential

location in the central city will result in "less" accessibility, using

the broad definition of accessibility given above.

This conclusion appears to contradict the traditional residential

land use models discussed previously. One should recall, however, that

these models viewed accessibility in terms of the journey to work,

which represents a limited definition of accessibility. The fact that

land rents are higher in the central city, as depicted in rent-bid

curves, is not inconsistent with the broad definition used in the model

in 3.3. This is because households must compete with business for








sites in the central city to a gri (ter degree than in the suburbs.

Land rents will accordingly decline from the central city.

The Rent-Bid Curves

The rent-bid curves depicted in Figures 1-3 will clarify this

analysis. Figure 1 is representative of land rents in a mononuclear

city, where employment and shopping are concentrated in the central

city. The rich would occupy the most accessible sites.

Figure 2 represents the decentralization of firms and households.

The slope of the rent-bid curvw is reduced, and a secondary peak is

established. From the model in 3.3, this results from two effects:

PH'(k) and TR'(k). The former depends on suburban neighborhood amenities

(and is assumed positive), and the latter refers to increased accessibility

that is determined by suburban development. Decentralization implies

that density in the suburbs has increased, and Figure 2 is the result.

When a government sector is introduced, the rent-bid functions will

not be continuous if there is fiscal variation between the city and

the suburbs. The discontinuity would be produced by the effects of

G'(k), PG'(k), aPH//FV and FV'(k), and it is depicted in Figure 3.

It should be noted that the impact of government also produces a change

in the slope of the rent-bid function in this example. However, the

shift and/or slope change depends on which income group derives a fiscal

advantage in each jurisdiction.

The rent-bid curves in Figures 1-3 are used to illustrate the

effects of location on utility. It has been argued that the government

sector is an important determinant of residential location, and this

has been demonstrated in both the graphical and mathematical analyses.

The next step is to relate this model to the literature on the Tiebout

hypothesis.









The Relation to the Tiebout Literiiure

The theoretical literature analyzed in Chapter 2 was primarily

concerned with the efficiency aspect of the Tiebout hypothesis. Buchanan

and Goetz point out that efficiency in the public sector is limited

in two respects. First, resources in the private sector are not

ubiquitous, and the population distribution between jurisdictions that

is optimal in the private sector may produce a nonoptimal solution in the

public sector. Second, an inmigrant into a community can impose

congestion costs which are greater than the increased cost-sharing of

the tax burden.

Hamilton argued that zoning, defined as a minimum expenditure

for housing, could produce efficiency in the public sector. In this

example, the property tax becomes an efficient pricing mechanism that

does not carry an excess burden. Hirsch and Margolis develop a model

which disputes the conclusions derived by Hamilton. They argue that

the property tax is not an efficient pricing mechanism for public goods.

This results in a distortion in the housing market, whereby a nonoptimal

substitution occurs between the location of single and multifamily

housing.

The primary conclusion drawn from these models is that a movement

toward Tiebout equilibrium would require residential segregation by income.

Zoning ordinances would be required to maintain this equilibrium.

The model developed in section 3.3 clearly demonstrates the restrictive-

ness of the Tiebout model, which requires that 3PH/ FV, PG'(k) and

FV'(k) must equal zero. Furthermore, the analysis of Buchanan and Goetz

demonstrates that PH'(k) must also equal zero. In other words, Tiebout

efficiency can exist only when location is not capitalized in the price








of housing or in the price for public goods. The conclusions drawn

from the model in 3.3 and Figures 1-3 suggest that Tiebout efficiency

is not likely to be realized.

The empirical models discussed in Chapter 2 are primarily concerned

with the issue of Tiebout-induced mobility. The models of Aronson and

Schwartz and Bradford and Kelejian demonstrate that fiscal variations

are a determinant of residential location. This implies that the

parameters cited above are not equal to zero.

Haurin and Tolley develop a model which calculates the welfare

losses that result from inefficiency in the central city public sector.

These welfare losses are derived from distortions in the housing and

public goods markets. The assumption that upper income groups should

reside in the suburbs is crucial to their analysis. However, the model

in section 3.3 demonstrated that under certain conditions, it is

optimal for an upper income household to locate in the central city.

Location, as defined in 3.3, becomes an inferior good under these

circumstances.

Primary Conclusions

The purpose of this chapter has been to extend the basic results

obtained from traditional residential land-use models and the Tiebout

literature. By dropping some of the restrictive assumptions of such

models, more realistic concepts of housing services and accessibility

can be formulated, and testable hypotheses can be developed.

Of more critical importance is the introduction of the government

sector into a model of residential location. Two major conclusions

can be deduced from the model. First, Tiebout efficiency is extremely

unlikely in the context of a metropolitan area. This point has been







developed in prior studies. Second, residential segration is not

optimal under certain conditions. The concept of location as an

inferior good is a sufficient condition for this result, and it has

not be consider in the literature. Again, it should be recognized

that the theoretical model in this chapter explicitly assumes that the

residential response to fiscal variations across jurisdictions is

achieved primarily by a change in locational choice, rather than by

the formation of coalitions or clubs to achieve budgetary responses

in existing locations.

The model in the following chapter will empirically test the

hypothesis that residential location can be explained by accessi-

bility, neighborhood quality and fiscal advantages. The model will

estimate the determinants of location for three income groups, and

the sample will be divided into growing and declining central cities.

The theoretical model has developed utility functions for individual

households. It will be assumed that the actions of income groups

represent an aggregate response. Therefore, instead of looking at

individual households, the dependent variable will relate the

relative concentration of various income classes to the locational

attributes developed in this chapter. The sensitivity of location to

fiscal variations will be determined by simulating the effects of the

institution of a consolidated government. It is assumed that

consolidation will eliminate the sources of fiscal variation within

a metropolitan area. Therefore, spatial quality differentials with

respect to public services will be ignored. In terms of the model in

3.3, k will drop out of the equations for public services (G) and the

tax price (PG), and the price for housing services (PH) will no longer
C H








be influenced by FV. Thus the sensitivity of residential location

to fiscal variations can be ascertained.

The utility function demonstrates that households will respond to

disequilibrium conditions. Attempts to measure this response will

cross-section data may not be fruitful. It should be noted that the

empirical tests of the Tiebout hypothesis and of other residential

location models typically have been done with cross-section data. The

theoretical model in this chapter, therefore, raises serious questions

about the received body of empirical tests on the residential location

response to disequilibrium conditions.














CHAPTER 4

THE EMPIRICAL MODEL AND RESULTS

4.1 The Data

4.11 The Sample

The sample in this study consists of 50 metropolitan areas, all

of which had central city populations in excess of 100,000 persons in

the 1960 census. In the sample, 24 central cities had populations

which increased between 1960-1970, and 26 central cities suffered

population declines. Excluded from the sample were those SMSA's in

which the primary city was located in more than one county. This was

necessary because the simulation assumes consolidation will occur

between a central city and a surrounding county. An example of this

exclusion rule would be Atlanta, Georgia.

Table 4.1 gives the population of the central cities, the suburbs

and the 1960-1970 percentage change in population in the central city.

The suburban population is defined to be the county population minus

the central city population. This definition is deficient for two

reasons. First, some large counties may include rural areas which are

not true "suburbs." Second, the surrounding county in heavily urbanized

areas may not comprise some areas which are suburbs. However, since

the model in this study assumes consolidation will occur between

a central city and a surrounding county, this derivation of the respective

central city suburban populations will be utilized.

One can see from Table 4.1 that most of the central cities with

growing populations were located in the south and west, Some exceptions








to this trend include two rapidly growing university communities

(Lansing, Michigan and Madison, Wisconsin) and four central cities

which had positive population growth due to annexation (Peoria, Illinois;

Tulsa, Oklahoma; Columbus, Georgia; and Corpus Christi, Texas).

Conversely, most of the central cities in the sample with declining

populations are located in the north and east. Therefore, this sample

is consistent with recognized demographic trends of the 1960's.

The sample provides many contrasts. First, the central city

populations range from Chicago, Illinois (3.4 million) to Duluth,

Minnesota (100,600). Second, the suburbs range in population from

2.1 million in Chicago to 13,300 in Columbus, Georgia. Finally, the

percentage of central city population to the total county population

varies from a low of 19% (Hartford, Connecticut) to 92% (Columbus,

Georgia). Therefore, the sample is characterized by regional diversity

and substantial differentials with respect to population.

Significant differences can also be noted with respect to the

population characteristics of the central cities. Seven central cities

in the north and east had population densities of over 9000 persons per

square mile. Alternatively, fourteen central cities in the sample had

population densities of less than 3000 persons per square mile, eleven

of which were located in the south and west. In addition, blacks

comprised less than 10% of the total population in nineteen central

cities in the sample. Eight of these cities are located in the southwest

and west. This figure is somewhat misleading, though, since most of

these cities have substantial concentrations of Mexican-Americans which

represent the "minorities" in these areas.

Finally, twenty-three central cities had declining civilian

employment between 1960-1970. As expected, these cities correspond









exactly to those which had a net ,,rease in population during this

period. The erosion of the tax base in these cities comes from two

sources: the movement of residents (predominantly middle and upper

income) from the core city to the suburbs and the decentralization of

firms. However, many households and firms left the northeast entirely

and relocated in the sunbelt states. It is worthy to note that all of

the suburban areas in the sample had net increases in civilian employ-

ment. The only exceptions to this trend were those areas Twhich had

annexations.


4.12 The Calculation of the Income Class

The empirical model in this study estimates a location equation for

three income groups, designated as lower, middle and upper income classes.

Since this classification is used to develop the endogenous variables of

the regression equations, an acceptable method for determining the

respective income groupings is extremely important. Bradford and

Kelejian (see 2.1) developed a rather sophisticated income distribution

series in which the income groupings were designated on a percentile

basis for their cross-section analysis. The strength of this Lorenz

curve procedure is obvious. By altering the percentiles of the various

income groups, tests of robustness are possible. However, they define

the poor in terms of a single definition of the poverty level ($3800 in

1960) that ignores regional differences in the distribution of income.

One would expect that a poverty level in Mississippi would be substantially

less than in New York, for example. Bradford and Kelejian do not disclose

the source of their data, and it is not possible to determine how their

income series were generated.

Census data, which is utilized in the following model, measures the

distribution of income on a discrete rather than a continuous basis.










Table 4.1


City (County)
Birmingham, Al. (Jefferson)
Mobile, Al. (Mobile)
Phoenix, Az. (Maricopa)
Tucson, Az. (Pima)
Little Rock, Ark. (Pulaski)
Fresno, Cal. (Fresno)
Sacramento, Cal. (Sacramento)
San Diego, Cal. (San Diego)
San Jose, Cal. (Santa Clara)
Hartford, Conn. (Hartford)
St. Petersburg, Fl. (Pinellas)
Savannah, Ga. (Chatham)
Columbus, Ga. (Muscogee)
Chicago, Ill. (Cook)
Peoria, Ill. (Peoria)
Evansville, Ind. (Vanderburgh)
Des Moines, Iowa (Polk)
Wichita, Kan. (Sedgwick)
Topeka, Kan. (Shawnee)
Louisville, Ky. (Jefferson)
Flint, Mich. (Genesee)
Lansing, Mich. (Ingham)
Grand Rapids, Mich. (Kent)
Minneapolis, Minn. (Hennepin)
Duluth, Minn. (St. Louis)
Jackson, Miss. (Hinds)
Omaha, Neb. (Douglas)
Newark, N.J. (Essex)
Jersey City, N.J. (Hudson)
Albuquerque, N.M. (Bernalillo)
Buffalo, N.Y. (Erie)
Rochester, N.Y. (Monroe)
Syracuse, N.Y. (Onandango)
Greensboro, N.C. (Guilford)
Charlotte, N.C. (Mecklenburg)
Cleveland, Ohio (Cuyahoga)
Cincinnati, Ohio (Hamilton)
Dayton, Ohio (Montgomery)
Tulsa, Ok. (Tulsa)
Pittsburgh, Pa. (Allegheny)
Erie, Pa. (Erie)
Providence, R.I. (Providence)
Houston, Tex. (Harris)


1970
Central City
Population
(in thousands:
300.7
190.0
581.6
262.9
132.5
166.0
254.4
696.6
446.5
158.7
216.1
118.3
154.1
3362.8
127.0
138.7
200.8
276.7
124.9
361.5
193.4
131.6
197.5
434.4
100.6
154.0
347.4
382.4
260.5
243.8
462.8
296.2
197.3
144.2
241.2
751.0
452.6
243.5
331.8
520.2
129.2
179.2
1232.4


Central City
Population
1960-1970
S% Change
-11.7
-2.5
32.4
23.5
22.9
23.9
34.1
21.6
118.7
-2.6
19.2
-20.7
32.8
-5.1
23.1
-2.0
-3.6
8.6
4.6
-7.4
-1.8
21.9
11.5
-10.0
-5.9
6.6
15.0
-5.7
-5.7
21.2
-13.1
-7.0
-8.7
20.5
19.7
-14.3
-10.2
-7.4
26.2
-13.9
-6.7
-13.7
31.4


1970
Suburban
Population
(in thousands)
344.3
127.3
385.9
88.8
154.7
247.0
377.1
661.2
618.2
658.0
306.2
69.5
13.3
2125.5
68.3
30.1
85.3
74.0
30.4
333.6
251.0
129.4
213.5
525.7
120.1
61.0
42.1
547.6
348.8
72.0
650.7
415.5
275.4
144.4
113.5
970.3
471.5
362.6
69.9
1084.8
134.5
401.1
509.5









Table 4.1 (continued)


1970
Central City
Population
(in thousands)


City (County)


Beaumont, Tex. (Jefferson)
Corpus Christi, Tex. (Nueces)
Salt Lake City, Utah (Salt Lake)
Seattle, Wash. (Pierce)
Madison, Wise. (Dane)
Milwaukee, Wisc. (Milwaukee)


116.0
204.6
175.8
154.6
173.2
717.1


Central City 1970
Population Suburban
1960-1970 Population
% Change (in thousands)


-1.4
22.0
-7.2
4.3
35.6
-3.2


128.8
32.9
282.8
256.4
117.1
337.0


Source: County and City Databook 1972, U.S. Dept. of Commerce, Bureau
of the Census.