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1/98 c/Clmms-ou

DETERMINANTS OF PUBLIC SERVICE EXPENDITURES IN
FAST GROWING LOCAL GOVERNMENTS OF MICHIGAN

By

GETACHEW W. BEGASHAW

A DISSERTATION

Submitted to
Michigan State University
in partial fulﬁllment of the requirements
for the degree of

DOCTOR OF PHILOSOPHY

Department of Agricultural Economics
1998

ABSTRACT

DETERMINANTS OF PUBLIC SERVICE EXPENDITURES IN
FAST GROWING LOCAL GOVERNMENTS OF MICHIGAN

By

Getachew W. Begashaw

This study analyzes the factors that determine the variations in per capita public
service expenditures of forty-six fast growing local governments in the State of Michigan.
Fast growing local governments were deﬁned as cities and townships that had 5,000 or
more residents by 1990 and had grown by at least 1,000 persons between 1980 and 1990.
All the seventeen cities and twenty-nine of the ﬁfty-two townships that qualiﬁed as fast
growing communities in the state were included in the study. Categories of public services
considered in the study included general government, public safety, public works, public
services, health and welfare, and recreation and culture.

The study was based on US Census population ﬁgures of 1980 and 1990 and the
1994 population projection of the Michigan Department of Management; public service
expenditures from the Comprehensive Annual Financial Report (1981 to 1995) of the local
governments; state equalized value of properties (1981 to 1995) of the all the
communities; public safety data of 1990 and 1905 for all cities and townships in the study;
and roads and streets expenditure for selected communities. An expenditure decision
model of local governments was developed assuming that the general objective of local

governments is to provide the best possible public services (maximizing service beneﬁts)

with minimum expenditures. A rigorous method of data preparation for the purpose of
such analysis was developed and a Fixed Eﬂects econometric model was employed to
analyze the huge panel data sets.

The empirical results showed that: in terms of 1995 constant dollars, per capita
public service expenditures of fast growing communities in Michigan vary widely; cities
and townships of different population sizes have different expenditure patterns (while
cities with smaller population size spend more than cities with larger population size,
townships with larger population size spend more than smaller townships); and
communities located in Southeast Michigan spend more than those in the rest of the state.
More importantly, while the explanatory power of all variables varied across community
groups, the per capita state equalized value of total property was found to be a
consistently signiﬁcant variable in explaining the variations in expenditures of local
governments. The more wealth, the more spending.

The general policy implication derived from the empirical ﬁndings was that more
people could be added to the existing smaller communities to decrease per capita
expenditures. Ifsmall communities were to grow to achieve economies of scale in utilizing
the existing service infrastructures, they need not contribute to sprawl since sprawl refers
to low density development, not growth in population. If re—directing population growth
into smaller size communities is to be actualized, the savings that could be obtained ﬁ'om
the joint impact of increased population and a dense new residential development could be

substantial.

I dedicate this dissertation to my children Noah and Gabrielua through whom I remember

my past and in whom I ﬁnd meaning for my life in the future.

iv

ACKNOWLEDGMENTS

I would like to convey my thanks and gratitude to all who have served in my thesis
committee. First and foremost, my indebtedness goes to Prof. A Allan Schmid, my
mentor, major professor, and thesis supervisor. His unﬂagging support and thoughtful
guidance have been so much invaluable to me and were critical in my successful
completion of my graduate studies, including writing this dissertation. I have immensely
beneﬁted from his insightful and scholarly discussion and comments to improve the quality
and focus of my research.

I also want to thank Prof. James F. Oehmke who has always been a source of
motivation and guidance for me ever since I joined the department. His prompt response
to many of the questions I had and the keen interest he had in my research have played
vital role in shaping the focus and content my thesis.

I am extremely grateful to Prof. Lynn R. Harvey, who not only served as a member
of my thesis committee, but also provided me with the most needed data for my research.
Many of his sharp comments have been valuable in reﬁning the makeup of my dissertation
and highlighting the germane policy issues that are of interest to local governments.

I would also like to sincerely thank Dr. Raymond D. Vlasin for serving in my thesis
committee and giving me several helpful suggestions that helped me to improve my
dissertation in form and content. In addition, I wish to acknowledge that it was a privilege
for me to have both Professors James T. Bonnen and Paul W. Strassmann for having

served in my committee before their retirement.

Well, I can never thank enough Dr. James E. Jay, Assistant to Vice-Provost of
CANK for helping me out with ﬁnancial assistance at the very critical time in my graduate
program in the university. I am extremely thankful to him and the Ofﬁce of Diversity and
Pluralism for the ﬁnancial help I received for three years as a Graduate Assistant. I also
esteem the assistantships and fellowships given to me at different times by the Urban
Aﬂ'airs, Graduate School, the College of Agriculture and Natural Resources, and
Department of Agricultural Economics.

My sincere appreciation is also for all my graduate colleagues in the department
that have made my stay in the university ﬁ'uitful and pleasant. My special mention goes to
Dr. Georges Dimithe, Dr. Berhanu G. Medhin, and Mr. Adnan Ozair, who have in one
way or another contributed towards my success in writing this dissertation.

I would like to mention my deepest gratitude to all clerks, treasurers, accountants,
planners, and staﬁ‘ of all the forty-six local governments that are included in this study for
ﬁrlly cooperating and providing me with all the data and information I used in this
research.

Finally, but most importantly, I would like to express my admiration and
appreciation to my wife Senait G. Tsadik. During those difﬁcult times, when I was
struggling with my research, she raised our two little children, Noah and Gabrielua.
Despite the precious time she sacriﬁced to help me ﬁnish my dissertation, she also
managed to make time for a successful completion of her graduate studies with high

honor. Indeed, I am blessed to have her as part of my life.

TABLE OF CONTENTS

List of Tables .....................................................................................................
List of Figures ....................................................................................................

CHAPTER 1. AN INTRODUCTION TO PUBLIC SERVICE

EXPENDITURES .....................................................................

1.1 Introduction .....................................................................................
1.2 Background .....................................................................................
1.3 Problem Statement ...........................................................................
1.4 Research Objectives .........................................................................

CHAPTER 2. LITERATURE REVIEW............ ...........................................

2.1 Introduction .....................................................................................
2.2 Public Service Expenditure Studies ..................................................
2.3 Lessons From the Studies .................................................................

CHAPTER 3. CONCEPTUAL FRAMEWORK TO ESTIMATE

DETERMINANTS OF PUBLIC SERVICE
EXPENDITURES .....................................................................

3.1 Introduction .....................................................................................
3.2 The Expenditures Model ..................................................................
3.3 The Dependent Variable ...................................................................
3.4 The Independent Variables ...............................................................
3.4.1 Population Size ..................................................................
3.4.2 Population Growth Rate ....................................................
3.4.3 Population Density ............................................................
3.4.4 Property Value and Land Use Characteristics .....................
3.5 Attributes of Services and Model Speciﬁcation ..................................
3.6 Omitted Variables .............................................................................
3.6.1 Inter-govemmental Revenue Transfers ...............................
3.6.2 Household Income .............................................................
3.7 Unit of Observation and Categories of Analysis .................................
3.7.1 Types of Government .........................................................
3.7.2 Geographic Location ..........................................................
3.7.3 Population Size Groups ......................................................

vii

Page

x
xiii

l

l
4
7
10

11

ll
11
39

44
44
44
45
45
46
48
48
49
50
51
51
52
53
54
55
56
56

CHAPTER 4. ANALYTICAL METHODS FOR ESTIMATING
DETERMINANTS OF VARIATIONS IN PUBLIC
SERVICE EXPENDITURES .....................................................

4.1 Introduction ......................................................................................
4.2 The Data ...........................................................................................
4.2.1 Population ..........................................................................

4.2.2 Expenditures ......................................................................

4.2.2.1 General Fund ......................................................

4.2.2.2 Special Funds ......................................................

4.2.2.3 Debt Service Funds .............................................

4.2.2.4 Capital Projects Funds .........................................

4.2.3 Adjusting Expenditures ......................................................
4.2.4 Excluded Fund Types .........................................................
4.2.5 Netting Out Expenditures ...................................................
4.2.6 Inflation Adjustment ...........................................................

4.2.7 Amortization ......................................................................

4.2.8 State Equalized Value of Properties ...................................

4.2.9 Population Density ............................................................

4.3 The Empirical Method of Analysis ....................................................
4.3.1 The Fixed Eﬂ‘ects Econometric Model ................................
4.3.2 Assumptions of the Fixed Effects Regression ......................
4.3.2.1 Heterogeneity of Units of Observations ................

4.3.2.2. Stochastic Relationship..................................

4.3.2.3 The Residuals .....................................................

4.3.3 Mathematical Representation of the
Fixed Effects Model .........................................................

CHAPTER 5. DETERMINANTS OF PER CAPITA PUBLIC SERVICE
EXPENDITURES IN FAST GROWING COMMUNITIES
OF MICHIGAN .........................................................................

5.1 Introduction .....................................................................................
5.2 The Variables ...................................................................................
5.2.1 Population ..........................................................................
5.2.2 Equalized Value of Properties ............................................
5.2.3 Total Land Area and Population Density .............................
5.2.4 Per Capita Public Service Expenditures ...............................
5.3 Data Classiﬁcation ............................................................................
5.3.1 Classiﬁcation by Types of Government ...............................
5.3.2 Sub-Classiﬁcation by Population Size
and Geographic Location ..................................................

viii

57

57
57
58
62
64
66
66
67
67
68
70
71
74
78
80
82
83
84
84
84
85

86

88

88
88
89
92
97
98
102
102

105

5.4 Characteristics of the Study Communities

by Sub-Classiﬁcation ....................................................................... 106

5.4.1 Cities .................................................................................. 106

5.4.1.1 Cities of Larger Population Size ........................... 106

5.4.1.2 Cities of Smaller Population Size .......................... 107

5.4.1.3 Cities in Southeast Michigan ................................ 107

5.4.1.4 Cities in the Rest of the State ............................... 108

5.4.2 Townships .......................................................................... 108

5.4.2.1 Townships of Larger Population Size ................... 109

5.4.2.2 Townships of Smaller Population Size .................. 109

5.4.2.3 Townships in Southeast Michigan ........................ 110

5.4.2.4 Townships in the Rest of the State ....................... 110

5.5 Regressions and Model Speciﬁcations ............................................... 112

5.5.1 Diagnostic Regressions ....................................................... 112

5.5.1.1 Results of Diagnostic Regressions ........................ 113

5.5.1.2 Results of Diagnostic Regressions - Cities ............ 115

5.5.1.3 Results of Diagnostic Regressions - Townships 118

5.5.2 Fixed Effects Regressions .................................................... 120

5.5.2.1 Regression Results ............................................... 121

5.5.2.2 Regression Results for Cities ............................... 121

5.5.2.3 Regression Results for Townships ....................... 130

5.6 Comparison of Regression Results by Types of Government ............. 135

5.7 Impact of Location on Expenditures ................................................... 137

5.8 Reliability Test of the Model ............................................................. 138

CHAPTER 6. CONCLUSIONS, IMPLICATIONS AND FUTURE

RESEARCH .............................................................................. 141

6.1 Introduction ...................................................................................... 141

6.2 Conclusions ....................................................................................... 142

6.3 Policy Implications ............................................................................ 152

6.4 Future Research ................................................................................ 155

BIBLIOGRAPHY .............................................................................................. 158

APPENDICES .................................................................................................... 163

163

Appendix A: Summary Statistics ....................................................................... 169

Appendix B: Correlation Analysis of the Variables ........................................... 170

Appendix C: Diagnostic Regression Results ...................................................... 178

Appendix D: Fixed Effects Regression ............................................................. 188

Appendix E: General Linear Model Regressions ................................................ 190

Appendix F: Fixed Eﬂ‘ects Regression With Location Variable .......................... 191
Appendix G: Sample Regression Data .................................................................

ix

Table 2.1

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 4.11:

Table 4.12:

LIST OF TABLES

Summary of Selected Studies on
Public Service Expenditures ....................................................

All Fast Growing Cities in Michigan .......................................
All Fast Growing Townships in Michigan ..............................
Townships Selected for the Study ...........................................

Combined Statement of Revenues and Expenditures,
Meridian Township, 1994 .......................................................

Deﬂators of Operating and Capital Project
Expenditures ..........................................................................

Unadjusted Public Service Expenditures of Meridian
Township ...............................................................................

Adjusted and Amortized Total Expenditures of Meridian
Township ...............................................................................

Amortized and Nominal Capital Project Expenditures of
Meridian Township .................................................................

Amortized and Adjusted Capital Project Expenditures of
Meridian Township .................................................................

Per Capita Public Service Expenditures of
Meridian Township .................................................................

State Equalized Value of Properties, Meridian
Township ...............................................................................

Total Land Area and Population Density of
Meridian Township .................................................................

Page

14
59
60

61

65

72

73

75

76

77

78

79

80

Table 4.13:

Table 5.1:

Table 5.2:

Table 5.3:

Table 5.4 (a):

Table 5.4 (b):

Table 5.4 (c):

Table 5.4 (d):

Table 5.5(a):

Table 5.5(b):

Table 5.6:
Table 5.7:
Table 5.8:

Table 5.9:

Table 5.10:

Table 5.11:

Total Land Area of the Fast Growing Local

Governments in the State of Michigan ................................

Mean, Minimum, and Maximum Values of

Selected Variables ..............................................................

Average Total Population of the Fast Growing Cities

in Michigan ........................................................................

Average Total Population of the Sampled Fast

Growing Townships in Michigan ........................................

Average PCSEV of Business Properties,

Cities .................................................................................

Average PCSEV of Residential Properties,

Cities .................................................................................

Average PCSEV of Business Properties,

Townships .........................................................................

Average PCSEV of Residential Properties,

Townships .....................................................................

Townships with Average Population Density

of 1,000 or More ...............................................................

Cities with Average Population Density

of 1,000 or More ...............................................................
Average Expenditures and Population, Cities .....................
Average Expenditures and Population, Townships .............

Single Factor ANOVA, by Types of Government, ..............

Single Factor ANOVA, by Geographic Location of

Local Governments ............................................................

Summary of Basic Characteristics of Fast Growing

Cities in Michigan ..............................................................

Summary of Basic Characteristics of Fast Growing

Townships in Michigan .....................................................

81

89

90

91

94

94

95

96

97

98

100

101

104

105

108

111

Table S.12(a): Results of the Diagnostic Regressions , Cities
and Townships ......................................................................

115
Table 5.12(b): The t-statistics of the Diagnostic Regressions,
Cities and Townships ..............................................................
115
Table 5.13(a): Results of the Diagnostic Regressions, Cities .........................
117
Table 5.13(b): The t-statistics of the Diagnostic Regressions, Cities ............
117
Table 5.14(a): Results of the Diagnostic Regressions, Townships ................
1 18
Table 5. 14(b): The t-statistics Results of Diagnostic Regressions,
Townships .............................................................................
1 19
Table 5.15: Fixed Eﬂ‘ects Regression Results, Cities ................................
122
Table 5.16: Ranking of the Independent Variables by the
Level of Signiﬁcance, Cities ...................................................
129
Table 5.17: Fixed Effects Regression Results, Township .........................
131
Table 5.18: Ranking of the Independent Variables by the
Level of Signiﬁcance, Townships ...........................................
134
Table 5.19: Comparison of the Ranking of Independent
Variables by Types of Government ........................................
136
Table 5.20 Results of the Reliability Test, Cities .....................................
139
Table 5.21 Results of the Reliability Test, Townships ............................
140

xii

LIST OF FIGURES

Page
Figure 5.1 Average Population and Expenditures,
all Cities ................................................................................ 124
Figure 5.2 Average Population and Expenditures
Cities Outside of Southeast Michigan .................................... 124
Figure 5.3 Average Population and Expenditures of
Cities in Southeast Michigan ................................................ 125
Figure 5.4 Average Population and Expenditures,
Large Crtres .......................................................................... 125
Figure 5.5 Average Population and Expenditures of 126
‘ Cities with Smaller Population size .....................................
Figure 5.6 Average Population and Expenditures of 132
. all Townships ........................................................................
Figure 5.7 Average Population and Expenditures of 132
Townships in Southeast Michigan .....................................
Figure 5.8 Average Population and Expenditures of 133
Townships Outside of Southeast Michigan ........................
Figure 5.9 Average Population and Expenditures of 133
Townships with Large Population Size ...............................
Figure 5.10 Average Population and Expenditures of 134

Townships with Small Population Size ..............................

xiii

CHAPTER ONE
AN INTRODUCTION TO PUBLIC SERVICE EXPENDITURES
1.1 Introduction
"T wo factors of practical eﬂiciency may be applied to the
government of a city: What does it provide for the people, and
what does it cost the people? " (James Bryce, 1914)

As municipal corporations, authorized by their respective charters, local
governments in Michigan provide basic public services like police protection, ﬁre control,
roads, water and sewer, parks and recreation, public improvements, planning and zoning,
and general administrative services to the residents in their jurisdictions. These services
have associated costs that are commonly referred to as public service expenditures. The
services provided and expenditures incurred are, more or less, similar for most local
governments in Michigan. They are paid for by the residents in form of taxes, charges,
assessments, and state transfers. Yet, there are signiﬁcant variations in the amount and
range of the per capita public service expenditures across most communities in Michigan,
ranging ﬁ'om $34 to $1,029 in constant 1995 dollars. From where do these variations or
diﬁ‘erences in expenditures come?

Although each local government in Michigan gets a sizable amount of dollars ﬁ'om
the state revenue sharing, they ﬁnance most of the public services they provide through
the revenues they generate locally. The public service revenue sources include taxes on

properties, businesses, and income. These revenue sources largely depend on how

communities use their lands. For instance, communities characterized by agricultural or
residential properties will be quite different from communities characterized by industrial
or commercial developments in their revenue generating ability.

All communities do not have equal number of residents (or population) and they
do not necessarily grow at equal rate. Public services are neither exclusionary nor rival in
their consumption. But, there are limits to how much services could be provided to a
growing number of people without reducing the quality of life (or services) and incurring
additional costs to the existing residents. On average, there is a threshold of population
size to a given level of public service beyond which the marginal cost of providing the
services could rise immensely.

There are several ways in which residents of adjoining communities could create
costs to communities in which they do not live or pay for the costs they create. Roads,
police and ﬁre, public libraries and parks are few such services ﬁ'om which outsiders can
not be excluded. Then, is it settlement congestion, as measured by location of
communities, or population size, grth rate, and density that drive expenditures of
communities? Or, it is the land use or development patterns of each local government that
is the sources of variations in expenditures of communities in Michigan?

Inquiry into this topic is not new; it has been around since the early 1900. Several
studies have been conducted; but, no consensus has evolved. The current study attempts
to contribute its share in clarifying the factors that drive public service expenditures of
local governments by: (1) developing a rigorous method of organizing and using relevant
data sets, and (2) enriching the method of analysis by employing the Fixed Eﬂects

Regression analysis of the extensive time-series cross-section (panel) data of Michigan.

The chapters are organized as follows: problem statement and research objectives
including this section of introduction are presented in Chapter One. Chapter Two contains
the literature review in which several major works in the topic are reviewed and the
lessons ﬁ'om the studies are highlighted. Chapter Three develops the conceptual
ﬁ'amework of the research and explains the model, the variables, and the classes of
analysis. Chapter Four discusses the analytical methods of the study and explains the
methods of adjusting and organizing the data, the econometric model chosen, and the
mathematical representation of the regression equation. Chapter Five presents the
empirical results and discussion of the analysis and the reliability test of the model. Finally,
Chapter Six summarizes the ﬁndings obtained from the study, policy implications for local

governments, and future research needs.

1.2 Background

Michigan, with a population of 9.5 million and a job base of 4.9 million in 1995,
has 83 counties and about 2,100 local governments. Nearly 50 percent of the population
and employment are located in the Southeast Michigan region, which comprises only
seven counties; Livingston, Macomb, Monroe, Oakland, St. Clair , Washtenaw, and
Wayne. It is projected that the population of Michigan will grow by 1.1 million people and
670,000 new jobs between 1995 and 2020. According to this projection, 38 and 44
percents of the new population and jobs respectively will be in Southeast Michigan
(MSPO: 1995; Burchell: 1997).

The Michigan Society of Planning Ofﬁcials reported that if the current pattern of
development continues, the state will incur signiﬁcant costs for new infrastructure as well
as the costs of urban decline. It further notes that this pattern of development is not
inevitable and an informed public could achieve different ﬁxture through coordinated and
integrated land-use planning and have a dramatic effect on the public and private resources
consumed for land development (MSPO: 1995). Thus, among many critical settlement
issues that need further research and knowledge are where and how to settle the increased
population to save on resources consumed and the associated public service expenditures
(Burchell: 1997; Schmid: 1997).

Observing that many of the cities in the US have increased their public service
expenditures by more than 40 percent between 1951 and 1954 alone, Harvey E. Brazer

suggested that this rapid increase in expenditures by American cities emphasizes the

importance of extending our knowledge into the study of the relationship between public
service expenditures and the factors that inﬂuence such expenditures (Brazer: 1959).

Michigan provides an excellent environment to study the factors that inﬂuence
increases and variations in public service expenditures, because it is one of the states that
have the highest per capita public service expenditures in the nation. Citizens Research
Council of Michigan (CRC) reported that in 1972/73 Michigan had a relatively higher per
capita expenditures (combined per capita expenditures for state and local governments) in
comparison with the national average and with those of the eight competitor states;
Indiana, Ohio, Wisconsin, New York, Illinois, Pennsylvania, New Jersey, and Michigan.
Michigan, with an average of $809.00 per capita public service expenditures, was the
second highest alter New York in 1972. That same year, its exceeded the national average
per capita by $97.00 (CRC, 1975).

The general ﬁll‘ld expenditures in Michigan increased by 66 percent (from $1.55
billion to $2.57 billion) between 1970 and 1974. The average annual increase was about
13.5 percent. Similarly, total expenditures ﬁ'om all operating funds increased by 58.2
percent (from $3.13 billion to $5.37 Billion) during the‘same period. These increases in
expenditures had given rise to increases in the general tax levels, including 10 percent
increase in the state and local personal income tax combined (CRC, 1975).

Similarly, the US Bureau of Census for ﬁscal 1987/88 reported that the state and
local governments in Michigan had both relatively high revenues and expenditures
compared with the national average and the average of the ﬁfteen states with populations
of over ﬁve million people. The ﬁfteen most populous states are California, New York,

Texas, Florida, Pennsylvania, Illinois, Ohio, Michigan, New Jersey, North Carolina,

Virginia, Massachusetts, Indiana, and Missouri. During this ﬁscal year, state and local
expenditures in Michigan were the ﬁfth highest per capita and second highest per
$1,000.00 personal income. The per capita expenditures were 7 percent higher than the
average of the ﬁfteen states and 9 percent higher than the national average (CRC, 1990).
In contrast to this steady increase in per capita public service expenditures in
Michigan, the per capita personal income rose by only 11 percent in real terms from 1979
to 1988. During this period, the ﬁfteen states had a remarkable average of 23 percent
increase in personal income and the national average was 21 percent (CRC, 1990). But,
Michigan ranked ﬁﬁh among the ﬁfteen states in collecting more revenue, especially
revenue ﬁom property and personal income taxes. The average per capita revenue for
Michigan, the ﬁfteen states, and the US were $3,107, $3,005, and $2,958 respectively (US

Bureau of the Census, Government Finances in 1987/1988).

1.3 Problem Statement

Recently, the Southeast Michigan Council of Governments (SEMCOG) had
commissioned two studies relating to the costs of alternative settlement patterns in
Michigan. The ﬁrst was a study on Fiscal Impacts of Alternative Land Development
Patterns in Michigan by Robert Burchell of Rutgers University. The other was a study on
Impact of Population Growth and Distribution on Local Government Expenditures in
Michigan by Allan Schmid of Michigan State University.

The Burchell study focused on the resource consumption and public service costs
of two alternative patterns of settlement, namely current trend (i.e. sprawl) and contained
developments (i.e. dense). The study was a micro density study that compared the costs of
infrastructure, housing, land, and public services at each selected study community level
under the two scenarios and informed which one of the two will save resources and costs.
This study, while very useful for the purpose of micro-settlement management, did not
explain what the underlying factors other than settlement density were responsible for the
steady increase in and variations of public service expenditures across communities in
Michigan.

The Schmid study was a macro-density approach focusing on the impact of
population size and location of the community in relation to metropolitan area and
investigated their impacts on public service expenditures. By employing a cross-sectional
regression analysis for 1990 and 1995, it determined the most important explanatory

variables that shaped the variations in public service expenditures.

Generally, population grth could be expected to increase the tax base and
revenue sources of a community (Oakland & Testa: 1995). On the other hand, as
population increase reaches a certain threshold, demands for more and improved public
services increase. This increase in demand, in turn, will place more pressure on local
government budget and public service expenditures. Most of the public services (public
safety, water and sewer, and roads for example) are congestablc goods with capacity
constraints. Thse classes of goods may be having scale economies over a certain range of
population and have a zero marginal cost as the number of users increases from zero to
some given number. As congestion sets in, the addition of more users reduces the utility of
services of all users and the marginal cost of additional users begins to rise sharply as an
absolute capacity constraint is reached (Randall: 1987). It is a conventional wisdom that
local governments need to invest more on public services in order to keep the quality and
quantity of services ﬁom declining as a result population growth and congestion.
However, many of the earlier studies have indicated that population growth and
congestion are just few of the many other factors that explain the forces that drive public
service expenditures of communities.

Most of these studies were based on the use of a single year cross-sectional data.
A cross-section analysis may be important not only for understanding of the underlying
factors of local government expenditures as they are, but also for what it may hint about
the possible future changes. However, as will be explained more in the literature review
section, these studies were not able to create consensus on which variables are the most
signiﬁcant factors in shaping public service expenditures. It is this lack of uniformity in the

ﬁndings of the diﬂ‘erent studies that motivated the current study that employs diﬁ‘erent

approach and methods of studying the topic. Accordingly, the two strategic research
questions that guide this study were: (1) what are the determinants or the signiﬁcant
factors that explain the variations in public service expenditures across communities in
Michigan?; and (2) what are the policy implications of the ﬁndings for ﬁxture population

settlement and growth strategies for local governments Michigan?

10

1.4 Research Objectives

This study attempts to identify the signiﬁcant factors (determinants) that are behind
the variations in per capita public service expenditures of fast growing communities (local
goverrunents) in the State of Michigan. The analysis seeks to underscore how the
association between per capita expenditures of the selected study communities and the
explanatory variables will be affected by population size groups, types of government (city
or township), and location (Southeast Michigan or rest of state). More speciﬁcally, the
study attempts:

(a) to establish a method of collecting, adjusting, and using local and state

governments expenditures data to conduct a study of public service

expenditures for different communities of Michigan;

(b) to establish a method of comparing public service expenditures of
different communities in Michigan;

(c) to determine if there are signiﬁcant diﬁ‘erences in public service
expenditures across communities in Michigan by population size, types of
government, and geographic location;

(d) to determine the signiﬁcance of selected variables in inﬂuencing the
variations in public service expenditures across fast growing communities
in Michigan; and

(e) to discuss the policy implications of the ﬁndings for future population
settlement policies and grth strategies in Michigan.

CHAPTER TWO
LITERATURE REVIEW OF STUDIES
ON PUBLIC SERVICE EXPENDITURES

2.1 Introduction

The ﬁrst section of this chapter reviews some of the major public service
expenditure studies conducted so far. It focuses on the economic variables considered
frequently and itemizes the important ﬁndings of the studies. It also describes the types of
data used and methods of analysis applied in detail. The objectives, variables, and research
outcomes of the studies are also presented in a form of summary (Table 2.1). The second
section presents a brief summary and critique of the studies and points out how the current
study will be different from them in the methods and approaches it used. This form of
presenting the review was selected with the aim of providing better opportunity to identify
and incorporate the most important economic variables frequently used by prior

researchers into the current empirical model and analysis.
2.2 Public Service Expenditures Studies

Although costs of governments had been interest of research for long time, the
importance of more focused research on this vital area of concern, especially on the

factors inﬂuencing public service expenditures, was spurred by the rapid increase in public

11

12

service expenditures of state and local governments in the US after the World War H
(Brazer, 1959; Schmandt and Stephens, 1963).

As the US was leaving the war period, the surpluses accumulated by state and
local governments had to be used and some capital outlay and maintenance, deferred
during the war, were resumed. Thus, interest in inquiring into the budgets and
expenditures of state and local governments to determine if expenditures were extravagant
or eﬁicient, taxes were too high or low, and whether borrowing was for planned
developments or for beneﬁt of interest groups grew (Berolzheimer, 1947). As a result,
mainly in 1950s and 19605, several major studies and number of specialized articles on
various aspects of local government ﬁnance appeared in professional literature. For
example, Josef Berolzheimer wrote on “Inﬂuences Shaping Expenditure and Economic
Structure in the United State” in 1952; Amos H. Hawley published an article on
“Metropolitan Population and Municipal Government Expenditures in Central Cities” in
1952; Solomon Fabricant published his book titled The Trend of Government Activity in
the United State Since 1900 in 1952; Scott and Feder examined the relationship between
municipal expenditures and some selected variables for 192 cities in California in 1957;
Brazer presented his study on City Expenditures in the United States in 1959; Johannes
Delphendahl of Michigan State University wrote his doctoral dissertation on Expenditure
Patterns and Services Rendered by Michigan Townships in 1961; Schmandt and Stephens
contributed the article on “Local Government Expenditure Patterns in the United States’
in 1963; Woo Sik Kee wrote his doctoral dissertation on Metropolitan Area Finance

Studies in 1964 and published an article on “Central City Expenditures” in 1965.

13

Public service expenditures are all public resources expended by state or local
governments to produce certain public goods and services (such as police protection, ﬁre
control, public education, public health, roads, water and sewer systems. park and
recreation, etc.) to improve the welfare and quality of life of the residents of that political
jurisdiction. The focus of the researchers including those mentioned in the following table
were the factors that derive or inﬂuence the public resources expended to provide these
services. Different researchers had submitted different answers, and some others have
supported each others ﬁndings.

Berolzheimer (1947) analyzed the expenditure of operation of states and local
governments in the US using the data reported by the Bureau of Census for the ﬁscal year
1942. The cities were divided into ten population size groups and a correlation analysis
was done on the assumption that the independent variables that affect state and local
expenditures were population size and density, income payments, and the volume of
government functions. On the expenditures side, it was only the expenditure for operations
that was considered. The operation expenditure, according to the author, was one
signiﬁcant part of expenditures and was sufﬁcient, by itself, to provide tentative
explanation relating to the association between state and local expenditures and the
independent variables. That was because operation expenditure comprised all public pay
rolls, current materials, current maintenance, public assistance payments, and other

operations, representing most of the annually recurring costs of government.

l4

 

 

Table 2.1 Summary of Selected Studies on Public Service Expenditures
Study Objectives Variables Findings
Berolzheimer( (1) To explore the Dependent variable: the cost (1) City expenditures were
1947) factors shaping state [expenditures] of public correlated with population
and local operation operations size, (2)excepting for
expenditures, (2) to counties with population
identify systematic Independent variables: total less than 10,000, county
ways of classifying and population, population density, expenditures did not vary
comparing public income payments, volume of markedly with population
ﬁnances functions. size
Hawley, 1951 Testing the Dependent variable: per capita (l) The per capita
interdependence of all government expenditures, government expenditures
operating expenditures, and were more closely related
populauons lying capital improvement to population residing
within and without the expenditures. outside the city than to
b0 1 'es of local population within the city,
Independent variables: and
governments involving .
population size, density, and (2) operating were
the use of the more related to population
. . growth rate, number m labor residing
mumcrpal government
force, number in white collar outside the city than
expenditures
occupation, number of houses, population within the city

houses per square mile, area in
square miles, percent of
population incorporated, and
percent of total district

population.

 

Table 2.1 (Cont’d)

15

 

 

Study Objectives Variables Findings
Brazer, (l) establishing Dependent variable: total (1) population density and
1959 ms of differences operation and functional intergovernmental revenue
category expenditures per per capita were the most
m per capita capita signiﬁcant variables in
expenditures of cities, explaining all categories of
(2) analyzing the Independent variables: expenditures.
iation between population size, population (2) population m and
population growth rate were
city expenditures per densrty, pop ulatron growth of least importance in
capi ta and l 1e rate, median farmly income, shaping crty expenditures,
economic variables percentage of population and
(3) median family income
employed, and
was signiﬁcant in explaining
intergovernmental revenue.
variations in functional
categories only.
Schmandt and (1) give an overview of Dependent variable: mean (1) state aids and median
Stephens, 1963 local goverrunent per capita expenditures of family income were the most
expenditure patterns by total and functional important variables
geographic regions, categories inﬂuencing per capita
and spending by county area
(2) indicate the factors Independent variables: total aggregate, and
that inﬂuence local population, population (2) total population and
ndin levels densrty, terntorral area state density did not aﬁect total
spe g aids, median family income
per capita expenditures

appreciably

 

Table 2.1 (Cont’d)

l6

 

 

Study Objectives Variables Findings
Woo Sik Kee, (1) Discuss critical Dependent variables: Determinants of each of the
1965 differences of socio- (1) total general expenditures, dependent variables by
economic and (2) non-educational ranking were:
governmental expenditures. and (l) for total general
characteristics (3) non-aided expenditures expenditures: state aid, ratio
between the city and of central city population to
areas outside the Independent variables: its SMSA population. per
central city. (1) per capita income, capita income, ratio of state
(2) Show the (2) owner-occupied housing and local expenditure
relationships between units as percent of total responsibility, and owner-
occupied units, occupied housing units as
the level or per capita (3) population density, percent of total occupied
city expenditures and (4) ratio of central city units;
selected explanatory population to total SMSA (2) for per capita non-
variables population, (5).ratio of state educational expenditure: state
and local functional

responsibility, and
(6) per capita state aid

aid, owner-occupied housing
units as percent of total
occupied units, ratio of
central city population to its
SMSA population, and ratio
of state and local expenditure
responsibility; and non-aided

expenditure.

 

Table 2.1 (Cont’d)

l7

 

 

Study Objectives Variables Findings

Masten and Explain that the Dependent variable: total city (1) The coefﬁcient of multiple

Quindry, relative importance of per capita current general determination (R’) was low for

1970 the popular expenditure purpose expenditures cities ranging from 5,000 to
factors, other than 20,000 and high for cities with
population and Independent variables: population of 20,000 to
intergovernmental population, population density, 100’000’
transfers, can be most (2) The contributions of the
meaningfully assessed per cap ita adjusted gross independent variables to the
only for areas of income, per capita full value of coefﬁcient of multiple
relatively homogenous assessed property, and land determination vary by city
population sizes. sizes.

area.

Schmid, (1) Investigate if public Dependent variable: total (1) expenditures and

1997 service expenditures expenditures per capita. population size matters for
could be reduced by townships;
altering macro-patterns Independent variables: total (2) location mattersfor cities;
of future settlement (or population, population growth and
development). rate, location, total state (3) cities in southeast
(2) Determine if growth equalized value of property, Michigan had higher total
location and population and percent of state equalized expenditures per capita than
size have effect on value of residential property cities in the rest of the state
public service while townships did not show
expenditures. such diﬁ'erence

 

18

The correlation analysis revealed that city expenditures were highly correlated with
population size. Per capita city expenditures ranged from $72.69 (in cities with
populations over one million) to $11.22 (in cities with populations less than 2,500). The
direction of changes in population size and expenditures followed the same direction
without any exception; i.e., expenditures increase when population sizes increase and
expenditures decrease when population sizes decrease.

In contrast to the variation in city expenditures in relation to population, the per
capita county expenditures did not vary signiﬁcantly among population size groups
excepting for the smallest group. While all of the four county population size groups
(over 250,000; 50,000 - 250,000; 25,000 - 50,000; 10,000 - 25,000; and under 10,000)
had per capita county expenditures within the range of $12.38 to $13.76, the smallest
counties with populations less than 10,000 had per capita expenditure of $22.72 showing
diseconomies of scale.

Amos H. Hawley’s 1952 study was based on two major assumptions. (1) City
services which were bought with municipal government expenditures were developed to
meet the total need generated by activity carried on within the city. (2) Some of those
activities, and hence some of the need for city services, arose from the population residing
outside the city boundaries. According to Hawley, the outlying population uses the city
streets and public buildings; it creates more police problems, thus affecting the expenditure
of that service; it causes additional ﬁre risks which must be factored in allocation of ﬁrnds
for ﬁre protection; and its movement in and out of the city is a factor in the budget of the
health department of the city. Then, the hypothesis arising ﬁom these assumptions was

that the annual expenditures of city governments should vary with the sizes of populations

l9

occupying adjoining areas. A corollary hypothesis of these assumptions was that the
larger the proportion of the total population living outside the city, the heavier should be
the tax burden on the population living within the city.

Hawley used the 1940 Bureau of Census data for seventy six cities with
population over 100,000 to perform correlation analysis. The correlation between all per
capita expenditures of city government and city population was found to be was slightly
curvilinear ( y = 0.51). However, he believed that the curvilinearity may be due to lack of
control of related variables and assumed, but not tested, that multiple correlation analysis
could correct the problem.

The zero-order correlation coefﬁcient was computed for each of the three
dependent variables (namely, all government expenditures, operating expenditures, and
capital improvement expenditures) with the eight demographic variables of the city
governments and the remainder of the districts (population size, population density,
population grth rate, number in labor force, number in white collar occupation, number
of houses, houses per square mile, area in square miles, percent of population
incorporated, and percent of total district population). The per capita expenditures of the
governments (computed on the population residing within the city) were more closely
related to population living outside the city than to the population residing within the city.
The per capita operating costs also revealed similar result. Based on this general
observation, the major hypothesis that stated the annual expenditures of city
governments should vary with the sizes of populations occupying adjoining areas appeared

to hold. However, the study showed that the capital improvement expenditures were only

20

slightly associated with the independent variables reﬂecting, according to the author, the
inadequacy of a single year data for a study of capital improvement expenditures.

The operating expenditures were more sensitive to variations in population than
were capital improvement expenditures. Likewise, government expenditures were more
closely associated with density of population within the city (r = 0.53) than with the size of
city population (r = 0.40)

The correlation between population growth rate and the dependent variables was
found to be slight and inverse in Hawley’s study. The cities and their surrounding districts
also showed no appreciable differences in this respect. Similarly, the association between
the labor force and government expenditures was insigniﬁcant for both the cities and the
remainder of the districts. However, the result became highly correlated when it was for
the number of people employed in white collar occupations and government expenditures.
Housing density was also found to be more consistently related to government
expenditures than the number of houses in the city or the total area of the city in square
miles.

Taking note of the major ﬁnding of his study, Hawley focused more on the
correlation of population and the dependent variables and asked to what extent the
association between expenditures and population was inﬂuenced by variations in other
independent variables. Then, multiple correlation (R) for government expenditures and
population was computed by successively adding each of the other variables speciﬁed for
the cities and the remainder of the districts. Of all the variables, the density of population
within the cities was found to exert signiﬁcant inﬂuence on the association of all

expenditures and population size; the measure of the population and government

21

expenditures changed from r = 0.40 to R = 0.55. The inﬂuence of the rest of the variables
was found to be not signiﬁcant.

The extent to which all the independent variables (8 for cities and 10 for the
surrounding metropolitan districts) explain the variations in all city government
expenditures was computed and R2 of 0.57 was obtained . That is, the total effect of all
the independent variables accounted for only 57 percent of the variation in all municipal
expenditures in the cities. The R2 for operating expenditures and capital improvement
expenditures were found to be 0.59 and 0.54 respectively

Forty percent of the variation in city government expenditures remain unexplained.
The existence of such large residue, according to Hawley, may have been due to
inadequate deﬁnitions of jurisdictional areas (like metropolitan districts) employed by the
Bureau of Census or missing important variables in the model. For instance, consideration
of per capita income may be important in that it reﬂects the ability and willingness of the
population to support the city governments expenditures. Similarly, the nature of the local
economy could be important in that the economic characteristics of the surrounding cities
have signiﬁcant impact on the budget and expenditures ofthe city under consideration.

With the main objectives of establishing patterns of differences in per capita
expenditures of cities and analyzing the association between city expenditures per capita
and important economic variables, Harvey E. Brazer studied per capita expenditures of
462 US large cities in 1951 and per capita expenditures of the 40 largest of these cities in
1953. The expenditure categories included were total general operating and six ﬁrnctional
categories (police, ﬁre, highways, recreation, general control, and sanitation). Capital

outlays, largely reﬂecting construction programs, were excluded from the study because

22

the author considered this category of expenditure to vary from year to year. Yet, the
capital expenditures of police, ﬁre, and general control were not netted out because the
Census Bureau data used for the study did not provide a breakdown between capital and
current expenditures of these functional categories by individual cities.

Measures of variations of expenditures per capita, as computed from the data of
Bureau of the Census, Compendium of City Government Finances (1950), for all the 462
cities indicated that the variation coefﬁcient for total general operating was 54.3 and 22.8
for common ﬁrnctions'. These variations coefﬁcients reﬂected the diﬂ‘erences among cities
in the distribution of ﬁrnctional responsibilities.

The mean, lowest, and highest total general operating expenditures for all the 462
cities were $47.57, $12.86, and $165.16 respectively; and $28.26, $11.31, and $80.66 for
common ﬁrnctions. The data, when evaluated by geographic divisional means, showed that
there was a variation in the per capita total general operating expenditure ranging ﬁ'om
$28.28 for cities of the West North Central states to 89.19 for cities in the New England
states. The highest per capita expenditures were found to be in the older cities of New
England, Middle Atlantic, and South Atlantic states, where, the author believed, traditions
of local autonomy in government were strongest and their cities had retained
responsibilities for most of the optional functions of city governments. Most of these
ﬁrnctions were administered by the state, school district, or county elsewhere in the nation.
In contrast, the per capita total general operation expenditure was the lowest for newer
cities of West North Central and West South Central states, where cities generally enjoy

fewer measures of political and economic importance.

23

Taking California, Ohio, and Massachusetts as states for regional comparison,
Brazer found that the variation coefﬁcients of the total general operating expenditure for
cities in these states were very different ﬁom that of the 462 cities considered together.
They were 23.5 for 35 cities in California, 8.8 for 30 cities in Ohio, and 25.0 for 32 cities
in Massachusetts compared to 54.3 for all the 462 cities across the nation. The between
states and within states variance of the total general operating per capita expenditure
category were 6,097.58 and 215.48 respectively with F value of 28.3, while those for the
common ﬁrnctions category were 468.40 and 47.28 with 9.9 F value.

The correlation analysis of the association between expenditure categories revealed
that only two sets of functional categories (police protection and ﬁre control and police
protection and general control) had a correlation coefﬁcient greater than 0.5. Ifall
functional categories were shaped or inﬂuenced by same explanatory variable(s), the
author explained, high coeﬁicient of correlation would have been obtained among all
categories. Moreover, the budgetary patterns among cities were extremely diverse
suggesting that no single factor accounted for the variation among cities in per capita
expenditures. Therefore, there was no compelling evidence to expect cities within
individual states to follow a consistent pattern than in the case of the 462 cities taken
together.

The least-square multiple regression analysis was used to describe the average
relationship between the per capita expenditure and the selected independent variables.
The cities were divided into ﬁve sub-groups: the 462 cities with population greater than

25,000 in 1950 (because complete data for that year was available for places with

 

1 Common function category included were police, ﬁre, highways, recreation, general control, and sanitation.

24

population of 25,000 or more sizes); 35 cities in California; 32 cities in Ohio; 30 in cities in
Massachusetts (the three states were selected as three sub-groups for the purpose of
holding the factors peculiar to individual states constant); and 40 cities, excluding
Washington DC, with population greater than 250,000 in 1950 (because they form
homogeneous group in terms of population and expenditure data for their overlying units
of governments were available. These data were required to compute the ratio of the city’s
population to that of its metropolitan area).

The basic assumption of the analysis was that all of the relationships among the
variables were linear and the sum of the squared deviations of the estimated values were
reduced to their least possible magnitude. The regression results were presented in terms
of estimated coefﬁcients ([3), elasticities, and multiple correlation coefﬁcients. The
estimated coefﬁcients were the weight assigned to a particular independent variable. The
elasticities were the measure of percent change in the dependent variable induced by 1
percent change in the speciﬁed independent variable. The multiple correlation coeﬁcients
measure the degree of association between the dependent and independent variables.

The coefﬁcients of multiple correlation of the regression analysis range ﬁ'om 0.76
for total general operating to 0.24 for ﬁrnctional category of recreation. That means, the
highest ability of the model to explain the factors behind expenditures was 58 percent at its
best and 6 percent at its lowest. However, some instructive generalization had emerged
from the exercise. With a due caution of census data error, the analysis had shown that the
association between population size and almost all, but police, per capita expenditures was

not statistically signiﬁcant as measured by its [3 value and elasticity measure (.015).

 

25

In a sharp contrast to the role of population size in explaining expenditure
variations for the 462 cities, population density had shown a remarkable association with
all types of expenditures with the exception of recreation. Excepting for its minor
association with total operation and ﬁre protection expenditures, population grth did
not appear to have role in shaping municipal expenditures. The median family income,
excepting for total general operating expenditure, had statistically signiﬁcant positive
association with all expenditures of ﬁrnctional categories. Ratio of employment had a sort
of mixed results. The association between employment in manufacturing, trade, and
service sectors and per capita expenditures appeared to increase as population increased.
But the regression coefﬁcients relating this variable with most of the expenditures were
not compelling. Of all the six independent variables in the regression model, it was only
the intergovernmental revenue per capita that was signiﬁcant in explaining all expenditure
categories.

The research conducted by Schmandt and Stephens (1963) was national in scope,
covering all the 3,096 counties in the nation. Using the 1957 Census of Government data,
it employed county area aggregates (in which expenditures by all local goverrunents and
special and school districts were grouped together) as unit of analysis.

The 3,096 counties were sub-divided into the traditional nine regions classiﬁcation
of the Bureau of Census (New England, Middle Atlantic, East north Central, West North
Central, South Atlantic, East South Central, West South Central, Mountain, and Paciﬁc).
Like in Hawley’s (1952), zero order correlation analysis was used to determine the
relationship of the mean per capita expenditures of county area aggregates and the

independent variables. The independent variables were total population, population

26

density, territorial area, state aids, and median family income. The total expenditures were
composed of two expenditure categories: total current expenditures and capital
expenditures. The functional categories included in the study were highways, public
education, police, ﬁre, parks and recreation, general control, sewerage and sanitation, and
health and welfare.

The descriptive statistics of the data showed wide differences in the regional
aggregate per capita total expenditures ranging ﬁ'om an average low of $80.56 (for the
East South Central States of Alabama, Kentucky, Mississippi, and Tennessee) to average
high of $221.06 (for the Paciﬁc region including California, Oregon, and Washington). In
general, the Southern states were at the low end of all the per capita expenditures and the
western states were toping the list, followed by the Middle Atlantic States of New York,
New Jersey, and Pennsylvania. The ranking by functional categories also followed the
same pattern.

The computation of the expenditures data for counties in all regions, excepting the
East South Central, indicated that those counties with population less than 5,000 had the
highest operating expenditures of all population size categories. However, the authors
cautioned that care must be taken in making a generalized assumption of systematic
relationship between per capita expenditures and population size because of the existence
of considerable variations within size groups as well as between them. In addition, the data
used in this particular study suggested that both the very large and very small counties
suffer ﬁom diseconomies of scale yielding the usual “U” shaped curve on the population-

per capita expenditures space.

27

The population per capita expenditure scenario appeared to be a little different
when the capital improvement expenditure was considered separately. Although the
counties with population under 5,000 spent more than the subsequent four population size
categories of higher order, the difference was very small. The steeper upswing started with
the population size category of 50,000 - 100,000 and the per capita expenditures of capital
improvements kept increasing with each subsequent class. The largest jump occurred in
counties with population over one million. Although the mean per capita for capital
improvement indebtedness followed the same pattern, the authors were a bit cautious that
comparisons among jurisdictions on the basis of a single ﬁscal year may prove unreliable
because capital expenditures of governmental units tend to move unevenly over time.

The percentage of budget allocated to schools and roads indicated a negative
relationship to population size, but that expended on health and welfare, police, ﬁre,
sewerage and sanitation, and parks and recreation showed positive association. The
authors argued that the explanation for this observation depended on the facts that local
governments in rural counties may discharge their principal responsibilities when they
provide for the education of the children and see that their residents have adequate
network of passable roads. Urbanization, on the other hand, brings with it the need and
demand for sewerage disposal, public health measures, recreational facilities, better police
and ﬁre protection, and similar type of services.

Schmandt and Stephens, found several important associations between per capita
expenditures (total and ﬁrnctional categories) and the ﬁve independent variables.

Amongst several conclusions that could be drawn from their analysis were:

28

(1) state aids, followed by median family income, emerged as the most important variable
inﬂuencing per capita expenditures by county area aggregate. State aids and family
income were measures of the availability of resources and reﬂect what communities

can aﬂ‘ord to expend on public services.

(2) while per capita expenditures tended to rise in all functional categories with increase in
median family income police and ﬁre, welfare, highways, and public education were

more influenced by State aids.

(3) although they showed signiﬁcant association with functional categories like protective
services (police and ﬁre), total population and density did not affect total per capita
expenditures appreciably. The reason for this relationship was, according to the
authors, that population and density were inversely related to expenditure for streets
and highways because the per capita mileage to be maintained decreases as population
and density rise. The protective services, on the other hand, were urban type ﬁrnctions

and their magnitude increased as population and population density increased.

(4) while state aid showed little relation to population size, median family income was
signiﬁcantly associated with population size and population density. This was a
reﬂection of the greater economic opportunities and wealth that exist in the large

urban centers.

29

(5) total current expenditure per capita showed higher association with territorial size of

the counties than with total population and population density.

Woo Sik Kee (1965) observed that most of the empirical studies regarding
expenditure behavior of central cities had not been satisfactory because, (1) they were
limited in scope (in terms of areas, class of governments, or ﬁrnctions they considered);
(2) they did not recognize the ﬁscal interdependence between state and local governments
on the one hand, and among the local governments on the other. Thus, in his attempt to
augment the previous studies with a research that considered intergovernmental ﬁnancial
interdependence and one with broader scope he set two speciﬁc purposes for his study.
They were: (1) discussing critical differences of socio-economic and governmental
characteristics between the city and areas outside the central city’, and (2) showing the
relationships between the level of per capita city expenditures and selected explanatory
variables by incorporating the effects of intergovernmental ﬁscal responsibilities into
multiple regression analysis.

Thirty six Standard Metropolitan Statistical Areas (SMSAs) showing variations in
geographic location, population size, patterns of state and local governmental system,
were selected. Public services of these 36 SMSAs were provided by a total of 4,482 local
units of governments. Using the 1957 Census Bureau data six explanatory variables (per
capita income, owner-occupied housing units as percent of total occupied units,

population density, ratio of central city population to total SMSA population, ratio of

 

2 The deﬁnition of 'central city‘ established by the US Bureau of the Census, which Kee adopted, was a city
or adjoining (twin) cities within 20 miles of each other that contain total of 50,000 or more inhabitants

30

state and local functional responsibility, and per capita state aid) were regressed on three
dependent variables (total general expenditures, non-educational expenditures, and non-
aided expenditures).

The central cities and the rest of the metropolitan areas had substantial variations
($61.22 for Savannah, GA to $256 for Sacramento, CA and New York) with regard to
per capita total expenditure and other major expenditure categories such as education,
welfare, health, and highways. The variations were attributed to the differences in
population characteristics, degree of urbanization, the level of income, and social and
economic preferences in the study areas. Yet, the major hypothesis of the study was that
the large part of the differences in per capita local expenditures within metropolitan areas
was attributable to the differences in the distribution of governmental responsibilities
between the state and its political subdivisions and the attendant share of state aid.

Although it was true that substantial variations existed between central cities and
the rest of the metropolitan areas (sub-urban areas) in total per capita expenditure, it was
not evident from the data that central cities spent more than the rest of the metropolitan all
the time. For example, while the total expenditure of New York sub-urban areas was
$259.38, it was only $256.22 for New York City. Likewise, cities of Albany, Bridgeport,
Buffalo, Norwalk, Stamford, Syracuse and Utica spent less than their sub-urban areas.
This observation was a serious challenge to the earlier ﬁndings of Hawley (1952) and
Brazer (1959 and 1962) that state (1) the total per capita expenditure of the central cities
was closely related to the ratio of the central cities to the total population of their
metropolitan districts, and (2) higher total expenditures were consistently incurred in the

central cities (Brazer, 1962). According to Kee’s argument the mere fact that central

31

cities, in many instances, spend relatively more than the sub-urban areas does not establish
the evidence that the residents of the sub-urban areas impose a net expenditure burden on
the central cities. In cases where the sub-urban communities spend more than the central
cities, he argued that it was so because of the relatively greater state aid to the areas
outside the city.

Woo Sik Kee cautioned that expenditure burdens of central cities and sub-urban
areas are much more difﬁcult to be explained by simple comparison of expenditures in that
central cities, quite often, incur additional functions like urban renewals that could make
the level of expenditure look higher at one point in time, where as some features of sub-
urban areas (voluntary community services like ﬁre ﬁghting and privately operated
sanitation) are ignored, there by making the level of expenditure look lower. Instead, he
suggested that contrasting individual ﬁrnctions would be a more adequate method of
comparison between the two places. Accordingly, he computed the coefficient of
variation3 for each ﬁrnction in the central cities and sub-urban areas to compare the
relative dispersions of the various classes of expenditure. The computation revealed that,
excepting for health and hospitals, the coefﬁcients of variations for per capita total general
expenditure, total education, highways, and public welfare were higher for the sub-urban
areas than the cities. Kee claimed that these variations of per capita expenditures of each
category indicate that there is a great difference in the allocation of functional

responsibilities between state and local governments.

 

3 The coefﬁcient of variation (V) is a measure of variation used to compare inter-functional and inter-
jun'sdictional per capita expenditures. The formula used to calculate was V = slx‘, where s is the standard
deviation aid x‘ is the arithmetic mean of the 36 selected central cities and areas outside the cities.

32

Masten and Quindry (1970), using the 1966 per capita expenditures gathered
through the Wisconsin State Department of Revenue, studied city expenditure
determinants of 567 cities and villages in the State of Wisconsin in 1970. The sub-
groupings of these 567 cities and villages consisted of 477 cities and villages with total
population of less than 5,000, 62 cities and villages with total population of 5,000 -
20,000, and 25 cities and villages with population of 20,000 - 100,000. The relative
importance of expenditure determinants for cities and villages of diﬂ‘erent population sub-
groupings were examined with the use of basic regression and correlation models.

When all cities and villages were analyzed together, the regression analysis
revealed that the estimated [is of the ﬁve independent variables, namely, total population,
population density, per capita adjusted gross income, per capita full value of assessed
property, and land area were 0.179, 0.161, 0.138, 0.688, 0.485 respectively. This showed
that the per capita full value of property has the highest explanatory power than all other
variables. The ranking of the independent variables in accordance to their contribution of
increasing the coefﬁcient of multiple determination (R) was found to vary by city and
population sizes. For places with population less than 5,000 the ranking by descending
order was per capita ﬁrll value of assessed property, per capita adjusted gross income, land
area, population density, and total population. For places with population 5,000 - 20,000
it was per capita ﬁrll value of assessed property, total population, population density, per
capita adjusted gross income, and land area. For places with population 20,000 - 100,000
it was population density, per capita full value of assessed property, per capita adjusted

gross income, land area, and total population.

33

This study highlighted that the ability to pay taxes (revenue for city services) was
very important for the ﬁrst and second sub-groupings, and second most important,
following population density, for the third sub-grouping. In contrast, total population
(excepting for its second place in the second sub-grouping) was the least important in
inﬂuencing the coefﬁcient of multiple determination.

Population density variable was the strongest expenditure determinant for 25 cities
and villages in the 3rd sub-grouping. More importantly, as cities became more populated,
the changing positions and importance of the determinants suggested unique growth
process. For instance, for the ﬁrst two sub-groupings with population less than 20,000 the
ability to pay for city services, as measured by property value, was the most inrportant
variable. When rapid urbanization phase was reached and the city expanded beyond a
certain population size, street improvement, improved sewerage facilities, modernized ﬁre
ﬁghting equipment, and other departmental expansions necessitated more than
proportional increase in per capita expenditures and this phenomenon was represented by
the increasing importance of the density factor as an explanatory variable in cities of the
next higher population sub-grouping (20,000- 100,000). Conﬁrming some ﬁndings of
some other earlier studies, in particular that of Schmandt and Stephens (1963), they
suggested that the interrelationship between per capita value assessed property, population
density, and total population on the one hand and per capita expenditures as city size
changed on the other reﬂected economies or diseconomies of scale in the provision of city
services.

The deviations and confusions between most of previous studies on factors

inﬂuencing expenditures of local governments, according to Masten and Quindry, were

34

attributed to the general lack of data of cities and villages and the varying circumstances
under which the studies were conducted. For instance, they cited the rejection of city size
by pervious studies while it was later found to be very important in determining the
relative explanatory ability of other socioeconomic factors as an example. Finally, they
underscored the fact that the expenditure impact of the ﬁve basic variables considered as
signiﬁcant in previous expenditures studies, varied with city sizes; and all but one, land
area, were found to be signiﬁcant explanatory factors for cities and villages in the State of
Wisconsin.

The most recent study of the association between public service expenditures and
selected explanatory variables was the one conducted by A. Allan Schmid (1997) for the
State of Michigan. This study was original not only in its methodological approach but
also in the type and quality of data it used. Seventeen cities and twenty-nine townships,
representing different geographic locations and population size groups in Michigan, were
purposefully selected out of the 71 communities in the State that have grown by a
population of at least 1,000 between 1981 and 1990 and have a population of 5,000 or
more.

Fifteen years total expenditures data (excluding enterprise funds) was used in this
study. The data was collected directly from the annual reports of cities and townships
included in the research. The data was superior in quality when compared with all other
data used in prior studies because: (1) they were actual expenditures (as opposed to
budgeted expenditures) audited by certiﬁed public accountants and ﬁled with the Michigan
Department of Treasury; (2) the total operation expenditure were adjusted for the general

inﬂation and were in 1995 constant dollar; and (3) the total capital improvement

35

expenditure was adjusted and amortized over a stand period (30 years) to avoid the erratic
nature of capital investment expenditure.

Multiple regression of cross sectional data for 1990 and 1995 were performed to
determine the association between the dependent variable (total expenditures per capita)
and the selected explanatory variables (total population, population growth rate, location,
total state equalized value of property, and percent of state equalized value of residential
WOW)

The study had revealed several ﬁndings that were both in agreement and
disagreement with previous studies. For instance, where most of previous studies indicate
that there is strong association between population and expenditures in general, Schmid
found that the relationship between city population and expenditures were negatively
correlated and statistically not signiﬁcant. His simple regression of population over
expenditures per capita showed that only 12% of the variation in city expenditures was
explained by population size. However, when similar analysis was done for townships
separately from cities, total population and per capita expenditures showed statistically
signiﬁcant and positively correlated association. The simple regression of population over

expenditures per capita also showed that 57%‘ of the variation in township expenditures

 

‘ The table below was reproduwd here just to show the impressive predication ability of the single variable
regression model that explained only 57% of the variations in expenditures of townships. The per cmita
expenditure prediction was calculated by multiplying the total population of the given township by the [3 value
(which is 0.003) of the model (p. 33).

 

Predicted Actual 1990
Township Per Capita per capita
Expenditure Expenditure
Clinton 342 321
Waterford 282 313
W. Bloomﬁeld 252 278

 

36

were explained by population size. According to the author, while the offsetting of some
of the increasing cost tendencies in cities by some other decreasing costs over some size
ranges may explain the observed relationship of population and expenditures, new service
needs and associated jump in expenditures as townships grow indicate the positive
association between population and expenditures. Moreover, unlike the townships, large
and small cities provide similar services and there will not be dramatic jumps in
expenditures as they grow in size. Therefore, it will not be inconsistent that population
size and expenditures exhibit inverse relationship.

The multiple regression results of this study showed that all the selected
explanatory variables jointly explained 75 and 60 percents of the variations in the 1990
expenditures of townships and cities respectively with similar results for 1995. For the
townships, population size, state equalized property value, and proportion of residential
properties were statistically signiﬁcant. While population and property value were
positively associated with expenditures, proportion of residential property was negatively
correlated. The broad speciﬁcation of location (as Southeast Michigan or not) and
population growth rate, however, did not contribute to the explanations of per capita
expenditures of townships signiﬁcantly.

For the cities, the only statistically signiﬁcant variable was location. Population
was not signiﬁcant and population grth rate (also not signiﬁcant) was negatively
correlated. The model revealed a slightly different results for 1995: population growth

rate, location, and proportion of residential property were barely signiﬁcant.

 

Meridian 192 255
Macomb 162 110
Fruitport 132 122

37

Similar analysis was performed using per household expenditures as the dependent
variable with the same explanatory variables. For cities, using the 1990 data, none of the
explanatory variables was signiﬁcant. But, for townships, with a slightly decreased ability
of the joint explanatory variables in explaining expenditures (69% vs. 75%), the same
variables (population size, state equalized property value, and proportion of residential
property value) remained signiﬁcant.

The rate of expenditure analysis of the study revealed that: ( 1) increase in
expenditures for fastest growing townships was no different than the average for all
townships, (2) large townships had higher expenditures regardless of their rate of growth,
(3) the rate of growth in expenditures and population followed the same direction for
cities, and (4) regardless of their grth pattern, larger cities did not exhibit higher
expenditures.

In order to give more insight into the relationship between expenditures and
population size, the study presented some historical perspectives of the ﬁfteen years total
expenditures and individual expenditures of some functional categories (general
government, public safety, roads and streets, and water and sewer) by dividing the sample
communities into seven population size groups without distinction between the form of
government (city or township) and location. The functional categories, according to the
author, were public service types that mark certain expenditure threshold as population or
density increase.

The analysis revealed some observations that explain the relationship between

expenditures of functional categories and population size. For example, it showed that the

 

38

expenditure for public safety in townships increases at a decreasing rate with rise in
population; and while mid-sized cities have shown increase in roads and streets per capita
expenditure over a range of period, large and small size group cities do not show any ﬁrm
pattern in per capita spending.

Schmid started out the study with two major questions: (1) do population size and
location of local governments have effect on public service expenditures? and (2) if they
do, could public service expenditures be reduced by altering macro-pattems of future
settlement (or development)? The answer to both questions was yes. Population size and
location may affect cities and townships differently, but there is evidence from the study
that the macro pattern of population location and the micro pattern of size and density of

population are policy tools that can reduce the public service expenditures levels.

39

2.2 Lessons From the Studies

It can be summed from the foregoing review that population size and growth rate
have been found to be the most important variables that explain variations in public service
expenditures by Berlozheimer (1947) and Schmid (1997), as it only related to townships.
0n the other hand, for Hawley (1951), Brazer (1959), Schmandt and Stephens (1963),
Kee (1965), and Masten and Quindry (1970) population size and growth rate were of the
least importance. Instead, excepting for Masten and Quindry, population density and the
ratio of the population of the community to that of its metropolitan district were very
important.

In addition to the authors reviewed above, other distinguished early researchers
had also attempted to show which of these variables inﬂuence public service expenditures
most. For instance, Mabel L. Walker (1930), in her study of municipal expenditures, had
found that per capita costs of government increase rapidly as the population increases.
Supporting her conclusion, Donald H. Davenport (1947) studied 56 cities around New
York and determined that there was positive correlation between per capita expenditures
of cities and population size. Hansen and Perloff (1944) and Solomon Fabricant (1952)
have also conﬁrmed these ﬁndings.

Contrary to the conclusion of these researchers, Gerhard Colm et al (1936),
aﬂirmed that density of population is of utmost importance in the cost of public services to
the taxpayer. Nevertheless, since the authors believed that industrialization and wealth
inﬂuence density of population, they had enjoined that it is diﬂicult to isolate the genuine
inﬂuence of density on public costs and it could be further assumed that density can

decrease per capita costs in certain area of functional categories. Five years later, Arnold

4O

Brecht (1941) also published a research, which supports Colm er a] by concluding that it is
only density of population that is highly correlated with per capita expenditures of
municipal services.

Scott and Feder (1957), on the other hand, published a totally different ﬁnding.
They studied 192 California cities with 1950 population of 2,500 or more and examined
the relationship between the municipal expenditures per capita (excluding public service
enterprise expenditures and those ﬁnanced through special assessments) and the
explanatory variables they considered. The independent variables they used in the model
were retail sales per capita, rate of growth of population, median number of persons per
occupied dwelling unit, total population, population density, and adjusted property
valuation per capita. They attributed expenditure differences in California cities to
variations in tax paying ability of the population. The analysis showed that it was the
adjusted property valuation per capita that had statistically signiﬁcant regression
coefﬁcient. But four years later, Shapiro (1961) came with an other different conclusion
ranking land area of a local government as the most important explanatory variable.

It can be said that little agreement existed amongst the researchers reviewed here
as to which independent variables are most important in explaining local government
expenditures. As a result, there is no single formula or rule that satisfactorily explains the
casual relationships involved. Nevertheless, there are some variables that are more
ﬁ'equently offered as the leading factors. That includes, total population, population
grth rate, population density, median household (family) income, land (territorial) area,

inter-governmental revenues, and property value.

41

To their credit, most of the authors recognize that public service expenditures are
determined not only by the economic elements which have been considered here, but also
by many political, social, and personal factors (Walker, 1930; Colm et al, 1936; Brazer,
1959; Schmid, 1997). Although these social, political, and personal inﬂuences could have
eﬂ‘ect only within a ﬁamework set by the economic factors determining the requirements
for and costs of public services and the resources available for ﬁnancing them, the .
ambition of an able governor, mayor or legislator, for example, may have an important
inﬂuence on the kind and size of public expenditures in a state or local government.
Unfortunately, there is no deﬁnite and ready measure of such variables that could help the
analysts to quantify its effect on the casual relationships between public service
expenditures and the factors involved.

Notwithstanding Woo Sik Kee’s criticism, most of the studies reviewed, excepting
that of Schmid, are of national or regional scope. Studying public service expenditures at
larger levels of system of government (state, regional, or federal) could have both
advantages and disadvantages. On the advantage side, (1) it creates ease of comparing
public service expenditures among states and regions for which data are readily available
ﬁ'om the Census Bureau, and(2) it eliminates the inﬂuence of differences in the distribution
of service responsibilities among the various types of local governments of city, township,
or school district (Schmandt and Stephens, 1963).

On the disadvantage side, it hinders the ability of a researcher to compare
expenditure patterns among and between the smallest units of governments and suppresses
the role of each variable that has different explanatory ability for different size and types of

local government. For instance, Masten and Quindry found that population density was

42

the most important variable in explaining the expenditure behavior of all the 25 cities and
villages with a population range of 20,000 - 99,999 in the State of Wisconsin in 1966. But,
at the same time, they found that population density ranked fourth, out of ﬁve explanatory
variables, in its ability to explain the expenditure behavior of all the 567 cities and villages
in Wisconsin considered together. Hence, it will be difﬁcult to accept results based on the
ﬁndings of larger set of cities without qualiﬁcation.

Similarly, the Michigan study by Schmid (1997) revealed that population size was
the most important variable that explained the expenditure patterns of 29 Michigan
townships, while it, at the same time, showed no signiﬁcant association with the
expenditures of the 17 cities considered in the study. Distribution of service
responsibilities vary among cities and townships. Accordingly, their revenue collection
ability and patterns of expenditures are different. Therefore, it will be inaccurate to put all
local governments in one pot and analyze the casual relationships of the variables that are
of interest without making any distinction to their form and structure.

Finally, the type of data used by most of the researchers are susceptible to
inadequacy. First, the data were collected by the Bureau of Census and it is not clear as to
how much these data are ﬁtting the objectives of the researchers without any adjustment.
Some of the researchers have noticed the discrepancy between the data they needed and
what was available to them. This discrepancy had created deﬁnite constraints on their
ability to carry out a reliable analysis. Secondly, most of the researchers relied on a single
year cross-sectional data to perform the analysis. Some were aware of the drawbacks that
the use of a single year data was imposing on their analysis. As a result, some of them

were forced to abandon the consideration of capital improvement expenditures from their

43

analysis all together. Others have some how went ahead with the one year data available
to them and cautioned that the ﬁndings be seen only as an ad hoc. Even if the problem
surrounding abandonment or use of capital improvement expenditure is to be tolerated,
how much could the results of all other expenditures based on a single year data be
reliable?

The main point of departure between the current study and the prior studies is
around this question. The method of analysis applied and types of data used are very
diﬂ'erent. The current study used ﬁfteen years time-series cross-section data on
population, expenditures, and state equalized value of properties along with other
supplementary data of individual service categories. 1t performed rigorous and extensive
statistical and regression analysis of panel data for forty six fast growing local
governments of different population size groups, geographic location, and types of

government in the State of Michigan.

CHAPTER 3
CONCEPTUAL FRAMEWORK TO ESTHVIATE
DETERMINANTS OF PUBLIC SERVICE EXPENDITURES

3.1 Introduction

This chapter develops a conceptual framework that can be used to estimate the
determinants of per capita public service expenditures (expenditures, here after) in the fast
growing communities of Michigan. The model derived can also be viewed as a local
government expenditure decision model. Expenditures patterns of communities are
expected to vary by types of government (city or townships) and are further sub-classiﬁed
by geographic location and population size groups. Furthermore, expenditures are
assumed to be functions of total population size, population growth rate, population

density, residential property as percent of total property, and value of properties.

3.2 The Expenditures Model

Following the general models developed by Masten and Quindry (1970) and
Schmid (1997), the model of analysis of was speciﬁed as follows:

expend = ﬁpoptotal, popgrwth, popdenst, rsdntprp, totalprp)

Where: poptotal = total population
popgrwth = population grth rate
popdenst = population density

44

45

rsdntprp = residential property
totalprp = total property

The general objective of local governments was assumed to be providing the best
possible public services (maximizing service beneﬁts) with minimum expenditures.
However, eﬂiciency of the governing bodies (or public service providers) on the one hand
and quality and quantity of the public services provided on the other were variables that
were very diﬂicult to measure, at least for this study. Consequently, they were not

included in the model speciﬁcation.

3.3 The Dependent Variable

The dependent variable was the per capita total expenditures for public services. It
was computed by dividing total expenditures by total population of each study community.
The total expenditures were adjusted for inﬂation and were in 1995 constant dollars. The
functional categories for which the total expenditures were computed included general
government, public safety, public works, welfare and social services, culture and

recreation, capital outlay, and debt service.

3.4 The Independent Variables

There were ﬁve independent variables considered in this study. They were total

population, population growth rate, population density, residential property as percent of

total property, and equalized value of total properties.

46

3.4.1 Total Population

Total population of communities was one of the variables that was often offered as
the most important variable that affects expenditures in much of the literature (Donald H.
Davenport, 1926; Brazer, 1959; Census Bureau, 1951; Schmid, 1997). It was, therefore,
hypothesized that the higher the population size, the higher the expenditures will be.
Furthermore, changes in per capita expenditures and total population were expected to
move in the same direction.

The hypothesis relied on the assumption that demands for more and improved
public services will increase as the population of a community grows. The increase of
demand for public services, holding quality of public services constant, will place more
pressure on local government budget and will increase public service expenditures.

Most of the public services (public safety, water and sewer, and roads for example)
are congestablc goods with capacity constraints. These classes of goods may be having
scale economies over a certain range of population and may have a zero marginal cost as
the number of users increases from zero to some given number (capacity threshold). But,
as population keeps increasing, the addition of more users reduces the utility of services
and quality of life of all users and the marginal cost of additional users begins to rise. As
the absolute capacity constraint is reached, the marginal cost of additional user will
increase sharply (Randall, 1987). Then, governments are expected to invest more on
public services and their related infrastructures to at least keep the quality and per user

quantity of services constant when faced with growing population.

47

Diseconomies of scale may also be a factor that raises the expenditures of
communities that have passed a certain population threshold. As the total population of a
community increases beyond a certain level, different types of services may become
economically feasible or necessary. Some communities may grow to a population size that
may require them to provide their own services (like police and/or ﬁre protection, for
instance) instead of contracting from other agencies or jurisdictions. Or new types of land
development that may have been necessitated by population growth (more multi-family
dwellings vs single family dwellings, or more commercial developments vs residential
developments) may require better and more ﬁre trucks, more and wider streets than the
existing ones, etc.

Most of the infrastructures of public services are lumpy in nature. At times,
improving infrastnrctures and services by increment may not be possible. It may become
necessary to totally scrap the old infrastructures and build new ones. This will cause a
large capital expenditure. Furthermore, the per capita expenditures on the construction,
maintenance, and service of these new lumpy infrastructures could stay high because it
may take a while for the optimal number of people making use of them to settle.

Population could also have indirect impacts on expenditures through other factors
that have direct relationship with expenditures. For instance, income could be a ﬁrnction of
population (Brazer, 1959). Mostly, economic opportunities are higher where population is
the highest. As a result, income could be high where economic opportunities are high.
Then, the high income population could be more willing to demand and able to pay for

higher quality of public services.

48

3.4.2 Population Growth Rate

Although it was assumed that the needs and demand for public services increase as
the population of communities grow, it was hypothesized that expenditures and the rate
of population growth will not necessarily ﬂow in the same direction. Even if population
may be growing at a faster rate, new expenditures on infrastructures may not be necessary
as existing facilities could be used more intensively because the existing service facilities
may have excess capacities, or simply budgetary allocations commonly do not keep pace
with the expansion of service requirements (Brazer, 1959; Schmid, 1997). Budget
allocation is a function of several factors, including political choices and tax payers
willingness to ﬁnance the service investment. That means, the service expenditures do not
necessarily grow proportionately with the rate of increase of population. Some earlier
studies have indicated that governmental infrastructures and institutions, once established
for minimum purposes, grow with population but at a rate less than population. Therefore,

inverse relationship between population grth rate and expenditures was expected.

3.4.3 Population Density

Population density, as a measure of the extent to which people live close to each
other, was considered in this study because levels of expenditures of the major public
services were reported to be functions of density in several earlier studies. In the case of
highways and streets, for example, it had been reported that as the density of population

increases road per capita expenditure will decline (Colm, et al, 193 6). As density increases

49

per capita mileage of roads to be maintained should fall and it is unlikely that greater
traffic volume resulting from higher density will offset this beneﬁt (Brazer, 1959). On the
other hand, the need for police and ﬁre protection, for example, may be increasing as
population density rises. Therefore, it is hypothesized that population density and total per
capita public service expenditures are highly associated; but the sign of the correlation
depends on the budget share of each functional category. If, for instance, police and ﬁre
protections constitute major share of the total public service expenditures, it should be

expected that the sign of estimated coefﬁcient and correlation would be positive.

3.4.4 Property Value and Land Use Characteristics

Land use in the State of Michigan could be divided into four major groups;
agricultural, commercial, industrial, and residential. Different types of land use will require
different types of public services. If, for instance, a community is characterized as rural
and agricultural, its road, ﬁre and police protection, or water and sewer requirements will
be different from those of commercial or industrial communities. Industrial communities
may require more governmental services than agricultural communities. The demands for
highways, sanitary services, communication, protection, etc. increase inevitably with
industrialization and urbanization. Therefore, it was hypothesized that there is a systematic
relationship between land use and public service expenditures. Residential property is
expected to have inverse relationship with expenditures whereas industrial and commercial

properties will be positively related to expenditures.

50

The state equalized value of all types of preperties are used as proxies to measure
the impacts of land use characteristics on expenditures. Property value captures both the
wealth and tax paying ability of a community and many earlier studies have established
that general government expenditures of a community are closely related to income and
wealth in that jurisdiction (Schmid, 1997). Therefore, since public services are
predominantly determined by the resources available for expenditures, it was hypothesized
that the value of total property will determine the relationship between the effective

demand for public services and services provided by local governments.

3.5 Attributes of Services and Model Specification

Most of the past studies of public service expenditures have recognized the
possible relationship between efﬁciency of governments and quantity and quality of
services on the one hand and per capita public service expenditures of local governments
on the other. But, they did not attempt or, may be, they were unable to develop a method
of analyzing the association between these attributes of local government and public
services and the associated expenditures. For example, the same amount of dollar outlays
to construct a water and sewer infrastructure in different geographic or topographic areas
may not produce the same physical amount or unit of infrastructure at these different
places. If it did, then, the inﬁ'astnrctures at these different places must be of diﬂ‘erent
quality or are done with a varying degree of efﬁciency. But, how can we measure this type
of association between these attributes and expenditures at national, regional, state, or

local levels? Unfortunately, much remains to be explored in solving this problem. Still to

51

date, there is no meaningful statistical or any other empirical method that could be used to
measure the different elements of these attributes and their impacts on public service
expenditures (Colm, et al., 1936 ; Brazer, 1959; Schmid, 1997).

Consequently, this study analyzed impacts of selected economic variables on
expenditures of local governments rather than on costs of a given quality and per capita
quantity of services provided by local governments. Also, little data on service levels (per
capita quantity of services provided) are available. For example, we may know the exact
number of police ofﬁcers in a given community and that number (and the expenditure)
may appear to be too high in comparison with other similar community of equal size. But
it will not be known if that community has decided to have that many ofﬁcers because
crime is more common in that community or just because the community chose to have a

higher level of services such as faster response time.

3.6 Omitted Variables

Two revenue variables that were used by many of the earlier researchers were not
considered in this study for several reasons. These variables were inter-govemmental

revenue transfers and household (family) income.

3.6.1 Inter-governmental Revenue Transfers
Does the source of revenue affect the level of expenditures? Or conversely, would
there be difference in expenditures whether the expenditures are paid for by revenues ﬁ’om

intergovernmental transfers or taxes collected from the residents? Intergovernmental

52

revenue transfer was not speciﬁed as an independent variable in this study. However, it
has been offered by some of the earlier researchers as one of the leading factors
inﬂuencing the level of expenditures. Indeed, it was one of the major contributors to
revenues of most of fast growing local governments in Michigan (over 20% for many of
the cities and townships). Nonetheless, this analyst did not ﬁnd it to be compelling to
consider this variable in the model because he argues that changes in expenditures of local
governments would ﬂow in the same direction with changes in intergovernmental revenue
transfers. Ifthe revenue transferred to a local government from the state is high, that local
government is now getting more money to spend on new services or to improve on the
quality and quantity of existing services. Ifthe revenue transferred is less, that local
government will have less to spend. Unless it is intended to investigate whether
intergovernmental revenue transfer is associated with other economic variables (say,
population size, density, or growth rate), which was not the objective of this study, there
was no need to consider it in the model as an independent regression variable apart from
the other public revenues. Furthermore, it had been indicated in some of the earlier studies
that intergovernmental revenues and per capita expenditures are signiﬁcantly and -

positively correlated (Schmandt and Stephens, 1963; Woo Sik Kee, 1965).

3.6.2 Household (Family) Income

Some of the earlier studies have used household (family) income in their studies of
public service expenditures. Using this variable may have not caused any signiﬁcant
problem in their analysis because: (1) they did not include other economic variables that

have strong correlation with it in their models; and (2) they were using a single year cross-

53

sectional data. However, this variable was excluded from the model of the current study
exactly for the two reasons it was used by earlier researchers. First, a correlation analysis
performed with the 1992 median household income in the 46 fast growing corrununities in
Michigan showed a very high correlation (0.88) with the equalized value of residential
property. Such high correlation creates a multicollinearity problem in the regression
analysis and will make the model weak in explaining factors that drive the variations in
expenditures of the communities . Second, household income data is neither available on
yearly basis nor could it be projected. The current study requires the exact income data for
the ﬁfteen years period covered. Therefore, household income was dropped ﬁom the
model and, instead, the equalized values of properties were used as proxy of wealth and

income of the study communities.

3.7 Unit of Observation and Categories of Analysis

The analysis in this study was conducted using a local governments as a unit of
observation. All the data were for municipalities and townships. However, in order to
make a meaningful comparison by creating homogeneity among the units of analysis, the
local governments were categorized by type of government (city or township), two
general geographic locations (Southeast Michigan or Rest of State), and two arbitrary

population size groups (equal to or more than 50,000 and less than 50,000).

54

3.7.1 Types of Government

Different local governments have different responsibilities and taxing power in
provisions of public services. The two types of governments in Michigan that were
included in this study are cities and townships. These governments operate under diﬂ‘erent
laws and they are different in their distribution of public service responsibilities. For
example, cities have to provide their own road and street services, while the responsibility
of constructing and maintaining roads and streets in townships is assigned to the County
Road Commission since 1931 (Delphendahl, 1961).

In most of the cases, cities have more responsibilities in providing public services
to their residents when compared to townships and, as a result, they have higher
expenditures. On average, in 1995, for instance, the sampled fast growing cities in
Michigan spent more per resident than the townships. Townships may use some of the
services provided by adjoining cities or counties free or with minimal pay. Consequently,
they could have less expenditures.

Furthermore, cities and townships differ in their taxing power. For example, a
charter township can levy 5 to 10 mills with a vote of the people, while cities may levy up
to 20 mills. These differences in service provision responsibilities and revenue collection
authority have signiﬁcant impacts on the patterns and extent of expenditures. The
seventeen cities and twenty nine townships included in this study have signiﬁcant
difference in expenditures. Therefore, cities and townships can not be mixed and

compared. .

55

3.7.2 Geographic Location

Location of a local government was used as a sub-category of comparison. It was
expressed as whether a place is in Southeast Michigan (SEM) or Rest of the State.
Southeast Michigan is the most populous region of the state where more than 50% of the
population is currently residing. Cities and townships in this region are more clustered
than anywhere in the state. That is, local governments in Southeast Michigan are located
close to each other and exhibit a degree of settlement congestion. Per capita public service
expenditures of communities in a relatively congested area would be expected to be
higher because a considerable portion of the expenditures would be caused by residents of
the adjoining communities. The residents of the adjoining communities are attracted by
activities and facilities in that particular community. The effective population of a local
government, where high settlement density is observed, is considerably greater than what
is contained within the incorporated boundaries of that political jurisdiction (Hawley,
1952; Schmid, 1997).

The impacts of the economic variables in explaining expenditures by location was
investigated by separating the sample cities and townships into the two locations
mentioned above. Location does not vary from period to period and remains to be a
constant in the panel. Moreover, the econometric model chosen for the study, Fixed
Eﬂects regression, does not allow the use of individual level covariates in the model.

Therefore, it was not considered as an independent regression variable in the model.

56

3.7.3 Population Size Groups

Population has a unique position in the public service expenditures of all local
governments. Unlike geographic location, for instance, it can serve as a sub-category of
comparison and, because it varies ﬁom year to year, can be used as an independent
variable of regression in the model at the same time. Many of the earlier studies have
presented different reports on the association between expenditures and different sizes of
population. The impact and ranking of the explanatory power of other variables, for
instance, were reported in some of the earlier studies to have been dependent on the sizes
of population. Thus, in order to comprehend the signiﬁcance of the variable in shaping
expenditures of communities, it was decided to thoroughly analyze the relationship
between population and expenditures in this study at two levels with a data set that

considers the continues changes in population.

CHAPTER FOUR

ANALYTICAL METHODS FOR ESTIMATING DETERMINANTS
OF VARIATIONS IN PUBLIC SERVICE EXPENDITURES

4.1 Introduction

The main purpose of this chapter is to develop an empirical method of estimating
the determinants of per capita public service expenditures in the fast growing local
governments in the State of Michigan. Two major tasks are accomplished in the chapter.
First, the data used in the empirical analysis are described in detail and all the procedures
and processes involved in cleaning, adjusting, and organizing all the data are presented in
several sub-sections. Finally, the econometric method employed for the analysis is

discussed and the regression equation is developed.

4.2 The Data

The data used in this study include: US Census population ﬁgures of 1980 and
1990 for all the fast growing communities in Michigan and the 1994 population projection
of the Michigan Department of Management; public service expenditures of all service
categories (general government, public safety, public works, recreation and culture, capital

outlay, debt service, etc) from the Comprehensive Annual Financial Report (1981 to 1995)

57

58

of the forty-six communities; state equalized value of agricultural, commercial, industrial,
personal, and total properties (1981 - 1995) of the all the forty-six communities; public
safety data of 1990 and 1995 for all cities and townships in the study; and roads and

streets expenditure for selected communities.

4.2.1 Population

The study covered the period between 1981 to 1995. Population data of the US
Census Bureau were only available at ten years interval and the 1980 and 1990 population
ﬁgures were used to determine the fast growing local governments that were included in
the study. Communities with a population greater than 5,000 and had grown by 1,000
people between 1981 and 1990 were purposeﬁrlly deﬁned as fast growing local
governments. However, townships of Alpine in Kent County and Muskegon and Fruitport
in Muskegon County, which have grown by less than 1,000 residents, were included in the
study for the purpose of having a reasonable geographic distribution and representation of
the local governments in the study. That brought the total number of local governments in
Michigan deﬁned as fast growing communities to sixty-nine (17 cities and 52 townships).
While all the seventeen cities (100%) were included in the study, a sample of twenty-nine
townships out of total population of ﬁfty-two (56%) were selected. These twenty-nine

townships fairly represent different population sizes and geographic locations.

59

 

 

 

 

 

 

Table 4.1: All Fast Growing Cities in Michigan, 1980 - 1990
Pop Pop Pop Change
City 1980 1990 1980 - 1990
Sterling Htsw 108,999 117,810 8,811
Portage 38,157 41,042 2,885
Wyoming 59,616 63,891 4,275
Troy 67,102 72,884 5,782
Farmington H181 58,056 74,652 16,596
Rochester Hill 40,779 61,766 20,987
Kenlwocd 31.438 37 .826 7,388
Novi 22,525 32,998 10,473
Holland 21,767 25,086 3,319
Graidville 12,412 15,624 3,212
Walker 15,088 17,279 2,191
Aubm Hlsr 15,598 17,076 1,478
Wixom 6,705 8,550 1,845
Marysviller 7,345 8,515 1,170
Lapeer 6,198 7,759 1,561
Brighton 4,268 5,686 1,418
Walled Lake 4,748 6,278 1,530

 

 

 

 

 

60

 

 

 

 

 

 

 

 

 

 

 

Table 4.2: All Fast Growing Townships in Michigan, 1980 - 1990
Pop

Township Pop Pop Change
1980 1990 80 - 90
Clinton 72,400 85,866 13,466
Shelby 38,939 48,655 9,716
Waterford 64,437 66,692 2,255
W. Bloomﬁeld 41,962 54,516 12,554
Canton 48,616 57,040 8,424
Meridian 28,754 35,644 6,890
Georgetown 26,104 32,672 6,568
Delta 23,822 26,129 2,307
Plainlield 20,611 24,946 4,335
Chesterfield 18,276 25,905 7,629
Harrison 23,649 24,685 1,036
Macomb 14,230 22,714 8,484
Contmerceu 23,757 26,955 3,198
Independence 21,537 24,722 3,185
Orion 22,473 24,076 1,603
Van Buren 18,940 21,010 2,070
Delhi 17,144 19,190 2,046
Holland 13,739 17,523 3,784
Pittsfield 12,997 17,668 4,671
Northville 12,987 17,313 4,326
Garﬁeld 8,747 10,500 1,753
Allendalet 6,080 8,022 1,942
East Bay 6,212 8,307 2,095
Oshtemo 10,958 13,401 2,443
Alpine] 8,934 9,863 929
Byron 10,104 13,235 3,131
Cascade 10.120 12,869 2,749
Gaines 10,364 14,533 4,169
Grand Rapid 9,294 10,760 1,466
Spata 6,934 8,447 1,513
Hamburg 11,318 13,083 1,765
Washington 10,213 13,083 2,870
Brandon 9,526 12,051 2,525
Lyon 7,078 9,450 2,372
Milford 10,187 12,121 1,934

 

 

 

 

 

61

 

 

 

 

 

 

 

 

 

 

 

 

Table 4.2: (Cent'd)
Pop
Township Pop Pop Change
1980 1990 80 - 90
Oxford 10,569 1 1,933 1,364
Springfield 8,295 9,927 1,632
Grand Haven 7,238 9,710 2,472
Park 10,354 13,541 3,187
Antwerp 7,744 9,293 1,549
Scio 8,029 11,077 3,048
F ’ 10,646 11,485 839
Muskegon 14,557 15,302 745
Kinross 1,891 6,566 4,675
Long Lake 3,823 5,977 2,154
Texas 5,643 7,711 2,068
Ada 6,472 7,578 1,106
Algoma 4,411 5,496 1,085
Caledonia 4,927 6,254 1,327
Cannon 4,983 7,928 2,945
lra 4,316 5,587 1,271
Northlield 4,672 6,732 2.060
Table 4.3: Townships Selected for the Study.
Clinton Delhi
Shelby Holland
Waterford Pittslield
W. Bloomfield Northville
Canton Alpine
Meridian Cascade
Georgetown Grand Rapid
Delta Sparta
Plainiield Milford
Chesterfield Fruljgort
Harrison Muskegon
Macomb Long Lake
Commerce lra
Orion Norlhlield
Garfield

 

 

 

 

 

62

A simple arithmetic method was used to compute the annual total population of
each community. The annual population growth rate between 1980 - 1990 was obtained
by computing the percentage change between 1980 and 1990 and dividing that by 10:
[(popoo - popmypopgoylo. The annual total population between 1980 and 1990 were
interpolated by multiplying the preceding year’s population by one plus the annual growth
rate. For instance, if the annual growth rate of a community was 2%, 1981 population of
that community will be 1980 population plus the computed annual growth,

i.e., popan, = popm, x(1+0.02).

Similar calculation was used for the period between 1991 and 1994 on the basis of
the 1994 population projection of the Michigan Department of Management and Budget.
The population ﬁgures of all the communities for 1995 were extrapolated by using the

same growth rate calculated for the period between 1991 and 1994.

4.2.2 Expenditures

Tables 4.4 through 4.8 display the expenditures data for ﬁfteen years period
(1981-1995).obtained from Comprehensive Annual Financial Report (CAFR) and annual
audit of local govemments'. CAFR are prepared by certiﬁed independent public
accountants and are approved by Michigan Department of Treasury. A 1994 revenue-

expenditure balance sheet of all Governmental Funds Types for Meridian Township was

 

' There were few instances, like in the case of City of Walker, Kent County, where CAFR of some years
were missing. Interpolation of estimated expenditures head on the averages of the prewding and
succeeding years in conjunction with data from F-65 for the missing years had been applied to complete the
data requirements.

63

presented in Table 4.4 as an example of a typical ﬁnancial statement for a local
government in Michigan.2

A closer look at the CAFR of all the local governments indicates that their
revenue-expenditure accounts are organized on the basis of different types of funds and
account groups. A ﬁrnd is a separate accounting entity with a self-balancing set of
accounts. Each of the account groups are considered a separate accounting entity and
contain information related to assets, liabilities, ﬁrnd equity, revenues, and expenditures.
Public resources are allocated to an individual type of fund based upon the purpose for
which they are to be used. They are grouped into seven fund types (General Funds,
Special Funds, Debt Service Funds, Capital Project Funds, Enterprise Funds, Internal
Service Funds, Trust Funds). These ﬁmd types are grouped within three broad categories;
namely, Government Funds, Proprietary Funds, and Fiduciary Funds.

The Government Funds, the only funds category used in this study, is for those
funds through which most typical governmental ﬁrnctions are ﬁnanced. As shown in Table
4.4 above, four types of government funds are included in this category: General Fund;
Special (Selected) Revenue Funds; Debt Service Funds; and Capital Projects Funds. Debt
Service Funds are not used in the empirical analysis for reasons explained elsewhere in

this chapter.

 

2 All the sample tables and figures on expenditures and state equalized values of properties presented in this
chapter are those of Meridian Township. There is no particular reason why Meridian is chosen over the other
locd govemrmnts. The same tables and figures are done for all the 46 local governments included in this
study. It is decided to stick to one local govemment for the purpose of showing the logic and sequence of
cleaning, adjusting, and organizing the data. All data pertaining to the 1994 fiscal year are highlighted.

64

4. 2. 2.1 General Fund

This is the basic and primary operating fund for general government operations. It
records ﬁnancial resources used for day-to-day general government service activities, such
as municipal administration, public safety, parks and recreation, environmental health, etc.
This fund receives the majority of its ﬁnancing from such sources as property taxation,
state shared revenues, fees and charges for services, investment income, and an annual
operating transfer from other departmental funds in accordance with provisions in the

governmental charter.

 

65

 

 

 

 

 

 

 

 

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H: 23

 

4.2.2.2 Special Revenue Funds

These are fund types used to account for the proceeds of speciﬁc revenue sources
(other than special assessments, expendable trusts, and major capital projects) that are
legally restricted to expenditures for speciﬁed purposes. They include funds like the
Highway and Major Streets Fund, Highway and Local Streets Fund, both established by
State of Michigan Public Act 51 of 1951, County Road Tax Fund established by the State
of Michigan Public Act 283 of 1909, Public Library Fund, Police Criminal Justice Training

Fund, etc.
4.2.2.3 Debt Service Funds

These are fund types used to account for the accumulation of resources for and
the payment of principal, interest, and related costs of general long-term debt obligation
and special assessment long-term debt. The general obligation debt service fund accounts
for the servicing of current maturity requirements (that include principal, interest, and
agent fees) on general obligation bonds like building authority bonds and other bonds
issued by Authority of State of Michigan Act 40. The revenues to ﬁnance such debt
service obligations are derived from property taxation, transfers from other funds, and
investment income. Special assessment debt service funds account for the servicing of
outstanding long-term debt in the form of special assessment bonds. Revenues to ﬁnance

these debt service obligations arise from special assessments levied against beneﬁting

67

property owners in approved special assessment districts for which the bonds were

originally issued.
4.2.2.4 Capital Projects Funds

These are ﬁmds used to account for ﬁnancial resources utilized for the acquisition
or construction of major capital assets or inﬁa-structures other than those projects
ﬁnanced by Proprietary Funds and Expendable Trust Funds. Financing for these kinds of
projects include operating transfers from other funds, special assessments, private sector
donations, and grant funding. Each of the projects in this group of funds are normally
budgeted and accounted for as multi-ﬁscal year to encompass revenues and expenditures
that span the entire open period of the speciﬁc project ﬁ'om inception to completion.
However, project revenues and expenditures are also recognized by individual ﬁscal year

for annual ﬁnancial purposes.
4.2.3 Adjusting Expenditures

Although the data in the CAFR of the local governments are of high quality and
reliable, they needed to be adjusted and rearranged in a way that they ﬁt the objectives of
the study. Consequently, some of the data speciﬁc to some service categories were
excluded; some of the ﬁmd types and categories were netted out; all of the expenditures
and equalized values of property data were adjusted for inﬂation; and the capital project

expenditures were amortized.

68

4.2.4 Excluded Fund Types

Three types of funds were purposefully excluded from the study. They were
Enterprise Funds, Internal Service Funds, and Fiduciary Funds. The ﬁrst two types of
funds are used to account for the local government’s ongoing organizations and activities
similar to those found in the private sector. They are accounted for on a cost of service or
capital maintenance measurement focus. All assets and liabilities associated with their
activity are included on their balance sheets, and operating statements present increases
and decreases in net total assets.

Enterprise funds account for: (a) operations that are ﬁnanced and operated in a
manner similar to business entities, where the intent of the service provider is that the
expenses, including depreciation, of providing goods and services to the general public on
a continuing basis be ﬁnanced primarily through user charge; or, (b) operations where the
governing body has decided that periodic determination of revenues earned, expenses
incurred, and/or net income is appropriate for capital maintenance or other purposes.
Examples of such funds are water and sewer fund, power utility funds, parking lots fund,
municipal airport fund, depot operations fund, and recycling pickup fund.

Internal Service Funds are used to account for the ﬁnancing of goods and services
provided by one department or activity of a city or township to other departments or
activities of the government; and/or to other governmental units on a cost-reimbursement
basis. These funds are established, managed, and Operated as a proprietary type operation,
providing ﬁnancial accountability for (a) operating and non-operating revenues and

expenses, (b) current assets, restricted assets, capital assets, liabilities, and fund equity.

69

Examples of these funds include information services fund, equipment revolving fund as
mandated by State of Michigan Act 51 of 1951, postage services fund, telephone services
fund, ﬁre vehicle and equipment ﬁJnd, vehicle and property insurance fund, health and
dental insurance fund etc.

Fiduciary Funds, also referred to as Trust and Agency Funds, are used to account
for assets held by the local government in a trustee capacity or as an agent for individuals,
private organizations, other governments, and/or other funds. These include Expendable
Trust, Non-expendable Trust, and Agency funds. The Expendable Trust Fund is
accounted for in essentially the same manner as a Governmental Fund, which means both
principal and earnings are spendable. The Pension Trust Fund is accounted for in the same
manner as Proprietary funds (only earnings are spendable). The Agency Funds are
custodial in nature and do not involve measurement of results of operations.
Disbursements from these funds are made in accordance with trust agreements or
applicable legislative enactment for each individual fund. Examples of these funds are:
Expendable Trust Funds: utilities guaranteed fund, police community relations fund, and
municipal airport donations fund; Non-expendable Trust Fund: cemetery perpetual care
ﬁJnd, library endowment fund; and Agency Fund: current tax collections fund, employee
deferred compensation plan fund, and employee flexible spending fund.

Moreover, including Enterprise Funds such as water and sewer fund creates
problem when comparing expenditures across communities. The service boundaries of
such service categories may not necessarily coincide with the political boundaries of local
governments (Schmid, 1997). Some local governments may not serve all the residents of

their political boundary and others may extend the service to residents of other political

70

jurisdictions. Pittsﬁeld Township, for instance, has an area where its sewer service does
not reach and those residents use their own septic systems. On the other hand, the water
authority of the Detroit Metropolitan Water authority is serving many of the local

governments in Southeast Michigan.

4.2.5 Netting Out Expenditures

A special care was taken to avoid double counting and over stating expenditures.
The special revenue and debt service sections of the expenditures account present such a
problem. Debt service appears as both ﬁmctional category and (ﬁnd types at the same
time (see Table 4.4). It accounts for principal retirement and interest and fees paid out of
both the special revenue and debt service ﬁrnds.

It was assumed here that debt services are mostly related to capital project outlays.
Careful examination of the CAFR of each local government in the study did not indicate
otherwise. Moreover, capital project outlays are signiﬁcant in the calculation of
expenditures of all local governments. For example, the beginning and ending fund
balances of the 1994 ﬁnancial statement of Meridian Township indicate that the capital
project fund accounts for more than 50% of the total Ending Fund Balance. Similarly, the
ﬁnancial statements of the 46 local governments for the ﬁfteen years show that capital
projects outlay is an essential part of local governments expenditures. Unlike most of
prior studies that have ignored it, it is deemed necessary to consider the capital project
expenditures along with the total operating expenditures of all local governments in the

study.

71

However, including both the capital project outlays and debt service expenditures
in the calculation of the total capital project expenditures poses the problem of overstating
the total expenditures of the local governments. The debt service expenditures could
include: (1) the capital outlays incurred prior to the study period; and (2) part of payment
on capital project expenditures already entered under its own ﬁJnd type, depending on
when such expenditure was incurred in the ﬁscal year. Hence, it was necessary to: (l)
exclude the debt service fund all together, (2) net out the capital outlay expenses in the
special revenue account; and (3) amortize all entries under the capital project ﬁrnds to
account for only the study period expenditures and avoid over/under stating yearly
expenditures. Table 4.6 was presented below to show the necessary ﬁrst step in adjusting

public service expenditure accounts, especially columns e and f.

5.2.6 Inﬂation Adjustment

The operating and capital project expenditures of all the study communities were
adjusted by a national index of deﬂators shown in Table 4.5. This was done for the
purpose of accounting for inﬂation and generating comparable expenditure ﬁgures in
terms of constant dollars. The operating and capital project expenditures have different
deﬂators and were computed accordingly. For example, in 1994 Meridian Township had a
total operating expenditures of $9,710,919 (Table 4.6). When adjusted for inﬂation, the
expenditure was equal to $10,011,257 in 1995 dollars. Adjusted and amortized total
expenditures of Meridian Township are displayed in Table 4.7 as a sample. It must be

noted, however, that the adjustment of capital project expenditures was diﬂ‘erent from that

72

of operating expenditures. It involved two steps of operations. First, the yearly total
capital project expenditures were amortized. Then, the amortized yearly expenditures were

adjusted by the corresponding deﬂators. This will be discussed in the next section.

Table 4.5: Deﬂators of Operating and Capital Project Expenditures

 

 

Operation Exp. Capital Project Exp.

Year. Deﬂator 1%) Deﬂator (96)
1981 59.5 73.1
1982 63.1 73.4
1983 65.5 74.0
1984 68.7 76.4
1985 71.6 80.6
1986 73.9 82.2
1987 76.6 83.0
1988 79.9 86.8
1989 83.2 89.5
1990 86.7 91.0
1991 89.7 91.6
1992 92.2 91.5
1993 94.6 93.6
1994 97.0 96.7
1995 100.0 100.0

 

 

 

Source: Survey of Current Businesses

73

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74

4.2.7 Amortization

As noted above, the capital project expenditures of all the study communities were
standardized by amortizing the actual capital spending that had occurred during the study
period. The amortization was for 30 years period at a ﬁxed 5% interest rate. This
approach was selected for several reasons. First, it showed the underlying production cost
of services without confusing them with how local governments might have decided to
ﬁnance them (Schmid, 1997). Second, each year’s capital project spending is distributed
into the future, mostly 30 years, through bond issuance and similar means. Although actual
cash disbursement in full amount of the project cost might have taken place during one
ﬁscal period of a local government, assigning the total amount of that disbursement to
that particular year’s expenditure will be overstatement. Analogously, it will be under
statement of the expenditures of the subsequent years. Third, the total expenditures of the
study period will not be affected by expenditures prior to 1981 because debt service
expenses were netted out.

The amortization process is depicted in Tables 4.8 and 4.9 below. For example, if
the 1981 Meridian Township capital project expenditure of $99,472 is amortized for 30
years at 5% interest rate, there will be equal annual payments of $6,471 each year for 30
years before inﬂation adjustment. The capital project expenditures entered for each of the
ﬁfteen years were the horizontal sums of the amortized and adjusted capital project
expenditure in Table 4.7. For example, the 1994 capital project expenditure of Meridian
Township is $483,762. This is the sum of all the annual capital project payments from

1981 to 1994. But, in 1994 Meridian Township had incurred an actual spending of

75

 

 

Table 4.7: Adjusted and Amortized Total Expenditures of Meridian Township
Adjusted Adjusted Amortized
Year 0p Exp. CP Exp. Op Exp. CP Exp.

1981 3,668,436 99.472 6,165,439
1982 4,321,659 236,613 6,848,905
1983 4,421,958 97,717 6,751,081
1984 4,823,647 1.873.457 7,021,320 196.
1985 5,415,421 316.631 7,563,437 211 771
1986 5,712,405 377,991 7,729,912 237.
1987 5,855,134 43.447 7,643,778 238.67
1988 6,145,325 35,976 7,691,270 , 230.9
1989 6.855.610 30,536 8.239.916 226.17
1990 7,604,565 1.242.594 8,771,125 311 2
1991 8.837.046 1.477.270 9.851.779 414 1
1992 9,793,884 440,707 10,622,434 445
1993 0.052.948 83,216 10,626,795 441 71
1994 9,710,919 835,579 10,011,257 483 78
1995 9,827,968 605,378 9,827,968 507 17

 

 

 

$835,579 (see Tables 4.4, 4.5, 4.7, and 4.8). Out of this $835,579, it is only the amortized

and adjusted value of $56,211 that entered as part of the 1994 capital project expenditures

(see Table 4.9). The amortized balance of this $835,579 actual spending (excepting the

payment of $54,356 in 1995) will be carried into future periods that are outside the time

range of this study. The grand total expenditures of all the study communities was

computed by summing the total operating and capital project expenditures reported in

Table 4.7 after completing all the netting out of the total operating expenditures,

amortizing the capital project expenditures, and adjusting both expenditures for inﬂation.

Each year’s grand total expenditures were divided by the corresponding total population

to obtain the total per capita public services expenditures (see Table 4.10)

76

 

 

 

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77

 

 

 

 

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ad 333.

 

78

 

 

Table 4.10 Per Capita Public Service Expenditures of Meridian Township

Grand Total Total Exp.

Year Exp. Population Per Capita
(a) (b) (0) (NC)
1981 6,174,291 29,443 210
1982 6,878,691 30,132 228
1983 6,789,215 30,821 220
1984 7,217,774 31,510 229
1985 7,775,209 32,199 241
1986 7,967,475 32,888 242
1987 7,882,456 33,577 235
1988 7,922,196 34,266 231
1989 8,466,094 34,955 242
1990 9,082,402 35,644 255
1991 10,265,929 35,770 287
1992 11,068,368 35,896 308
1993 11,068,507 36,022 307
1994 10,495,019 36,148 290
1995 10,335,147 36,274 285

 

 

4.2.8 State Equalized Value of Properties

 

The ﬂﬁeen years state equalized value of properties in the forty-six local
governments were collected directly from the report of State Tax Commission,
Department of Treasury. Following the same procedure of inﬂation adjustment, all of the
equalized values were adjusted by the capital expenditure deﬂators. The section labeled
“other” includes properties listed under Timber-Cut-over Real Property, Developmental
Real Property, and Personal Property. The ﬁrst two real properties are seldom available in
all the communities and were very insigniﬁcant. They were added with Personal Property

and labeled “Other” just to account for 100% equalized property value in a community.

79

89 . 62 6233.500 x8. 085 ”8.58

 

 

 

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838.8 88.8.8 03.8.88 «8.8.88 8«.8«.5« 83.8.— 82
282.888 8.88.8 838.88 «8.288 2.3.2.888 «8.8.8.— 82
88.88.88 838.2. 8«.2«.«8 §.8o.« «3.88.8. «8.88 82
«8.25.8 «8.28.8 28.388 88.83 28.82.82 «8.«: 82
2a8q8« 88.8.8.2. 8.88.88 88.828 «888.82 «8.88 82
$85.88 28.82:. 2882.82. 28.38.. 2.2.3.82 38.83 82
5.838 2888.8 «88.8.. 08.83 888.5 «8.82 82
2.83.88 5.88.; «88qu 28.8: 88.5.8. 88.22.. 82
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“:..« 032.

 

4.2.9 Population Density

Population density was one of the signiﬁcant variables in the empirical analysis of
this study. The yearly population densities were calculated by dividing the total population
by the land area of the communities. Table 4.12 shows the changes in annual pepulation
density of Meridian Township as an example while Table 4.13 displays the total land area

of each local government in the study,. Similar population density tables were prepared for

all the study communities.

Table 4.12: Total Land Area and Population Density of Meridian Township

80

 

 

 

 

 

Land Area Density
Year (sq. mile) (persons/Sq. Mile)
1981 33 892
1982 33 913
1983 33 934
1984 33 955
1985 33 976
1986 33 997
1987 33 1,017
1988 33 1,038
1989 33 1,059
1990 33 1,080
1991 33 1,084
1992 33 1,088
1993 33 1,092
1994 33 1.095
1995 33 1,099

 

 

81

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£8.55 .882 .882 528.5 8.38 e... 8953 E
.82 8.8.5 282 e... 8...... saw .0 .5588 E .858

 

 

 

 

 

 

 

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8 E 28.8 3 Q 2%: 8
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8 E 232 8 E 8.2.58 8 Q as: 88.2....
8 E .2 0888 8 E 2.8 8
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82

4.3 The Empirical Method of Analysis

The data set used in this study is interchangeably called panel, longitudinal, or
crossfsection time-series data. Fiﬁeen years of observations on cross-section of forty-six
local governments, a total of 690 observations, were made available. There were sixty-
nine local governments that qualify as fast growing communities according to the
deﬁnition adopted for this particular study. Forty-six local governments representing
diﬂ‘erent population sizes, geographic location, and government types were selected as
samples.

Two major inferences were drawn from earlier studies that relate to this research.
The ﬁrst one was that variations in public service expenditures across communities can not
be fully explained by an analysis of a historical data for a single variable of observation (a
local government in this case) over a certain period of time only. This suggested that a '
time-series analysis that uses a set of observation drawn ﬁom one observational variable at
a number of points in time should not be used alone. Secondly, an observation of a single
year data of many observational variables did not help to produce consensus on factors
explaining the variations in public service expenditures. Consequently, cross-section
analysis that uses a sample of a number of observational variables all drawn at the same
point in time should not be used alone. Therefore, panel data, that comprises both cross-
sectional and time-series data, was collected and organized and a corresponding panel data
analysis technique that combines the above two methods of analysis in a single

econometric equation was employed.

83

4.3.1 The Fixed Eﬂects Econometric Model

The econometric model used to analyze this data set is called the Fixed Eﬁ’ects
model. Indeed, there is one other model, the Random Effects model, that could have been
considered as an alternative to the use of Fixed Effects model. But, because (a) the
random effects model presupposes the existence of an overall intercept for all units of
observation (local governments), and (b) it assumes that the random error associated with
each cross-section unit is uncorrelated with other or missing regressors, it is not applicable
for this particular study. For instance, if public service expenditures per capita is regressed
on total number of population, and that demography (which is actually a missing variable
in this particular study) can affect the intercept, then, running the regression with random
eﬁ'ect model will create correlation between the error term and population, because
population and demography are likely to be correlated. The ﬁxed effect modeL however,
avoids these sorts of problems and produces results conditional on the units in the data set
only (Greene, 1997).

Moreover, while Random Effects model is suitable for a small sample data drawn
from a larger population at random, Fixed Effects is usually used for a data set that
exhausts the population (Kennedy, 1992). In the case of this study, the sample data set
used exhausts the population in that it consists of all the cities (100%) and twenty-nine of
the ﬁfty-two townships (56%). Therefore, the choice and use of the Fixed Effects model

was justiﬁed.

84

4.3.2 Assumptions of the Fixed Effects Regression

The use and application of the Fixed Eﬂects regression technique in this study are
based on the three basic assumptions of the model: heterogeneity, stochastic relationship,

and residuals.

4.3.2.1 Heterogeneity of Units of Observations.

Heterogeneity across the observation units in the context of this study was
considered to be essential. It was based on the assumption that the constant term, a), of
the regression equation (model) vary across the local governments and the time periods

and the differences across units can be captured in differences in the term.

4.3.2.2 Stochastic Relationship

Preliminary observation of the expenditure data set showed that the relationship
between the public service expenditures and the explanatory/independent variables were
not ﬁxed, exact, or detemiinistic. Since the study was conducted under a non-experimental
and uncontrolled environment, it was necessary to assume that the relationship between
the explanatory variables and the dependent variable (the per capita public service

expenditures) are stochastic in nature.

85

4.3.2.3 The Residuals

This is a critical assumption in that it is based on the assertion that the relationship
between the dependent and the independent variables of the model is signiﬁcantly
inﬂuenced by the disturbance or error terms (commonly called residuals). In other words,
the estimation of the unknown or and [3 parameters of the independent variables largely
depends on the nature of the error terms.

Error terms could arise in this study from one or combinations of the following
factors. First, several variables (like demography and politics, for instance) that may have
systematic and/or irregular inﬂuences on public service expenditures were not included in
the model. This omission could constitute speciﬁcation error that leads to inaccurate
estimation of the economic relationship between public service expenditures and the
independent variables.

Second, because of data collection difﬁculties and the inherent measurement
problems in some of the variables, measurement errors could be committed. For example,
the ﬁgures used for density were more or less approximation. That is, besides dividing the
total population by the total land area of the local governments, the exact measure of
density for the communities was not available.

Third, people decided public service expenditures. Usually, people randomly make
diﬁ‘erent decisions under identical circumstances that can not be explained or measured
with identiﬁable variable. The Fixed Effects regression technique, by taking all these
assumptions into consideration, performs a complex statistical analysis that controls these

and similar error terms and yield more reliable empirical results.

86

4.3.3 Mathematical Representation of the Fixed Effects Model

The basic framework of the Fixed Eﬂects model utilized here to describe the
average relationships between the dependent and the independent variables was as

developed by William Gould (1997) and Greene (1997):

yr: = a+ﬂn +vr +5.1 (1)

where:
ya. = dependent variable (per capita public service expenditures of unit iat time t)
x5. = vector of all independent (explanatory) variables (of unit i at time t)
a = constant (intercept)
B = estimated coefﬁcients of the independent variable
v = unit-speciﬁc residual (differs between i units but constant for any
particular unit)
a = “usual” residual (with mean 0, uncorrelated with itself, uncorrelated
with v, and homoscedastic)

From equation (1) it follows that

y, = a+f,.,6+v,. +5,
where:

j", , f, , and e.- are averages of y... x... and a... In other words, they are within-group
means.

Subtracting equation (2) from (1), we obtain
y. - Y.- = (x. - 37.- W + (8.. - a. (3)
Equation (3) is the most common form of the Fixed Eﬂects estimator. But, in this
' formula, (1 remains unestimated. Therefore, with ﬁirther mathematical manipulation, it

follows from equation (1) that

87

j) = Siﬂ + V + 5 (4)
where
j", 52, V , and t? are the grand averages of y", x", v, and 5..
The computation of the grand averages follows the formula,

9 = {(ZZym N}

i=l l=l

where N = number of observations

Summing equations (3) and (4), we obtain

yrr“yr+.9=a+(xrr—f+£)ﬂ+(£rr-Er+v)+é (5)

Then, the Fixed Effects regression estimates the above equation under the
constraint v = 0. That means, it estimates

y“ -7,. +5) = a+(x,., -f+x),6+noise 3;

 

3 It should be noted that adding in grand means to the left and right hand sides of the equation has no effect
on the estimated 8.

CHAPTER FIVE

DETERMINANTS OF PER CAPIT A PUBLIC SERVICE
EXPENDITURES IN FAST GROWING COMMUNITIES OF MICHIGAN

5.1 Introduction

This chapter presents results of the statistical analysis of the variables described in
previous chapters and the empirical output of the Fixed Effects regression model
developed in Chapter Four. Descriptive statistics of the selected variables are discussed in
detail. Methods used for data classiﬁcations are presented and the diagnostic regression
performed to check for existence of any statistical problem in the model is explained. The
ﬁnal regression results of the model are displayed in their respective categories and,

ﬁnally, the result of the reliability test of the model is shown.

5.2 The Variables

Although all of the forty six local governments selected for this study are generally
classiﬁed as fast growing communities, they are very diverse in their population size,
population growth rate, population density, land use characteristics, and level of total
expenditures per resident. They range from Sparta Township in Kent County, which

spent only $34 per person (in 1981) to City of Auburn Hills, Oakland County that

88

89

spends $1,029 (in 1995). A general summary of the selected explanatory variables of the

communities is presented in Table 5.1.

Table 5.1: Minimum. Maximum, and Mean Values of Selected Variables, 1981 - 1995.

 

 

 

 

 

 

 

 

 

 

Variable Mean Minimum Maximum

Expenditure Per Capita 287 34 1,029
Total Population 28,745 4,038 119,929
Population Growth Rate 0.018 -0.01 0.06
Population Density 1.086 112 3383
Agricultural Property 281 O 2.259
Commercial Property 3,542 392 12,177
Industrial Property 1,602 0 12,335
Personal Property 2,254 351 10,731
Residential Property 11,879 5,107 34,706
Business Property 7,399 789 25,945
Total Property 19,558 8,558 58,331

Total Land Area 28 3 57

 

5.2.1 Population

 

The annual population growth rate ﬁ'om 1981 - 1995 for most of the communities
is about 2% on average. However, there are a few cases where population increases and
decreases have deviated from the general pattern of steady growth. For example, the 1994
projected population data for Cascade Township, Kent County, indicated a decline of
population to 12,352 in 1994 from 12,896 in 1990. This has resulted in a projected 1%
decline in annual population growth rate of the township between 1991 and 1995. On the

other hand, there are some places that have shown sharp increase much above the average

90

for all communities between 1981 and 1990. Macomb Township, for example, had a

growth rate of 4 to 6 percent each year during the period.

Table 5.2: Average Total Population of the Seventeen Fast Growing Cities
in Michigan, 1981 - 1995.

 

 

 

 

 

 

 

City Avegqe Population Counties
Sterling Htsw 115,590 Oakland
Troy 72,686 Oakland
Farmington Hills 71,133 Oakland
Wyoming 63,157 Kent
Rochester Hills 57,569 Oakland
Portage 49,303 Kalamazoo
Kentwood 36,127 Kent
Novi 31,277 Oakland
Holland 24,336 Ottawa
Auburn Hills 17,085 Oakland
Walker 17,011 Kent
Grandvillei 14,992 Ottawa
Wixom 8,311 Oakland
Marysville- 8,259 St. Clair
Lapeer 7,534 Lapeer
Walled Lake 5,942 Oakland
Brightonl 5,452 Livingston ,

 

 

 

The population distribution in the study communities ranged ﬁom 4,038 in Long
Lake Township in 1981 to 119,929 in the City of Sterling Heights in 1995 with a grand
mean of 28,745 (Long Lake Township had a population of 5,977 in 1990 to be included in
the study). Most of the communities with the largest population are cities and townships in
Southeast Michigan. Four of the ﬁrst ﬁve cities in Table 5.2 (Sterling Heights, Troy,
Farmington Hills, and Rochester Hills) with the highest average population for the study
period are cities in Southeast Michigan. Likewise, there is no fast growing township

outside of Southeast Michigan that has a population of 50,000 or more or is in the group

91

of the ﬁrst ﬁve townships with the highest average population during the study period. In
general, fast growing big cities and townships in Michigan are concentrated around the

City of Detroit, in Southeast Michigan.

Table 5.3: Average Total Population of the Sampled Fast Growing Townships
in Michigan, 1981 - 1995.
Township Average Population Counties
Clinton 83,597 Oakland
Waterford 67,262 Oakland
Canton 55,762 Wayne
W. Bloomﬁeld 51,711 Oakland
Shelby 46,535 Macomb
Meridian 33,703 lngharn
Georgetown 30,660 Ottawa
Commerce 26,726 Oakland
Delta 25,882 Clinton
Harrison 24,741 Macomb
Plaintield 24,358 Kent
Chesterfield 24,164 Macomb
Orion 24,143 Oakland
Macomb 20,733 Macomb
Delhi 19,032 lngham
Holland 17,047 Ottawa
Pittsfield 16,717 Washtenaw
Northville 16,466 Wayne
Muskegon 15,096 Muskegon
Cascade 11,941 Kent
Milford 11,879 Oakland
Fruitport 11,382 Muskegon
Grand Rapid 10,313 Kent
Garﬁeld 10,178 Grand Traverse
Alpine - 9,686 Kent
Sparta 8,047 Kent
East Bay 7,835 Grand Traverse
Long Lake 5,560 Grand Traverse
Ira 5,369 St Clair

 

 

 

 

 

 

 

 

 

 

 

 

92

5.2.2 Equalized Value of Properties1

The distribution of per capita state equalized values of properties (“properties”
henceforth) in these communities has some identiﬁable patterns. All cities and townships
combined, the residential properties range from $5,107 to $34,706 and business
properties2 range from $789 to $25,945. Overall, the mean value of residential property in
the entire study communities is more than that of business property by nearly $4,500.

Many of the seventeen cities, with the exception of the cities of Portage, Novi,
Holland, and Lapeer, do not have agricultural land at all. Even in these four cities, the per
capita value of agricultural properties is insigniﬁcant when compared to those of other
types of properties. In the case of townships, however, all the twenty-four townships in
the study have some agricultural properties. Those townships that do not have agricultural
properties are Clinton, Harrison, and West Bloomﬁeld townships in Southeast Michigan
and Cascade and Grand Rapids in Kent County (outside of Southeast Michigan). In sum,
agricultural property is the type of property with the lowest mean, minimum, and
maximum per capita value in all the study communities. Its contribution to the per capita
value of total properties is insigniﬁcant; it is just a little more than 1 percent of the total
properties.

All cities and townships, excepting Long Lake Township in Grand Traverse
County, have both commercial and industrial properties. Long Lake Township did not

have industrial properties from 1981 - 1991. The value of its commercial properties for the

 

' Unless stated otherwise, all references to diﬁ‘erent types of properties must be understood in
terms of per capita state equalized values (PCSEV).

2 It should be noted that business properties are expressed in terms of per capita value and not a
per business value.

93

period between 1981 - 1995 was also not signiﬁcant; it ranged between $392 - $574 in
comparison to the $3,542 mean for all places.

Four of the ﬁve communities (Table 5.4) with the highest average value of
business properties (Wixom, Troy, Auburn His, and Novi) are cities located in Southeast
Michigan. But, ﬁve of the communities with the highest average value of residential
properties consist of three townships (W. Bloomﬁeld, Cascade, and Northville) and two
cities (F armington His and Troy). However, still four of the ﬁve communities, with the
exception of Cascade Township again, are located in Southeast Michigan". It is worth
noting that (1) Cascade Township, with a combined business and residential per capita
value of $41,006, tops all communities included in the study, and (2) most of the

communities that have the highest average value of residential properties are townships.

 

3 Average values of business properties are the sum of average PCSEV of industrial, commercial,
and personal properties.

Table 5.4 (a):

Table 5.4 (b):

94

Average PCSEV of Business Properties, Cities, 1981 - 1995

 

 

 

 

 

 

 

City Business Properties
Wixom 22,161
Troy 18,966
Auburn Hills 13,793
Novi 13,572
Marysville 13,289
Brighton 11,515
Walker 11,390
Kentwood 11,350
Farmington Hills 10,012
Wyomigg 8,653
Portage 7,969
Lapeer 7,700
Sterling Hts 7,178
Grandville 6,773
Walled Lake 6,058
Rochester Hills 5,767
Holland 5,345

 

Average PCSEV of Residential Properties, Cities, 1981 - 1995

 

 

 

 

 

 

City Residential Properties
Farmington Hills 17,366
Troy 17,166
Rochester Hills 16,557
Novi 14,460
Sterling Hts 12,069
Marysville 11,240
Brighton 10,731
Grandville 10,304
Walled Lake 9,550
Holland 9,144
Kentwood 9,058
Walker 8,874
Portage 8,770
Wyoming 8,061
Wixom 7,835
Auburn Hills 5,907
Lapeer 5,605

 

 

 

 

95

Table 5.4 (c): Average PCSEV of Business Properties, Townships, 1981 - 1995

 

 

 

 

 

 

 

 

Township Business Properties
Cascade 15,719
Garﬁeld 12,296
Pittsﬁeld 12,071
Delta 10,597
Holland 8,858
Milford 7,596
Chesterﬁeld 6,093
Meridian 5,639
Grand Rapid 5,553
Commerce 5,504
Orion 5,365
Waterford 4,941
Shelby 4,896
Alpine 4,755
Ira 4,532
Plainﬁeld 4,331
Canton 4,173
East Bay 4,099
Northville 3,956
Muskegon 3,741
Sparta 3,732
Harrison 3,608
Clinton 3,573
W. Bloomﬁeld 3,314
Delhi 2,772
aorgetown 2.509
Macomb 2,260
Fruitport 1,446
LongLake 925

 

 

96

Table 5.4 (d): Average PCSEV of Residential Properties, Townships, 1981 - 1995

 

 

 

 

 

 

 

 

 

Township Residential Properties
W. Bloomﬁeld 26,440
Cascade 25,287
Northville 17,827
Grand Rapid 16,191
LMe 16,094
Commerce 15,496
Milford 14,379
Shelby 13,789
East Bay 13,685
Meridian 13,527
Orion 13,327
Macomb 13,027
Harrison 12,736
Delta 11,822
Georgetown 1 1,613
Waterford 1 1,539
Canton 11,356
Clinton 10,973
Plainﬁeld 10,581
Chesterﬁeld 10,535
Garﬁeld 9,357
Fruitport 9,051
Delhi 8,785
Holland 8,684
Pittsﬁeld 8,284
Alpine 8,152
Ira 7,612
Sparta 7,359
Muskewn 6,236

 

 

97

5.2.3 Total Land Area and Population Density

The average land area for all the communities in the study is 28 square miles. It
varies from the smallest area of 3 square miles, Walled Lake City, to 57 square miles,
Orion Township, both in Southeast Michigan. The average density over the 15 years
period is 1,086 persons per square mile and ranges from 112 persons per mile in Long
Lake Township in 1981 to 3,383 persons per square mile in Clinton Township in 1995.
Generally, most of the communities with the highest population density are cities. While
thirteen of the seventeen cities in the study have a population density of 1,000 or more
only seven of the twenty nine townships have a population density that is comparable to
the cities. Furthermore, excepting for the cities of Wyoming, Holland, Kentwood, and
Portage, nine of the thirteen cities are located in Southeast Michigan(see Table 5.5b).
Similarly, with the exception of Meridian Township (Ingham County) all of the six
townships in this category are also in Southeast Michigan (see Table 5.5a). Generally,

most of the populated communities are currently located in Southeast Michigan.

Table 5.5(a): Townships with Average Population Density (persons per sq. mile)
of1,000 or More,1981-1995

 

 

 

 

 

Township Density Location
Clinton 2,986 SEM
Waterford 2,156 SEM
Harrison 2,019 SEM
W. Bloomﬁeld 1,981 SEM
Canton 1,549 SEM
Shelby 1,330 SEM
Meridian 1,021 ROS

 

 

Note: In Tables 5.5a and 5. 5b SEM stands for Southeast Michigan and ROS for Rest of
the State.

98

Table 5.5(b): Cities with Average Population Density of 1,000 or More, 1981 - 1995

 

 

City Density Location
Sterling Hts 3,211 SEM
Wyoming 2,429 ROS
Farmington Hills 2,156 SEM
Troy 2,019 SEM
Walled Lake 1,981 SEM
Holland 1,868 ROS
Rochester Hills 1,599 SEM
Kentwood 1,571 ROS
Marysville 1,376 SEM
Brighton 1,363 SEM
Portage 1,297 ROS
Lapeer 1,256 SEM
Novi 1,009 SEM

 

 

 

 

 

5.2.4 Per Capita Public Service Expenditures

The mean per capita public service expenditures for all communities combined
over the ﬁfteen year period is $287 and individual community mean expenditure range
ﬁ'om $34 to $1,029 in constant 1995 dollars. There is a clear pattern of expenditures in
relation to type of government and geographic location of communities. Over all, cities
spend more per person than townships, and communities located in Southeast Michigan
(cities or townships) spend more than those in the rest of the state. However, as an
exception to this observation, out of the twenty-nine townships of the study communities,
three townships in Southeast Michigan (Shelby, Clinton, and Waterford) have spent a little

more than three cities (Rochester Hills, Kentwood, and Grandville).

99

Inter city comparison reveals that cities in Southeast Michigan spend more than
cities in the rest of the state. It is only the City of Holland in Kent County, outside of
Southeast Michigan, that is among the top ten cities with the highest per capita
expenditures. For townships, they are only Delta, Meridian, and Muskegon townships,
outside of Southeast Michigan, that are among the top ten with the highest expenditures.

The association between total population size and expenditures is not conclusive
when all communities are combined. This is because there is no clear pattern of association
between population and expenditures for cities. Nonetheless, it is observed that smaller
population size cities spend more than larger population size cities on the average. For
example, seven of the ten cities with the highest expenditures are from the smaller
population size group (see Table 5.6). In the case of townships, however, there is a
general trend of positive association between per capita public service expenditures and
total population size. The larger the population size, the higher the expenditures (see

Table 5.7).

Table 5.6:

100

 

 

 

 

 

 

Average Expenditures and Population, Cities, 1981 - 1995

Cities Expenditure Population
Lapeer 791 7,534
Marysville 636 8,259
Auburn Hills 618 17,085
Holland 604 24,336
Brighton 569 5,452
Wixom 514 8,311
Walled Lake 514 5,942
Troy 503 72,686
Sterling Hts 457 115,590
Farmington Hills 450 71,133
Novi 449 31,277
Walker 440 17,011
Wyoming 376 63,157
Portage 335 49,303
Grandville 317 14,992
Rochester Hills 292 57 .569
Kentwood 285 36,127

 

 

 

 

Table 5.7:

101

Average Expenditures and Population,

Townships, 1981 ~1995

 

 

 

 

 

 

 

 

 

 

Township Expenditure Population
Shelby 325 46,535
Clinton 307 83,597

Waterford 296 67,262
Canton 275 55,762

Delta 262 25,882

W. Bloomﬁeld 257 51,711
Meridian 254 33,703
Pittsﬁeld 233 16,717
Harrison 225 24,741

Muskegoi 206 15,096

Northville 198 16,466

Cascade 192 11,941
Holland 183 17,047

Commerce 176 26,726

Delhi 164 19,032
Chesterﬁeld 141 24,164
Garﬁeld 139 10,178
Orion 137 24,143
Grand Rapid 128 10,313
Milford 119 11,879
Plainﬁeld 111 24,358
Macomb 102 20,733
Georgetwon 102 30,660
Fruitport 101 11,382
East Bay 100 7,835
Ira 92 5,369
Alpine 91 9,686

Long Lake 68 5,560
Sparta 52 8,047

 

 

102

5.3 Data Classification

Preliminary review of the study data indicates that the local governments in the
study sample are very different in many respects. For instance, cities and townships have
substantial diﬁ‘erences in services they provide and expenditures they incur; local
governments in Southeast Michigan have expenditures that are signiﬁcantly higher than
those of municipalities and townships in the rest of the state; and townships with a larger
total population size have higher per capita expenditures than townships with a smaller
population size. These differences in patterns and levels of expenditures call for
classiﬁcation of the study communities into some homogeneous or uniform sub-groups of
communities in order to carry out a meaningful empirical investigation. This analyst
contends that ignoring these observable differences and performing a general empirical
analysis by putting all the study communities in one group may make the results ﬂawed

and less important for ﬁrture use.

5.3.1 Classification by Type of Government

As noted earlier, cities and townships are very different in their service
responsibilities and ﬁnancing authority. For example, cities have to provide for the
construction and maintenance of roads and streets in their jurisdictions. Townships, to the
contrary, are not required to provide road services; they are served by county road
commissions. Consequently, road and street expenditure, which is very signiﬁcant in terms

of annual ﬁnancial outlay of a community, creates signiﬁcant difference between a city and

103

township budgets. Because townships do not have this huge expenditure, their budget
appears to be signiﬁcantly lower than those of city budgets.

Furthermore, cities in the study provide their own police and ﬁre protection,
whereas townships could contract such services from a neighboring jurisdiction, county,
or the state. While all the cities have their own police and ﬁre departments, by 1995 there
were only ten of the twenty-nine townships (Canton, W. Bloomﬁeld, Shelby, Waterford,
Pittsﬁeld, Clinton, Meridian, Chesterﬁeld, Grand Rapids, and Ira) that had their own
public safety departments. The remaining nineteen townships were contracting the services
ﬁ'om the adjoining city or county departments. This also contributes to the disparity
between city and township budgets and expenditures. Therefore, it is necessary to separate
the communities by their respective type of governments (city or township) ﬁrst and
foremost.

It is possible to investigate the impact of type of government on expenditures of
communities by specifying it as one of the independent variables in the regression analysis
using other econometric techniques like the Ordinary Least Square (OLS). But, since this
study is using a Fixed Eﬂects regression model of panel data type of government can not
be used as an explanatory variable because it remains as a constant within the panel
throughout the ﬁfteen years period of the study. Because it does not change year by year
(a community is a city or a township throughout the period) it can only be represented by
dummy variables 0 or 1 in the model. Since individual level covariates are not compatible

with the Fixed Eﬂects regression model, the variable will automatically be dropped ﬁ'om

104

the regression analysis if included‘. Therefore, the opportunity of regressing expenditures
(dependent variable) on type of government (independent variable) without using other
regression model is not available in this study.

A single factor analysis of variance (ANOVA) is performed to test the
appropriateness of separating the study communities by types of government. The result
obtained (see Table 5.8) shows the existence of signiﬁcant difference between cities and
townships and the classiﬁcation is justiﬁed. The associated two-sample t-test, which
indicates the source of the differences also gave a t-statisticss of 26.7 at 0.05 conﬁdence

level with a P-value of 0.

Table 5.8: Single Factor ANOVA, by Type of Government

 

 

 

 

 

 

 

Type of Average
Gov’t Count Expenditure Variance F value P-value
Cities 255 475 28594
Townships 435 174 7351
Between
Groups 964 0

 

 

 

 

 

‘ A Fixed Eﬂects regression was performed with location as an independent variable to illustrate
how such variables that remain constant in the panel will be treated by the model. While its
inclusion does not affect the regression result, the variable will just be dropped (see Appendix F).
Same result would have been obtained if similar regression was performed with type of government
variable.

5 All t-statistics in this study are at 0.05 conﬁdence level and critical value of 1.96

105

5.3.2 Sub-Classification by Population Size and Geographic Location

The study communities are further sub-classiﬁed by population size and
geographic locations. Cities and townships are respectively sub-grouped into two
population sizes (large and small) and two general geographic locations (Southeast
Michigan and Rest of the State). These sub-classiﬁcations are necessitated because the
preliminary review of the data indicated that population size and geographic location are
signiﬁcant in shaping the level and patterns of expenditures of the communities. The
determination of the two population size groups (more than 50,000 and less than 50,000)
is arbitrary. The broad locational sub-categorization is conﬁrmed by the test and result of a
Single Factor ANOVA and a two-sample t-test assuming unequal variances yielding a t-

statistics of 10 and 0 P-value.

Table 5.9: Single Factor ANOVA, by Geographic Location

 

 

 

 

 

 

 

 

 

 

Average
Location Count Expendihrres Variance F value Povalue
Southeast Michigan 360 351 42826
Rest of State 330 214 19802
Between Groups 101 0

 

 

6 The average expenditure indicated here is computed before disaggregating the communities into
their respective types of government.

106

5.4 Characteristics of the Study Communities by Sub-Classiﬁcation

This sub-section will present the descriptive statistics of all the study communities
arranged by the major classiﬁcation of type of government and the sub-classiﬁcations of
population size and geographic location. To ﬁrrther highlight the differences between the
communities of different sub-class, two summary tables, one for cities and one for

townships, will be presented.

5.4.1 Cities

The seventeen fast growing cities of Michigan included in this study are
characterized by average expenditures of $479, total population of 35,633, population
growth rate of 2%, population density of 1,547 per square mile and total property value of
$21,478. While only six of the seventeen cities have larger population size (more than
50,000) in 1990, four of them are located in Southeast Michigan. Moreover, eleven of all

the fast growing cities (65%) are again in Southeast Michigan.

5.4.1.1 Cities of Larger Population Size

The six cities in this population size group are Sterling Heights, Troy, Farmington
Hills, Wyoming, Rochester Hills, and Portage. On the average, this group spends about
$402, which is $77 less than all cities combined. Consistent with the average population
growth rate for all fast growing cities, this group has average population of 71,573 with

nearly 2% annual growth rate. The average per capita value of its total properties is

107

$23,084 and it is slightly over the average for all cities by $1,607. Its population density is

much higher (by 573 persons per square mile) than the average for all cities.

5.4.1.2 Cities of Smaller Population Size

Cities of Kentwood, Holland, Novi, Auburn Hills, Walker, Grandville, Wixom,
Marysville, Lapeer, Walled Lake, and Brighton make this group. The group spends $522
per person on the average (that is $120 more than cities with larger population size) and
$43 more than the average of all cities combined. The average population is 16,030 and
the growth rate is more or less consistent with all cities combined. The value of its average
total properties is less than that of larger cities by nearly $2,500. Its population density is

signiﬁcantly less than that of the larger cities by 884 persons per square mile.

5.4.1.3 Cities in Southeast Michigan

The fast growing cities in Southeast Michigan are Sterling Heights, Troy,
Farmington Hills, Rochester Hills, Novi, Auburn Hills, Wixom, Marysville, Lapeer, Walled
Lake, and Brighton. The average expenditure of this group $527, which is $48 more than
that of all cities combined. Its average total population size is a little more than the
average of all cities combined (by 807), while its average annual population growth rate
(2.2%) is signiﬁcantly higher than all other categories. It has the highest average per
capita value of total properties and slightly higher population density than the average for

all cities. ,

108

5.4.1.4 Cities in the Rest of the State.

The fast growing cities outside of southeast Michigan are Wyoming, Portage,
Kentwood, Holland, Walker, and Grandville. This group spends $134 less per person than
cities in Southeast IVﬂchigan. Its average total population is less than the average for all
cities combined by 1,478 and for larger cities by 2,285. Its annual population growth rate
(1.5%) is the slowest when compared to all sub-classes of communities. It also has the
lowest average value of properties ($3,853 less than that of all cities combined) and

population density only higher than the communities with smaller population.

Table 5.10: Summary of Basic Characteristics of Fast Growing Cities in Michigan
1981 - 1995

Variables Small SE Rest of Sale All

402 522 527 393 479
Total 71 1 440 34 155

Grth . Rate 1.9 2.0 2.2 1.5 2.0
119 1 1 13 1 425 1
Value 17 21 478

 

5.4.2 Townships

Out of the total ﬁfty-two fast growing townships in Michigan twenty-nine (56%)
are included in this study. While fourteen of these townships are in Southeast Michigan the
other ﬁfteen are in the rest of the state. On the average, this sample group is characterized

by per capita expenditure of $174 (which is $305 per person less than that for the cities),

109

population of 24,707, population growth rate of 1.8%, population density of 816 persons
per square mile (almost half of the cities) and per capita property value of $18,432 (nearly
$3,000 less than the average of the cities). There are only three townships in the entire
group of the fast growing townships in Michigan that have a population size greater than

50,000 by 1990 and all three of them are located in Southeast Michigan.

5.4.2.1 Townships of Larger Population Size

The three townships in Southeast Michigan that make the large population size
group are Waterford, Clinton, and W. Bloomﬁeld. This group has an average expenditure
of $287, which is more than the average for all townships combined by $104. Its average
population size is 67,523 and its annual growth rate of 1.6% is close to the average of all
the townships combined. The population density in this group is very high, 2,193 persons
per square mile and is almost three times that of all the townships. Its average per capita

value of properties exceeds that of all townships combined by $1,800.

5.4.2.2 Townships of Smaller Population Size

Twenty-six of the twenty-nine sample townships are in this group. These
townships spend $161 per person, signiﬁcantly less (by $126) than the townships with
larger population size. The average population size is 19,768 and the annual population
growth rate is equal to that of the average for all townships (1.8%). It has a low

population density of 658 persons per square mile. This is less than a third of that of the

“0

larger population size townships. The average per capita value of its properties is also less

than that of larger townships by $2,057.

5.4.2.3 Townships in Southeast Michigan

The fourteen sample townships in southeast Michigan are Clinton, Waterford, W.
Bloomﬁeld, Commerce, Orion, and Milford in Oakland County; Shelby, Harrison,
Chesterﬁeld, and Macomb in Macomb County; Canton and Northville in Wayne County;
Pittsﬁeld in Washtenaw County; and Ira in St. Claire County. Their average per capita
expenditure ($206) is more than the average for all townships by $32. The group average
population is about 34,000 with an average annual growth rate of nearly 2%, higher than
the population growth rate for all townships combined. The average per capita property

value and population density are also greater than those for all townships combined.

5.4.2.4 Townships in the Rest of the State

Townships in the rest of the state are Plainﬁeld, Cascade, and Grand Rapids in
Kent County; Meridian and Delhi in Ingham County; Holland and Georgetown in Ottawa
County; Delta in Clinton county; Muskegon and Fruitport in Muskegon County; and
Garﬁeld, East Bay, and Long Lake in Grand Traverse County. These townships spend $62
less per person than townships in Southeast Michigan. Their average population (16,048),

annual grth rate (1.6%), per capita total property value ($17,966), and population

Ill

density (511 persons per square mile) are also considerably less than those of Southeast

Michigan.

Table 5.11: Summay of Basic Characteristics of Fast Growing Townships in
Michigan. 1981 -1995

Variables Small SE Rest of aate

287 161 206 144
Total 67 19 768 986 1

Growth . Rate 1.6 1.8 2 0 1.6

193 658 51 1
Value 20 1 17

 

112

5.5 Regressions and Model Specification

This study uses a ﬁfteen-year panel data set utilizing the Fixed Effects regression
method. The amount of data used in this study is so large that it was necessary to be
concerned about the existence of possible statistical problems in the model. For example,
there could be a signiﬁcant change in the regression coefﬁcients if one adds or omits an
independent variable in the process of model speciﬁcation. As a result, the estimated
standard errors of the ﬁtted coefﬁcients would be inﬂated, or the estimated coefﬁcients of
the explanatory variables may not be statistically signiﬁcant even though a statistical
relation exists between the dependent and independent variables. Therefore, before
embarking on the actual regression analysis a diagnostic regression is performed on all
data sets. The diagnostic regression employed is primarily focused on the problem of
correlation between the independent variables and the test showed the existence of

multicollinearity problem in the initial model of the study.
5.5.1 Diagnostic Regression

One of the frequent problems observed in several studies like this one is when the
explanatory (independent) variables are highly correlated (multicollinearity). Two of the
independent variables (square of total population and total land area) that were initially
included in the model speciﬁcation are detected by the diagnostic regression to have

caused such a problem in the regression analysis of this study.

113

Square of total population was included in the model for the purpose of adjusting
for the non-linearity that may exist between total population and expenditures. Total land
area was included because many of the prior researchers have used it. Even some of them,
Shapiro (1961) for example, had found it to be the most signiﬁcant variable in explaining
the expenditures of local governments.

Variance of Inﬂation Factor (vif) analysis is utilized following the diagnostic
regression in order to measure the degree of multicollinearity between the independent
variables and to calculate the level of tolerance for each of the variables in the model.
Most analysts rely on informal rules of thumb applied to the vif (Chatterjee and Price,
1991). Some use the vif value of 30 and others use the more restrictive value of 10. The
diagnostic linear regressions and the corresponding vg'f values of this study are presented

below in Tables 5.12 A - 5.14 B
5.5.1.1 Results of Diagnostic Regression for all Communities

When all communities are considered together, the maximum vrf values for the
total population and population density in the diagnostic linear regression that
incorporates both square of population and land area are 28.7 and 14.14 respectively
(Table 12 A). This is mostly because of the high correlation between these two variables
and the square of population (0.95 and 0.8 respectively, see Appendix B). When square
of population is removed from the model, the vif value of total population improved
signiﬁcantly (by 47%) and its t-statistics (which indicates its explanatory signiﬁcance)

doubled (jumped ﬁom -2.32 to -4.83, see Table 12 B). However, the change in vrf value

114

and t-statistics of population density is not signiﬁcant. This indicates that although the
correlation between square of population and population density is very high, the impact
of this variable on the explanatory signiﬁcance of population density is insigniﬁcant. The
dramatic change in the vif vale and t-statistics of population density comes when the total
land area is removed ﬁom the model; vff improves by 78% and t-statistics changes from
10.61 to 27. 10. As expected, since population density is calculated from total population
and land area, the result reveals that the explanatory signiﬁcance of population density is
much affected by total land area.

The removal of both variables from the model improves the mean and individual
vrf values of all variables without any impact on the explanatory ability of the model.
Furthermore, results of the diagnostic regression indicate that signiﬁcance of square of
population as an explanatory variable in the model is very low. It has a t-statistics of -1.7
or less at 0.05 conﬁdence level conﬁrming that its contribution in explaining the variations
in expenditure of the study communities is insigniﬁcant.

In summary, when the two variables are removed from the model, three
remarkable results are observed: (1) the mean and individual vif values of all variables in
the model declined signiﬁcantly and fall in the range of the acceptable threshold ; (2) the t-
statistics of all of the independent variables improved; and (3) the adjusted R2 of the model
did not decline because of a loss of the variables. These results conﬁrm that square of

population and land area are not useful variables in the model.

Table 5.12 (A):

Results of Diagnostic Regressions, Cities and Townships

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Variance Inﬂation Factor
Wrth Land Area Wrthout Land Area
Variables Wrth Pop? Wrthout PopZ Wrth PopZ Wrthout Pop2
Total Pop. 28.70 15.30 11.50 3.26
Pop. Density 14.14 13.92 3.17 3.12
Sq. of Pop. 10.61 ~- 10.16 ---
Pop. Gr. Rate 1.03 1.03 1.03 1.03
Resid. Prop. 2.71 2.70 2.53 2.48
Total Property 2.53 2.53 2.37 2.36
Land Area 5.83 5.58 -—-- -—-
Mean VlF 9.36 6.84 5.13 2.45
Table 5.12: (B) The t-statislics the Diagnostic Regressions, Cities and Townships
t-statistics
Mth Land Area Wrthout Land Area
Variables Wrth PopZ lMthout PopZ Wrth PopZ Wrthout PopZ
Total Pop. 232 -4.83 -7.24 -15.47
Pop. Density 10.29 10.58 27.10 27.14
Sq. of Pop. -1.77 --- -1.19 ---
Pop. Gr. Rate 2.47 2.54 2.46 2.51
Resid. Prop. 46.75 -16.64 -18.05 -18.05
Total Property 21.56 21.51 22.91 22.87
Land Area -2.96 ~2.65 ~— -
Adjusted R2 0.70 0.70 0.70 0.70

 

 

 

 

 

 

5.5.1.2 Results of Diagnostic Regression for Cities

The individual and combined impacts of square of population and land areas

become more clear when the communities are classiﬁed by types of government. Inclusion

or omission of these variables in the model have dramatic impacts for cities. Total

 

116

population, as an explanatory variable for expenditure patterns of cities, would be
rendered useless if the two variables are included in the model. The vg'f value of 117.89
(Table 5.13 A) is very far from the tolerance threshold of even the most generous cutting
point of 30. There would be a serious multicollinearity problem that will drop all the
contributions of population variable in the analysis. Just removing square of population
will bring down the vif near the 30-point threshold indicating that the multicollinearity
problem in the model is signiﬁcantly reduced. Although the magnitude is not the same, the
vrfvalues of all the remaining explanatory variables have improved or have remained the
same.

However, unlike in the case of all communities combined, removing the square of
population from the model reduced the explanatory signiﬁcance of all the variables
(excepting that of population grth rate, which is not signiﬁcant in the model anyway)
and reduced the explanatory ability ﬁom 44% to 43% (see Table 5.13. B).

This trend is reversed when land area is removed. The W] values of all variables
improved signiﬁcantly (with only population and its square being in excess of the 10 points
threshold). Leaving the explanatory ability of the model at 43%, the explanatory
signiﬁcance of all the variables (with a small exception of population grth rate again)
improved dramatically.

The omission of both variables assures near complete absence of any
multicollinearity problem in the analysis. All variables have vg’f value of less than 3.1 and
the mean drops to 2.49 from 27.79. Again with the small exception of population growth
rate, the signiﬁcance of all explanatory variables improves substantially. However, the

model’s ability to explain the variations in expenditures of cities declines by 4%.

Table 5.13 (A):

117

Results of Diagnostic Regressions, Cities

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Table 5.13:

 

 

 

 

 

 

 

 

 

 

 

 

Variance Inﬂation Factor
Wrth Land Area Wrthout Land Area
Variables Wrth PopZ Wrthout Pop? Wrth PopZ Wrthout Pop2
Total Pop. 117.89 30.09 12.05 2.24
Pop. Density 16.61 12.48 3.40 2.86
Sq. of Pop. 26.04 --- 13..15 ---
Pop. Gr. Rate 1.28 1.28 1.27 1.26
Resid. Prop. 3.49 3.48 3.20 3.05
Total Proper 2.66 2.58 2.29 3.04
Land Area 26.58 13.43 -- ---
Mean VIF 27.79 10.56 5.89 2.49
(B) The t-statistics of the Diagnostic Regressions, Cities
t-statistics
Wrth Land Area Wrthout Land Area
Variables Wrth Pop2 Wrthout Pop? Wrth Popz Wrthout Popl
Total Pop. -1.67 0.25 -7.99 903
Pop. Density 2.16 1.29 6.62 8.66
Sq. of Pop. 2.08 -—- 3.85 ---
Pop. Gr. Rate 0.89 0.90 0.80 0.44
Resid. Prop. 399 -3.86 4.45 -5.28
Total Propery 7.64 7.34 8.61 9.01
Land Area 093 335 ~— ~—
R2 0.44 0.43 0.43 0.40

 

 

 

 

 

 

 

118

5.5.1.3 Results of Diagnostic Regression for Townships

The impacts of the two variables in the case of townships is considerably different
from that of cities. Indeed, removal of population square or land area or both improves
the vrfvalues of all the variables (Table 14. A). However, the t-statistics of all variables
(excepting population grth rate) decline with a removal of any of the variables.
Likewise, the explanatory ability of the model declines by 5%. Although there is no
strong case in itself for removing square of population and land area ﬁ'om the model for
townships, because there is no variable with a vif value that is signiﬁcantly greater than the
liberal 30 points threshold of tolerance, the need to use uniform analysis for both cities and

townships in this study necessitate the omission of these variables.

Table 5.14 (A): Results of Diagnostic Regressions, Townships

 

 

 

 

 

 

 

 

 

 

 

Variance Inﬂation Factor

Wrth Land Area Wrthout Land Area

Variables Wrth PopZ Wrthout Pop2 Wrth Pop2 lMthout PopZ
Total Pop. 30.78 21.03 16.14 6.91
Pop. Density 22.79 22.55 7.57 7.23
Sq. of Pop. 13.41 --- 13.41 --—-
Pop. Gr. Rate 1.07 1.05 1.07 1.05
Resid. Prop. 5.00 4.89 4.91 4.79
Total Property 4.71 4.68 4.67 4.63
Land Area 3.21 3.21 -- ---
Mean VIF 11.57 9.57 7.96 4.92

 

 

 

 

 

 

 

Table 514(8):

119

The t-statistics of the Diagnostic Regressions, Townships

 

 

 

 

 

 

 

 

 

 

 

 

t-statistics
Wrth Land Area Wrthout Land Area
Variables Wrth Popz Wrthout Pop? Wrth Pop2 Wrthout Popz
Total Pop. 10.36 6.70 9.14 4.93
Pop. Density 1.14 0.30 9.00 7.12
Sq. of P0p. 789 ~- -7.56 ———-
Pop. Gr. Rate -1.58 -2.63 -1.33 -2.37
Resid. Prop. 955 -7.91 -10.05 -8.45
Total Property 15.54 13.97 15.66 14.17
Land Area -5.14 -4.65 ~- --
R2 0.77 0.74 0.76 0.72

 

 

 

 

 

 

120

5.5.2 Fixed Eﬂects Regression

Fixed Eﬂ’ects regressions are performed for each sub-class of cities and townships
with the ﬁve explanatory variables (as developed in chapter three) using equation 5 in
chapter four:

M: ‘y:' -.Y" = a +(xrr ' x! - Jl“9.3+ (a. - 8.’+ v') + e"

The preliminary regression analysis of the data indicated that while industrial,
commercial, and personal properties have positive association with expenditures,
residential and agricultural properties, as expected, show negative association. Because
the share of agricultural properties in the study communities is very small and its ability to
explain variations in expenditures of communities is insigniﬁcant, it is decided not to treat
it as a different variables from the rest. Residential property, however, has to be treated as
a separate variable because of its large share in total property and very signiﬁcant

explanatory power in the model.

121

5.5.2.1 Regression Results?

The regression results presented in Tables 5.15 for cities and 5.16 for townships
show: (1) the expenditures of the two classes of analysis (cities and townships) are
aﬁ'ected differently by each of the explanatory variables; (2) the different sub-groups
within the same class of analysis have different sets of ranking of the independent variables
in accordance with their contributions in explaining the variations in expenditures of their
respective sub-groups; (3) while almost all variables are signiﬁcant in explaining the
variations in the expenditures of cities (last column of Table 5.15), it is only the total
property variable in the model that is signiﬁcant for townships (last column of Table 5.16);
(4) the regression model does a better job in explaining the variations in expenditures of

townships than cities.

5.5.2.2 Regression Results for Cities

The regression model explains 68% of the variations in expenditures of all fast

growing cities in Michigan. Total property, followed by residential property, is the most

signiﬁcant variable with the highest explanatory power. While both population growth rate

 

7 It should be noted that the values that are used for total property and residential property are.
different. While per capita value is used for total property, proportion of residential property as
percentage of total property is used for the later. Therefore, the interpretation of the coeﬁicients of
the two variables are different. Take the regression result for cities as an example: The (3 value for
total property is 0.17. That means, a 1% change in per capita value of total property is followed by
$0.17 change in per capita total expenditure. In the case of residential property, the coefﬁcient of -
734.8 is stating that if the proportion of residential property as a percentage of total property
changes by 1%, the per capita total expenditure will change by $7.35.

122

and density have some statistical relation with expenditures, total population is the third
signiﬁcant variable in the model that explains the variations in expenditures of cities.

The empirical ﬁnding ﬁom the regression analysis of all cities combined does not
support the hypothesis of a positive correlation between population size and expenditures.
The hypothesis developed in chapter three states that the higher the population size, the
higher the expenditures will be. This statement does not make any distinction between

government types, city or township.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Table 5.15: Fixed Effects Regression Results, Cities
Large Small SE Michigan Rest of State All

Variable Coeii t stat 0081. t stat Coat. t stat Coei. t stat 00811. t stat
Total Population 001 -1.8 -0.02 -4.0 -0.01 -4.7 0.00 0.2 -0.01 -4.8

Pop Growth Rate -103 0.3 2003 2.7 1407 2.0 2.5 0.0 953.7 1.8
Residential Property -169 -1.4 -621 -5.5 -753 -6.7 -326 -1.1 -735 -7.8
Total Property 0.01 7.7 0.02 10.6 0.02 9.5 0.01 5.2 0.17 11.1
Population Density 0.51 1.9 0.02 0.3 0.14 2.0 -0.09 -0.4 0.122 2.0
Constant 221 2.0 533 7.6 679 8.3 409 1.7 659.3 9.5

R2 0.77 0.74 0.72 0.54 0.68

 

 

 

 

 

 

 

 

Total population, excepting in the case of the six cities outside of Southeast
Michigan, is negatively correlated with expenditures of all classes of cities. These six
cities outside of Southeast Michigan are Grandville, Walker, Holland, Kentwood, Portage,
and Wyoming. Scatter diagrams, showing the trend of correlation between average
population and expenditures over the ﬁfteen years period, for all classes of cities are
presented. Cities outside of Southeast Michigan indicates the positive association between
population and expenditures while all classes of cities show negative

(see Chart 5.2).

123

Public service expenditures are driven not only by the quality and quantity of
services provided, but also by the infrastructures and agencies that make the services
possible. Overhead expenditures for running and maintaining the service inﬁ'astructures
are part of ﬁxed costs in the public service production function of local governments.
Total average cost of producing and maintaining certain units of public services will be
relatively higher in those communities that have smaller population size because there are
fewer people among whom the expenditures could be distributed.

Furthermore, if the service boundaries of a local government are greater than its
political boundaries, its expenditures will be overstated because the effective population
served is greater than the population by which the expenditures is computed. For instance,
Schmid reports that the City of Lapeer extends its ﬁre protection service to adjoining
townships. This will increase Lapeer’s ﬁre protection expenditures ﬁgure. If the
computation of the per capita ﬁre protection expenditures does not count the actual
number of population served and it is only divided by those who consider Lapeer as a
place of their abode, the expenditures of Lapeer is bound to be overstated. Similarly, if all
residents of a political jurisdiction are not served, but the computation of the per capita
expenditures of that service does not exclude those not served, the expenditures of that
community is bound to be understated. In general, disparity between effective population
that gets the service and the population by which the per capita is computed could cause

misrepresentation of the expenditures ﬁgures and change the sign of association.

124

Chart 5.1 Average Population and Expenditures, all Cities, 1981 - 1995

800 w.
700 ...
600 +.

O

o
500 ~~ o
o o o o
g 400 -~ .
o

 

300 r .
200 - ~
1 00 . -

 

 

 

50.000 100.000 150.000
Population

Chart 5.2 Average Population and Expenditures of Cities Outside of
Southeast Michigan, 1981 ~1995

 

TN
60041 O
8500)
O
4004 .
ﬁscal o .0
“32(1)“
100»

 

 

 

20.000 40,000 60,000 80,000

Population

125

Chart 5.3 Average Population and Expenditures of Cities in Southeast
Michigan, 1981 ~1995

 

 

 

 

20,00 40,00 60,00 80,00 100,0 120,0
0 0 0 0 00 00

Population

W
.'§§§§§§§s
O
O
00
0

Chart 5.4 Average Population and Expenditures, Large Cities, 1981 - 1995

 

Expendituea
888888
0
O
0

AL A
I 7

20,000 40,000 60.000 00,111.30 100.00 120,“)
0 0

 

 

 

Population

126

Chart 5.5 Average Population and Expenditures of Cities with Smaller
Population size, 1981 - 1995

 

eoo~—¢
300. 0 O Q
80 .
400‘ °
0 O .
200‘»

 

 

 

- 100) 20,00 30,00 40,00 50,!”
0 0 0 0 0

Population

It is generally observed from the descriptive statistics that smaller cities are
associated with higher per capita expenditures and the larger cities with lower
expenditures. This inverse relationship between population size and level of expenditures
is captured by the regression results as well. In cases of both larger and smaller population
size groups, signs of the estimated [3 coefﬁcients and the t-statistics are negative. This
conﬁrms the association of high population with lower expenditures and low population
with higher expenditures.

Five of the six cities that show negative association between total population and
expenditures belong to the smaller population size group. Then, why do the cities outside
of Southeast Michigan, that are predominantly in the smaller size group, show positive
correlation between size of population and expenditures? Indeed, these cities as a group
spend less than cities in Southeast Michigan. But, does this positive correlation indicate
that expenditures increase as a result of secular growth of population, as stated in the

hypothesis, or are there diseconomies of scale that result from sheer increase of residents

127

to be served? Unambiguous answers for this question may not be drawn ﬁom the data at
hand. Thus, this analyst proposes ﬁrrther inquiry in this area.

Although population density shows positive association with expenditures of all
cities combined, the variable is found to be inconclusive when all the sub-classes of cities
are treated separately. Population growth rate, however, not supporting the hypothesis
that it will have an inverse relationship with expenditures, shows a positive statistical
relationship. this suggests that the rate at which residents of a community is increasing has
a direct eﬁ‘ect on changes in services provided, thereby causing increase in expenditures.

The independent variable with the highest explanatory ability at all levels of
classiﬁcation of the cities is the per capita value of total property. The regression results
support the hypothesis that total property and expenditures are positively associated while
residential property and expenditures are inversely related. This ﬁnding is a conﬁrmation
of the hypothesis that total property, as a proxy of real wealth and income, enables
residents to demand and pay for more and improved public services. The ﬁnding regarding
residential property is consistent with the explanation of the hypothesis in chapter three in
that the estimated inverse relationship between residential property and expenditures is
evidence that expenditures may not need to rise as residential development increases. New
residential development may not require signiﬁcant ﬁnancial outlays for new public
services because of the existing economies of scale in some of the infrastructures and the
types of its service requirements. In fact, the data shows that most of the cities and
townships with high value of residential properties have very low per capita expenditures.

A signiﬁcant portion of total property consists of business properties (commercial,

industrial, and personal). Business developments will affect public service expenditures in

128

two ways. The ﬁrst one is through the expanded tax base they create for a community.
More government revenue will be generated from new business developments and can be
used for more or improved public services. The second is that new business activities may
require new services and infrastructures that may duplicate the already existing ones
thereby causing increase in expenditures. Both scenarios contribute to the positive
association between total property and expenditures.

With a clear exception of total property, which invariably is the most signiﬁcant
variable for all classes of cities, the degree of impact of each variable on expenditures of
communities vary signiﬁcantly. Population density, for example, is the second most
important variable in explaining the expenditures of larger cities while it is actually the
least signiﬁcant variable in the case of smaller cities. See Table 5.15 for details.

The overall regression estimate, which is the estimated per capita public service

expenditures equation for all cities combined, can be represented as:

Y, = 659.3 - (.01)xI + (953.7)x2 - (734.8)X3 + (0.016)x. + (0.12)x,'

where Y;, = Expenditure
X) = Total Population
X2 = Population Growth Rate
X3 = Residential Property as % of Total Property
X4 = Total Property
X5 = Population Density
or = Constant (659.3)

 

' Similar per capita public service expenditures equation for cities with large and small population
size and in Southeast Michigan and the rest of the state can be obtained from Table 5.14

129

 

 

 

 

 

 

 

 

 

 

 

Table 5.16: Ranking of Independent Variables by Level of Signiﬁcance, Cities
Large Small SE MMan Rest of State All

Total Total Total Total Totd

Property Property Property Property Prope
Population Total Total Population Total Residential

Density Population Population Prope
Told Residential Residential Population Total
Population Property Property Density Population
Residentid Population Population Residential Population

Property Growth Rate Density Property Densi
Population Population Population Population Population
Growth Rate Density Growth Rate Growth Rate Growth
Rate

 

 

Although it was not possible to include geographic location in the model as an
independent variable, a multiple regression that treats each year’s observation as an
independent record was used to just see how expenditures of communities would be
aﬂ‘ected by location. It was found that it was statistically signiﬁcant with estimated 0 value
of 90. 26. This indicates that if the variable was to be used in the model, it would
contribute a value of 90.26 to the or constant in the estimated expenditure equation of fast
growing cities in Southeast Michigan. The same analysis was done for townships and it
was found to be statistically signiﬁcant with (3 value of Of -10.67. This would reduce the or
constant of the estimated expenditure equation of fast growing townships in Southeast

Michigan by 10.67

130

5.5.2.3 Regression Results for Townships

The regression model does a better job in explaining the variations in expenditures
of fast growing townships in Michigan than for cities. It has an adjusted R2 of 0.72 for all
townships combined, which is 4% more than that of the cities. This comparison is more
obvious when it is done between the sub-groups of both cities and townships. For
instance, the adjusted R25 of townships with larger population size, townships in Southeast
Michigan, and townships in the rest of the state are greater than the R’s of cities of similar
categories by 15, 6, and 17 percent respectively. Nonetheless, it should be noted that this
model performs slightly better (by 5%) in explaining the expenditures of smaller
population size cities than townships with comparable population size.

Total property is very signiﬁcant in explaining the variations in expenditures of
townships. (1) It is the only statistically signiﬁcant variable in explaining variations in the
expenditures of townships when all the twenty-nine townships are grouped together. (2) It
is the variable with the highest contribution to the R2 regardless of the class of townships.

All of the other variables are not signiﬁcant when all the townships are combined.
This is indicated by their respective t-statistics (see Table 5.17). However, this observation
changes when the townships are classiﬁed by a broad geographic location. The
signiﬁcance of almost all variables improves when townships are classiﬁed by location.
Classiﬁcation by population size, however, did not improve the statistical signiﬁcance of

the variables.

131

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Table 5.17: Fixed Effects Regression Results, Townships
La e Small SE Michigan Rest of State All
Varlable Coefi t stat 00811 t stat Coefi t stat Coeff t stat 00811 t stat
Total Population 002 -1.6 0.00 1.1 0.01 2.7 «0.03 -3.9 0.002 0.9
Pop. Growth Rate -15 «0.0 96 0.7 -193 -1.2 369 1.9 56.5 0.4
Residential Property -77 -0.4 -35 -0.8 134 2.3 -117 -1.7 -28.1 -0.7
Total Property 0.01 4.8 0.01 14.9 0.00 8.3 0.01 10.9 0.006 17.4
Population Density 0.63 2.1 0.09 1.1 -0.01 -0.1 1.1 4.3 0.093 1.3
Constant 26 0.1 -31 -1.0 -178 -3.9 9 0.2 -38.04 -1.2
R2 0.92 0.69 0.78 0.71 0.72

 

 

 

 

 

 

 

The regression results displayed in Table 5.17 support most of the hypothesis:

total population, population grth rate, and total property show positive association with

 

expenditures; residential property conﬁrms the inverse relationship. Total population,
which is negatively related to expenditures of all cities combined, has positive association
with expenditures of all townships. This positive association may be explained by the fact
that many townships are not required to have all types of service facilities, but can
contract ﬁ'om others. The services purchased from other units of government and fees
paid for the service may be proportional to the number of people served. Or, the
townships may decide to acquire new service facilities in response to new demand arising
from growing population. In general, economies and diseconomies of scale of service
facilities may not play a role to force an inverse relationship between population and
expenditures.

An inverse relationship between population size and expenditures is obtained in
communities with larger population size and those outside of Southeast Michigan when
townships are broken down into different classes. Those in smaller population size and

the rest of the state show positive association and are consistent with all the communities

I32

combined. The general trends of the relationship between population and expenditures of

diﬁ'erent classes of townships are shown with the help of the charts below.

Chart 5.6 Average Population and Expenditures of all Townships, 1981 - 1995

 

350 e
“‘1’ . . .
2504 ’0 0
’0
200«
e".
1500 .
10043 0°.
504°.

 

 

 

- 20,000 40,000 60,000 80.000 100.000
Populdion

Chart 5.7 Average Population and Expenditures of Townships
in Southeast Michigan, 1981 - 1995

 

350
300
250 .. .
200 0 O
150
100
50

 

 

 

20.1” 40,00 60,00 800) 100.0
0 0 0 0 00

Population

Chart 5.6

133

Average Population and Expenditures of Townships Outside

of Southeast Michigan, 1981 - 1995

Chart 5.9

 

300
250
gay.
i...
100..
50

 

 

° 0
0..
e
8
0.0 ° 0
.0

 

10.000 20.000 30.000 40.000
Population

Average Population and Expenditures of Townships with Large

Population Size, 1981 -1995

 

 

310 ‘
300 1r
0

290
280 <-

O
270
260 O
250 4

 

20,1!) 40$” 60,11) 80,00 100,0
0 0 0

Population

0

 

Chart 5.10

Table 5.18:

134

 

 

 

 

 

 

 

 

 

 

Average Population and Expenditures of Townships with Small
Population Size, 1981 -1995
350 0
3m 4
250 . .0 e
200 . ‘ .
150 .. 9 .
100 .. :9} e 0 e
50 .. e
10.00 20,00 30,00 40,00 50,00
0 0 o o 0
Population
Ranking of Independent Variables by Level of Signiﬁcance, Townships
La_rge Small SE Michigan Rest of State All
Total Total Total Total Told
Property Property Property Property Property
Population Total Total Population Population Population
Density Population Density Density
Total Population Residential Total Totd
Population Density Property Population Population
Residential Residential Population Population Residential
Property Property Growth Rate Growth Rate Property
Population Population Population Residential Population
Growth Rate Growth Rate Density Property Growth Rate

 

 

 

 

 

 

The independent variable that had the highest explanatory ability in the model at all

levels of classiﬁcation of the townships was the per capita value of total property.
Variables that were least important in the model varied by class of townships:
(1) population growth rate was the least signiﬁcant for all townships grouped together and
classiﬁed by population size, and (2) population density and residential property were the

least important variables for townships classiﬁed by location. Finally, there was no

 

135

observable pattern of ranking of the rest of the variables for the second, third, and fourth
places in accordance to their contribution to the R2.
The estimated per capita public service expenditures equation for all townships

grouped together can be represented as:
Y,. = -38 + (.002)X, + (56.5))(2 - (28.1)X3 + (0.05)X4 + (0.09)X5
5.6 Comparison of Regression Results by Type of Government

Cities and townships are basically different in many respects. On average, cities
spend $301 per person more than the townships; have 10,000 or more residents than
townships; have population density of almost double that of townships; and have about
$3,000 more in per capita state equalized value of total properties, $5,500 more in
business property, and $2,500 less in residential property.

While total property and rate of population growth variables were the highest and
the least in terms of statistical signiﬁcance in their contributions to the R2 for both
aggregated classes of communities, the ranking of residential property, total population,
and population density vary by classiﬁcation. Moreover, total population plays different
roles in determination of city and township expenditures. It was observed that increase in
population size decreases expenditures for cities while it increases expenditures of

townships.

136

Table 5.19: Comparison of Ranking of Independent Variables, by Types of Government

Cities T
Total Total
Residential

Total Total
Residential
Growth Rate Growth Rate
68 R2 72

 

Further observation into the regression results of both class of communities
revealed that almost all independent variables, excepting total property, were statistically
signiﬁcant for cities but not for townships. Yet, the R2 for cities was less than that of
townships. This ﬁnding suggests that more explanatory variables in addition to the ones
used in the model are needed to ﬁnd the unexplained factors that determine city
expenditures. On the other hand, the relatively higher R2 of townships suggests that total
property, with little contribution from the other variables, is the single most important
variable in shaping expenditures in townships. The signiﬁcance of this variable is further
observed when townships are sub-divided by population sizes. Townships with larger
p0pulation size have an R2 of 0 .92 with only total property having a signiﬁcant value of
t-statistics. The importance of total property in determining the expenditures of townships
becomes more marked with smaller population size where it is the only signiﬁcant

explanatory variable with t-statistics of 14.9.

137

5.7 Impact of Location on Expenditures

It should be remembered that location was not treated as independent variable in
the model because (1) individual level covariates can not be used in a ﬁxed effects model,
and (2) it will be dropped grom the regression results if entered because it is a constant
within the panel (see Appendix F). Therefore, for a purpose of showing the signiﬁcance of
location on expenditures, a multiple regression of the Generalized Linear Model was
performed using dummy variables (1 for Southeast Michigan, 0 for the Rest of the State).
It was found to be statistically signiﬁcant for both cities and townships with 8 values of

90.3 for cities and -10.7 for townships (see Appendix E).

138

5.8 Reliability Test of the Model

Ten cities out of seventeen and twenty four townships out of the twenty nine were
arbitrarily and randomly selected to test the validity of the estimated equation of the
model. The 1995 data on expenditures and the independent variables were selected
purposefully for the validity test because all expenditure and property data were all in

constant 1995 dollars.

The estimated equations used for cities and townships were respectively:
Y5. = 659.3 - (.01)X1 + (953.7)X2 - (734.8)X3 + (0.016)X4 + (0.12)X5
and
Y,. = -38 + (.002)X1 + (56.5)X2 - (28.1)X3 + (0.05)X4 + (0.09)X5
where:
Y5, = Expenditure
X1 = Total Population
X2 = Population Grth Rate
X3 = Residential Property as % of Total Property
X. = Total Property
X5 = Population Density
or = Constant

Over all, for adjusted R25 of the model (0.68 for cities and 0.72 for townships), the
reliability test showed that the equations have estimated the variations of expenditures
within the bound of 32% under or over the actual expenditures for cities and 28% for
townships. Excepting in the case of the cities of Wyoming and Walled Lake (two out of
ten) and townships of Fruitport, Alpine, and Ira (three out of twenty four), the ability of
the equations in estimating expenditures was very impressive. In sum, given the length of
time considered in the study and the nature of the data, this validity test has shown the

strength and accuracy of the model (see Tables 5.19 & 5.20).

Table 5.20:

139

Results of the Reliability Test, Cities, 1995

 

 

 

 

 

 

Actual Estimated Over/Under

Cih/ Expenditure Expenditure Estimated (96)
Troy 569 456 020
Wyoming 438 261 -0.40
Novi 519 627 0.21
Holland 684 449 034
Walker 530 669 0.26
Auburn Hills 974 988 0.01
Marysville 698 819 0.17
Lapeer 779 721 -0.07
Walled Lake 498 679 0.37
Brighton 665 881 0.33

 

 

Table 5.21:

Results of the Reliability Test. Townships, 1995

140

 

 

 

 

 

 

Actual Estimated Over/Under

Township Expenditure Expenditure Estimated (‘16)
Waterford 332 373 0.12
Canton 382 334 -0.13
W. Bloomﬁeld 340 417 0.23
Meridian 285 241 -0.15
Delta 295 207 0.3)
Delhi 188 130 031
Commerce 255 253 -0.01
Chesterﬁeld 215 202 -0.06
Macomb 171 182 0.06
Holland 236 180 —0.24
Harrison 214 270 0.26
Plainﬁeld 193 164 -0.15
Orion 182 203 0.11
Northville 269 228 -0.16
Fruitport 110 70 -0.36
Cascade M 325 293 «0.10
Alpine 139 92 034
Grand Rapid 211 182 -0.14
Garﬁeld 181 153 -0.16
Sparta 56 60 0.08
Milford 184 163 -0.1 1
East Bay 140 105 -0.25
Long Lake 73 72 -0.02
Ira 107 69 -0.35

 

 

CHAPTER SIX

CONCLUSIONS, IMPLICATIONS AND FUTURE RESEARCH

6.1 Introduction

The main objective of this study was to identify the signiﬁcant factors that
determine the variations in per capita public service expenditures of local governments in
the State of Michigan. Public services considered in the study include general government,
public safety, public works, public services, health and welfare, and recreation and culture.
The impacts of selected explanatory variables (total population, population density,
population growth rate, per capita state equalized value of total property, and per capita
value of residential property as percent of total property) on per capita expenditures were
investigated in the context of different types of government (city or township), population
size groups (large or small), and geographic location (Southeast Michigan or the rest of
the state). The conceptual framework of the analysis was formulated as an expenditure
decision model of local governments. A rigorous method of data preparation and
management for the purpose of such analysis was developed and an econometric model

using Fixed Eﬂ'ects regression was employed to analyze ﬁfteen-year panel data sets.

I41

142

6.2 Conclusions

The conclusion of this study focuses on three important aspects. First, the overall
empirical results are summarized. Then, ﬁndings regarding the impacts of each
independent variable on per capita expenditures of communities and their explanatory
power in the model are discussed. Finally, the impact'of geographic location variable is

discussed separately.

6.2.1 General

One of the important ﬁndings in this study was the conﬁrmation of the existence of
identiﬁable patterns of variations in expenditures (all reference to expenditures and
property values are in per capita unless stated otherwise) of fast growing communities in
the State of Michigan. On average: (1) per capita public service expenditures of fast
growing communities in Michigan vary widely (between $34 and $1,029 in terms of 1995
constant dollars); (2) cities and townships categorized by different population sizes have
diﬁ‘erent expenditure patterns. While cities with smaller population size spend ($120 per
person) more than cities with larger population size, townships with larger population size
spend ($126 per person) more than smaller townships; (3) cities spend considerably more
($305 per person) than townships; and (4) communities located in Southeast Michigan
spend more than those in the rest of the state ($143 per person for cities and $62 for

townships).

143

6.2.2 The Independent Variables

With exception for the total property variable, the signiﬁcance of the independent
variables considered in this study vary across groups of communities. Variables that are
statistically signiﬁcant in expenditures of cities are not for townships; or variables that are
signiﬁcant for cities in Southeast Michigan are not for cities in the rest of the state.
Likewise, a variable that has a positive association with expenditures of cities may have an
inverse relationship with expenditures of townships; and the variable that was inversely
related to expenditures of townships in Southeast Michigan may be positively associated '
with expenditures of townships in the rest of the state. In sum, the ranking of the
signiﬁcance of the independent variables and their impacts in explaining the expenditures
of local governments vary by types of government, population size, and geographic
location of the communities. Therefore, results pertaining to each independent variable are

discussed separately.
6.2.2.1 Total Property Value

The most important factor that explained the variations in the expenditure patterns
of all classes of communities was the per capita value of total property. The values of
industrial and commercial properties (collectively called business properties) have positive
association with expenditures. Business properties affect expenditures in two ways: (1)
they create expanded tax base for communities. More tax revenues generated from these

properties and business related activities make more expenditures on public services

144

possible; and (2) new developments may require new and improved public services and
inﬁastructures that may replace or duplicate existing ones In general, the value of total
property was statistically signiﬁcant in the expenditure model and the value of its
estimated coeﬁicient was very large such that any ch'ange in its value will be followed by

signiﬁcant change in expenditures of local governments.

6.2.2.2 Mix of Land Use

Mix of land use can affect the demand and need for services. For example,
residential property, as percentage of total property, was found to be inversely related
with expenditures of most of the communities. That means, new residential developments
may not require as much new inﬁestructure of public services as business developments.
Accordingly, it was observed that most of the communities with high residential property
value have very low expenditures (less than $200).

Nevertheless, it should be noted that the regression results for townships indicated
that the residential property variable and expenditures of townships in Southeast Michigan
were positively associated. Although the data sets used in this study do not help to ﬁrmly
determine the reasons as to why such relationship was observed, the diﬁ‘erences between
types of residential: properties in Southeast Michigan and the rest of the state could be
considered as a starting point for further study. In addition to the costs of settlement
congestion that characterize Southeast Michigan, the preponderance of multi-family multi-
story residential properties may contribute to increasing expenditures in certain types of

public services. For instance, high rise multi-family dwellings and ofﬁce buildings in

145

Southeast Michigan require an aerial ﬁre truck equipped with more sophisticated
equipment which may not be needed in single family residential communities that are

outside of Southeast Michigan.

6.2.2.3 Population:

The population variable impacts expenditures of cities and townships diﬁ‘erently.
Expenditures in cities decrease as total population increase and expenditures increases in
townships as population increase. Public service expenditures are driven not only by the
quality and quantity of the ﬂow of services, but also by the costs of the inﬁ'astructures of
the services. In addition to the day to day cost of running the services and agencies that
provide the services, communities incur considerable overhead expenditures to maintain
existing service infrastructures. These expenditures could be considered as ﬁxed costs in
the public service production ﬁrnction. In smaller population size cities the per capita cost
of producing certain units of public services will be higher because there are fewer people
among whom the ﬁxed costs could be distributed.

In the case of townships, however, increasing and discontinuous jumps in public
service expenditures could be observed as a result of increase in demand for better quality
and quantity of services as population increases. Most of the more populated townships
produce their own public services such as police and ﬁre protection and have higher
associated expenditures compared to the less populated townships that may contract such
services ﬁ'om other units of governments like county sheriﬁ‘ and state police or may do

with whatever general level of service is provided by the county government.

146

Finally, it should be noted that this population-expenditure relationship could be
misleading due to the incongruity that may exist between service and political boundaries
of communities. Ifthe service boundaries are greater than the political boundaries, the
expenditures of the community will be overstated because the eﬁ'ective population served
is greater than the population by which the per capita expenditures are computed. For
instance, the City of Lapeer extends its ﬁre protection service to adjoining townships. This
will obviously increase Lapeer’s ﬁre protection expenditure. However, if the computation
of the per capita expenditure for the City of Lapeer does not count the actual number of
people served and is only based on those who consider Lapeer as a place of their abode, .
then, the expenditure will be overstated. To sum up, disparity between effective
population receiving the service and the number of people by which the per capita is
computed will cause over/understatement of the expenditures because data on population

of service areas is not generally available.
6.2.2.4 Population Density

Population density, while statistically signiﬁcant for cities, was found to be not
signiﬁcant for townships. However, care must be taken in interpreting results of this
variable. First of all, the computation of density itself has a serious problem. Dividing the
total population by the total land area of a local government does not tell how the
population is distributed across the landscape of the jurisdiction. Two communities with
equal population size and land area may have a different distribution of settlement. One

may distribute all its residents on all the land under its jurisdiction and the other may only

147

conﬁne its residents to a certain portion of its area. These different types of population
distribution will have diﬁ‘erent impacts on expenditures in that constructing and
maintaining service infrastructures over the entire land area or over a limited section will
have diﬂ‘erent service and associated expenditure requirements.

Second, types of service categories for which the impact of density is being
investigated do matter. Diﬁ‘erent classes of services will be impacted diﬁ‘erently by
increasing population density. In the case of road construction and maintenance, for
instance, the per capita expenditures would be expegted to decrease with increasing
density of population up to a point because increased volume of traﬁc is not expected to
offset the average cost advantage that arises from increased density. On the other hand,
ﬁre and police expenditures could rise if congestion (as a result of increasing density) sets
in. Hence, the overall impact of density will be determined by the share of each service
category in the expenditures of local government.

In this study, population density was found to be negatively associated with
expenditures of cities outside of Southeast Michigan and Townships in Southeast
Michigan when communities are disaggregated by geographic location. But, it was found
to have positive association when all cities and townships were aggregated in their
respective types of government. A negative 8 coefficient in the former case indicates that
increasing population density will decrease expenditures of local governments because
economies of scales are captured in the infrastructures of the services. Most of the cities
outside of Southeast Michigan, generally small in population size, have ﬁrll inﬁastructures
and services. If these communities are able to increase their population density, it is very

likely that they could reduce their expenditures.

148

All of the large townships are in Southeast Michigan and have long grown over the
threshold of getting by with services provided counties. Indeed, excepting for Meridian
Township, all the townships, big or small, that have their own police departments are in
Southeast Michigan. Ifthese communities are able to increase their density, it is possible
that they would also be able to reduce their expenditures because they would achieve
economies of scale in several service categories up to a point.

The ﬁnding regarding these two sub-classes of communities was in agreement with
a recent study of eighteen communities in Michigan. Burchell (1997) estimated that there
would be considerable savings in four major areas (land consumption, infrastructures,
housing cost, and ﬁscal impact) if new grth were added in a greater density than the
existing level. The more people along a mile of water or sewer pipeline, the lower the cost
per person. The study by Burchell utilized a single year cross sectional data and was based
on synthetic projections that included formulas for the costs of roads and water and sewer.
But the current study used actual historical data sets of ﬁfteen years and did not include
expenditures of water and sewer for all the forty six study communities and expenditures
of roads for the twenty nine townships. Therefore, the positive sign of the population
density coemcient for other classes of communities should not be considered as a
conﬂicting result because the studies were conducted with different sets of data and
purpose. For instance, if water and sewer were omitted from Burchell’s study, the
remaining expenditures, including those for police and ﬁre, are for services where density
is associated with congestion and greater expenditures instead of economies.

The regression results indicated that cities in Southeast Michigan have statistically

signiﬁcant positive association between density and expenditures. It was also observed

149

that this association was positive when all cities were all grouped together. This was
because eleven of the seventeen cities are in Southeast Michigan and the negative
correlation for cities in the rest of the state was counterbalanced or lost because of larger
aggregation of cities.

Although the data set used in this study does not show congestion thresholds, the
positive association between density and expenditures of these commwities could be seen
ﬁ'om a settlement congestion perspective. All the larger cities in the study groups are
located in Southeast Michigan. It is possible that most of these large cities may have
passed over the threshold for economies of scale and are experiencing high costs
associated with congestion in some service categories. For example, the conditions of
road, police, and ﬁre services in Southeast Michigan are very different from those in the
rest of the state. Frequency of calls for police protection and ﬁre emergencies require
many patrol omcers and ﬁre ﬁghters on duty, more police vehicles, jails, and ﬁre trucks.
All these are costs associated with congestion resulting in a positive correlation between

population density and expenditures.
6.2.2.5 Population Growth Rate

The population growth rate variable was found to be statistically not signiﬁcant for
either cities or townships when they all are grouped in their respective types of
government. However, when communities were analyzed in their respective sub-groups, a

closer look at the regression results of cities in Southeast Michigan and smaller population

150

size group indicated that the variable was statistically signiﬁcant and the sign of the
estimated coefficient of the variable was positive.

The implication of the observed positive correlation between expenditures of these
communities and population growth rate is that it is the rate at which the population
grows that contributes to the increase in expenditures rather than the actual number of
residents (since actual population size is inversely related with expenditures). This is
because faster population growth will be accompanied with increasing demands for
expansion of services and inﬁastructures. The faster the population grows, the higher the

service expenditures will be.

151

6.2.3 Impact of Location

The role of geographic location in driving expenditures of cities and townships was
captured by the Single Factor Analysis of Variance (Table 5:9), summary statistics (Tables
5:10 & 11), and the regression results of the Generalized Linear Model presented in
Appendix E. It should be remembered that location was not treated as independent
variable in the model because individual level covariates can not be used in a Fixed Eﬁ’ects
model alone and all constant within the panel will be dropped from the regression results if
entered (see Appendix F). Therefore, Ordinary Least Square regression was performed for
the purpose of showing the signiﬁcance of location on expenditures. The variable was
found to be statistically signiﬁcant for both cities and townships. However, it showed
diﬂ‘erent signs of correlation with the expenditures of cities and townships in Southeast
Michigan. It was positive for cities and negative for townships. According to this result,
controlling for all the variables in the model, location alone will make the expenditures of
cities in Southeast Michigan higher than those in the rest of the state by $90 and the
expenditures of townships in Southeast Michigan lower than those in the rest of the state
by $11. The ﬁnding for cities was conﬁrmed by the summary statistics of cities (see Table
5:10). The summary showed that cities in Southeast Michigan spend $134 more than those
in the rest of the state. But townships in Southeast Michigan, despite the inverse
relationship between expenditures and location, spend $62 more than those in the rest of
the state (see Table 5:11).

Why would townships in Southeast Michigan have higher expenditures when they

are having cost advantage related to their location? The Fixed Ejects regression results

152

showed that total population and residential property variables in the estimated
expenditures equation have positive association with expenditures of townships in
Southeast Michigan. In the case of the current study, the positive (3 values of these two
variables in the equation had outweighed the negative correlation of location and
expenditures such that the expenditures of the townships in Southeast Michigan became
higher than the expenditures of townships in the rest of the state. Analogously, because
these two variables are inversely related to the expenditures of the townships in the rest of
the state (see Table 5:16), their negative [3 values in the equation had made the
expenditures of townships in the rest of the state less than the expenditures of townships in
Southeast Michigan. In sum, the reasons why expenditures of townships in Southeast
Michigan are more than the expenditures of townships in the rest of the state are better

explained by variables other than location.

153

6.3 Policy Implications

Many people in Michigan are concerned about population settlement patterns. The
Michigan Society of Planning Oﬁcials is currently conducting a series of studies and
conferences dealing with the impacts of settlements. Two major studies by academics
(Burchell, 1997; Schmid, 1997), for instance, were recently commissioned. Furthermore,
there is enough evidence from news media that indicate citizens of different communities
are very much concerned about the increasing costs of public services provided by their
local governments. Therefore, one could cautiously conclude that both the local and state
policy makers on the one hand and the citizens of different communities on the other share
common concerns relating to population settlement patterns and their impacts on costs
and resources in Michigan.

The basic assumption of this study was that the objective behind local government
expenditures is providing the best public services with minimum per capita costs. Hence,
the regression estimates of the per capita public service expenditures equations that
emerged ﬁom the analysis in Chapter 5 present the opportunity for policy makers to
identify the important policy instruments that could be used to control expenditures.

According to the empirical results, whether all communities were grouped only by
their respective types of governments or different sub-classes of population size and
geographic location, the most signiﬁcant factor that emerged to explain expenditures was
the per capita value of total properties as measured by the state equalized value. In the
case of townships, for example, it was only this variable that was statistically signiﬁcant in

the model (see Table 5:16). Yet, the model did a good job of explaining 72 percent of the

154

variations in public service expenditures of the twenty-nine townships. This was a very
strong ﬁnding and clearly calls for a further study. It appears that communities that have
wealth to tax do so and spend the revenue. At the same time, wealthier communities
demand more and higher quality services. No one would advocate becoming poor or
rejecting high valued land use in order to hold down expenditures. To the contrary,
communities try to attract high valued land uses. They offer reduced taxes now to get
more wealth in the future.

Michigan has created eleven tax-ﬁee Renaissance Zones (six urban, three rural,
and two military bases) located throughout the State where businesses and residents pay
virtually no taxes up to fifteen years. This tax waiver includes the single business tax,
personal income tax, real property tax, utility users tax, state education tax, local income
tax, and local personal property tax (Michigan Job Commission, 1997). Such measures are
expected to attract more commercial and industrial developments that could utilize
existing inﬁ'astructures and achieve economies of scale. While an increase in tax base will
increase spending, it may help to keep the tax burden of the established residents lower in
the future than it might otherwise be. Therefore, the statistical signiﬁcance of total
property does not warrant land use regulations as policy instruments to hold down
expenditures. What matters is not the level of expenditures but the ability of residents to
pay for the services they demand.

Most of the communities with high expenditures are the smaller cities. Almost all
cities provide most of the services (excepting water and sewer in a few cases) on their
own, while smaller townships do not. Because of the lumpy nature of many of the

services, underutilization of the existing public service infrastructures results in high public

155

service expenditures. Consistent with the ﬁndings of Burchell (1997) and Schmid (1997),
such a population-expenditure relationship implies that more people could be added to the
existing smaller communities and spending per capita would decrease. A small city
following a dense settlement policy has two things going for it that can reduce per capita
expenditures. (1) If small cities were to grow to achieve economies of scale it need not
contribute to sprawl since sprawl refers to low density development, not grth in
population whether it be around a metro or non-metro area. (2) City population is
negatively correlated with expenditures. This ﬁnding supports a policy to increase the
number of residents of existing communities. Ifthis is to take place in smaller size
communities, the savings that could be obtained from the joint impact of increased
population and a dense new residential development could be substantial.

Settlement, nonetheless, follows jobs. Currently most of the jobs in the State are
concentrated in cities and townships of Southeast Michigan where per capita expenditures
are the highest (the exception is the Grand Rapids area). The projected future job growth
is also in Southeast Michigan. But, if local governments outside of Southeast Michigan
could use diﬁ‘erent policy instruments to promote job opportunities in their areas by
attracting new businesses, it could mean that expenditures would drop in outstate cities
(that are in a sense now too small) and Southeast Michigan cities (that are or will be too
large). Growth outstate could beneﬁt Southeast Michigan by removing some of the
pressure for increased spending. Outstate regions need 'new and coordinated growth
strategies that will direct businesses and settlement into their areas. But, such strategies
are unlikely to materialize if growth efforts are not coordinated at regional or state levels

and if Southeast Michigan can not see that it is also to their advantage.

156

6.4 Future Research

This research was conducted using ﬁfteen-year data sets that include population,
expenditures of public services, and state equalized value of properties. However, it
remains desirable if data on other variables like measures of congestion, quality of
services, income and employment in minor civil divisions (MCDs), water/sewer
expenditure, and county supplied roads were available. The paucity of these types of data
sets could be considered as shortcomings of this research.

The lack of measures of quality of service creates problems of quantifying the
actual beneﬁts that may arise from population grth for some communities and the
actual costs of population congestion for others. In many of related studies, congestion
has been identiﬁed as a variable that increases the costs of public services. On the other
hand, higher population density is suggested as a variable that could reduce these costs.
Then, the question becomes what level of congestion will offset the beneﬁts of higher
population density, or what level ofpopulation density brings in congestion. The major
service categories in this study that are affected by these countervailing eﬂ‘ects of
congestion and population density are water and sewer systems, ﬁre and police
protections, and roads and highways. The questions posed above can be answered only if
it is possible to measure quality of services at different level of population density and
obtain relevant data of these service categories.

Public service expenditures largely depend on the resources available in a
community. Household income and place of employment of residents of a community

make up the larger share of resources available for public services. But, household (family)

157

income and employment information are not available at a lower MCD (city or township)
level. The census data of these variables is only available at a county level. That is not that
much helpful for this type of research that focuses to the lowest level of government
structure because there is no way of knowing the exact share of employment and income
in the community of interest. A city or a township is only a part of a county.

Expenditure data on water and sewer service areas need to be included to obtain
the whole picture of expenditures of local governments. But these data are very difﬁcult to
collect. The political boundaries of communities and the service areas covered by the
system are often diﬁ‘erent.

Finally, expenditure on roads and major streets is one of the problems encountered
in this study. Cities provide their own construction and maintenance of roads and streets
while townships are served by county road-commissions. Counties do not keep
expenditure records by townships, but by road or street that may run through several
townships. Thus, because it is difficult to assign the exact amount of expenditure to the
share of road miles in a particular township, expenditure data for this service category is
not available for townships.

Collecting and adjusting most of the data mentioned here may not be an easy task.
However, it may be possible to reduce the magnitude of the problem through survey and
primary data collection methods if reasonable ﬁnancial and technical supports are

available.

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APPENDICES

APPENDIX A:

SUMMARY STATISTICS

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“mesa
aumamuou
Qumucomu
Qummcmn
ADZHUQOQ
Hmuoumoa
ncmmxm

manmﬁum>

downwaﬂmom HOHHmEm gawk uaﬂuwo Am.H2<v

bmHm.vmw
Hammmm.m
www.mamm
mmm.mo>v
wm>.mmom
Hmmamao.
mo.avomm
mommv.mm

mmm.mHHN
bmmma.¢m
mo.vmomm
vm.ammma
hmv.>mbm
mmmmmao.
ba.MhmHh
boom.HO¢

uncoo
owned
Quaamuou
Quaucvmu
Qummcmn
nuzuomom
Hmuoumoa
ocwmxm

lllllllllllllllllllllllllllllllllllllllllllllllllllll +lllllllll

.>ma .num

mﬂnmﬂum>

coauuaaaom uooumq and: uoauao .v.H:<.

166

momm.omh
Hahmo.oa
vmv.ammm
vmm.vmmm
vha.nmmm
NbeHHo.
Hm.vmmNN
mmmva.hm

.>mo .num

cm0w£0ﬁz unmouaom a“ uawsocsoa

mHHm.vmw
Homvvm.m
Ham.Hth
bmv.vmvm
mom.hm>m
vaomao.
Hm.mmoma
mvovh.mm

.>ma .num

mmm.mvaa
mmN¢H.Hm
m.NmmmH

hm.mbmma
Hmm.vmam
mmommao.
Ha.mmmmm
bmmm.mom

Hmmv.wam
hammo.am
mv.vamH
hh.mvaH
Hmh.hbvm
Nmmwbao.
m.ronwm

vbmm.mra

umcmn
“coca
Quaamuou
Quaucvmu
Qummcmn
cashmmom
Hmuoumoa
ncmmxm

magmaum>

AN.N.$

uncov
Hausa
Quaamuou
Qumuccmu
Quamamn
nuzumaom
amuouaom
ocmaxm

maanum>

DQMSuc3OB HH(_AH.N.¢9

167

mmma.mmm
mmhbmv.m
www.momb
mom.mmmh
mmo.mMHH
mmamoao.
Hv.vhova
memm.om

.>mo .oum

scandaamom kahuna gawk unﬁnnczoa

bmvm.mvm
NmvaN.m
av.mvmm

owm.HbNm
mom.vaov
«maomao.
vN.Nvmm

Hmmwm.mh

.>ma .cum

mmm.NmHN
mmmmm.Hm
mH.>hNON
vv.>amma
www.mvmm
0H0.

Ha.mmmhm
mmmm.mmm

mbmo.HHm
mMMMH.Nm
vm.mmmha
hv.HobHH
NH.mmbm
mmao.
mo.mvomH
NNvm.mvH

umcov
amend
Quaamuou
Quaucomu
Qummcmn
nu3uomoa
Hmuoumoa
ucmmxm

manmﬂnm>

3&2:

umGoU
Mecca
Quaamuou
aumucomu
mummCmQ
nuzumaoa
Hmuouaom
ocoaxo

magmaum>

«anon on» no once as» ea nagguczoa .m.u.¢e

168

mmmm.oov
momwmb.m
mvo.mmm>
www.mmmv
mnm.vmmm
hmmmmao.
MH.VHHNH
mpmmH.mb

.>mn .num

coauaaaaom uoaﬁmem nuns nannuczoa

mvmm.bmm
Hmmmm.am
mm.mHNmH
MN.POHNH
Hm.vmmm

mommbao.
hm.hmhma
mmmw.omH

uncov
Mecca
Qumamuou
muaucomu
QHQmCmQ
casummom
Hmuoumoa
ucomxm

wanmacm>

.m.~.5

APPENDIX B:

CORRELATION ANALYSIS OF THE VARIABLES

169

HmHN.or

oooo.a

vao.o
Hamo.o
oooo.H

mmbH.o
hvmo.o
mem.o
oooo.H

Nvma.0|
homo.o
mnoo.o:
ommo.o
oooo.H

ovom.o
wvmo.o
vmoo.ot
mvHH.o
mmmo.or
oooo.H

mmmm.o
vwoa.o
mome.o
vaH.o
mmmo.or
mmmm.o
oooo.H

mNNh.o
OOHH.OI
Hmbm.o
mmmm.o
thH.OI
mvvm.o
HNNb.o
oooo.H

_uwcmumoa
_umvcH
_Qumamuou
_Quaucnmu
_nu3uvmom
_vmmom
_Hmuouaom
_Uchxo

IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII +IIIIIIII.
Hmuoumoa vcoaxo

mmam.o
oooo.H

Quaamuou Qumucvmu nuzumaoa

uawnuc3oa .ooHQMwun>

mHmN.0I
moHo.o
mmom.o
mmNN.o
oooo.H

Ummoa

neoocoaoocu on» no coaunaauuoo .~.m.

HHNm.o
Nmmm.o
Hmma.o
Namv.o
mmvm.or
oooo.H

Nmmb.o
Hmom.o
HmHN.o
vmom.o
ova.0I
mmvm.o
oooo.a

wao.0I
mwmv.or
mvHN.o
vmo~.or
moao.o
thH.OI
mmmN.OI
oooo.a

_umcooaom
Cong
.muaamuou
_Qumucvmu
_nu3uoaoa
_Umaoa
_HMuoqum
_ocoaxm

IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII +Iu.l.ll||.l.l
Hmuoumoa vcwmxm

momo.o mmbm.o
Hmvm.o Harv.o
oooo.H mmo>.o
oooo.H

Quaamuou

Qumucvmu suzuomom Unmoa

nowuao .uoHAMMun>_ucoo:oaoocH «no mo coauaaouuoo .H.m.

APPENDIX C:

DIAGNOSTIC REGRESSION RESULTS

170

mmmo.oom
mammmom.
Hammom.m
mmmmwﬂo.
mmmmroo.
Hm.ommw

wormmm.v
thmooo.

mm.hNH n
mmHv.o
mmmv.o
oooo.o

m>.>~ _ mH> cmoz

llllllllllllllllllllll +lllllllll
mmHHm>.o m~.H _ nuzumaoa
mommpm.o mm.~ . mundane»
mmmom~.o mo.m _ auaucnmu
mmaomo.o Hm.wH _ umcmnaom
moammo.o vo.m~ _ vmaoa
mmmpmo.o mm.m~ _ umuca
mmemoo.o mm.>HH _ Hmuouaom
IIIIIIIIIIIIIIIIIIIIII +.l.ll.l.|||l.l
mH>\H mH> _ manmﬂum>
mmH.mmH ooo.o Hmv.v mvﬁmm.>> «amm.>¢m _ mcou
mommmoo. Hmo.o va.~ «sheave. NmOmFOH. _ umcmnaoa
Hmmmmm.mu ~mm.o mmm.ou «mmamm.m mmmpmﬂ.mu _ “mead
hammmoo. ooo.o one.» pmmpaoo. mmmmmﬂo. _ auaamuou
mmmmﬁmo.n ooo.o mmm.mu «Hmomoo. momaeao.t _ auaucnmu
pﬁm.m¢mn mﬁm.o mmm.o mvmm.~mn mmvotmmm _ nusuoaoa
moummm.H mmo.o mmo.~ moumm~.H mouovm.m _ emaoa
Hmomoﬁo.s mmo.o onw.au Hummmoo. mombvoo.u _ Hmuouaoa
llllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllll +Illllllll
.ucoo wmma _u_Am u .uum .eum .umoo _ ucmaxm
mm: uoom mmmm.mmam~ «mm am.mmmmmae _ Hmuoa
voumsvmrm mom IIIIIIIIIIIIIIIIIIIIIIIIIIIIII + IIIIIIIII
umumsvmum Hamm.m¢mwﬁ new HH.Hmmemov _ Hmsoﬂmmm
m A beam vom.mmam¢v n mm.mm~mﬁﬂm _ Hmnoz
Ahvm .h am It: .......... t ......... untuuua+ ..... n---

vN.bN
mmm

mno no no

£852 m2 up mm _ condom

uoauao .noanuaun> Add nuﬂz_.eoauuoumem oauuocmuao .H.a.o.

I71

memﬁmb.o
Novbmm.o
mmormm.o
mvaomo.o
mmvvbo.o
mmmmmo.o

hH> cmmz

nuzummom
Qumamuou
Qumucnmu
umcmnmoa
Hanna

Hmuoumom

mammammm
mmmNHvH.
vmmmvm.ml
mbmHch.
Nmmmmoo.t
HHH.omNN
mmmﬁmoo.

mmom.mbN

mmhvmmo.l
hammm.NHI
wmvmmoo.

HmmNHNo.I
mmma.v¢ml
mhbvmoo.l

whoom.0h
Nﬁvmmvo.
mmbHNv.N
vmmrﬁoo.
momwmoo.
mmvo.mmh
movvaoo.

mwo.hH¢
mmmmo.
mvmmHH.ml
mathHo.
Hmbovao.l
mmwm.>or
mmmooo.

mcool

umcmomoa
Hanna

Qumamuou
mumucomu
nu3ummom
Hmuoumom

Hr.mNH u
mHHv.o
bmwv.o
oooo.o
¢m.om
mmN

mmz uoom
noHMSUmtm mom
boundvmrm
m A noum
Amvm .w
who no Honﬁdz

Cm

wom¢.mwmma mvN
NmH.mmmbom w
llllllllllllllllllllllllllllll +|llllllll

m2

MU

ma.mm~moa¢
mH.bmmmvom

mm

Hmsoﬁmmm
Hmnoz

ouusom

nowuuo .co«uudnmom uo Cunard u:onua3..c0duuouuom Own-ocmdda Aw.ﬁ.uv

172

0mmmmh.0
¢0mwmv.0
v0m~am.0
mmmmmm.0
000000.0
HN00>0.0

hH> cmmz

£u3uamom
mumamuou
Qumucnmu
uncoomom
Hmuoumom
Unmom

mem.hmm
HO0Hmma.
hmmeao.
mNHmmoo.
www.mmam
00rﬂmo.m
wdmvmoo.

mmom.m0m
vowvaH.
mamboao.

bv0MNN0.I
Hm0N.mamt

00t0mm.a

00H0000.I

mNN00.Hv
mmbvwwo.
0mNmH00.
mmbvmoo.
mwb¢.mhh
wormbm.m
Hmomooo.

thv.00N
mommmva.
mmmmmao.
mmmvmao.l
000m.maw
molmvm.m
m¢MN>00.I

mcool

uncovaom
Qumamuou
mumucumu
nusummoa
vmmom

Hmuoumoa

wNNm.mmHON va
llllllllllllllllllllllllllllll +l'l'l'll'
mmmm.mmmma mvm
00H.0HO0Hm w

IIIIIIIIIIIIIIIIIIIIIIIIIII +nl'lI-III'II

N0.bNH
mmHv.0
wmmv.0
0000.0
mw.am
mmm

mm: uoom
nwumsvmrm nod
noumsvmrm
m A noum
Amen .0
who no Honﬁdz

0m

m2

we

vm.wmmmmﬁb

HN.mhmHm0v
MH.HO0NOHM

mm

Hmsnﬂmom
Hmuoz

condom

Coaudu .IOH<_UGIA unocuak..co«uuoumtm aﬂauocunﬂa AM.H.UV

173

0Nv0.HmN
m00HmNN.
mvamao.
0mvmaa0.l
mhm.mama
mbmmm00.I

wvaw.~vﬁ
Hmmmﬁeﬁ.
mmmwaﬁo.

mmonN0.I
mp0.HNNHI
meamoo.t

vmammh.0
mmvwv¢.0
mmmmvm.0
mommmm.0
NOHONM.0

vmomm.bm
ambaamo.
Nmmmaoo.
hmmvmoo.
Hmm.mmh
bwqooo.

>0PH.0HN
Nmmmmma.
mammvao.

Hb0v0H0.t

¢H0m.wvm

mbHNv00.t

hH> cmwz

Suzummom
Quaamuou
unconmom
Hmuoumom
Qumucomu

mcool

umcmnmom
Qumamuou
Qumucnmu
nusuoaom
Hmuoumom

lllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllll +llllll|ll

Ham>uoucH

.ucoo wmmﬁ

.uum .vum

wNNm.m0HmN va
llllllllllllllllllllllllllllll +lllllllll
mmH0.mvaH mvm
m0m.mbmﬁbm m

llllllllllllllllllllllllllllll +lllllllll

Nm.HMH u
hbmm.0
hmmm.0
0000.0
0H.mm
mmN

mm: uoom
noumsvmrm mom
ooumswmrm
m A noum
Amam .m
who no Honssz

0m

m2

MU

vm.mmwmmﬂb

Hm.0mmvmmv
mm.bbmmmmm

mm

Hmsoﬂmom
Hove:

wousom

anUAU .IIH¢_chA val coauddsnom no Oulnvm uSO£UdB_.coququOm oauuocmldo .v.n.ov

174

m®m00.m0
mmmmmvo.
0¢mvm.at
vaHOHo.
vvmawoo.
mmvmm.mm
00I0NF.N
mmwoboo.

mva0.NN
00NMNH0.I
00NNH0.MI
Hmwmhoo.
I Hvﬂmmoo.t
N¢N.H00I
I 00I0Nm.vl
mwﬂmvoo.

Ham>umucH .ucoo wmmg
mmHm¢.Hmm> «ma
llllllllllllllllllllllllllllll +ll|llll|l
mmomm.mmma has
mob.mo>~mm n

lllllllll Illllllllllllllllllll+lllllllll

h0H.Hv
H0bb.0
thb.0
0000.0
m0.00m
mmv

mm: uoom
u omumsvmlm mod
n noumsvmrm
m A noum
u .bmv .b 0m
n one no Hmnﬁdz

_u_Am

mma.ml
0vm.ma
0mm.ml
mbm.HI
wmm.bl
wmm.0H

u

mmmamm.0
«FOHHM.0
NDNNHN.0
Nm000N.0
hvmvho.0
wbmmv0.0
Nm¢Nm0.0

mmvﬂh.mﬂ
mbmmvﬁo.
mmmmmmv.
vmhmooo.
m000000.
«Nm0.mma
00IMmm.v
thmooo.

.uum .cum

MU

bmbam.mm
mmmmao.
«vmth.NI
0000000.
mvmhhoo.t
mmm0.hmml
00I0N0.MI
vammoo.

.uooo

0v.HNmomHm

Nm.mmmHNh
wm.bmmmmvm

mm

_ hH> Gmmz

_ £u3ummom
_ Hausa

_ Qumamuou
_ Qumuccmu
_ Unmom

_ uncovmoa
_ Hmuoumom

_ mcoul
_ umcmnmom
_ amped
_ Qumamuou
_ Qumucvmu
_ £u3ummom
_ Unmom
_ Hmuouaom

''''''''' IIII-In"I"I-l'nl'lu'l'I'InT'l-I-II'"-

_ ncomxo

_ Hmsnﬁmmm
_ Hobo:

_ wousom

ands-csoa .uoanuaun> Han nuaz_.eo«uuoumom cauuoeuaao .H.u.o.

175

Nmﬂmmm.0
mNNHHm.0
mwhmam.0
N00¢0N.0
mvmbv0.0
Hmmvv0.0

hH> cmmz

cuzummom
mecca

Qumamuou
mumucomu
Hmuoumom
umcmoaoa

mmmm.0HH
maobmmo.
N00¢HN.HI
mvmmmoo.
mN00m00.I
mvam.0HHI
0vmmv00.

m0m00.mm
00Hm0N0.I
wmmmm.ml
vmovboo.
Hmvv000.I
waH.MN0I
¢00¢N00.

wvm.vl
www.ma

.HHm.bI

HwaH.mH
thbmao.
mohamm¢.
Mbﬂwooo.
mvm0000.
mmm~.mha
mr0m000.

mombh.mm
«Hmmvoo.
Hmwm0H.Nl
hHNwmoo.
0N0b000.t
00¢0.0hvl
wbmmmoo.

mcool

uncoomom
Hausa

mumamuou
ammucnmu
nusuomom
Hmuoumom

0mamv.amm> vmv
llllllllllllllllllllllllllllll +lllllllll
momav.amma 0Nv
0H0.mhmmmm m

llllllllllllllllllllllllllllll +lllllllll

mvm.mv u
Mbmr.0
movh.0
0000.0
mm.m0m
mM¢

mm: uoom
noumsvmrm wed
nmumsvmrm
m A noun
Ammv .0
mno no Honesz

vb

m2

MU

0v.HNm00Hm

hm.hvmmmm
HH.vh0m0mm

mm

Hmsowmom
Hove:

oousom

nmﬂnu::oa .COAUIdamom uo lunnvm uaonudz_.coaunouuom Daunocmaan AN.«.OV

176

0thmm.0
00mvHN.0
mmbmom.0
thNma.0
mmmv00.0
mvma00.0

mH> cmmz

nusuomom
mumﬂmuou
Qumucnmu
umcmomom
Unmom

Hmuouaom

v00000v.
000v000.
000v0H0.
mv00000.t
00NN.0HH
00I0¢0.NI
Nmmbvoo.

moro0.~mt

v00H00.
vhmamoo.

0500000.!
0000.0hml
00Im00.vl

mm00m00.

bmm.0
000.0H
0v0.0HI
vmm.HI
000.5!

N00000.0
v00h000.
mm00000.
mvmmooo.
mmv.¢ba

00Im0h.v
mhmvooo.

00000.0HI
vbmambo.
wmmmoo.
NO0N000.t
mm00.mmml
00t0h0.Ml
Hammoo.

mcool

uncoumom
Qumamuou
Qumucumu
£u3ummoa
Unmoa

Hmuoumom

Hm.Nv u
0000.0
0000.0
0000.0
Hh.mNN
mmv

mm: uoom
noumsvmrm hum
umumsvmtm

m A noum

Ammv .0

0m

mno mo Monﬁsz

bmmma.omba 0Nv
mv0.h00v0v 0
llllllllllllllllllllllllllllll +lllllll||

m2

up.

vNN.th00h
0N.Nvmvmwm

mm

Hmsuwmmm
Hobo:

mousom

unﬁnuctoa .ﬂlnt baud uaonuwz..cownn0um0m adv-ocmuﬂn Am.N.Uv

177

mm.o _ mH> coo:
llllllllllllllllllllll +||I|l|lll
omommm.o mo.H _ nuzuoooo
Hammam.o mo.¢ _ ouoamoou
Hormo~.o me.v _ monocomu
mm»a¢a.o Hm.o _ Honouooo
mmmmmﬁ.o m~.h _ omcooooo
llll llllllllllllllllll +1 llllllll
mH>\H .mH> _ mannaum>
moamo.¢m mommmo.m moo.o Hmm.~ oevmmm.> mompm.ma _ mcoon
mmmommo. mmeapqo. ooo.o HNH.F oovamoo. Hoaamoo. _ umcooaoo
mmqaoﬂo. oarmpoo. ooo.o pmﬂ.¢ﬁ mmmoooo. abommoo. _ ouoaouoo
Noaomoo.u mmmomoo.u ooo.o hov.mu mommooo. «mamboo.u _ monocomu
smmﬁb.mpu mvhm.vm>- mﬁo.o mom.~- ~m~m.mma msqo.¢mvu . nozuoooo
Hmomoo. mommooo. ooo.o mmm.v enamooo. mmmvﬂoo. _ Hmoooooo
llllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllll +lllllllll
Ham>uouoH .ucoo mmmH _u_Am o .uum .oum .uooo _ ocoaxo
mm... u mm: boom mmamo.ﬁmme an. mv.H~momHm _ Hobos
>v~>.o u oouosomum nod uuuuuuuuuuuuuuuuuuuuuuuuuuuuuu + uuuuuuuuu
mpmb.o u ooumsomum mmNHH.v~o~ mm. ve¢.¢vmmom _ Hmsoﬂmom
oooo.o u m A ooum Hoa.mmvvmv m Ho.>eammm~ _ Hoooz
mv.m- u Ammo .m an uuuuuuuuuuuuuuuuuuuuuuu s ...... +unu ......
mmv u ago no noossz m2 no mm _ oousom

ands-c308 .uOnt ﬁend val coauddamom Ho Chunvu uaonudk..cowuuoumtm Oduuocmada Av.N.U.

APPENDIX D:

FIXED EFFECTS REGRESSIONS

rm

Amoﬂuoomumu bay

H00v.m0b
mmom0mN.
vm0v0a0.
0000.0vml
0N0.0POH
0000000.!

.Hm>umucH

00NH.0N0
0NHOv00.
HOMHO.
M000.0H0I
HN¢0V.H>I
m0bva0.r

.ucoo mmmg

0NHm.0m0
N000HNH.
0H000H0.
0HN0.vm>I
qomh.mm0
m0N0H0.I

maoul

umcoomom
muaamuou
Quaucomu
nuzummom
Hmuoumom

|":ll'-l'-|"'l'|ll|'l'll'lll'l'|'|""II"|'|-"|'|I'I|"I"|'|II"II'|I'I|

0000.0
00.00

000N.0
00NN.0
MH00.0

ma
5H
mmm

m A poem
Ammm .m Vb
Hamuo>o

coo3uon
capo“: omum

mpo no nonadz

«wanna ”do

Nmm.mm u Ammm.oﬂvm
mmm.m voHNH.mo
pmo.~ Hemommo.
moo.HH Hmmvﬂoo.
omm.p- mmoom.mm
mmm.a momm.o~m
map..- mmmﬂmoo.
o .uum .oom
mmom.o- u
mmvm.om~ u
nmpom.mm. u
osmm.vbm u

.cowuuouoou

Anx .xlsvuuoo

Axl: + uHxHoVUm

3 xsaom
s. so.

.caouaz. uuoouuouooxwu .H.H.o.

179

Ammﬂuoooumo 0V

V000.va
000v00.H
0000H0.

N000H.¢0
00v0.000
000VH00.

000000N.I
5000000.:
00HH000.
H00.H0vl
0vmb.m0ml
000N0N0.I

m00h.0NN
H0000H0.
0NON000.
v000.00HI
v0N0.N0HI
MHH0MH0.I

uncooaoa
Qumamuou
mumucomu
nuzumaom
Hmuoumoa

llllllllllllllll +ll|lll|ll

0000.0
v0.00

H0hH.0
000H.0
vm>>.0

0H
0
00

a A ooum
.mb .m

Hamuo>o
cmmxuon

00

canon: om-m

mno mo Honﬁsz

ooaoao noun;

mmm.oH u Ame.mvm
mmm.a momo.HHH
H00.H Nvmﬁwhm.
h00.> 0m>oaoo.
mvv.Hu v0>o.>HH
m0m.ou Hmov.~0m
Hom.Hu mmmbboo.
u .uum .oum
mvm>.ou u
b0¢0.0¢ﬂ n
0H>N0.>~ u
n00m.mvﬁ u
.cowuuouoou

Anx .xlsvuuou

Axis + uHxloVUm

Au xHovom
3. son

.oanuaz. ouoouuouooxdm .u.H.o.

180

Amoﬂuoomumo HHV ooo.o

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APPENDIX E:

GENERAL LINEAR MODEL REGRESSIONS

188

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FIXED EFFECTS REGRESSION WITH LOCATION VARIABLE

190

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APPENDIX G:

SAMPLE REGRESSION DATA

 

 

191

 

 

 

 

 

 

 

 

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