NOT ALL PROPERTY TAXES ARE CREATED EQUAL:
INEQUITY FROM POLICY AND PRACTICE
By
Timothy R. Hodge

A DISSERTATION
Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of
Agricultural, Food, and Resource Economics - Doctor of Philosophy
2013

ABSTRACT
NOT ALL PROPERTY TAXES ARE CREATED EQUAL:
INEQUITY FROM POLICY AND PRACTICE
By
Timothy R. Hodge
This dissertation consists of three essays examining the effect of Michigan’s assessment
growth limit and assessment practices on property tax equity in Michigan and Detroit. The first
essay evaluates the extent to which Michigan’s assessment growth cap has redistributed tax
payments across economic and demographic groups throughout Michigan. Using survey data
collected in the winter of 2008 and summer of 2012, I show the length of homeownership is
negatively correlated with the homeowner’s effective property tax rate. I also document a
regressive relationship between income and effective tax rates. Finally, a relationship between
age and effective tax rates emerges in 2012 – older homeowners enjoy reduced rates.
The second essay evaluates the degree to which the assessment growth cap has created
substantial differences in effective tax rates among residential properties within the City of
Detroit. Using parcel-level tax data collected from the City of Detroit’s assessment division,
results show the cap creates substantial horizontal and vertical inequities. An important potential
implication of the cap is that it may constrain mobility; these concerns are validated as I measure
the “lock-in” effect created by the cap.
In the final essay, I examine property tax inequity created by assessment practices in
Detroit. Using the same parcel-level data from essay 2, I show that current assessment practices
create a wide range of property tax payments across properties of similar value, and similar tax
payments for properties of different values.

ACKNOWLEDGEMENTS

I am very grateful to my major professor and mentor, Dr. Mark Skidmore. His guidance,
encouragement, and friendship throughout my years at Michigan State have made this
dissertation and other projects not only possible, but also extremely enjoyable. He has been
influential in shaping me as an individual, and my interests as an economist. I am also grateful
to my committee members, Dr. Scott Loveridge, Dr. Charles Ballard, and Dr. Leslie Papke,
whose efforts and suggestions have greatly improved the quality of this research. I also thank
Dr. Gary Sands and Dr. Daniel McMillen for providing guidance, encouragement, and insightful
feedback throughout this process, and the Lincoln Institute of Land Policy for their financial
support.
To my friends, I thank you for your time listening to ideas, your kind and encouraging
words, your jokes and laughter, your thoughtful insight on work and life, and your genuine
camaraderie. Each of you has been influential in making my graduate school experience very
enjoyable and a time in my life I will remember fondly. Specifically, I would like to thank
Andrew, Mary, Sung, Tina, Tim, Adam, and Dale.
Finally, I would like to thank my wife, Drea, and my daughter, Adelyn. Drea, your love,
encouragement, and patience have provided the support I needed to get through these last six
years. You are my best friend and I am glad to have shared this experience with you. Addy,
although you have only been a part of my life for a short period, your laughter and smile at the
end of each day makes the bad days good, and the good days great. I love you both with my
whole heart.

iii

TABLE OF CONTENTS

LIST OF TABLES ......................................................................................................................... vi
LIST OF FIGURES ..................................................................................................................... viii
CHAPTER 1: Introduction ............................................................................................................. 1
CHAPTER 2: The Property Tax: A Review of Michigan Policies and Practices .......................... 4
2.1 Assessment Growth Limit in Michigan and Detroit ............................................................. 4
2.2 Abatement Programs in Detroit ............................................................................................ 7
2.3 Assessment Practices in Detroit .......................................................................................... 11
CHAPTER 3: Literature on Property Tax Limitations and Assessment Inequity ........................ 14
3.1 Property Tax Limitations .................................................................................................... 14
3.2 Assessment Inequity ........................................................................................................... 17
CHAPTER 4: Property Value Assessment Growth Limits and Redistribution of Property Tax
Payments: Evidence from Michigan (2008 and 2012) ............................................................. 20
4.1 Introduction ......................................................................................................................... 20
4.2 Methods and Data ............................................................................................................... 20
4.2.1 Effective Tax Rates and Tax Payments in Michigan ................................................... 20
4.2.2 Data and Descriptive Statistics, 2008 .......................................................................... 21
4.2.3 Data and Descriptive Statistics, 2012 .......................................................................... 25
4.2.4 Empirical Strategy and Econometric Issues ................................................................ 28
4.3 Empirical Analysis .............................................................................................................. 32
4.4 Conclusions ......................................................................................................................... 46
APPENDICES .......................................................................................................................... 49
Appendix 4.A ........................................................................................................................ 50
Appendix 4.B ........................................................................................................................ 52
Appendix 4.C ........................................................................................................................ 53
Appendix 4.D ........................................................................................................................ 54
Appendix 4.E ........................................................................................................................ 55
CHAPTER 5: Inequity from Michigan’s Assesment Growth Limit: The Case of Detroit........... 56
5.1 Introduction ......................................................................................................................... 56
5.2 Methods and Data ............................................................................................................... 57
5.2.1 Effective Tax Rates in Detroit ..................................................................................... 57
5.2.2 Model ........................................................................................................................... 60
5.2.3 Examining Effects on the Full Distribution: Quantile Regression Analysis ............... 61
5.2.4 Data and Descriptive Statistics .................................................................................... 64
5.3 Empirical Analysis .............................................................................................................. 67
5.3.1 Traditional Analysis: Measuring the Average Effect .................................................. 67
5.3.2 Quantile Regression Analysis: Examining the Full Distributional Effect ................... 73
iv

5.3.3 Quantile Regression Analysis: Horizontal Inequity .................................................... 76
5.3.4 Quantile Regression Analysis: Vertical Inequity......................................................... 88
5.4 Assessment Growth Limit and Mobility in Detroit ........................................................... 90
5.5 Conclusions ......................................................................................................................... 97
APPENDICES .......................................................................................................................... 99
Appendix 5.A ...................................................................................................................... 100
Appendix 5.B ...................................................................................................................... 101
Appendix 5.C ...................................................................................................................... 111
CHAPTER 6: Assessment Inequity in a Declining Housing Market: The Case of Detroit ....... 112
6.1 Introduction ....................................................................................................................... 112
6.2 Methods and Data ............................................................................................................. 115
6.2.1 Assessment Ratio and Equity..................................................................................... 115
6.2.2 Vertical Equity ........................................................................................................... 116
6.2.3 Horizontal Equity ....................................................................................................... 117
6.2.4 Quantile Regression Analysis .................................................................................... 119
6.2.5 Data and Descriptive Statistics .................................................................................. 120
6.3 Empirical Analysis ............................................................................................................ 124
6.3.1 Traditional IAAO Measure of Regressivity............................................................... 124
6.3.2 Vertical Inequity: Traditional Statistical Analysis ..................................................... 126
6.3.3 Vertical Inequity: Quantile Regression Analysis ....................................................... 129
6.3.4 Horizontal Inequity: Traditional Statistical Analysis ................................................ 137
6.3.5 Horizontal Inequity: Quantile Regression Analysis .................................................. 140
6.4 Property Tax Implications................................................................................................. 151
6.5 Conclusions ....................................................................................................................... 154
APPENDICES ........................................................................................................................ 156
Appendix 6.A ...................................................................................................................... 157
Appendix 6.B ...................................................................................................................... 158
Appendix 6.C ...................................................................................................................... 160
CHAPTER 7: Conclusion ........................................................................................................... 167
REFERENCES ........................................................................................................................... 171

v

LIST OF TABLES

Table 2.1 NEZR and NEZN Requirements .................................................................................... 9
Table 2.2 Millage Rates and Tax Payments for Qualified Abatement Zone Property ................. 10
Table 4.1 Summary Statistics, 2008 ............................................................................................. 24
Table 4.2 Summary Statistics, 2012 ............................................................................................. 27
Table 4.3 OLS Effective Tax Rate Regression Results ................................................................ 33
Table 4.4 Heckman Effective Tax Rate Regression Results ........................................................ 34
Table 4.5 OLS Effective Tax Rate Regression Results ................................................................ 40
Table 4.6 Heckman Effective Tax Rate Regression Results ........................................................ 41
Table 4.7 Pooled OLS Effective Tax Rate Regression Results .................................................... 44
Table 4.8 Pooled OLS Effective Tax Rate Regression Results .................................................... 45
Table 4.9 Variable Definitions...................................................................................................... 50
Table 4.10 Heckman Selection Equation Estimation Results....................................................... 52
Table 4.11 Heckman Selection Equation Estimation Results....................................................... 53
Table 4.12 Length of Homeownership Regression Results, 2008 ................................................ 54
Table 4.13 Length of Homeownership Regression Results, 2012 ................................................ 55
Table 5.1 Summary Statistics ....................................................................................................... 66
Table 5.2 OLS Effective Tax Rate Regression Results ................................................................ 69
Table 5.3 OLS Effective Tax Rate Regression Results: Mean Effect of Taxable Value Cap across
Property Value Groups ................................................................................................................. 71
Table 5.4 Average Tax Payments across Property Value Groups ................................................ 72
Table 5.5 Effective Tax Rate Quantile Regression Results .......................................................... 74

vi

Table 5.6 Effective Tax Rate Quantile Regression Results for Years of Ownership across
Property Value Groups ................................................................................................................. 77
Table 5.7 Probit Estimation Results.............................................................................................. 93
Table 5.8 Marginal Effect on the Probability of Sale ................................................................... 94
Table 5.9 Effect on the Probability of Sale across SEV Deciles .................................................. 96
Table 5.10 Variable Definitions.................................................................................................. 100
Table 6.1 Tests for Vertical Inequity in Property Tax Assessments........................................... 117
Table 6.2 Outlier Trimming ........................................................................................................ 122
Table 6.3 Summary Statistics ..................................................................................................... 123
Table 6.4 Traditional Assessment Performance Measures ......................................................... 125
Table 6.5 Traditional Results for Vertical Inequity .................................................................... 127
Table 6.6 Quantile Regression Results for Vertical Inequity ..................................................... 130
Table 6.7 Traditional Results for Horizontal Inequity ................................................................ 139
Table 6.8 Quantile Regression Results for Horizontal Inequity ................................................. 142
Table 6.9 Assessment Equity ...................................................................................................... 152
Table 6.10 Vertical and Horizontal Inequity .............................................................................. 153
Table 6.11 Horizontal Inequity (Market Value = $13,000) ........................................................ 153
Table 6.12 Variable Definitions.................................................................................................. 157

vii

LIST OF FIGURES

Figure 2.1 Michigan Residential SEV vs. TV ................................................................................ 6
Figure 2.1 Detroit Residential SEV vs. TV .................................................................................... 6
Figure 2.3 Tax Abatement Zones in Detroit, 2010 ....................................................................... 11
Figure 5.1 Average Effective Tax Rates of Owner-Occupied Residential Properties by Detroit
Neighborhood, 2010 ..................................................................................................................... 59
Figure 5.2 Parcel-Level Effective Tax Rates Among All Taxable Properties, 2010 .................... 60
Figure 5.3 Effect of Assessment Growth Cap on Estimated Effective Tax Rate Densities ......... 76
Figure 5.4 Effect of the Assessment Growth Cap on Horizontal Equity by Decile (SEV) .......... 79
Figure 5.5 Effect of Assesment Growth Cap on Vertical Equity ................................................. 89
Figure 5.6 Standard Quantile Coefficient Estimates................................................................... 101
Figure 5.7 Shift in the Effective Tax Rate Distribution as a Result of the NEZH Program ....... 111
Figure 6.1 Regression Estimates ................................................................................................. 128
Figure 6.2 Nonlinear Regression Estimates for Sales > $30,000 ............................................... 129
Figure 6.3 Nonlinear Quantile Regression Results ..................................................................... 132
Figure 6.4 Nonlinear Quantile Regression Results: $0 to $5,000............................................... 133
Figure 6.5 Nonlinear Quantile Regression Results: $5,000 to $30,000...................................... 134
Figure 6.6 Nonlinear Quantile Regression Results: $30,000 to $60,000.................................... 135
Figure 6.7 Nonlinear Quantile Regression Results: $60,000 to $90,000.................................... 136
Figure 6.8: Conditional Quantile Distributions, by Sale Price Quintiles .................................... 137
Figure 6.9 Quantile Distributions: House Age ........................................................................... 144
Figure 6.10 Quantile Distributions: Living Area ........................................................................ 145
Figure 6.11 Quantile Distributions: Lot Size .............................................................................. 146
viii

Figure 6.12 Quantile Distributions: MI Resident ....................................................................... 147
Figure 6.13 Quantile Distributions: PRE .................................................................................... 148
Figure 6.14 Quantile Distributions: Districts 1 through 4 .......................................................... 149
Figure 6.15 Quantile Distributions: Districts 5 through 7 .......................................................... 150
Figure 6.16 Quantile Distributions: Districts 8 through 10 ........................................................ 151
Figure 6.17 Standard Quantile Coefficient Estimates: Vertical Equity ...................................... 158
Figure 6.18 Standard Quantile Coefficient Estimates: Horizontal Equity.................................. 160

ix

CHAPTER 1
Introduction

Over the last 20 years, the residential property market in Michigan experienced a
dramatic transformation: housing prices rose rapidly in the mid- to late-1990s, slowed in the
mid-2000s, and then declined rapidly through the recent real estate crisis. Parallel with this
transformation, Michigan’s residential property tax underwent two key changes. First, the
1

property value assessment growth limit was enacted in 1994. This policy restricts the rate at
which individual property tax payments can increase, and was enacted to mitigate large yearover-year increases experienced by homeowners during periods of rapidly rising house prices.
Second, assessors in some areas are currently over-assessing property values for tax purposes.
With the dramatic decline in property values, residents are no longer concerned with large yearto-year increases in their property tax payments. Rather, the focus has shifted to assessment
accuracy; and this concern is not without merit as assessors experience pressure to prevent
assessments from following the downward spiral of the housing market to curtail property tax
revenue declines.
My primary interest in writing this dissertation is to measure the effect of the the taxable
value cap and assessment practices on property tax equity. My evaluation consists of three
essays. The first essay (Chapter 4) evaluates the extent to which the taxable value cap has
redistributed tax payments across economic and demographic groups throughout Michigan.
Using survey data collected in the winter of 2008 and summer of 2012, I show the length
homeownership is negatively correlated with the homeowner’s effective property tax rate. I also
1

The terms assessment growth limit, assessment growth cap, and taxable value cap are used
interchangeably throughout this dissertation.
1

document a regressive relationship between income and effective tax rates in 2008: All else
equal, middle- to high-income homeowners have lower effective property tax rates, relative to
low-income homeowners. By 2012, the relationship between income and effective tax rates is
altered; only high-income homeowners experience lower effective tax rates as a result of the cap.
Finally, a statistically significant relationship between age and effective tax rates emerges in
2012 – older homeowners are receiving reduced rates.
In the second essay (Chapter 5), I examine the degree to which Michigan’s assessment
growth cap has created substantial differences in effective tax rates among residential properties
within the City of Detroit. Using tax data collected from the City of Detroit’s assessment
division, I examine how the assessment growth cap alters effective tax rate distributions within
and across property-value groups. Results show that the cap creates a wide range of effective tax
rates across properties of similar value (horizontal inequity), and similar tax payments for
properties of different values (vertical inequity). My analysis also reveals market inefficiencies
created by the taxable value cap. That is, I show that the cap reduces mobility, new evidence of
a “lock-in” effect.
Finally, my third essay (Chapter 6) examines the role of assessment practices in Detroit
with regard to equity. Using the parcel-level data described in Chapter 5, I show that current
assessment practices in Detroit create a wide range of property tax payments across properties
with similar market values, and similar tax payments for properties of different market values.
In the next chapter, I provide a description of the property tax environment in Michigan
and Detroit, thoroughly discussing the policies and practices I evaluate in this dissertation.
Chapter 3 provides a brief literature review of the most relevant research examining equity issues
related to similar property tax policies and practices throughout the United States. Chapters 4

2

through 6 include the analyses described above, and Chapter 7 concludes with a summary of my
main findings.

3

CHAPTER 2
The Property Tax: A Review of Michigan Policies and Practices

In this chapter, I summarize the institutional details of the property tax in Michigan and
Detroit to provide context for the empirical analyses presented in Chapters 4 and 5. In particular,
I discuss property tax rates in Michigan and the variation in effective tax rates stemming from
the taxable value cap and various abatement programs. In the final section of this chapter, I
discuss assessment practices in the City of Detroit, which provides context for the analysis
undertaken in Chapter 6.
2.1 Assessment Growth Limit in Michigan and Detroit
Michigan’s assessment growth limit was part of Proposal A, a sweeping education
2

finance reform approved by referendum in 1994. Prior to the passage of Proposal A, property
3

taxes were based on the state equalized value of property (SEV). After 1994, the growth of
residential property values for tax purposes was limited to the lesser of the rate of inflation or 5
4

percent, regardless of any increase in the property’s SEV. Thus, in a market where housing
prices are growing more rapidly than the general price level, the taxable value (TV) of a property

2

For an extensive review of Proposal A, see Feldman, Drake, and Courant (2003).

3

A property’s state equalized value is equal to 50 percent of the property’s assessed market
value (or true cash value). In Michigan, the SEV of each property is determined by December
31 of the previous year.
4

Since the passage of Proposal A, the growth in taxable value has been restricted solely by the
rate of inflation since it has been less than 5 percent each year.
4

5

will lag behind the SEV. However, Proposal A also specifies that the taxable value of a
property must return to its current market-based SEV whenever a property is sold or transferred.

6

The effective property tax rate of each homeowner is therefore a function of the changes in
property value, the rate of inflation, and the owner’s length of residence.
To begin seeing how Proposal A changed Michigan’s property tax environment, Figure
2.1 highlights the divergence between TV and SEV in Michigan since 1994. As shown in the
graph, average housing values in Michigan grew faster than the general price level from 1994
through 2004. During this period, taxable value fell further and further below state equalized
value. The largest differential between TV and SEV occurred in 2004 when the taxable value
was 76 percent of state equalized value. In 2005, the difference began to narrow and TV was 89
percent of SEV by 2010. Figure 2.2 highlights the divergence between TV and SEV in Detroit
since 1994. Although the relationship between the taxable value and state equalized value in
Detroit is similar to the relationship at the state level, there are two key differences. First, the
gap between the taxable value and state equalized value in Detroit was larger than the gap at the
state level before narrowing; TV was only 53 percent of SEV in 2002. Second, the gap between
the taxable value and state equalized value in Detroit remained larger in 2010; TV in Detroit was
77 percent of SEV in 2010.

7

5

The gap between the TV and SEV will diminish in a housing market where SEV is stable or
declining. The TV (and tax payment), however, may continue to increase until the taxable value
equals the state equalized value.
6

This “pop up” effect includes the transfer of property from one family member to another.

7

Although Figures 2.1 and 2.2 highlight the aggregate difference between taxable values and
state equalized values, my analysis focuses on the difference at a single point in time.
5

Figure 2.1 Michigan Residential SEV vs. TV

Figure 2.2 Detroit Residential SEV vs. TV

Source: State equalized values and taxable values from 2000 through 2010 were obtained from
the State Tax Commission, Michigan Department of Treasury,
http://www.michigan.gov/treasury/0,4679,7-121-1751_2228---,00.html. The values from the
previous years (1994-1999) were obtained from the State Equalization Department, Michigan
Department of Treasury.

6

It is important to note that Proposal A was not the first mechanism for restraining
property tax revenues in Michigan. Prior to Proposal A, property tax revenues were already
8

limited by the “Headlee Amendment,” which was passed in 1978. While Proposal A limits
statutory millage rates and imposes a limit on the growth in taxable values, the Headlee
Amendment puts a direct limitation on property tax revenues. The Headlee Amendment restricts
property tax revenue growth to the rate of inflation (with an adjustment for new construction).
Any jurisdiction with potential revenue increases exceeding the Headlee limit is required to
reduce property tax rates and bring revenues into line with the revenue-growth restriction. This
9

type of tax-rate reduction is known as a “Headlee rollback.” Prior to the introduction of the
taxable value cap, rapidly rising property values resulted in numerous Headlee rollbacks. After
Proposal A, however, rollbacks were greatly reduced, both in number and in magnitude.
Thus, before Proposal A, the Headlee Amendment provided a mechanism for limiting
property tax rates, in a uniform manner across all properties in a jurisdiction. Proposal A
effectively instituted a new system for limiting effective property tax rates, but the Proposal A
mechanism did not treat all properties in a jurisdiction uniformly. Instead, under Proposal A, the
taxable value cap reduced effective tax rates for existing homeowners, but not for new
homebuyers.
2.2 Abatement Programs in Detroit
To provide an accurate measurement of effective tax rates and isolate the effect of the
assessment growth cap on horizontal and vertical equity, I must also consider the property tax

8

The Headlee Amendment is named for its author, Richard H. Headlee.

9

Local residents can choose to exceed the Headlee limitation by referendum, but this occurrence
is relatively uncommon. Note that the taxable value cap can interact with Headlee rollbacks.
7

abatement programs in Detroit. Two programs offered in Detroit include Neighborhood
Enterprise Zones (NEZ) (PA 147 of 1992) and Renaissance Zones (RZ) (PA 376 of 1996).
Under the Neighborhood Enterprise Zone program, three property tax reductions are available to
residential property owners: Rehabilitation (NEZR), New (NEZN), and Homestead (NEZH).

10

The goal of the NEZR and NEZN portions of the Neighborhood Enterprise Zone program is to
rehabilitate or develop housing in economically distressed communities. Table 2.1 provides a
summary of NEZR and NEZN requirements by dividing them into three stages: preimprovement, improvement, and post-improvement. NEZN beneficiaries receive a reduced
millage rate equal to half the statewide average millage rate, and NEZR beneficiaries have their
property taxes frozen at the pre-rehabilitation amount. Finally, the NEZH program is designed to
provide tax relief to current property owners, as opposed to inducing new investments. To
qualify, homeowners must have purchased their home after December 31, 1997, in a subdivision
platted before January 1, 1968. Furthermore, homeowners must make qualifying improvements
to the property of at least $500 within the first three years of qualification. The NEZH provides
a 50 percent reduction in city and county operating millage rates.

11

10

For more detail concerning Neighborhood Enterprise Zones, see: 1)
http://www.michiganadvantage.org/cm/Files/Fact-Sheets/NeighborhoodEnterpriseZone.pdf and
2) http://www.michigan.gov/documents/taxes/NEZ_FAQ_276616_7.pdf
11

NEZR, NEZN, and NEZH beneficiaries may receive program benefits from 6-15 years,
depending on location and type of project.
8

Table 2.1 NEZR and NEZN Requirements
Pre-improvement
-Applications for NEZ
certificates must be filed
before the building permit is
issued for rehabilitation or
new construction
-A copy of the building
permit must be submitted to
the local unit of
government.
NEZR only:
-The structure must be an
existing structure (or portion
of an existing structure)
with a true cash value of
$80,000 or less per unit.

Improvement
NEZR only:
-If a licensed contractor does
the improvements, the cost of
rehabilitation must equal the
lesser of 50% of true cash
value or $5,000 per owneroccupied unit ($7,500 per
non-owner-occupied unit).
-If an owner does the
improvements, the cost of
materials (excluding labor)
must equal at least $3,000 per
owner-occupied unit ($4,500
per non-owner-occupied unit).

Post-improvement
-Owners must file an affidavit
that the property is their
principal residence.
-NEZ certificates may be
transferred to new owners
within 12 years
NEZR only:
-The structure must be zoned
residential with no more than
eight units.
NEZN only:
-The structure must be
primarily residential with no
more than two units.

The Renaissance Zone (RZ) program eliminates all property taxes for residents and
businesses in the designated zones, excluding the taxes for local bond indebtedness, school
sinking funds, and special assessments.

12

In Detroit, this abatement makes the statutory tax rate

of those within a zone equal to 21.91 mills – a substantial reduction from the initial 66.61 mills
on homestead property.

13

As in the case of the NEZ program, Renaissance Zone benefits are not

automatically granted to properties. Rather, property owners are required to meet two
12

The property taxes eliminated for those in a Renaissance Zone include: local real property
taxes (including city and county taxes), personal property taxes, and the 6-mill State Education
Tax (SET). In addition to the property tax abatements, Detroit Renaissance Zones exempt the
state personal income tax and the utility users tax for qualified applicants.
13

One mill is defined as $1 due in taxes per $1,000 of the property’s taxable value. Along with
the taxable value cap, Proposal A reduced the statutory property tax rate of owner-occupied
properties by introducing a distinction between “homestead” and “non-homestead” property. A
homestead is defined as the homeowner’s principal residence. Specifically, Proposal A limits
the statutory millage rate that local school districts can impose on qualified homestead property
for public school operating purposes to 18 mills. In Detroit, where tax rates are particularly high,
homestead properties received a 17.83 mill reduction in their statutory millage rate (homestead
properties are subject to a tax rate equal to 66.61 mills, down from 84.44 mills).
9

stipulations (in addition to being within the zone): 1) participants may not be delinquent in any
local, county, or state taxes; and 2) participants must apply to receive benefits. Once the
property owner qualifies, the exemption is provided throughout the duration of the program
without reapplying.

14

Table 2.2 provides a summary of the millage rates for each type of abatement zone. In
addition, Table 2.2 provides an estimated tax payment for a property with an assessed land value
equal to $10,000 and an improvement equal to $20,000. The tax payment column provides a
sense of the savings accruing to beneficiaries (excluding benefits from the NEZR program).
Figure 2.3 shows the locations of the Neighborhood Enterprise Zones and Renaissance Zones in
Detroit.

Table 2.2 Millage Rates and Tax Payments for Qualified Abatement Zone Property
Abatement
Land
Improvement Tax Payment
$1,998
66.61
66.61*
NEZR
$971
66.61
15.24
NEZN
$1,743
66.61
53.82
NEZH
$657
21.91
21.91
RZ
*This rate is multiplied by the pre-rehabilitated taxable value of qualified properties

14

The typical RZ provides benefits for twelve years, followed by a three-year phase in to full
taxation.
10

Figure 2.3 Tax Abatement Zones in Detroit, 2010

15

2.3 Assessment Practices in Detroit
In addition to the inequities stemming from the Michigan policies, assessment practices
in Detroit may also be creating inequitable tax payments. However, before assessment inequity
is discussed (Chapter 6), I must first highlight the institutional details concerning assessment
practices in Detroit. All taxable properties in the City of Detroit are assessed on an annual basis
by the City’s assessment division. To accomplish this task, city assessors are responsible for two
basic functions: 1) inventory all property within the City;

16

and 2) equitably value all taxable

15

There are 77,221 properties within Neighborhood Enterprise Zones and 2,392 properties
within Renaissance Zones. Not all properties within designated zones receive tax abatements.
The map highlights areas within the city for which a property is eligible to receive an abatement.
16

Assessors inventory properties by: identifying and tracking property by tax descriptions and
parcel numbers, changing tax descriptions if properties are split by being re-platted or sold, and
analyzing property improvements/losses.
11

property in accordance with Michigan’s General Property Tax Law.

17

Assessors calculate

property values by inspecting new construction, analyzing recent sales of comparable properties,
and observing neighborhood advantages and disadvantages affecting market value. Assessors
are required to establish the market value of each property in the jurisdiction as of December 31
of the previous year (a.k.a. Tax Day).
After Tax Day, additional steps are taken to monitor the accuracy of the municipality's
assessed values and to ensure assessments are both equitable and at the appropriate level. By
March, the City assessor must complete an assessment roll, submit a copy of each assessment to
the property owner, and submit the assessment roll to the March Board of Review. That is, the
assessor must provide the true cash value (i.e., fair market value), assessed value (i.e., 50 percent
of true cash value), and taxable value of each property in the jurisdiction. At this time, property
owners who disagree with the assessor’s valuation may file a petition to the Board of Review.
Finally, upon the Board’s examination and approval of the assessment roll, the assessor delivers
the roll to the Wayne County equalization division and the Michigan State Tax Commission.

18

If property owners remain dissatisfied with the Board of Review’s assessment rulings, they may
file an appeal to the Michigan Tax Tribunal.

19

17

According to Michigan law, property must be assessed uniformly at 50 percent of true cash
value. True cash value is also referred to as the properties “usual selling price” in an open
market, with the sale being an arm’s length transaction (Michigan Taxpayer’s Guide, 2011).
18

The assessment roll is to be delivered to the Wayne County equalization office either ten days
after the Board of Review approves the roll, or the Wednesday following the first Monday in
April, whichever date occurs first.

19

The Michigan Tax Tribunal handled 12,500 residential cases last year alone, of which 3,015
were from Detroit (McDonald, 2013).
12

Despite the formal procedures to monitor assessment accuracy, assessors have an
incentive to over-assess property to mitigate substantial declines in property tax revenue
stemming from the recent plummet of property values in Detroit. The purpose of Chapter 6 is to
evaluate the degree to which these guidelines are followed in an eroded real estate market.

13

CHAPTER 3
Literature on Property Tax Limitations and Assessment Inequity

In this chapter, I review the literature on property tax limitations and assessment inequity.
While the entire body of literature regarding each of these topics is too extensive to review here,
I highlight the research most relevant for my three essays. Specifically, I discuss the literature
examining the distributional consequences of assessment growth limits and assessment practices.
In addition, I discuss the literature highlighting constrained mobility resulting from assessment
growth limits – an issue I examine in Chapter 5.
3.1 Property Tax Limitations
Early empirical research on property tax limits, including property value assessment
growth constraints, tended to focus on determining the degree to which these emerging fiscal
institutions constrained the growth of property tax revenue (Dye, McGuire, and McMillen, 2005;
Mullins and Joyce, 1996; and Skidmore, 1999). More recently, researchers have focused their
attention on the distributional consequences and tax-payment inequities introduced by
assessment growth limits, and I focus on this research here.
Dye, McMillen, and Merriman (2006) consider the assessment growth cap introduced in
Cook County, Illinois, in 2004. They demonstrate that maintaining property-tax revenues after
introducing a taxable value cap for residential property (as in Cook County) requires taxes to
increase for properties receiving little or no benefit from the cap, unless there is an increase in
another source of revenue. Focusing on the increasing taxes of non-beneficiaries, two groups in
Cook County are highlighted: 1) industrial and commercial property owners; and 2) homeowners
with taxable values appreciating at a rate lower than the specified cap. Thus, tax increases
14

stemming from the cap create inequity between residential and industrial property classes and
among residential properties. Validating the proposition that taxes can increase for homeowners
who do not benefit from a taxable value cap, the Minnesota Department of Revenue (2007)
reported that 84 percent of residential homesteads in Minnesota paid a higher tax in 2006 than
they would have if taxable values had remained unrestricted, all else equal.
Muhammad (2007) evaluates the inequities resulting from the District of Columbia’s
taxable value cap policy, imposed in 2002. Using taxable values and estimated market values for
all homes in the District of Columbia, Muhammad uncovers a large degree of horizontal inequity
when he discovers that effective tax rates for homesteads worth $600,000 are as high as $0.79, or
as low as $0.01. Regarding vertical inequity, Muhammad highlights 24 homesteads worth more
than $2 million with tax liabilities equal to, or less than, the tax liabilities of non-tax capped
homestead properties worth $100,000 or less.
Mikesell and Mullins (2007) examine the determinants of residential tax payments, using
household-level data from the Public Use Micro Samples of the 2000 Census of Population and
Housing, along with subsequent Annual Community Surveys from the Bureau of the Census,
from 2000 through 2006. They find that a range of policies, institutions, and household
characteristics are correlated with household tax payments. From the perspective of the present
study, it is important to note that Mikesell and Mullins find that length of tenure in a home is
negatively correlated with tax payments as a proportion of income.
In addition to reducing tax revenues and creating horizontal inequities, the taxable value
cap could create a “lock-in effect”. In the words of Dye, McMillen, and Merriman (2006), the
tax cap “may discourage mobility, since the expanded exemption is lost when real estate is sold,
and, thus, may decrease the efficiency of the residential real estate market.” Several studies

15

examine the effect of property tax caps on household mobility. Nagy (1997), Stohs, Childs, and
Stevenson (2001), Wasi, et al. (2005), Stansel, Jackson, and Finch (2007), and Ferreira (2009),
Ferreira, Gyourko, and Tracy (2010) and Ihlanfeldt (2011) evaluate the lock-in effect a various
contexts. Nagy (1997), Stohs, Childs, and Stevenson (2001), Ferreira (2009), and Ferreira,
Gyourko, and Tracy (2010) study the potential lock-in effect resulting from California’s
Proposition 13. Stansel, Jackson, and Finch (2007) and Ihlanfeldt (2011) focus on Florida’s
Save Our Homes program.
Of the California studies, all but Nagy (1997) conclude that assessment growth limits
create a lock-in effect. Nagy (1997) and Wasi, et al. (2005) use data on mobility rates before and
after the imposition of Proposition 13 in California, relative to communities in other states
without a taxable value cap. With tax benefits accruing to stationary homeowners, the
expectation was that relative mobility rates would decline after Proposition 13. However, the
findings of the two studies differed, with Nagy failing to find evidence for a lock-in effect and
Wasi, et al. (2005) supporting the lock-in effect. Stohs, Childs, and Stevenson (2001) use a
cross-sectional approach to evaluate the lock-in effect. Specifically, they compare home sales
rates in California metropolitan areas with metropolitan areas in other states. They find sales
rates are relatively lower in California—a result consistent with a lock-in effect. However, as
pointed out by Ihlanfeldt (2011), omitted variable bias is a concern when estimating effects using
aggregate cross-sectional data.
Ferreira (2004) also examines residential mobility in California, but focuses on two
amendments to Proposition 13 allowing transferability of the implicit tax benefits to a new home
for head of households who are 55 or older. In a comparison with two age groups, he found that
mobility for the 55-year old group is about 25 percent higher than mobility for the 54-year old

16

group. In summary, these studies present empirical evidence for a link between California’s
assessment growth limit and household mobility.
There are also two studies that focus on Florida’s assessment growth cap (Save Our
Homes). Stansel, Jackson, and Finch (2007) compare the average home tenure of full-time
homeowners in 2002 and 2006 – before and after the implementation of the assessment growth
limit. The researchers hypothesize that average home tenure would be longer in 2006 because
homeowners would have accumulated tax savings and would be less willing to move. However,
their comparisons fail to support this hypothesis. Finally, Ihlanfeldt (2011) uses parcel-level data
from Duval and Miami-Dade Counties to examine the probability of home sale before and after
the imposition of Amendment One, which enabled homestead property owners to apply a portion
of the tax savings from the assessment growth cap to a new home. Ihlanfeldt finds compelling
evidence that household mobility increased after the passage of Amendment One.
3.2 Assessment Inequity
Early empirical research on assessment inequity focused on specifying the functional
form to measure vertical inequity (Paglin and Fogarty, 1972; Cheng, 1974; IAAO, 1978; Kochin
and Parks, 1982; Bell, 1984; Sunderman et al., 1990; Clapp, 1990), the functional form to
measure horizontal equity (Berry and Bednarz, 1975; Goolsby, 1997; Allen and Dare, 2002), and
the determinants of assessment inequity (Haurin, 1988; Birch, Sunderman and Hamilton, 1990;
Borland, 1990; Benson and Schwartz, 1997; DeCesare and Ruddock, 1998; Smith, Sunderman,
and Birch, 2003; Cornia and Slade, 2005; Cornia and Slade, 2006; McMillen and Weber, 2008;
Ross, 2011; Ross, 2012; McMillen, 2013).

20

Recently, researchers have shifted their attention to

20

Additional research has examined how the results of various vertical and horizontal
specifications may differ (Sunderman et al., 1990; Sirmans, Diskin, and Friday, 1995; Benson
and Schwartz, 1997; DeCesare and Ruddock, 1998; Smith, 2000; Cornia and Slade, 2005).
17

a more thorough examination of assessment inequity by analyzing the distribution of assessment
ratios. Since this latter line of research is most relevant to the present work, I provide a more
detailed review of these articles.

21

McMillen and Weber (2008) examine assessment ratios in Chicago to determine if an
increase in the number of sales in a census tract is associated with an improvement in assessment
uniformity (i.e., improved horizontal equity). While their analysis has important implications
regarding the determinants of assessment equity, the method they implement is of particular
interest for this study. Rather than follow traditional regression approaches, McMillen and
Weber use a multinomial logit model to examine assessment equity. With this approach, the
distribution of assessment ratios and uniformity of assessments are evaluated by determining
whether assessment ratios for particular properties are more (or less) likely to exist in the top or
bottom of the distribution as the number of sales in the neighborhood increases. In addition,
McMillen and Weber examine vertical inequity by testing whether higher sales prices increase
the probability that assessment ratios are in the bottom of the distribution (i.e., regressivity).
They conclude that high and low assessment ratios are more likely to occur in areas with fewer
comparable sales; however, they are unable to support the idea that thin markets are responsible
for more regressive distributions.
McMillen (2011) highlights that traditional regression analysis is unable to evaluate the
degree of variability in assessment ratios at different sales prices, and therefore is not well suited
for analyzing assessment regressivity (or progressivity). Instead, McMillen offers quantile
regression analysis as an approach that enables one to examine the way in which the full

21

For a review of papers examining horizontal and vertical inequity from assessment practices
prior to 2008, see Sirmans, Gatzlaff, and Macpherson (2008).
18

distribution of assessment ratios varies by sales price. Using quantile regression analysis to
analyze assessment data from the City of Chicago, McMillen observes assessment ratios with
high variability at low sales prices, whereas both the variability and average assessment ratio
decrease as the sales price increases. In other words, most of the regressivity is concentrated at
low sales prices where the variance is high – a result standard regression analysis would not
reveal. In contrast, McMillen also examines assessment ratios for DuPage County and observes
high ratios with low variance at low sales prices, but decreasing ratios with greater variance at
higher sales prices.
McMillen (2013) again examines assessment ratios in the City of Chicago, this time
focusing on the effect of appeals on assessment ratios. This work is also of particular relevance
to the current study as he examines the full distribution of assessment ratios using quantile
regression techniques, rather than focusing on central tendencies. McMillen observes that while
traditional methods indicate declining assessment ratios with increases in sales price, quantile
regressions reveal “...the most pronounced degree of regressivity occurs at very low sales
prices.” That is, the variation of assessment ratios is much greater for low sales prices, and this
“...suggests that much of the apparent regressivity in assessments is attributable to the number of
extremely high assessment ratios at low sales prices.”

19

CHAPTER 4
Property Value Assessment Growth Limits and Redistribution of Property Tax Payments:
Evidence from Michigan (2008 and 2012)

4.1 Introduction
The objective of this chapter is to determine the extent to which the taxable value cap has
redistributed tax payments across economic and demographic groups in Michigan. I examine the
distributional consequences of the taxable value cap using detailed data on property tax
payments and housing values, obtained through a survey taken in the winter of 2008. I also
examine how the distributional consequences of the taxable value cap have changed as a result of
the housing market crisis, using detailed data from a survey taken in the summer of 2012.
4.2 Methods and Data
4.2.1 Effective Tax Rates and Tax Payments in Michigan
As previously discussed, prior to the passage of Michigan’s assessment growth limit in
1994, the taxable value for each property was its state equalized value (SEV), where the SEV is
equal to one-half of the assessed market value. From 1995 on, the growth of taxable value for
any property not sold during the period cannot exceed the rate of inflation. If a property is sold,
the taxable value returns to SEV. Thus, the effective property tax rate for homestead i
(EFFECTIVE RATEi) is given by:
[4.1]

EFFECTIVE RATEi = (TPi/Vi) = f (Ti, Ci).

Equation [4.1] indicates that the effective property tax rate for homestead i depends on
the tax payment (TPi) and the market value of the home (Vi), which in turn depend on

20

community characteristics (Ci)

22

and the homeowner’s length of tenure in the home (Ti).

23

As

long as housing values rise at a rate faster than inflation, long-time homeowners will enjoy a tax
benefit over new homeowners, and the magnitude of the benefit will increase over time. This
discussion illustrates the way in which differences in property-tax payments and effective tax
rates can emerge as a result of the interaction between changing home prices and the taxable
value cap.
4.2.2 Data and Descriptive Statistics, 2008
To conduct the initial analysis, information on homeowner economic and demographic
characteristics must be matched with the characteristics of the communities in which they live.
To accomplish this, several questions about property tax payments and home values were added
to the State of the State Survey for winter 2008.

24

The questions regarding 2007 property tax

22

There may be variations in community characteristics within a given jurisdiction. Because of
data limitations, I abstract from these variations, and assume everyone within a given jurisdiction
has the same community characteristics.

23

The tax-payment portion of equation [4.1] for homestead i (TPi) is found by multiplying the
taxable value of the property by the statutory tax rate. The taxable value of a property depends
on (a) the value of the property at the time the property was last purchased, (b) the rate of
inflation over the period of ownership, and (c) the length of time the property has been owned
since passage of Proposal A (Ti). The statutory tax rate depends on the specific economic and
demographic characteristics of the community in which the respondent lives. Therefore, the tax
payment for homestead i depends on (a), (b), (c), and (d) the set of community-specific
characteristics (Ci) determining statutory tax rates. In this analysis, the variable Ti is truncated to
a maximum, given by the number of years since the enactment of Proposal A. Since Proposal A
was enacted in 1994 and the data are from 2007 and 2012, the maximum value for Ti is 13 and
18, respectively.
24

The State of the State Survey (SOSS) is a quarterly telephone interview survey of Michigan
adults, conducted by the Institute for Public Policy and Social Research, in the College of Social
Science at Michigan State University. More information on SOSS is available at
http://www.ippsr.msu.edu/SOSS. The winter 2008 survey, which is the 47th round of SOSS,
contains information from a stratified random sample of Michigan adults. The weighted sample
21

payments and home values were modeled after similar questions in the 2000 Census of
Population and Housing.
This survey resulted in completed interviews with 1,012 Michigan adults. However, 230
of the survey respondents were not homeowners. An additional 291 respondents failed to answer
some of the questions needed for the regression analysis, including one or more of the questions
on property taxes, home values, years of ownership, or other important variables. Finally, an
additional 37 respondents were excluded from the analysis because they provided inconsistent
information about age and homeownership.

25

Summary statistics for the variables used in this analysis are presented in Table 4.1, and
detailed definitions of all variables used in the analysis are shown in Appendix 4.A. Table 4.1
includes summary statistics for the entire sample, as well as for three sub-groups based on the
rates of population growth for the counties in which the respondents reside. These categories
split the full sample roughly into thirds. I expect that respondents who live in areas with higher
population growth to experience the largest effective tax-rate differentials between long-time
homeowners and new homeowners.

is representative of the Michigan adult population. All of the statistical analyses reported in this
article use the appropriate survey weights. The codebook and methodological report from the
winter 2008 SOSS are available at http://www.ippsr.msu.edu/SOSS/SOSSdata.htm.
25

For example, if a respondent says he/she is 30 years old and has owned the home for 20 years,
this person would have been only 10 years of age at the time of becoming a homeowner.
However, I also checked for robustness with respect to the decision to exclude these 37
observations and the inclusion of these observations yields similar estimates. In fact, the
absolute magnitude of the coefficient on years of ownership increases slightly when these 37
observations are included. Thus, the regressions I present are the more conservative estimates.
22

From Table 4.1, the average effective property tax rate is 27 mills, but there are
differences across sub-samples.

26

Respondents in slow-growth areas have an average effective

tax rate of about 30 mills, whereas the mean effective tax rate for respondents in high-growth
areas is about 25 mills. Note also that slow-growth areas have substantially lower per-capita
property values (measured by the WEALTH variable), and jurisdictions with higher populations
are likely to be located in slow-growth counties.

26

As expected, the average effective property tax rate (shown in Table 4.1) is somewhat smaller
than the average statutory tax rate (equal to 33.72 mill for homestead property in 2007). This is
consistent with the erosion of the property tax base as a result of the taxable value cap.
23

Table 4.1 Summary Statistics, 2008

Variable
EFFECTIVE RATE
POPULATION
(City or Township)
WEALTH
MOBILE HOME
DETROIT
URBAN CITY
URBAN TOWNSHIP
RURAL CITY
CONSECUTIVE YEARS
CONSECUTIVE YEARS SINCE A
BLACK
EDUCATION
INCOME
AGE
MARRIED
Number of
Observations

Full Sample
Mean
Std Dev
27.24
0.718

Slow Growth
Mean
Std Dev
30.04
1.297

Medium Growth
Mean
Std Dev
25.86
1.123

High Growth
Mean
Std Dev
24.92
1.199

92,491

12,543

189,418

29,733

32,207

4,328

26,490

4,315

41,946
0.031
0.070
0.398
0.082
0.131
15.89
10.46
0.088
14.59
50,279
53.71
0.707

1,212
0.009
0.014
0.031
0.019
0.018
0.716
0.244
0.017
0.131
1,185
0.870
0.027

32,259
0.031
0.177
0.589
0.033
0.120
16.57
10.303
0.201
14.62
49,304
52.37
0.673

1,585
0.015
0.035
0.047
0.016
0.029
1.197
0.413
0.039
0.224
1,924
1.194
0.043

48,760
0.023
0.275
0.150
0.171
17.50
11.26
0.003
14.56
51,354
55.11
0.698

2,546
0.012
0.052
0.043
0.038
1.380
0.381
0.003
0.236
2,190
1.708
0.051

47,659
0.040
0.274
0.074
0.116
13.15
9.776
0.030
14.58
50,418
53.98
0.763

1,832
0.018
0.050
0.036
0.026
1.037
0.449
0.019
0.217
2,042
1.693
0.049

443

176

24

125

142

4.2.3 Data and Descriptive Statistics, 2012
To examine how benefits from the taxable value cap have changed in the wake of the
housing market crisis, several questions about property tax payments and home values were
added to the State of the State Survey for summer 2012.

27

This survey resulted in completed

interviews with 1,015 Michigan adults. However, 128 of the survey respondents were not
homeowners. An additional 335 respondents failed to answer some of the questions needed for
the regression analysis, including one or more of the questions on property taxes, home values,
years of ownership, or other important variables. Similar to the 2008 sample, 54 respondents
were excluded from the analysis because they provided inconsistent information about age and
homeownership. Finally, a confounding issue in the survey data is the presence of effective tax
rate outliers. For example, one survey respondent stated his/her effective tax rate was 40,000
mills. Although an individual’s effective tax rate after the housing crisis may be greater than a
jurisdiction’s statutory rate due to over-assessment (see Chapter 6), it is very unlikely the
effective tax rate is this large. Using standard methods for determining outliers, six additional
observations are excluded from the analysis below.

28

Summary statistics for the variables used for this portion of my analysis are presented in
Table 4.2 and includes statistics for the entire sample, as well as for the three sub-groups
previously discussed. Again, I expect that respondents who live in areas with higher population
27

The summer 2012 survey, which is the 62nd round of SOSS, contains information from a
stratified random sample of Michigan adults. The weighted sample is representative of the
Michigan adult population. All of the statistical analyses reported in this article use the
appropriate survey weights. The codebook and methodological report from the summer 2012
SOSS are available at http://www.ippsr.msu.edu/SOSS/SOSSdata.htm.

28

I also checked for robustness with respect to the decision to exclude these six observations
and the inclusion of these observations yields a coefficient on years of ownership larger than the
results presented. Thus, the regressions I present are more conservative estimates.
25

growth to experience the largest effective tax-rate differentials between long-time homeowners
and new homeowners.
From Table 4.2, the average effective property tax rate is about 40 mills. This provides
initial evidence that the average benefits granted to residents are smaller after the housing market
crisis. Again, there are differences across sub-samples. Respondents in slow-growth areas have
an average effective tax rate of about 46 mills, whereas the mean effective tax rate for
respondents in high-growth areas is about 31 mills. It is interesting to note the difference
between the average mills observed for 2008 and 2012 across sub-samples; the slow-growth
communities had an increase in their average effective property tax rate of about 16 mills, while
the high-growth communities had an increase of only 6 mills.

26

Table 4.2 Summary Statistics, 2012

Variable
EFFECTIVE RATE
POPULATION
(City or Township)
WEALTH
MOBILE HOME
DETROIT
URBAN CITY
URBAN TOWNSHIP
RURAL CITY
CONSECUTIVE YEARS
CONSECUTIVE YEARS SINCE A
BLACK
EDUCATION
INCOME
AGE
MARRIED
Number of
Observations

Full Sample
Mean
Std Dev
39.54
1.441

Slow Growth
Mean
Std Dev
45.54
2.470

Medium Growth
Mean
Std Dev
39.03
2.285

High Growth
Mean
Std Dev
31.26
2.495

32,651

3,812

38,931

7,212

33,628

6,675

21,682

3,998

41,664
0.006
0.008
0.457
0.079
0.131
13.94
10.43
0.0282
14.75
60,650
53.53
0.751

2,056
0.004
0.002
0.062
0.032
0.024
1.241
0.814
0.015
0.156
1,323
1.570
0.048

36,912
0.021
0.500
0.055
0.115
14.25
10.05
0.073
14.46
59,436
50.06
0.826

2,223
0.007
0.097
0.031
0.035
2.028
1.065
0.039
0.175
2,160
3.159
0.046

40,035
0.006
0.431
0.125
0.126
15.05
11.70
0.003
14.68
59,741
55.60
0.685

3,895
0.006
0.112
0.073
0.044
2.035
1.377
0.003
0.318
2,649
1.607
0.103

51,341
0.015
0.433
0.046
0.161
11.78
9.071
15.28
63,922
55.62
0.738

4,642
0.014
0.113
0.038
0.045
2.359
1.762
0.295
1,471
1.783
0.074

492

207

27

130

154

4.2.4 Empirical Strategy and Econometric Issues
One possible strategy is to estimate property tax outcomes as a function of individual and
community characteristics, using ordinary least squares for the sample of homeowners who
answered all of the relevant survey questions. The basic ordinary least squares regressions are
represented by equations [4.2] and [4.3] below. Consider [4.2]:
[4.2]

EFFECTIVE RATEi = Ciα + δTi + ε

where EFFECTIVE RATEi is the effective property tax rate, Ci is a vector of community and
individual characteristics, Ti is the length of time homeowner i has owned his/her property since
the passage of Proposal A, and ε is the error term. Below, I will refer to the total length of
homeownership as CONSECUTIVE YEARS and the number of years of ownership since the
passage of Proposal A as CONSECUTIVE YEARS SINCE A.
In equation [4.2], the length of homeownership since Proposal A (CONSECUTIVE
YEARS SINCE A) enters the regression directly. However, the length of homeownership is
determined, in part, by the economic and demographic characteristics of the homeowner. In an
attempt to analyze the underlying determinants of effective property tax rates, Ti is replaced with
a vector of respondent economic and demographic characteristics. Equation [4.3] represents the
second set of property tax regressions:
[4.3]

EFFECTIVE RATEi = Ciη + Zi λ + γ

where Ci is a vector of community and individual characteristics, Zi is a vector of economic and
demographic characteristics of the respondent, and γ is the error term.
In all of the results reported below, the OLS estimates are presented first. However, since
a number of homeowners failed to answer questions about property taxes and home values, there
28

is potential for sample-selection bias. To correct for possible selection bias, I use the procedure
proposed by Heckman (1979).

29

In this context, before estimating equations [4.2] and [4.3], it is

necessary to estimate a first-stage selection regression. The selection equation is represented by:

[4.4]

1 if Ciα + X iβ + ui ≥ 0
Yi = {
0 if Ciα + X iβ + ui < 0

where Yi indicates whether the respondent provided information on all of the relevant questions,

Ci is a vector of community and individual characteristics, and Xi is a vector of variable(s)
excluded from the second-stage outcome equations (4.2 or 4.3). The variable(s) in X are used to
predict whether respondents report all of the relevant information. Specifically, in the estimates
presented, educational attainment (EDUCATION) and race (BLACK) are used as instruments for
the Heckman results.

30

Appendix 4.B and Appendix 4.C report the selection equation estimates,

showing educational attainment is a good predictor of whether a respondent reports his/her tax
payment and home value for the 2008 survey and race is a good predictor for the 2012 survey.
Selection bias is potentially present, although the direction of the potential bias in the
context of this analysis is not clear. Generally, little evidence of selection bias is found in the
regressions for effective property tax rates. As a result, the OLS coefficients are very similar to
the coefficients controlling for selection bias. For thoroughness, results for the OLS regressions
and for the regressions addressing sample-selection bias are presented. In the regressions

29

See Achen (1986) and Sigelman and Zeng (1999) for good theoretical and intuitive
discussions regarding the Heckman procedure.
30

EDUCATION is the number of years of schooling and BLACK is an indicator variable to
distinguish whether the respondent is African American.
29

correcting for sample-selection bias, the selection and outcome equations are jointly estimated by
maximum likelihood.
In estimating 4.2 and 4.3, whether by OLS or the sample-selection procedure, I control
for a range of individual and community characteristics. These include the population of the
community (POPULATION), the wealth of the community, measured as per-capita state
equalized value (WEALTH), whether the participant lives in the largest city in the state
(DETROIT), and whether the participant lives in an urban city, urban township, rural city, or
rural township (URBAN CITY, URBAN TOWNSHIP, and RURAL CITY, respectively, with the
excluded category being those who live in a rural township).

31

It is expected that those living in

urban areas and in cities may face higher statutory rates, all else equal, because these
jurisdictions have greater taxing authority and may offer a wider range of public services,
including services directed at low-income populations. It is interesting to note that 8.2 percent of
the residents in the 2008 sample live in urban townships (7.9 percent in the 2012 sample), and
13.1 percent live in rural cities for both 2008 and 2012 (see Tables 4.1 and 4.2). Because
properties located in mobile-home parks are exempt from the property tax in Michigan, I also
include an indicator variable (MOBILE HOME) to control for whether the respondent lives in a
mobile-home park.
Before discussing the regression results, one remaining estimation issue requires
attention. The estimation of equation [4.1] may potentially be further complicated by

31

URBAN was defined by identifying the community of residence for each survey respondent,
and then using the Census Bureau’s definition of an urbanized area to classify each community.
(The precise definition is shown in Appendix A.) In Michigan, cities have greater taxing
authority and provide a greater array of public services than do townships. It is important to note
that, as defined by the Census Bureau, a community characterized as a city is not necessarily a
part of an urbanized area. Thus, a city can be located in either an urbanized area or a rural area.
Similarly, townships can be either urban or rural.
30

interdependence between years of ownership and the effective tax rate. Recall the lock-in papers
discussed in Section 3.1, which indicated that assessment growth caps increase the length of
tenure in a home. Thus, causality may run both ways: On the one hand, as long as home values
are rising faster than the rate of inflation, effective tax rates fall every year a homeowner lives in
the same home. On the other hand, the taxable value cap provides an incentive for homeowners
to remain in their current home. This could potentially lead to a bias in the coefficient estimate
on the years of homeownership.
To examine the possible endogeneity of years of ownership, a test of endogeneity was
conducted, based on the techniques developed by Hausman (1978, 1983). The Hausman test
requires that I identify at least one variable that determines length of homeownership, but does
not directly determine effective tax rates. BLACK and EDUCATION have been identified as
potential instruments. In column (2) of Appendix 4.D and Appendix 4.E, I report a regression in
which the variable CONSECUTIVE YEARS SINCE A is regressed on homeowner economic and
demographic characteristics. CONSECUTIVE YEARS SINCE A is capped at 13 years for the
2008 sample and 18 years for the 2012 sample, because the assessment growth cap was
implemented in 1994; thus, in 2007, there was no additional gain from having owned a home for
more than 13 years. While BLACK is a significant determinant of CONSECUTIVE YEARS
(column (1) of Appendix 4.D and Appendix 4.E), unfortunately neither BLACK nor
EDUCATION is close to statistical significance in the regressions for CONSECUTIVE YEARS
SINCE A. Therefore, BLACK and EDUCATION are not good instruments, and I am unable to
examine the endogeneity issue formally. Nevertheless, my examination of the relationship
between CONSECUTIVE YEARS and effective tax rates is useful, in the sense that I use it to link
effective tax rates with the economic and demographic characteristics of homeowners. In a

31

further attempt to explore the endogeneity issue, CONSECUTIVE YEARS SINCE A is replaced
with the non-capped variable CONSECUTIVE YEARS, and then a Hausman test of endogeneity
is conducted. I did not find evidence of an endogenous relationship between effective tax rates
and CONSECUTIVE YEARS, lending credibility to the notion that I am measuring a causal
relationship between CONSECUTIVE YEARS SINCE A and effective tax rates.

32

4.3 Empirical Analysis
There are two approaches to estimating equations [4.2] and [4.3]: 1) estimate separate
regressions for each year, and 2) pool the data and estimate the results for each year together. In
the following discussion, I focus my attention on the results from the non-pooled regression.
However, I also present the pooled results as a robustness check.
The first set of estimation results are presented in Table 4.3 and Table 4.4. In Table 4.3,
columns (1) and (2) contain the OLS estimates from the 2008 survey, and columns (3) and (4)
contain the estimates from the 2012 survey. The results presented in columns (1) and (3) are
from equations not distinguishing among communities on the basis of their population growth
rates. However, communities in Michigan had substantial variation in their rates of population
growth during the period examined. These differences could be expected to be associated with
different degrees of appreciation in property values. Therefore, in columns (2) and (4) of Table
4.3, I present results in which the variable for years of ownership is interacted with indicator
variables for low, medium, and high rates of population growth. Table 4.4 is identical to Table
4.3; however, now I present the second-stage outcome estimates from each survey, corrected for

32

Even if I am only capturing correlations, this analysis succeeds in achieving a more modest
objective, in that I measure the differences in effective tax rates for (1) homeowners who have
lived in the same home for varying lengths of time, and (2) homeowners with different
demographic characteristics. These results are interesting, even if they are simply viewed as
correlations.
32

selection bias. This discussion focuses on the OLS estimates since the estimates based on the
Heckman correction for sample selection are very similar to the OLS estimates in most cases.

Table 4.3 OLS Effective Tax Rate Regression Results
(t-statistics in parentheses)
Dependent Variable: EFFECTIVE RATE
Independent Variable
Ln (POPULATION)
Ln (WEALTH)
MOBILE HOME
DETROIT
URBAN CITY
URBAN TOWNSHIP
RURAL CITY
CONSECUTIVE YEARS SINCE A
CONSECUTIVE YEARS SINCE A
x SLOW GROWTH
CONSECUTIVE YEARS SINCE A
x MEDIUM GROWTH
CONSECUTIVE YEARS SINCE A
x HIGH GROWTH
R-squared
Number of Observations

2008
(1)
1.049*
(1.83)
0.738
(0.57)
-28.94***
(-20.9)
1.784
(0.42)
6.670***
(3.42)

(2)
1.027*
(1.80)
1.243
(0.96)
-28.83***
(-20.9)
1.346
(0.31)
6.404***
(3.37)

2012
(3)
2.026
(1.37)
-7.915**
(-2.10)
-25.94***
(-7.22)
38.42***
(3.34)
4.525
(1.26)

(4)
2.431
(1.57)
-6.649**
(-1.79)
-25.45***
(-6.79)
35.07***
(2.99)
3.940
(1.09)

2.181
(0.86)

2.445
(0.95)

-2.495
(-0.33)

-3.536
(-0.47)

3.935**
(2.08)
-0.394**
(-2.31)

3.996**
(2.11)

4.107
(0.91)
-0.345*
(-1.65)

4.708
(1.06)

-0.293
(-1.56)

-

-0.478***
(-2.75)
-0.478**
(-2.31)
0.292

0.287
443

33

-0.074
(-0.30)

-

-0.318
(-1.29)
-0.754***
(-3.20)
0.153

0.136
492

Table 4.4 Heckman Effective Tax Rate Regression Results
(t-statistics in parentheses)
Dependent Variable: EFFECTIVE RATE
Independent Variable
Ln (POPULATION)
Ln (WEALTH)
MOBILE HOME
DETROIT
URBAN CITY
URBAN TOWNSHIP
RURAL CITY
CONSECUTIVE YEARS SINCE
A
CONSECUTIVE YEARS SINCE
A x SLOW GROWTH
CONSECUTIVE YEARS SINCE
A x MEDIUM GROWTH
CONSECUTIVE YEARS SINCE
A x HIGH GROWTH
Rho
Number of Observations
Censored
Uncensored

2008

2012

(1)
1.011*
(1.74)
0.862
(0.66)
-28.95***
(-20.7)
2.072
(0.48)
6.902***
(3.48)

(2)
0.994*
(1.72)
1.373
(1.06)
-28.83***
(-20.7)
1.580
(0.36)
6.594***
(3.43)

(3)
2.026
(1.37)
-7.916**
(-2.02)
-25.94***
(-5.62)
38.41***
(3.37)
4.525
(1.26)

(4)
2.436
(1.57)
-6.740*
(-1.77)
-24.85***
(-5.65)
35.22***
(3.03)
3.919
(1.08)

2.446
(0.95)

2.699
(1.03)

-2.494
(-0.33)

-3.375
(-0.45)

4.092**
(2.12)
-0.414**
(-2.39)

4.144**
(2.14)

4.107
(0.92)
-0.345*
(-1.65)

4.721
(1.07)

-0.306
(-1.61)

-

-0.499***
(-2.82)
-0.496**
(-2.36)
-0.092

-0.104
628
185
443

-0.069
(-0.28)

-

-0.310
(-1.26)
-0.748***
(-3.18)
-0.020

-0.0002
694
202
492

First consider the results for the control variables. For the 2008 survey, the coefficients
on POPULATION are positive and statistically significant: All else equal, communities with
larger populations have higher effective property tax rates. For the 2012 survey, the coefficients
on WEALTH are negative and statistically significant: All else equal, communities with greater

34

wealth have lower effective property tax rates. This is reasonable since one might expect
individuals who live in communities with greater per-capita wealth to have lower property tax
rates, because a larger tax base can generate a given amount of tax revenue with a lower tax rate.
For 2008, however, the coefficient on WEALTH falls well short of statistical significance.
Perhaps before the housing market crisis, the residents of affluent communities had strong
preferences for public goods financed with property taxes; the statistically insignificant
coefficients on WEALTH suggest this preference offsets the influences previously discussed.
The variable indicating whether a participant lives in a mobile-home park is highly significant
and negative for both surveys. This is to be expected, since Michigan residents living inmobilehome parks pay no property taxes on their mobile homes.
For the 2008 survey, the coefficients on the URBAN CITY indicator variable are also
significant, indicating that those living in urban-area cities pay higher effective rates of property
tax, all else equal, when compared with the excluded category of rural townships. The
coefficient estimates indicate that urban city dwellers pay approximately 6.7 mills more than
those who reside in rural townships, all else equal. Residents of rural cities pay about 3.9 mills
more than those living in rural townships, all else equal, and this relationship is statistically
significant. However, residents of urban townships only pay about 2.2 mills more than those
living in rural townships, but this difference is not statistically significant. These results are not
unexpected, since cities often provide more services and have greater taxing authority than do
townships. However, the results from the 2012 survey show a change: There are now no
observed difference in effective tax rates among cities and townships classified as urban and
rural.

35

I previously noted that property tax rates in the City of Detroit are exceptionally high.
However, the regression results are not consistent between the two datasets and only the 2012
survey results indicate Detroit residents are subject to effective tax rates that are substantially
greater than the rest of the State, after controlling for other factors. Perhaps an effect is not
observed for DETROIT in 2008 since the other factors were significant (such as POPULATION
and the trio of indicator variables, URBAN CITY, URBAN TOWNSHIP, AND RURAL CITY).

33

However, since none of these variables were significant in the 2012 survey, the coefficient on the
DETROIT indicator variables become significant and of reasonable magnitude.

34

Next, I turn to the effect of CONSECUTIVE YEARS SINCE A on effective tax rates, the
estimates for which are shown in columns (1) and (3) of Table 4.3. All else equal, effective
property tax rates are reduced significantly as the number of years of ownership increases.
Specifically, the estimates in column (1) of Table 4.3 show that homeowners’ effective property
tax rates are reduced by about 0.39 mills for every year of ownership, relative to a new
homeowner, all else equal. This is a reduction of approximately 1.43 percent per year. Thus in
2008, homeowners who lived in their home since 1994 (or earlier) faced an effective property tax
rate about 19 percent less than the effective rate faced by new homebuyers, all else equal. The
estimates in column (3) show that this benefit has been reduced by 2012. Specifically, effective

33

The large and statistically significant estimate may also stem from the low number of
observations in Detroit in 2012. These few observations are likely to have substantially different
effective tax rates than the remaining sample for two reasons: 1) Detroit residents are subject to
higher statutory tax rates, and 2) assessment practices may cause state equalized values to be
close to, or above, the property’s market value (see Chapter 6).
34

This is reasonable because the measured effect of Detroit residents paying 35 to 38 mills more
is close to the statutory difference of about 30 mills previously highlighted (as discussed in
section 2.1, the average statutory property tax rate in Detroit was 66.61 mills in 2009, whereas
the statewide average rate was only 39.13 mills).
36

property tax rates are reduced by about 0.35 mills (or 0.88 percent) for every year of ownership.
Thus in 2012, the effective tax rate of long-time homeowners (i.e., those owning their home
since 1994 or before) is about 16 percent less than the effective rate faced by new homebuyers,
all else equal.
The tax benefits for long-time homeowners in communities with different growth rates
can be seen in columns (2) and (4) of Table 4.3. These results indicate the reduction in effective
tax rates is smaller for long-time homeowners in areas with slow population growth compared to
those in areas with more rapid population growth. The tax-rate reductions for long-time
homeowners in slow-growth areas are relatively small, and the coefficients are less precisely
estimated. In 2008, however, the tax-rate reductions in areas with medium and high rates of
population growth are statistically significant. For areas with medium and high rates of
population growth, the estimates indicate that homeowners’ effective tax rates are reduced by
about 0.48 mills for every year of ownership. This is a reduction of about 1.8 percent per year,
which amounts to a 23 percent savings for long-time homeowners relative to new homeowners.
Again, these estimates have changed as a result of the housing market crisis.

35

In 2012, areas

with medium rates of population growth no longer experience effective tax rates that are
statistically different from areas with low rates of population growth. However, long-time
homeowners in areas of high population growth continue to have substantial benefits; their
effective tax rates have been reduced by about 0.75 mills (or 1.9 percent) for every year of

35

It may be unfair to blame the entire difference between 2008 and 2012 on the housing market
crisis. In fact, a difference in the survey respondents may also be a factor; however, the extent to
which differences between 2008 and 2012 occur from the sample of respondents is inconclusive.
The results, as reported, may thus be interpreted as a maximum effect of the housing market
crisis.
37

ownership. This amounts to a 34 percent savings for long-time homeowners relative to new
homeowners.
In Table 4.3, length of homeownership has been shown to play an important role in
determining effective property tax rates. I would also like to know which variables have an
influence on the length of homeownership. Appendix 4.D and Appendix 4.E contain the results
of regressions examining the relationship between the length of tenure in a home and the specific
socioeconomic characteristics of homeowners. In column (1) of Appendices 4.D and 4.E, the
dependent variable is CONSECUTIVE YEARS (years not capped at 13 or 18 years for the 2008
and 2012 surveys, respectively), while the dependent variable in column (2) is CONSECUTIVE
YEARS SINCE A (years capped at 13 years in Appendix 4.D and 18 years in Appendix 4.E).

36

In both columns, the number of years of ownership is not systematically related to living in
urban cities, urban townships, rural cities, or rural townships, all else equal. Both columns in
Appendix 4.D reveal that those who live in mobile homes have significantly shorter tenure, while
Appendix 4.E reveals that those in communities with greater wealth have shorter tenure.
However, the results between the columns in each appendix differ in some respects. The
coefficient on BLACK is significant and of similar magnitude in column (1) of Appendix 4.D and
Appendix 4.E, but insignificant in column (2).

37

The coefficient on AGE is statistically

36

Approximately half of the homeowners in the both surveys have owned their home at least
since the passage of Proposal A in 1994.

37

In both samples, the average number of years of homeownership for African Americans is
significantly less than for the general population (although homeownership rates for African
Americans have increased in recent years). The insignificance of BLACK in the CONSECUTIVE
YEARS SINCE A regression may be the result of the reduction in differences in homeownership
rates across demographic groups in recent years, combined with capping the length of
homeownership.
38

significant in each of the columns, but its magnitude is much smaller in column (2) of both
appendices.
The findings in Appendix 4.D and Appendix 4.E provide the basis for the next set of
regressions, reported in Tables 4.5 and 4.6. In these regressions, I replace CONSECUTIVE
YEARS SINCE A with socioeconomic characteristics, to map the relationship between effective
property tax rates and homeowner characteristics. Thus, Tables 4.5 and 4.6 are similar to Tables
4.3 and 4.4; the difference is that the number of years of homeownership is not used as an
explanatory variable.

38

In Table 4.5 and Table 4.6, several categories of household income are

introduced as explanatory variables. (The excluded category consists of homeowners with
annual incomes below $20,000.)

38

Note that the regressions shown in Tables 4.2 through 4.6 do not include BLACK or
EDUCATION as regressors. I explicitly excluded EDUCATION and BLACK from the reported
effective tax rate regressions because I used these variables as an instrument in the selection
equation.
39

Table 4.5 OLS Effective Tax Rate Regression Results
(t-statistics in parentheses)
Dependent Variable: EFFECTIVE RATE
Independent Variable
Ln (POPULATION)
Ln (WEALTH)
MOBILE HOME
DETROIT
URBAN CITY
URBAN TOWNSHIP
RURAL CITY
20k < INCOME < 40k
40k < INCOME < 70k
INCOME > 70k
AGE
AGE x (20k < INCOME < 40k)
AGE x (40k < INCOME < 70k)
AGE x ( INCOME > 70k)
R-squared
Number of Observations

2008
(1)
1.102*
(1.93)
0.627
(0.50)
-28.27***
(-18.7)
1.857
(0.44)
6.299***
(3.27)
1.469
(0.61)
3.807**
(2.12)
-7.146**
(-2.27)
-3.530
(-1.12)
-6.471**
(-1.98)
-0.035
(-0.61)
0.298
443

40

2012
(2)
1.095*
(1.93)
0.672
(0.53)
-27.99***
(-21.2)
2.216
(0.53)
6.159***
(3.22)
1.442
(0.59)
3.652**
(1.97)
0.028
(0.49)
-0.103**
(-2.39)
-0.041
(-0.94)
-0.098**
(-2.04)
0.294

(3)
1.817
(1.20)
-5.054
(-1.26)
-33.48***
(-5.19)
39.29***
(3.39)
7.900**
(2.26)
2.400
(0.37)
6.434
(1.47)
-0.892
(-0.15)
-4.753
(-0.88)
-11.47**
(-2.25)
-0.241**
(-2.50)
0.171
492

(4)
2.069
(1.39)
-5.019
(-1.27)
-33.22***
(-5.86)
38.36***
(3.32)
7.030**
(2.01)
1.454
(0.22)
5.985
(1.36)
-0.146
(-1.12)
0.007
(0.07)
-0.082
(-0.86)
-0.190**
(-2.03)
0.170

Table 4.6 Heckman Effective Tax Rate Regression Results
(t-statistics in parentheses)
Dependent Variable: EFFECTIVE RATE
Independent Variable
Ln (POPULATION)
Ln (WEALTH)
MOBILE HOME
DETROIT
URBAN CITY
URBAN TOWNSHIP
RURAL CITY
20k < INCOME < 40k
40k < INCOME < 70k
INCOME > 70k
AGE
AGE x (20k < INCOME < 40k)
AGE x (40k < INCOME < 70k)
AGE x ( INCOME > 70k)
Rho
Number of Observations
Censored
Uncensored

2008
(1)
1.081*
(1.87)
0.780
(0.62)
-28.36***
(-18.34)
2.120
(0.50)
6.495***
(3.32)
1.674
(0.69)
3.945**
(2.15)
-6.941**
(-2.26)
-3.558
(-1.13)
-6.636**
(-1.99)
-0.045
(-0.74)
-0.089
628
185
443

2012
(2)
1.070*
(1.87)
0.861
(0.68)
-28.07***
(-20.77)
2.533
(0.61)
6.402***
(3.28)
1.692
(0.68)
3.834**
(2.02)
0.018
(0.30)
-0.100**
(-2.35)
-0.043
(-0.97)
-0.101**
(-2.08)
-0.110

(3)
1.852
(1.21)
-5.305
(-1.30)
-31.90***
(-4.70)
39.64***
(3.44)
7.821**
(2.23)
2.997
(0.45)
6.496
(1.48)
-0.882
(-0.15)
-4.854
(-0.91)
-11.57**
(-2.26)
-0.239**
(-2.50)
-0.063

(4)
2.096
(1.39)
-5.211
(-1.29)
-32.01***
(-5.29)
38.63***
(3.37)
6.965**
(1.98)
1.894
(0.28)
6.032
(1.38)
-0.144
(-1.11)
0.007
( 0.07)
-0.082
(-0.87)
-0.191**
(-2.04)
-0.047

694
202
492

The coefficients on the income indicator variables are negative, and are statistically
significant for the $20,000-to-$40,000 income category in 2008 and the over-$70,000 income
category in 2008 and 2012. These negative coefficients indicate that, holding other factors
41

constant, the effective property tax rates are lower for these income classes, when compared to
those with incomes below $20,000. The results from the 2008 survey indicate that, all else
equal, those with higher incomes have lower effective tax rates, although the relationship is nonlinear. The results from the 2012 survey indicate a more linear relationship; only those with the
highest income have lower effective tax rates. Although I cannot be sure the taxable value cap is
the cause of the negative coefficient on income, these results are consistent with the idea that the
taxable value cap may have caused the property tax to be more regressive, or less progressive,
than it otherwise would have been (especially after the housing crisis).
In light of the estimates presented in Appendix 4.D and Appendix 4.E, a strong
relationship between AGE and effective tax rates was expected; however, the results in Table 4.5
are mixed. The coefficient for AGE in columns (1), (2), and (4) of Table 4.5 are not statistically
significant, but AGE is statistically significant in column (3). The 2012 survey results indicate
that a 63-year-old homeowner enjoys a reduction of 9.64 mills (or 24 percent), compared with a
23-year-old homeowner, all else equal. To explore the age-income effects further, additional
estimates are reported in columns (2) and (4). In these columns, I report on regressions in which
the three income categories are replaced by their interaction with AGE. Mirroring the income
results discussed above, the coefficients on AGEx(20k<INCOME<40k) and
AGEx(INCOME>70k) are negative and statistically significant in 2008, while only
AGEx(INCOME>70k) is negative and statistically significant in 2012. Overall, this indicates that
older homeowners in the highest income category have lower effective tax rates, relative to
younger homeowners with similar incomes, all else equal. Specifically, the estimates indicate
that a 63-year-old homeowner enjoyed a reduction of about 14 percent in his/her effective
property tax rate in 2008 and a reduction of about 19 percent in 2012, compared with a 23-year-

42

old homeowner, all else equal.

39

Taken together, the results from the 2008 and 2012 surveys

provide evidence that older and high-income homeowners appear to have benefitted most from
the taxable value cap, at the expense of younger and low-income homeowners.

40

In addition to the analysis already presented, I also test the robustness of my results by
pooling the datasets and including additional variables. Table 4.7 mirrors Table 4.3; however,
the sample is pooled and five additional county-level variables are included (MEDIAN AGE,
MEDIAN INCOME, % OWNER HOUSE, % COLLEGE DEGREE, and UNEMPLOYMENT).
Likewise, Table 4.8 is similar to Table 4.5, but the data are pooled and additional variables are
included. In Table 4.7, the 2008 coefficient for CONSECUTIVE YEARS SINCE A is nearly
identical to the previous result and the effect of the limit on jurisdictions with different rates of
growth is slightly altered. The effect is smaller in medium and high growth jurisdictions, and
slow growth communities experience an effect from the taxable value cap that was not
previously observed. However, the estimates for 2012 are no longer statistically significant.
There are no significant changes to the estimates reported in Table 4.8 as compared with the
results in Table 4.5.

39

To calculate this result, I use the coefficients for AGEx(INCOME > 70k), multiply by (63 –
23) = 40 years, and then divide by the average effective tax rate.

40

These findings are consistent with U.S. Census Bureau data on migration patterns.
According to the report, “Internal Migration of the Older Population: 1995 to 2000, Census 2000
Special Reports” (U.S. Census Bureau, 2003), mobility peaks between the ages of 18 and 30 and
then generally decreases until very late in life.
43

Table 4.7 Pooled OLS Effective Tax Rate Regression Results
(t-statistics in parentheses)
Dependent Variable: EFFECTIVE RATE
Independent Variable
Ln (POPULATION)
Ln (WEALTH)
MOBILE HOME
DETROIT
URBAN CITY
URBAN TOWNSHIP
RURAL CITY
CONSECUTIVE YEARS SINCE A
CONSECUTIVE YEARS SINCE A
x SLOW GROWTH
CONSECUTIVE YEARS SINCE A
x MEDIUM GROWTH
CONSECUTIVE YEARS SINCE A
x HIGH GROWTH
County Variables
MEDIAN AGE
MEDIAN INCOME
% OWNER HOUSE
% COLLEGE DEGREE
UNEMPLOYMENT
R-squared
Number of Observations

(1)

(2)

2008
-0.014
(-0.02)
-0.071
(-0.05)
-29.20***
(-17.12)
1.017
(0.22)
4.861***
(2.79)

2012
1.108
(0.80)
-9.300**
(-2.42)
-29.62***
(-7.85)
32.34***
(2.77)
-1.569
(-0.38)

2008
-0.004
(-0.01)
-0.018
(-0.01)
-29.17***
(-17.06)
1.116
(0.24)
4.890***
(2.81)

2012
1.221
(0.84)
-8.671**
(-2.17)
-29.62***
(-7.84)
32.33***
(2.72)
-1.405
(-0.33)

1.504
(0.71)

-5.505
(-0.87)

1.508
(0.70)

-5.661
(-0.87)

3.931**
(1.99)
-0.396**
(-2.30)

3.469
(0.82)
-0.077
(-0.36)

3.975**
(2.02)

3.848
(0.91)

-

-

-

-

-0.385*
(-1.93)

0.058
(0.22)

-

-

-

-

-0.397**
(-2.28)
-0.416**
(-2.16)

-0.080
(-0.31)
-0.310
(-1.10)

0.400
0.618
(1.51)
(1.04)
0.0004**
0.0006*
(2.33)
(1.74)
-0.841***
-1.511***
(-3.38)
(-2.75)
-0.184
-0.270
(-1.25)
(-0.79)
-0.455
1.223
(-0.78)
(1.10)
0.280
935
44

0.373
0.287
(1.32)
(0.43)
0.0004**
0.0005
(2.26)
(1.57)
-0.820***
-1.246**
(-3.07)
(-2.09)
-0.179
-0.204
(-1.18)
(-0.61)
-0.441
1.245
(-0.76)
(1.14)
0.283
935

Table 4.8 Pooled OLS Effective Tax Rate Regression Results
(t-statistics in parentheses)
Dependent Variable: EFFECTIVE RATE
Independent Variable
Ln (POPULATION)
Ln (WEALTH)
MOBILE HOME
DETROIT
URBAN CITY
URBAN TOWNSHIP
RURAL CITY
20k < INCOME < 40k
40k < INCOME < 70k
INCOME > 70k
AGE
AGE x (20k < INCOME < 40k)
AGE x (40k < INCOME < 70k)
AGE x ( INCOME > 70k)

(1)

(2)

2008
-0.117
(-0.21)
-0.051
(-0.04)
-29.43***
(-17.82)
2.484
(0.56)
4.739***
(2.78)

2012
0.735
(0.52)
-6.291*
(-1.70)
-37.50***
(-6.14)
35.27***
(2.96)
2.031
(0.53)

2008
-0.083
(-0.15)
0.041
(0.03)
-29.01***
(-19.43)
2.774
(0.64)
4.612***
(2.69)

2012
0.956
(0.69)
-6.454*
(-1.73)
-37.38***
(-6.91)
34.65***
(2.92)
1.091
(0.28)

1.064
(0.53)

-0.978
(0.17)

1.098
(0.54)

-1.860
(-0.32)

3.839**
(2.12)
-7.188**
(-2.21)

6.322
(1.52)
-2.250
(-0.35)

3.397*
(1.95)

5.695
(1.38)

-

-

-4.576
(-1.38)

-6.277
(-1.05)

-

-

-8.286**
(-2.40)
-0.050
(-0.94)

-12.78**
(-2.19)
-0.158
(-1.58)

-

-

-

-

-

-

-

-

0.031
(0.57)
-0.108**
(-2.39)
-0.063
(-1.34)
-0.133***
(-2.61)

-0.050
(-0.35)
-0.007
(-0.06)
-0.102
(-0.96)
-0.203*
(-1.93)

45

Table 4.8 (cont’d)
County Variables
MEDIAN AGE
MEDIAN INCOME
% OWNER HOUSE
% COLLEGE DEGREE
UNEMPLOYMENT
R-squared
Number of Observations

0.227
0.272
(0.87)
(0.47)
0.0003**
0.0007**
(2.10)
(2.16)
-0.761***
-1.426***
(-3.04)
(-2.75)
-0.112
-0.402
(-0.76)
(-1.20)
-0.492
0.888
(-0.85)
(0.82)
0.306
935

0.257
0.321
(0.98)
(0.56)
0.0003**
0.0007**
(2.08)
(2.18)
-0.767***
-1.436***
(-3.08)
(-2.76)
-0.118
-0.390
(-0.79)
(-1.17)
-0.531
0.810
(-0.91)
(0.76)
0.305
935

4.4 Conclusions
In this chapter, I evaluate the distributional consequences of the taxable value cap in the
property tax in Michigan, as well as the changes to these distributional consequences after the
housing market crisis, and demonstrate the link between the taxable value cap and a substantial
redistribution of property tax payments. I find the length of homeownership is negatively
correlated with the homeowner’s effective rate of property tax. Specifically, estimates from
2008 indicate that homeowners who have lived in their home since 1994 (or earlier) faced
effective property tax rates roughly 19 percent less than the effective rate faced by new
homebuyers, all else equal, and the effect increased to 23 percent in high growth areas. The
overall benefit of homeowners living in their home since 1994 (or earlier) was reduced in 2012.
Specifically, the effective tax rate of long-time homeowners (i.e., those owning their home since
1994 or before) was about 16 percent less than the effective rate faced by new homebuyers, all
else equal. However, the benefit received by those in high growth areas increased to 34 percent.
Thus, the taxable value cap leads to a redistribution of effective property tax payments, with

46

lower tax payments for long-time residents, and higher tax payments for relative newcomers. I
also find that after the housing market crisis, older homeowners enjoy a tax benefit over younger
homeowners, as seen in the negative and statistically significant coefficient on AGE. In addition,
among those within the high-income groups, older homeowners have enjoyed a tax benefit over
younger homeowners both before and after the housing market crisis. The estimates indicate
that, all else equal, a 63-year-old homeowner received a tax savings of about 14 percent over a
23-year-old homeowner in 2008 and a tax savings of about 19 percent in 2012.
I also document a regressive relationship between income and effective tax rates: All else
equal, high-income homeowners have lower effective property tax rates, relative to low-income
homeowners (with the 2008 data also showing middle-income homeowners benefitting). In fact,
nearly all of the tax features of Proposal A were regressive. In addition to the taxable value cap,
Proposal A reduced property taxes overall, and raised cigarette taxes.
When Proposal A was passed, voters were given a choice. Each of the two choices
involved reductions in property taxes, but the two choices differed in the method of making up
the lost property tax revenue. Voters could have chosen higher income taxes, but they chose
higher sales taxes instead. Thus, on the revenue side, Proposal A was nearly uniformly
regressive. On the expenditure side, however, Proposal A was undoubtedly progressive since it
provided disproportionate benefits to low-wealth school districts (Papke, 2005). This
combination of regressive taxes and progressive spending is not unique to Michigan. Many
European countries finance large public expenditures that are favorable to low- and middleincome residents, partly by relying on the revenue-raising power of a regressive value-added tax.
Home values have fallen across Michigan over the past few years. As discussed earlier,
some long-time homeowners have experienced increasing property taxes and falling home values

47

at the same time. This has led to considerable controversy, and a number of legislative proposals
have been put forth to deal with the issue. One proposal would prevent taxable values (and thus
tax payments) from rising in the face of falling home values. This proposal, which has received
some support in the state legislature, would preserve the horizontal inequities resulting from the
taxable value cap.
My analysis suggests it might be better to consider repeal of the taxable value cap.
Holding revenues constant, repeal of the taxable value cap would result in a broadening of the
tax base, which would make it possible to raise the same amount of revenue with lower statutory
tax rates.

41

Furthermore, repeal of the taxable value cap would avoid the potential distortions

created by future housing price increases. Haveman and Sexton (2008) recommend alternative
property-tax relief measures, such as circuit-breaker programs, partial exemptions on owneroccupied housing, and property tax deferral options. Each of these alternative tax-relief
measures is already in place in Michigan, in one form or another. If the taxable value cap were
to be removed, these other provisions of Michigan law, along with the Headlee tax-revenue
growth limit, could provide adequate checks against excessive growth of property tax revenues
in the future.
Finally, I acknowledge this analysis offers an evaluation of effective tax rates at two
points in time. Although some of the regressions include age and income as explanatory
variables, I do not claim this is a complete analysis of the life-cycle effects of property taxes.
Economists have shown the value of tax-incidence analyses tracing the changes in tax burdens
over the life cycle (Davies, St.-Hilaire, and Whalley, 1984; Fullerton and Rogers, 1993). In
future research, it may be useful to embed these results in a life-cycle framework.

41

The potential reduction in statutory rates would depend on the trajectory of housing prices.
48

APPENDICES

49

Appendix 4.A
Table 4.9 Variable Definitions
Variable
EFFECTIVE RATE

Definition
The effective property tax rate respondents pay, measured by the
tax payment divided by the state equalized value of the property.

POPULATION

The total population of the municipality or township in which the
respondent resides.

WEALTH

Wealth of the municipality or township in which the respondent
lives, measured by the per-capita state equalized value in the
municipality/township.

MOBILE HOME

Indicator variable to distinguish whether a respondent lives in a
mobile home park (1= respondent lives in a mobile home park,
and 0 otherwise).

DETROIT

Indicator variable to distinguish whether a respondent lives in
Detroit (1= respondent lives in Detroit, and 0 otherwise).

URBAN

Indicator variable to distinguish whether a respondent lives in an
urban area (vs. non-urban area). Calculated by using the Census
Bureau’s definition: an urban area has a population density of at
least 1,000 people per square mile, and has surrounding census
blocks with an overall density of at least 500 people per square
mile (1= respondent lives in an urban setting, and 0 otherwise).

CITY

Indicator variable to distinguish whether a respondent lives in a
city (1= respondent lives in a city, and 0 otherwise).

TOWNSHIP

Indicator variable to distinguish whether a respondent lives in a
township (1= respondent lives in a township, and 0 otherwise).

CONSECUTIVE
YEARS

Number of consecutive years a respondent has lived in his/her
home.

CONSECUTIVE
YEARS SINCE A

Number of consecutive years a respondent has lived in his/her
home since the passage of Proposal A (maximum value = 13
years for 2008 survey and 18 years for 2012 survey).

BLACK

Indicator variable to distinguish whether the respondent is African
American (1= African American, and 0 otherwise).

EDUCATION

Number of years a respondent was in school (e.g., high–school
graduate=12, college graduate=16).
50

Table 4.9 (cont’d)
Variable
20k < INCOME<40k

Definition
Indicator variable to distinguish respondents with a household
income ranging from $20,000 to 40,000 at the time of the survey.

40k<INCOME<70k

Indicator variable to distinguish respondents with a household
income ranging from $40,000 to 70,000 at the time of the survey.

INCOME > 70k

Indicator variable to distinguish respondents with a household
income above $70,000 at the time of the survey.

AGE

Age of the respondent.

MARRIED

Indicator variable to distinguish whether the respondent is married
(1= respondent is married, and 0 otherwise).

SLOW GROWTH

Indicator variable to distinguish if the respondent lives in a slow
growth county (1= county in which the respondent lives had an
overall population growth rate less than 5% between 1994 and the
time of the survey, and 0 otherwise).

MEDIUM GROWTH

Indicator variable to distinguish if the respondent lives in a
medium growth county (1= county in which the respondent lives
had an overall population growth rate between 5% and 12%
between 1994 and the time of the survey, and 0 otherwise).

HIGH GROWTH

Indicator variable to distinguish if the respondent lives in a high
growth county (1= county in which the respondent lives had an
overall population growth rate greater than 12 percent between
1994 and the time of the survey, and 0 otherwise).

MEDIAN AGE

The median population age of the county in which the respondent
resides.

MEDIAN INCOME

The median income of the county in which the respondent resides.

% OWNER HOUSE

The percent of owner-occupied housing in the county the
respondent resides.

% COLLEGE
DEGREE

The percent of the population with a Bachelor’s degree or higher
in the county the respondent resides.

UNEMPLOYMENT

The unemployment rate of the county in which the respondent
resides.

51

Appendix 4.B
Table 4.10 Heckman Selection Equation Estimation Results
(t-statistics in parentheses)
Independent Variable
Ln (POPULATION)
Ln (WEALTH)
MOBILE HOME
DETROIT
URBAN CITY
URBAN TOWNSHIP
RURAL CITY
CONSECUTIVE YEARS SINCE A
CONSECUTIVE YEARS SINCE A
x SLOW GROWTH
CONSECUTIVE YEARS SINCE A
x MEDIUM GROWTH
CONSECUTIVE YEARS SINCE A
x HIGH GROWTH
EDUCATION
BLACK
Rho
Number of Observations
Censored
Uncensored

Dependent Variable: Selection Indicator
2008
2012
0.069
0.067
-0.023
-0.003
(0.96)
(0.92)
(-0.26)
(-0.03)
-0.278*
-0.325**
0.450**
0.481**
(-1.88)
(-2.16)
(2.21)
(2.29)
0.090
0.065
-2.272***
-2.274***
(0.22)
(0.15)
(-4.33)
(-4.33)
-0.515
-0.497
0.548
0.396
(-1.35)
(-1.30)
(0.94)
(0.66)
-0.457*
-0.432*
0.159
0.143
(-1.95)
(-1.83)
(0.60)
(0.51)
-0.481
-0.523
-0.863
-0.816
(-1.46)
(-1.58)
(-1.58)
(-1.52)
-0.312
-0.329
-0.098
-0.073
(-1.49)
(-1.57)
(-0.40)
(-0.30)
0.035**
-0.042**
(2.26)
(-2.54)
0.025
-0.032
(1.43)
(-1.58)
0.044**
-0.050***
(2.46)
(-2.69)
0.036*
-0.0392**
(1.87)
(-2.35)
0.068**
0.069**
0.020
0.019
(2.28)
(2.29)
(0.42)
(0.41)
-0.027
-0.003
-1.150**
-1.171**
(-0.09)
(-0.01)
(-2.16)
(-2.22)
-0.104
-0.092
-0.0002
-0.020
628
694
185
202
443
492

52

Appendix 4.C
Table 4.11 Heckman Selection Equation Estimation Results
(t-statistics in parentheses)
Dependent Variable: EFFECTIVE RATE
Independent Variable
Ln (POPULATION)
Ln (WEALTH)
MOBILE HOME
DETROIT
URBAN CITY
URBAN TOWNSHIP
RURAL CITY
20k < INCOME < 40k
40k < INCOME < 70k
INCOME > 70k
AGE
AGE x (20k < INCOME < 40k)
AGE x (40k < INCOME < 70k)
AGE x ( INCOME > 70k)
EDUCATION
BLACK
Rho
Number of Observations
Censored
Uncensored

2008
(1)
0.049
(0.70)
-0.379**
(-2.48)
0.213
(0.52)
-0.493
(-1.37)
-0.458**
(-1.96)
-0.442
(-1.36)
-0.321
(-1.59)
-0.424
(-1.63)
-0.011
(-0.04)
0.230
(0.85)
0.019***
(3.63)

(2)
0.046
(0.65)
-0.379**
(-2.47)
0.175
(0.43)
-0.463
(-1.28)
-0.456*
(-1.95)
-0.430
(-1.33)
-0.334
(-1.62)
0.019***
(3.18)
-0.006
(-1.38)
0.0003
(0.08)
0.003
(0.68)
0.066*
(1.95)
-0.121
(-0.46)
-0.110

0.062*
(1.80)
-0.112
(-0.43)
-0.089
628
185
443

53

2012
(3)
(4)
-0.040
-0.041
(-0.46)
(-0.46)
0.446**
0.452**
(2.24)
(2.23)
-1.990***
-2.056***
(-3.67)
(-3.84)
0.444
0.437
(0.74)
(0.71)
0.171
0.179
(0.61)
(0.65)
-0.855
-0.842
(-1.59)
(-1.56)
-0.105
-0.112
(-0.44)
(-0.47)
-0.065
(-0.21)
0.188
(0.63)
0.061
(0.19)
-0.006
-0.005
(-0.88)
(-0.75)
-0.002
(-0.39)
0.001
(0.22)
-0.0007
(-0.14)
0.019
0.022
(0.37)
(0.44)
-1.042*
-1.042*
(-1.95)
(-1.92)
-0.051
-0.047
694
202
492

Appendix 4.D
Table 4.12 Length of Homeownership Regression Results, 2008
(t-statistics in parentheses)
Dependent Variable

Independent Variable
Ln (POPULATION)
Ln (WEALTH)
MOBILE HOME
DETROIT
URBAN CITY
URBAN TOWNSHIP
RURAL CITY
BLACK
20k < INCOME < 40k
40k < INCOME < 70k
INCOME > 70k
AGE
MARRIED
EDUCATION
R-squared
Number of Observations

CONSECUTIVE YEARS
SINCE A
(2)
-0.108
(-0.50)
-0.063
(-0.13)
-3.639***
(-3.10)
0.227
(0.12)
0.521
(0.75)
1.644*
(1.77)
0.075
(0.11)
-0.857
(-0.52)
0.624
(0.64)
0.466
(0.46)
0.705
(0.63)
0.121***
(7.41)
0.756
(1.44)
-0.081
(-0.72)
0.203

CONSECUTIVE YEARS
(1)
0.177
(0.31)
-1.529
(-1.16)
-6.386***
(-2.62)
4.132
(1.04)
2.204
(1.31)
2.076
(0.84)
1.045
(0.73)
-6.243*
(-1.77)
1.625
(0.53)
2.512
(0.89)
1.467
(0.50)
0.503***
(9.45)
1.068
(0.68)
-0.209
(-0.76)
0.346
443

54

Appendix 4.E
Table 4.13 Lenth of Homeownership Regression Results, 2012
(t-statistics in parentheses)
Dependent Variable

Independent Variable
Ln (POPULATION)
Ln (WEALTH)
MOBILE HOME
DETROIT
URBAN CITY
URBAN TOWNSHIP
RURAL CITY
BLACK
20k < INCOME < 40k
40k < INCOME < 70k
INCOME > 70k
AGE
MARRIED
EDUCATION
R-squared
Number of Observations

CONSECUTIVE YEARS
SINCE A
(2)
0.115
(0.17)
-2.403***
(-2.70)
-0.129
(-0.03)
2.159
(0.78)
-1.155
(-0.60)
-2.903
(-1.50)
-0.251
(-0.23)
-3.523
(-1.39)
-0.816
(-0.37)
-1.892
(-0.88)
-1.137
(-0.46)
0.243***
(8.91)
0.731
(0.51)
0.302
(1.17)
0.326

CONSECUTIVE YEARS
(1)
-0.298
(-0.28)
-5.695***
(-3.58)
-0.375
(-0.04)
3.600
(0.98)
0.061
(0.02)
-4.070
(-1.26)
-1.046
(-0.60)
-6.327**
(-1.97)
1.905
(0.59)
-1.842
(-0.56)
-2.159
(-0.61)
0.528***
(9.18)
4.050**
(2.26)
0.330
(0.74)
0.426
492

55

CHAPTER 5
Inequity from Michigan’s Assessment Growth Limit: The Case of Detroit

5.1 Introduction
The objective of this chapter is to assess property tax inequities in Detroit resulting from
the taxable value cap. In the context of property taxation, horizontal inequity occurs when tax
rates vary among houses with similar market values. Vertical inequity occurs when tax rates are
inconsistent across a range of market values; that is, higher valued properties do not always pay
more taxes than lower valued properties (Muhammad, 2007). To examine these issues, I use
detailed data on property tax payments and housing values, obtained from Detroit’s assessment
division.
A primary contribution I make to the existing literature is the use of quantile regression
techniques to assess the inequities resulting from the taxable value cap. Standard regression
analysis is not well suited for the evaluation of equity issues because such analysis considers
only central tendencies. As I discuss in detail later, the quantile regression technique reveals
how policies affect the entire distribution of effective tax rates, making this approach ideal for
examining equity issues with regard to property tax policies. This approach also reveals the
sources of the average effect observed in standard regression analysis – whether the effect is the
result of a location shift (i.e., a change in mean value), a scale shift (i.e., a change in variance), or
both. My findings provide a more complete understanding of the effects of these policies and
may encourage policymakers to consider systemic changes toward a more coherent, efficient,
and equitable property tax system.

56

5.2 Methods and Data
5.2.1 Effective Tax Rates in Detroit
Differences in effective property tax rates may emerge from both assessment practices
and tax policies. McMillen (2010) found that assessment practices can lead to substantial
inequities and can increase the regressivity (or reduce the progressivity) of the property tax.
While assessment practices are obviously an important component of the tax burden (see Chapter
6), the focus of this chapter is on the taxable value cap. Regardless of the degree of assessment
accuracy, state equalized values reflect what the base of the tax would be in absence of the
taxable value cap. My evaluation reflects this reality, not the notion that assessments ought to
accurately reflect market conditions.
Absent the assessment growth limit and property tax abatement programs, the propertytax payment of each parcel in Detroit would equal the property’s state equalized value multiplied
by the statutory rate (66.61 mills).

42

However, with the assessment growth cap and property-tax

abatements, the property-tax payment is equal to the property’s taxable value multiplied by the
applicable millage rate. The taxable value cap changes the tax base (resulting in a TV less than
the SEV), while abatements may change the tax rate. The effective tax rate is therefore a more
accurate measure of tax burden. The effective tax rate for residential property i (EFFECTIVE
RATEi) is given by the following equation:
[5.1]

EFFECTIVE RATEi = [(TPi)/(SEVi)] = f[Ti, r, Vi, Ci, Li]

42

The 66.61 millage rate reflects the rates properties with the homestead exemption are subject
to (see footnote 13 for a description of “homestead” versus “non-homestead” property). Without
the exemption, the statutory millage rate in Detroit is 84.44 mills.
57

Equation [5.1] shows the effective rate for homestead i depends on the tax payment (TPi) and the
state equalized value (SEVi), where SEV reflects the market or full value of the property.
Although all properties face the same statutory rate, the effective tax rate differs
considerably from property to property. The effective tax rate depends primarily on which
abatement programs the property benefits from and the degree to which the property is protected
by the taxable value cap. In this context, the effective tax rate is a function of the length of time
an individual has owned the property (Ti), the rate of inflation (r), the appreciation (or
depreciation) of property value (Vi), the characteristics of the property (Ci),
the property (Li).

44

43

and the location of

These factors illustrate the ways in which differences in effective tax rates

can emerge. The less a property owner benefits from the taxable value cap and various tax
abatement programs, the closer the effective rate will be to the statutory rate.
Figures 5.1 and 5.2 illustrate the variation in effective tax rates across Detroit. Figure 5.1
presents average effective tax rates of owner-occupied residential properties at the neighborhood
level, and Figure 5.2 shows the variation of effective tax rates among all taxable properties

43

Characteristics such as age of the house, lot size, house size, etc. are important determinants
of the sales price (related to SEV and TV).
44

The location of the property determines whether or not a property owner may benefit from
any of the targeted abatement programs. Also, location may influence the state equalized value
of the property since properties in nicer locations may experience larger growth in their assessed
and market values relative to properties in less desirable neighborhoods.
58

within a single Detroit neighborhood.

45

Together, these maps highlight the substantial variation

in effective rates across neighborhoods and among neighbors within a given neighborhood.

Figure 5.1 Average Effective Tax Rates of Owner-Occupied
Residential Properties by Detroit Neighborhood, 2010

Source: Neighborhood shapefiles and tax data to calculate effective tax rates provided by the
City of Detroit Assessment Division.

45

In Figure 5.1, crosshatched neighborhoods represent those without any owner-occupied
residential properties. Crosshatched parcels in Figure 5.2 represent nontaxable properties.
Figure 5.2 includes all taxable properties to highlight the wide variation in effective tax rates
between neighbors, including non-owner-occupied properties.
59

Figure 5.2 Parcel-Level Effective Tax Rates Among All Taxable Properties, 2010

Source: Parcel-level shapefiles and tax data provided by the City of Detroit Assessment Division.

5.2.2 Model
One approach for estimating the effect of the assessment growth limit on effective tax
rates is to use ordinary least squares, represented by the equation [5.2]:
[5.2]

EFFECTIVE RATEi = Ciτ +αNEZRi +βNEZNi +γNEZHi +ηRZi +δTi +θLi +ε

where EFFECTIVE RATEi is the effective property tax rate, Ci is a vector of property
characteristics, NEZRi through NEZHi are indicator variables representing whether property i is
benefitting from each portion of the Neighborhood Enterprise Zone program, RZi is an indicator
60

variable representing residential properties located within a Renaissance Zone, Ti is the length of
time homeowner i has owned his/her property since the imposition of the assessment growth cap
(Years of Ownership), Li indicates the neighborhood in which property i is located, and ε is the
error term. Of primary interest is Ti: I expect the effective tax rate to be lower the longer a
homeowner retains ownership.
5.2.3 Examining Effects on the Full Distribution: Quantile Regression Analysis
While measuring the effect of policies “on average” provides a good initial assessment,
observing only the mean effect yields a limited perspective since it ignores the effect of policies
on the distribution (Buchinsky, 1994). To determine how the conditional distribution of
effective tax rates varies given the covariates, I use quantile regression methods (QRM).

46

In

the context of effective tax rates, the quantile regression approach provides a more complete
evaluation of horizontal equity because it shows whether the assessment growth limit creates
more or less variable effective tax rates within property value groups. One could potentially use
standard regression techniques to examine central tendencies across points within the full
distribution of effective tax rates; however, one would need to identify and use the appropriate
functional form. As my QRM results demonstrate, identifying an appropriate specification can
be a difficult task given there is no a priori knowledge on how the limit is expected to alter the
distribution of effective tax rates.
Quantile regressions allow one to examine changes in the distribution of the dependent
variable because QRM allows the distribution of the dependent variable to differ from the
covariate’s underlying density – since the coefficients differ across quantiles. As an illustration

46

Koenker and Bassett (1978) first introduced the quantile regression model.
61

of the difference between the quantile regression and the linear regression approaches, consider
an example taken from McMillen (2012). Equation [5.3] provides the standard linear regression
equation:
[5.3]

E( y | X ) = β + β x +  + β x + u ,
0
1 1
i i

where y is the dependent variable, xi is independent variable i, and β is the coefficient. To see
the effect on the distribution of y by changing the value of the covariate x1 from δ0 to δ1 ,
consider equations [5.4] and [5.5]:
[5.4]

ˆ
ˆ
ˆ
E( y | X , x = δ ) = β + β δ +  + β x
1
0
0
1 0
i i

[5.5]

ˆ
ˆ
ˆ
E( y | X , x = δ ) = β + β δ +  + β x
1
1
0
1 1
i i

ˆ
ˆ
ˆ
ˆ
The distribution will shift right by β1 (δ1 − δ0 ) if β1 > 0 and will shift left by β1 (δ1 − δ0 ) if β1 < 0
, while retaining the assumed shape of the normal distribution. This is known as a location shift

(Hao and Naiman, 2007). While it may be reasonable to expect a parallel shift in the distribution
of y in many contexts, it is a limitation I do not want to impose since I am interested in
understanding how the distribution of y changes with respect to changes in the covariates.
To see how QRM enables one to estimate changes in the distribution of y as the
covariates change (i.e., allows both a location and a scale shift), consider a quantile regression
model similar to Hao and Naiman’s (2007), where the pth conditional quantile is specified as
follows:
[5.6]

Q

( p)

(y | X ) = β

( p)
( p)
( p)
+β
x ++ β
x +u
i
i
0
1 1

62

,

0<p<1

(
Here, the pth conditional quantile is determined by the quantile-specific parameters, β 0p)

through βi(p) , and the values of each covariate. This approach allows one to trace out the entire
conditional distribution of y as the quantiles are increased from 0 to 1 (Buchinsky, 1998). The
effect of covariates on the distribution of y across quantiles is illustrated by equations [5.7] and
[5.8]:
[5.7]

Q

[5.8]

Q

( p)

ˆ ( p ) + β ( p )δ +  + β ( p ) x
ˆ
ˆ
(y | X, x = δ ) = β
1
0
0
1
0
i
i

,

0<p<1

( p)

ˆ
ˆ
ˆ ( p ) + β ( p )δ +  + β ( p ) x
(y | X, x = δ ) = β
1
1
i
1 1
0
i

,

0<p<1

ˆ(
Since β1 p) varies across quantiles, the conditional quantile functions imply a full
ˆ(
distribution of values for y. In other words, changes to x1 results in both a scale shift ( β1 p)

differs across each quantile) and a relocation of the conditional distribution of y. To estimate a
similar effect using standard regression analysis, one would need to make assumptions about the
distribution and correctly specify the functional form. In the context of the present study, this is
a difficult task because there is no clear theoretical basis for predicting how the assessment
growth limit might alter the distribution of effective tax rates across property-value groups.

47

Use of quantile regression techniques offers a clear evaluation of: 1) how the assessment
growth cap changes the distribution of effective tax rates across all owner-occupied properties;
2) how the assessment growth cap alters effective tax rate distributions within property value
groups (i.e., horizontal inequity); and 3) how the assessment growth cap changes the effective
tax rate distributions across property value groups (i.e., vertical inequity).

47

Buchinsky (1998) also shows that relative to standard ordinary least squares, QRM is more
robust to outliers and more efficient when the error term is non-normal.
63

5.2.4 Data and Descriptive Statistics
The City of Detroit’s Assessment Division provided parcel-level information for this
research. Relevant information provided for each parcel in the City includes: property class,
taxable status, improvements, tax payment (by taxing authority), SEV, TV, last sale date, and last
sale price. Properties located in Neighborhood Enterprise Zones and Renaissance Zones were
also identified.
The data include information for 444,183 real and personal property parcels, of which I
focus on residential owner-occupied properties. I therefore exclude 72,864 non-residential
(commercial, industrial, and/or personal), 59,402 nontaxable, 62,504 unimproved, 14,486
properties for which key information is missing (e.g., property characteristics, property class,
sale date, etc.), and 124,857 non-owner-occupied residential parcels (rental or vacant housing
units). Given my focus is on equity implications for homeowners, the exclusion of nonresidential, unimproved, and nontaxable properties is appropriate. However, the exclusion of the
14,486 properties for which there is missing information could generate selection bias.

48

These

properties represent less than 15 percent of the total number of residential properties, and any
potential bias is minimal.
I must also exclude the 3,534 residential owner-occupied properties sold in 2010. For
these properties, the number of years of ownership is updated upon sale to reflect the new
ownership, but any changes in TV are not reflected in the assessment rolls until the following
year. Thus, TV in the first year of ownership reflects the previous owner’s TV and not that of
the new owner.

48

Of these properties, nearly 10,000 of them are NEZ properties without the required
information. A formal request for this information has been made with the City of Detroit’s
Assessment Division.
64

In total, there are 106,536 owner-occupied properties for which I have all of the needed
information to include in the analysis. Summary statistics for the variables used in the analysis
are presented in Table 5.1, and detailed definitions for these variables are provided in Appendix
5.A. Table 5.1 includes summary statistics for the full sample, as well as for ten sub-groups
based on the size of SEV.
From Table 5.1, the average effective property tax rate is 49.65 mills, but there are
differences across the sub-samples. Property owners with the lowest-valued properties have an
average effective tax rate that is much higher than the remaining groups, even though the average
number of years the properties are owned is similar across all groups. The relatively high
effective tax rates for low-valued properties may be the result of this group losing the most value
in the wake of recent housing market crisis, or it may be that these properties have not
appreciated as much over time. In the full sample, as with each property value group, it is not
surprising to see the average effective tax rate is less than the statutory tax rate in Detroit (66.61
mills). This differential is the result of the erosion of the property tax base as a result of the
taxable value cap, as well as the reduced rates for properties in Renaissance Zones and
Neighborhood Enterprise Zones.

65

Table 5.1 Summary Statistics
Variable
Effective Tax Rate
SEV
Living Area
Lot Size
House Age (in decades)
Condo
NEZ-R
NEZ-N
NEZ-H
RZ
Years of Ownership
# of Obs.

Full Sample
Mean Std Dev.
49.65
14.43
28,629
14,710
1,161
1,259
874.8
1,063
6.703
1.502
0.003
0.051
0.00003
0.005
0.001
0.031
0.002
0.047
0.001
0.031
13.08
4.672
103,027

Effective Tax Rate
SEV
Living Area
Lot Size
House Age (in decades)
Condo
NEZ-R
NEZ-N
NEZ-H
RZ
Years of Ownership
# of Obs.

SEV Decile 4
47.28
15.59
23,170
1,046
980.1
326.0
800.2
151.3
6.601
1.376
0.001
0.024
0.0001
0.010
0.001
0.028
0.0003
0.017
12.78
4.737
10,294

SEV Decile 1
SEV Decile 2
SEV Decile 3
Mean Std Dev. Mean Std Dev. Mean Std Dev.
56.39
13.91
47.32
16.23
46.10
16.23
7,244
2,724
14,470
1,596
19,193
1,232
1,077
432.6
1,048
352.8
1,022
340.6
776.1
248.3
763.6
174.5
777.6
153.7
8.256
1.453
7.773
1.524
7.200
1.471
0.008
0.091
0.002
0.042
0.000
0.022
0.0001
0.010
0.0001
0.010
0.006
0.079
0.001
0.028
0.001
0.035
13.75
4.229
13.01
4.663
12.80
4.788
10,461
10,379
10,327
SEV Decile 5
48.40
14.92
26,529
928.4
992.0
498.3
820.1
326.1
6.358
1.212
0.0005
0.022
0.0001
0.010
0.001
0.026
0.0001
0.010
12.77
4.746
10,272

66

SEV Decile 6
48.99
14.25
29,680
892.4
1,022
611.5
845.9
556.6
6.267
1.119
0.001
0.024
0.0001
0.010
0.001
0.038
0.0001
0.010
12.86
4.738
10,260

SEV Decile 7
50.51
13.22
32,756
891.3
1,050
436.5
853.4
317.6
6.163
1.082
0.0004
0.020
0.0002
0.014
0.002
0.043
0.0005
0.022
12.87
4.739
10,272

Table 5.1 (cont’d)
Variable
Effective Tax Rate
SEV
Living Area
Lot Size
House Age (in decades)
Condo
NEZ-R
NEZ-N
NEZ-H
RZ
Years of Ownership
# of Obs.

SEV Decile 8
SEV Decile 9
Mean Std Dev. Mean Std Dev.
50.66
12.57
50.04
12.19
36,163
1,111
41,101
1,882
1,121
823.1
1,258
701.5
881.2
744.3
896.1
551.4
6.052
1.074
6.037
1.215
0.001
0.037
0.004
0.065
0.001
0.030
0.004
0.061
0.002
0.047
0.003
0.058
0.0001
0.010
0.0001
0.010
13.03
4.692
13.22
4.706
10,239
10,261

SEV Decile 10
Mean Std Dev.
50.74
11.64
56,650 18,546
2,047
3,530
1,338
3,094
6.282
1.426
0.008
0.089
0.0002
0.014
0.005
0.068
0.012
0.109
13.68
4.541
10,262

It is important to note the number of properties qualifying for each portion of the NEZ
program in the full sample is small: about 200 properties qualify for the NEZH program; 100
qualify for the NEZN program; three qualify for the NEZR program; and 100 residential
properties are within Renaissance Zones.

49

Also, the number of owner-occupied properties

qualifying for these programs across SEV sub-groups varies greatly, with many of the groups
having zero properties benefitting from the zones.
5.3 Empirical Analysis
5.3.1 Traditional Analysis: Measuring the Average Effect
Following the traditional approach of measuring the effect of an assessment growth cap
on effective tax rates, this analysis begins with a standard OLS regression approach to measure
49

The number of properties qualifying for the NEZ program in my sample is low compared to
the total number of NEZ properties. A large number of NEZ properties are not included because
they are missing crucial information for the analysis. Specifically, the data provided by the City
of Detroit do not include the following (for most NEZ properties): floor area, year built, last sale
date, and last sale amount. A formal request for this information has been made with the City of
Detroit’s Assessment Division.
67

the mean effect across all owner-occupied residential properties. In Table 5.2, column (1)
reports the average effect of the assessment growth cap across all properties, and column (2)
includes an interaction term between the Years of Ownership and SEV. The Years of Ownership
x SEV interaction term provides an initial evaluation of the vertical inequity stemming from the
assessment growth cap.
Consider first the results of the property characteristics. The coefficient for House Age is
negative and statistically significant: all else equal, older properties have lower effective tax
rates. The coefficient for Condo is positive and statistically significant, indicating
condominiums have higher effective tax rates.
Next, consider the effects of abatement zones on effective tax rates. As expected,
properties qualifying for each type of Neighborhood Enterprise Zone receive large reductions in
effective tax rates. NEZ Homestead properties receive an average reduction of 10 to 12.5 mills.
This estimate is nearly identical to the full benefit of qualified properties (see Table 2.2).
Properties qualifying for NEZN benefits receive an average reduction of 12.5 to 15 mills. This is
a smaller reduction than one might expect given these properties are eligible for a reduced
millage rate equal to 15.24 mills for the improved portion of property, while the land portion of
the property is taxed at the full rate. However, since there is a three-year phase in to full taxation
for expiring zones and most NEZN properties are in zones nearing expiration, the average
benefits are less generous than anticipated. Perhaps the most interesting finding among the NEZ
programs is the effect from the rehab portion (NEZR). Recall that it is difficult to know
precisely how large NEZR benefits are because the improved portion of the property is frozen at
the pre-rehabilitated taxable value. The estimates in Table 5.2 show an average reduction in
effective tax rates of 27 to 33 mills, a 41 to 50 percent reduction as compared with non-NEZR

68

properties receiving no other benefits.

50

Finally, properties located within a Renaissance Zone

experience no change in their effective tax rate as the coefficient is statistically insignificant.
Table 5.2 OLS Effective Tax Rate Regression Results
Independent Variable
Constant
Living Area
Lot Size
House Age
Condo
NEZR
NEZN
NEZH
RZ
Years of Ownership
SEV

OLS
(1)
77.449***
(0.661)
-0.0005***
(0.0001)
0.0007***
(0.0001)
-0.751***
(0.040)
15.232***
(1.062)
-33.223***
(8.430)
-15.060***
(2.133)
-12.498***
(0.493)
0.877
(2.053)
-1.771***
(0.007)
-

(2)
85.848***
(0.677)
0.003***
(0.0002)
-0.002***
(0.0002)
-1.401***
(0.043)
13.522***
(1.094)
-27.256**
(11.635)
-12.715***
(2.089)
-10.246***
(0.527)
0.531
(1.947)
-1.870***
(0.019)
-0.0003***
(0.00001)
0.000004***
(0.000001)

Years of Ownership
x SEV
Yes
Nhood Fixed Effects
0.414
0.440
R-squared
# of Obs.
103,027
Notes: Standard errors are in parentheses. All regressions include all
control variables and are corrected for heteroskedasticity. Asterisks
denote significance at the 1% (***), 5% (**), and 10% (*) levels.

50

Recall that in my data I only have a few properties qualifying for and receiving the NEZR
abatement. I am therefore cautious in drawing strong conclusions from this estimate.
69

Consider now the effect of Years of Ownership on effective tax rates. All else equal,
effective property tax rates are reduced as the number of ownership years increases.
Specifically, the estimates in column (1) of Table 5.2 show an average reduction in effective tax
rates of 1.77 mills for each year of ownership. Thus, homeowners who have lived in their home
since 1994 (or earlier) face an effective property tax rate 28 mills (or 42 percent) lower than the
effective rates faced by new homebuyers.
To examine the vertical inequity stemming from the assessment growth cap, consider the
results in column (2) of Table 5.2. Here, the coefficient on the interaction between Years of
Ownership and SEV provides an initial evaluation of the effective rate reduction resulting from
the taxable value cap for different property value groups. The coefficient for Years of Ownership
shows the average effective tax rate decreases as the number of years of ownership increases, but
the effect diminishes as property values increase (Years of Ownership x SEV). Specifically,
homeowners receive a 1.87-mill reduction in effective tax rates for each additional year of
ownership, but this reduction decreases by 0.04 mills for each $10,000 increase in property
value. Therefore, properties in the lowest SEV decile receive an average reduction in their
effective tax rate of 1.84 mills for each additional year of ownership. For those owning property
since 1994, this is a reduction of approximately 29.4 mills, or 44 percent. Properties in the
highest SEV decile receive an average reduction of 1.64 mills for each additional year of
ownership (approximately 26.2 mill, or 39 percent, reduction for those retaining ownership since
1994). This provides evidence of a modest increase in the progressivity of effective tax rates as a
result of the assessment growth cap; however, this finding is misleading.
To further examine how the effect of the assessment growth cap is distributed across
property values, I interact the length of homeownership with ten indicator variables representing

70

SEV deciles. As presented in Table 5.3, these estimates show that properties in the middle
deciles tend to receive much larger effective-tax-rate reductions as a result of the assessment
growth cap (as much as two to three times larger than the lowest-valued properties). For
example, homeowners in the third SEV decile (properties with an SEV equal to roughly $19,000)
are subject to effective tax rates approximately 35 mills lower (or 52 percent less) than the
effective tax rates for new homebuyers with similarly valued properties. For the lowest decile
(SEV equal to 7,000), the average reduction is just 12.7 mills; for the highest decile (SEV equal
to $33,000), the average reduction is 26.2 mills.
Table 5.3 OLS Effective Tax Rate Regression Results: Mean
Effect of Taxable Value Cap across Property Value Groups
Variable

OLS
-0.792***
Years of Ownership x SEV1
(0.024)
-1.975***
Years of Ownership x SEV2
(0.023)
-2.186***
Years of Ownership x SEV3
(0.022)
-2.133***
Years of Ownership x SEV4
(0.022)
-2.072***
Years of Ownership x SEV5
(0.021)
-1.958***
Years of Ownership x SEV6
(0.020)
-1.817***
Years of Ownership x SEV7
(0.018)
-1.749***
Years of Ownership x SEV8
(0.018)
-1.637***
Years of Ownership x SEV9
(0.018)
-1.371***
Years of Ownership x SEV10
(0.020)
Notes: Standard errors are in parentheses.
Regressions include all control variables and are
corrected for heteroskedasticity. Asterisks
denote significance at the 1% (***), 5% (**),
and 10% (*) levels.
71

To provide a clearer summary of the estimates in Table 5.3, Table 5.4 provides estimated
average tax payments for each SEV decile. The column labeled “No Tax Benefit” is the average
tax payment of properties not benefitting from the taxable value cap (property sold in 2009) and
the “Full Tax Benefit” column is the average tax payment of properties receiving the maximum
reduction from the taxable value cap (property sold in 1994 or earlier). Finally, “Full Tax
Benefit/No Tax Benefit” shows the ratio of taxes paid by those receiving the full benefit to the
taxes paid by those receiving no benefit. As Table 5.4 highlights, the actual tax payments vary
significantly for otherwise identical properties (i.e., there is horizontal inequity). Specifically, a
homeowner may receive a tax bill 19 to 52 percent higher than a neighboring homeowner with a
property of similar value. Table 5.4 also illustrates vertical inequity. Properties enjoying full
benefits of the taxable value cap in the first five deciles pay less than $900 in taxes, while
properties receiving no benefits reach this tax level in the second decile. Thus, a home valued at
$26,500 (decile 5) pays as little as $894 with full tax benefits, whereas a property valued at
$14,500 (decile 2) owes as much as $967 without benefits.

Table 5.4 Average Tax Payments across Property Value Groups
SEV Decile

Decile Range ($)

1
2
3
4
5
6
7
8
9
10

$120 - $11,497
$11,499 - $17,038
$17,040 - $21,292
$21,293 - $24,923
$24,924 - $28,127
$28,130 - $31,220
$31,222 - $34,323
$34,327 - $38,205
$38,208 - $44,788
$44,793 - $434,167

No Tax
Benefit
$484
$967
$1,283
$1,549
$1,774
$1,984
$2,190
$2,418
$2,748
$3,788

72

Full Tax
Benefit
$393
$510
$612
$759
$894
$1,054
$1,238
$1,406
$1,672
$2,545

Full Tax Benefit
/ No Tax Benefit
81%
53%
48%
49%
50%
53%
57%
58%
61%
67%

5.3.2 Quantile Regression Analysis: Examining the Full Distributional Effect
I now turn to the quantile regression approach, which offers additional insight on how the
assessment growth cap altered effective tax rate distributions. The standard quantile regression
estimates are presented in Table 5.5, and the quantile regression coefficients for quantiles
ranging from p = 0.01, 0.02, ..., 0.99 are presented in Appendix 5.B. Consistent with the OLS
results, the estimates imply that effective tax rates are higher for more recently sold properties,
non-NEZ properties, and properties with newer houses. Focusing more specifically on the
coefficients for Years of Ownership across quantiles, the slope is much steeper at the 10 percent
quantile than at the 90 percent quantiles – indicating that effective tax rates diverge as the years
of ownership increases (i.e., the distribution’s variance increases with length of tenure). In fact,
most of the policy variables appear to increase the variance of the effective tax rate.
To examine whether the assessment growth cap and the abatement zones change the
effective tax rate variance (i.e., scale shift), I test differences between coefficient estimates
across quantiles. The difference between the 10 percent and 90 percent quantiles are presented
in the last column of Table 5.5. For the NEZR and NEZH abatements, the difference between
quantiles is not statistically significant. That is, these policies do not change the effective tax
rate variance; rather, the effective tax rate distribution uniformly shifts left. However, the
difference between the 10 percent and 90 percent for properties located in Renaissance Zones
(RZ), NEZNs, and those benefitting from years of ownership via the taxable value cap are
statistically significant. In these cases, the effective tax rate distribution shifts left and becomes
wider.

73

Table 5.5 Effective Tax Rate Quantile Regression Results
Quantile
Independent Variable

10%
57.351***
(0.617)
0.0003*
(0.0001)
-0.00008
(0.0002)
-1.166***
(0.046)
10.030***
(1.279)
-26.098***
(9.227)
-25.929***
(2.065)
-11.843***
(1.030)
-8.908***
(1.614)
-1.828***
(0.011)

50%
80.670***
(0.496)
-0.00003
(0.0001)
0.0002
(0.0001)
-1.052***
(0.037)
19.935***
(1.027)
-46.021***
(7.412)
-15.279***
(1.659)
-14.365***
(0.827)
2.955**
(1.297)
-1.894***
(0.009)

90%
90% - 10%
66.727***
9.376***
Constant
(0.490)
(0.814)
-0.000002
-0.0003**
Living Area
(0.0001)
(0.0001)
0.000003
0.00009
Lot Size
(0.0001)
(0.0001)
-0.0008
1.165***
House Age
(0.037)
(0.048)
0.019
-10.011***
Condo
(1.016)
(1.153)
-0.039
26.059
NEZR
(7.332)
(22.862)
-8.158***
17.771**
NEZN
(1.641)
(8.389)
-12.196***
-0.353
NEZH
(0.818)
(0.339)
0.002
8.910***
RZ
(1.282)
(3.278)
-0.004
1.824***
Years of Ownership
(0.008)
(0.014)
Nhood Fixed Effects
Yes
# of Obs.
103,027
Notes: Standard errors are in parentheses and the standard errors for the last column are
from 100 bootstrap replications. Asterisks denote significance at the 1% (***), 5% (**),
and 10% (*) levels.

While examining the changes in effective tax rate variance is relatively straightforward,
the results presented in Table 5.5 require some additional explanation. Interpretation of the
quantile regression estimates is perhaps most easily understood with graphical illustrations of
how the distribution of effective tax rates change as an explanatory variable takes on different
values. Focusing on the effect of the assessment growth cap via Years of Ownership, Figure 5.3
presents a graph of the estimated conditional density functions of effective tax rates for
properties sold in 1994 or earlier, sold in 2001, and sold in 2008. Figure 5.3 provides a clear

74

evaluation of the degree of inequity resulting from the assessment growth cap.

51

Effective tax

rates are clustered around the full millage rate for properties sold in 2008. However, as the
number of years of property ownership increases, the distribution shifts to the left and has a
much greater variance. Also, note the bimodal distribution for properties owned since 1994.
The small bump on the right represents properties sold in 1994 no longer receiving an effective
tax rate reduction from the assessment growth cap. For these properties, the tax benefits have
eroded as a result of property-value declines caused by the housing market collapse.

51

Similar changes in effective tax rates as a result of the different abatement programs were also
examined by looking at the estimated conditional density functions. The resulting distribution
shifts were as expected, given the nature of the programs and the results highlighted in Table 5.5.
A graph highlighting the result of the NEZH program is presented in Appendix 5.C. The
distribution shifts left, but there is little change in the variance.
75

Figure 5.3 Effect of Assessment Growth Cap on Estimated Effective Tax Rate Densities

5.3.3 Quantile Regression Analysis: Horizontal Inequity
Standard quantile regression estimates by SEV deciles are presented in Table 5.6, as well
as the differences between the 10 percent and 90 percent quantiles. These estimates show
effective tax rates are higher for recent purchasers of property across all SEV deciles. In contrast
to the previous results, the variance of effective tax rates does not always increase as the length
of tenure increases; rather, the variance increases as the length of homeownership increases only

76

for the first two deciles. The variance does not change for deciles three to five, and the variance
actually decreases as the length of homeownership increases for the remaining groups.

Table 5.6 Effective Tax Rate Quantile Regression Results
for Years of Ownership across Property Value Groups
Quantile
SEV Decile

10%
50%
90%
90%-10%
-1.109***
-0.346***
-0.0006***
1.109***
1
(0.048)
(0.047)
(0.0002)
(0.069)
-1.688***
-2.139***
-1.023***
0.665***
2
(0.043)
(0.027)
(0.082)
(0.158)
-1.900***
-2.300***
-2.051***
-0.150
3
(0.035)
(0.026)
(0.083)
(0.144)
-1.856***
-2.284***
1.707***
0.148
4
(0.030)
(0.022)
(0.065)
(0.142)
-1.915***
-2.153***
-1.914***
0.001
5
(0.023)
(0.023)
(0.048)
(0.089)
-1.846***
-1.980***
-2.004***
-0.158**
6
(0.031)
(0.026)
(0.035)
(0.078)
-1.689***
-1.861***
-1.966***
-0.277***
7
(0.023)
(0.022)
(0.037)
(0.085)
-1.660***
-1.801***
-1.927***
-0.267***
8
(0.024)
(0.019)
(0.043)
(0.089)
-1.559***
-1.664***
-1.926***
-0.367***
9
(0.034)
(0.018)
(-.032)
(0.086)
-1.311***
-1.344***
-1.633***
-0.321***
10
(0.049)
(0.018)
(0.035)
(0.105)
Notes: All control variables are included in the regressions. Standard errors are
shown in the parentheses (100 bootstrap replications for the quantile difference
results). Asterisks denote significance at the 1% (***), 5% (**), and 10% (*) levels.

For a clearer illustration of these estimates, consider Figure 5.4 which shows the
estimated conditional density functions of effective tax rates for properties sold in 1994 or
earlier, sold in 2001, and sold in 2008 for each SEV decile. Consistent with the variance results
shown in Table 5.6, the first two deciles have a greater variance as the years of ownership
increase, whereas the variance narrows in the last five property value deciles. Figure 5.4
highlights two dimensions of the horizontal inequity created by the assessment growth cap: 1)
77

not all property value groups experience the same level of reduced effective tax rates; and 2)
among similarly valued properties sold in the same year, effective tax rates vary widely and the
assessment growth limit creates greater variance in effective tax rates for deciles one and two,
and more narrow variances in effective tax rates for deciles six through ten. The second result
also illustrates the nature of how the OLS estimates were derived. The OLS results for the first
decile indicated an average reduction of 12.7 mills for properties benefitting fully from the
taxable value cap. As the graph in Figure 5.4 shows, this result is due primarily to an increased
variance in the effective tax rate, since only a small proportion of properties actually receive any
benefit. In contrast, deciles two and three experience large location shifts (leftward), with a large
proportion of properties having effective tax rates similar to the effective tax rate of recently
purchased properties (shown by the overlapping area between 1994 and 2008). Finally, in
deciles six through ten I observe smaller location shifts, with fewer properties receiving little to
no benefit from the taxable value cap.

78

Figure 5.4 Effect of the Assessment Growth Cap on Horizontal Equity by Decile (SEV)
st

1 Decile

79

Figure 5.4 (cont’d)
nd

2

80

Decile

Figure 5.4 (cont’d)
rd

3 Decile

81

Figure 5.4 (cont’d)
th

4 Decile

82

Figure 5.4 (cont’d)
th

5 Decile

83

Figure 5.4 (cont’d)
th

6 Decile

84

Figure 5.4 (cont’d)
th

7 Decile

85

Figure 5.4 (cont’d)
th

8 Decile

86

Figure 5.4 (cont’d)
th

9 Decile

87

Figure 5.4 (cont’d)
th

10 Decile

5.3.4 Quantile Regression Analysis: Vertical Inequity
To examine vertical inequity, consider how the distributions differ across property-value
groups. Figure 5.5 presents the estimated conditional density functions of effective tax rates, for
properties sold in 1994 or earlier, across selected SEV deciles.

52

The results highlighted by

Figure 5.5 are consistent with the OLS results previously discussed. Properties in the third SEV
52

Not all deciles are included because they would clutter the graphs beyond interpretation.
Deciles four and five are between three and six, and deciles seven through nine are between six
and ten.
88

decile receive the largest benefit from the assessment growth cap, properties in the first SEV
decile receive the smallest benefit, and properties in the remaining SEV deciles are in-between.
In other words, the assessment growth cap is regressive across deciles one through three and then
progressive across deciles three through ten. Figure 5.5 offers additional insight not provided by
the OLS analysis; high-valued properties have less variability in effective tax rates (are more
equitable), whereas low-valued properties have greater variability, holding other factors constant.

Figure 5.5 Effect of Assesment Growth Cap on Vertical Equity

Decile
st
1
nd
2
rd
3

89

Figure 5.5 (cont’d)

Decile
th

10

th

6
rd
3

5.4 Assessment Growth Limit and Mobility in Detroit
As described in the literature review, effective tax rate differentials resulting from an
assessment growth cap may create inefficiencies. For example, assessment growth caps may
inhibit normal residential market transactions and homeowner mobility. This phenomenon has
come to be known as the “lock-in” effect. A homeowner who enjoys a substantial tax benefit
may be less likely to sell because the cost of holding the property is low and tax benefits are lost
once the property is sold. In the analysis presented here, I offer an examination of lock-in

90

created by assessment growth caps, using the Detroit parcel-level data previously discussed in
this chapter.
To examine the effect of the assessment growth cap on the length of property ownership,
I must compare the average duration of property ownership for all residential properties with the
average duration for properties benefitting from the assessment growth cap. Following the
method presented in Stohs, Childs, and Stevenson (2001), average tenure is calculated by taking
the reciprocal of the turnover rate. For example, if the turnover rate (or percent of homes sold) is
10 percent, then the average household remains in its home for 10 years (1.00/0.10). In addition
to the 2010 tax data used above, I have also collected 2011 sales data for owner-occupied
residential properties.

53

The turnover rate for a given year is (# of sold properties)/(# sold + #

unsold). In 2011 the turnover rate among residential property owners in Detroit is 4.4 percent
(4,506/103,027) for homestead property owners. Based on this turnover rate, the average length
of tenure is about 22.9 years.

54

The average change in tenure as a result of the assessment growth cap requires a two-step
calculation. I must first estimate the change in effective tax rates as a result of the assessment
growth limit, and then estimate the effects of the effective tax rate on the probability of property
being sold. With these two estimates, I can calculate the effect of the assessment growth limit on
length of ownership.

53

Recall that houses sold in 2010 do not experience the “pop up” in taxable value until the 2011
tax year. Therefore, using the properties that sold in 2011 with the previously discussed tax data
allows me to measure how reduced effective tax rates affect the probability of sale.
54

Although this estimate is about 2.5 times than the 2011 national average (9 years), it is not
unreasonable. Approximately 15% of homeowners lived in their house for more than 21 years in
2011 (source: http://www.creditsesame.com/blog/how-long-are-americans-staying-in-theirhomes/).
91

The first step therefore requires me to estimate the effect of the number of years of
ownership on effective tax rates. This has been calculated in Section 5.3 and it was shown that
the longer a property owner retains ownership, the lower effective tax rates are. Specifically,
Table 5.2 highlights that effective tax rates are about 30 mills lower (a reduction of nearly 50
percent) for an owner who has retained his/her property since 1994. As discussed earlier, the
property owner stands to lose the tax benefit he/she currently enjoys when the property sells.
This creates a substantial incentive to retain ownership.
To examine how a marginal change in the effective tax rate affects the probability of
selling a property, I estimate the probability of selling a property as a function of effective tax
rates, while controlling for property and neighborhood characteristics. Following Ihlanfeldt
(2011), the probability of a property selling is equal to the probability that an owner will put
his/her property up for sale (P(U)) times the conditional probability that a buyer is found if the
property is for sale (P(B/U)):
[5.9]

P(S) = P(U) ⋅ P(B /U)

The probability of offering a property for sale depends on the loss of utility from being at
a suboptimal level of housing consumption (H*) and moving costs (MV) as originally framed by
Hanushek and Quigley (1978). The property owner offers his/her property for sale when the
utility loss from living at a suboptimal level of housing exceeds moving costs:
1 if U(H * −H) > MC
[5.10] P(U) = {
0 if U(H * −H) ≤ MC

To determine the effect of the taxable value cap on the probability of moving, I include a range
of variables controlling for differences in P(U) across property owners, property characteristics,
and neighborhood characteristics. The tax savings resulting from the taxable value cap are
92

embedded in MC (moving requires an individual to give up any tax benefit acquired over time).
I estimate the probability of a property being sold with a standard probit estimation
procedure. The core probit estimation results are presented in Table 5.7. In the probit
estimations, I include as control variables the number of years of ownership (to control for the
owner’s general propensity to move), a range of property characteristics (including tax
abatements), and neighborhood indicator variables. Note that both the effective tax rate and taxabatement indicator variables are included, to distinguish between the effect of the taxable value
cap and the effect of each of the zones.

55

Table 5.7 Probit Estimation Results
Variable

Coefficient
-1.8574***
Constant
(0.1129)
0.00003
Living Area
(0.00002)
-0.00002
Lot Size
(0.00002)
-0.0103
House Age
(0.0068)
-0.1643
Condo
(0.1898)
0.5287*
NEZN
(0.2714)
1.2549***
NEZH
(0.0848)
-0.3307
RZ
(0.3816)
0.0045***
Erate
(0.0007)
-0.0234***
YearsOwned
(0.0018)
Nhood FE
Yes
# of Obs.
103,027
Notes: Standard errors are in parentheses.
55

NEZR is excluded because no observations in this category were sold in 2011.
93

As highlighted in Table 5.7, the effective tax rate and NEZ variables are positively
correlated with the probability of sale, and these relationships are statistically significant. That
is, a lower effective tax rate reduces the probability of sale. Recall that the longer a property
owner retains ownership, the lower the effective tax rate. However, the number of years of
ownership also serves as a proxy for the owners’ general propensity to move (long-time property
owners are generally less likely to sell). I therefore included the number of years of ownership
as an explanatory variable to control for this important factor. The estimates confirm the notion
that the longer a property owner retains ownership, the less likely he/she will sell a property.

56

Controlling for these other factors, it is shown that the coefficient on effective tax rates
are positive and highly significant. That is, property owners with higher effective tax rates are
more likely to sell, all else equal. The marginal effects generated from the probit estimation are
presented in Table 5.8. Here the coefficient on the effective tax rate from the homestead
property regression is 0.0004; a one-mill increase (decrease) in the effective tax rate increases
(decreases) the average probability of selling a property by 0.04 percent. Although the effect
may seem inconsequential at first glance, the goal is to examine the effect of the assessment
growth cap on the length of property ownership (not just the impact of the effective rate on
probability of selling). Several steps are required to assess the magnitude of this estimate.
Table 5.8 Marginal Effect on the Probability of Sale
Variable
dy/dx
Effective
0.0004***
Tax Rate
(0.00006)
Note: Standard errors are in parentheses.
56

To obtain an unbiased estimate of the lock-in effect, I do my best to control for characteristics
making it more or less likely that a given property will be sold; years of ownership, an indicator
of property owners’ propensity to sell, is therefore potentially very important. Omitting this
variable leads to a much larger coefficient on the effective tax-rate variable; this provides some
comfort that I am generating a conservative and unbiased estimate of the lock-in effect.
94

Recall that the reduction in effective tax rates due to the taxable value cap is 30 mills for
those living in their home since 1994. The estimated change in tenure as a result of the
assessment growth cap is calculated using both the estimated millage reduction and the change in
the probability of selling a property due to a change in effective tax rates. The probability of
selling a property is estimated to decrease by 1.2 percent as a result of the reduced effective tax
rate generated from the assessment growth limit (30*0.0004 = 0.012). That is, a property owner
who receives a 30-mill reduction in the effective tax rate due to the taxable value cap has a 1.2
percent lower probability of selling their property. Considering the average turnover rate in the
data is 4.4 percent, a 1.2 percent reduction in this probability means the turnover rate for these
homeowners is reduced to 3.2 percent. This translates into an increase in the average duration of
property ownership from 22 years to 31 years (1.00/0.032) for those living in their homes since
1994. Of course, this is an upper limit on the magnitude of the effect, and so it is worth
calculating the average change in tenure length among all property owners (including those
selling their property post-1994). Repeating the calculations provided above for each year and
averaging across all years, the average change in tenure length among all properties increases
from 22 years to about 27 years. This analysis suggests a meaningful increase in the average
length of property ownership as a result of the assessment growth cap – evidence of a lock-in
effect.
Mirroring the analysis above, the effect of the assessment growth cap on mobility rates
can be examined across different sets of property values. Table 5.9 presents the marginal effects
for the effective tax rate variable across property value deciles. Also presented in Table 5.9 is
the average length of tenure as a result of the assessment growth cap (“Avg. Tenure (Years)”), as

95

well as the average change in the length of tenure as a result of the assessment growth cap
(“Tenure Change (Years)”).
Table 5.9 Effect on the Probability of Sale across SEV Deciles
Variable

dy/dx

Avg. Tenure
(Years)

Tenure Change
(Years)

-0.00028
22.9
0.0
(0.00017)
0.00030**
Effective Tax Rate x SEV2
26.0
3.1
(0.00014)
0.00038***
Effective Tax Rate x SEV3
27.7
4.8
(0.00013)
0.00053***
Effective Tax Rate x SEV4
30.0
7.1
(0.00013)
0.00086***
Effective Tax Rate x SEV5
38.5
15.6
(0.00014)
0.00067***
Effective Tax Rate x SEV6
31.9
9.0
(0.00014)
0.00080***
Effective Tax Rate x SEV7
33.5
10.6
(0.00015)
0.00090***
Effective Tax Rate x SEV8
34.9
12.0
(0.00015)
0.00104***
Effective Tax Rate x SEV9
37.0
14.1
(0.00016)
0.00064***
Effective Tax Rate x SEV10
28.0
5.1
(0.00016)
Note:Standard errors are in parentheses. Asterisks denote significance at the 10%
(*), 5% (**), and 1% (***) levels.
Effective Tax Rate x SEV1

The results in Table 5.9 show property owners with high-valued homes are locked into
ownership for longer periods than owners with low-valued homes. Specifically, homeowners in
the fifth SEV decile hold on to their properties for an estimated 38.5 years, whereas property
owners in the first SEV decile have no change in average tenure length. Clearly, the estimated
probability of selling among properties in the fifth decile is low. These results are not too
surprising given the benefits from the taxable value cap for those with higher property values are,

96

in general, much higher. However, consistent with the finding of non-linear vertical inequities, I
find there is also a nonlinear relationship between tenure and reduced effective tax rates across
property value deciles. For example, those with properties in the ninth SEV decile receive a
lower reduction than those in the third decile, but they retain their properties for a much longer
period as a result of the assessment growth limit. Furthermore, those in the tenth SEV decile
have an estimated tenure length similar to those in the second and third decile, despite receiving
a smaller reduction in their effective tax rates.
5.5 Conclusions
In this chapter, I offer a new evaluation of the degree of inequity created by Michigan’s
assessment growth limit. Using parcel-level data from the City of Detroit, quantile regression
analysis is used to assess the degree of inequity created across homeowners. The evaluation of
horizontal equity indicates that those who have lived in their homes since 1994, or earlier, face
effective property tax rates between 19 and 52 percent lower than the effective rates faced by
new homebuyers, all else equal. These rates are even lower for properties qualifying for the
Neighborhood Enterprise Zones program. Use of quantile regression techniques offers a clear
evaluation of how the assessment growth cap violates the principle of horizontal equity. In
addition, this analysis shows how the assessment growth cap generates significant vertical
inequity; properties nearly half as valuable may be required to pay as much as 8 percent more in
taxes. Perhaps more importantly, the analysis reveals how the assessment growth cap leads to
non-linearities in effective tax rates across property-value groups. One could make arguments
for more or less progressivity in effective tax rates across the property-value groups, but it is
more difficult to justify a non-linear distribution of tax burdens. Finally, Michigan’s assessment
growth limit has created non-uniform changes to effective tax-rate distributions; the effective tax

97

rates become more variable in some property-value groups and less variable in others – a result
both unknown and difficult to predict without quantile regression techniques.
This evaluation demonstrates clear violations of the principles of horizontal and vertical
equity, as well as inefficiency (i.e., lock-in effect), resulting from the assessment growth limit.
Are there any politically feasible approaches that would improve property-tax policy outcomes?
One proposal would be to permanently eliminate the taxable value cap for new homebuyers,
while retaining the cap for existing property owners until they sell their property. Such a
proposal would allow the tax base to broaden with property turnover, and as local housing
markets regain value. Over time, the horizontal and vertical inequities resulting from the
assessment growth cap would diminish. This proposal may be able to garner the political
support required to alter property-tax policies because it insures that longtime property owners
would not experience a sudden increase in tax burden as a result of the elimination of the taxable
value cap. Further, as the tax base broadens and property values increase, the Headlee
Amendment provides purchasers of property with protection against substantial tax payment
increases, but in a way that avoids the inequities resulting from the assessment growth cap (see
Skidmore, Ballard and Hodge, 2010 for a brief discussion). Haveman and Sexton (2008)
recommend alternative property-tax relief measures, such as circuit-breaker programs, partial
exemptions on owner-occupied housing, and property-tax deferral options. Each of these
alternative tax-relief measures is already in place in Michigan, in one form or another. If the
taxable value cap were to be removed, these other provisions of Michigan property-tax law,
along with other existing property tax-revenue growth limits, could provide adequate checks
against excessive growth of property-tax payments in the future.

98

APPENDICES

99

Appendix 5.A
Table 5.10 Variable Definitions
Variable
Effective Rate

Definition
The effective property tax rate each resident pays, measured by the
tax payment divided by the state equalized value of the property.

SEV

The state equalized value of the property, equal to one-half the
assessed market value.

Living Area

Size of the residential structure (square feet).

Lot Size

Size of the property associated with the residential structure (acres).

House Age

Age of the residential structure, estimated as continuous variable
with each number representing an additional decade.

Condo

Indicator variable to distinguish whether the property is a
condominium (1= property is a condo, and 0 otherwise).

NEZR

Indicator variable to distinguish whether the property is receiving
NEZR benefits (1= property receives benefits, and 0 otherwise).

NEZN

Indicator variable to distinguish whether the property is receiving
NEZN benefits (1= property receives benefits, and 0 otherwise).

NEZH

Indicator variable to distinguish whether the property is receiving
NEZH benefits (1= property receives benefits, and 0 otherwise).

RZ

Indicator variable to distinguish whether the property is located
within a Renaissance Zones (1= property is located within the zone,
and 0 otherwise).

Consecutive
Years Since A

Number of years a resident has lived in their home since the passage
of Proposal A (maximum value = 16 years).

100

Appendix 5.B
Figure 5.6 Standard Quantile Coefficient Estimates

101

Figure 5.6 (cont’d)

102

Figure 5.6 (cont’d)

103

Figure 5.6 (cont’d)

104

Figure 5.6 (cont’d)

105

Figure 5.6 (cont’d)

106

Figure 5.6 (cont’d)

107

Figure 5.6 (cont’d)

108

Figure 5.6 (cont’d)

109

Figure 5.6 (cont’d)

110

Appendix 5.C

0.020
0.015
0.000

0.005

0.010

Distribution

0.025

0.030

Figure 5.7 Shift in the Effective Tax Rate Distribution as a Result of the NEZH Program

0

20

40

60

80

Effective Tax Rate

Note: Dashed line represents NEZH properties and solid line represents non-NEZH properties

111

CHAPTER 6
Assessment Inequity in a Declining Housing Market: The Case of Detroit

6.1 Introduction
Michigan law requires property to be assessed uniformly at 50 percent of true cash value
(Michigan Taxpayer’s Guide, 2011).

57

In practice, however, the assessment ratio – assessed

value divided by the sales price – often varies considerably from this standard, exhibiting a
regressive relationship: high-priced properties have lower ratios than low-priced properties
within the same jurisdiction. Concerns regarding assessment practices have been the subject of a
growing list of topics of empirical research, including: 1) methods of measuring inequity; 2) the
underlying determinants of inequity; 3) the degree of horizontal and vertical inequity resulting
from assessment practices; and 4) the economic beneficiaries of assessment inequity. However,
little is known about the degree to which assessment practices have generated unequal tax
payments during a period of significant disequilibrium such as the one created by the recent
housing crisis. To examine this issue, data have been collected from one city hit particularly
hard by the housing crisis – Detroit, Michigan.
It is no secret that Detroit property values have dropped substantially over the last five
years. Detroit residential property assessments have dropped 46 percent between 2007 and 2012
(MacDonald, 2013). Despite the large decline in assessed values, evidence recently reported in
the media suggests assessors are not following the market closely enough, raising concerns over

57

True cash value is also referred to as the market value or the properties “usual selling price”
(Michigan Taxpayer’s Guide (2011)).
112

assessment accuracy and equity.

58

For example, houses that sold for $2,300 are being valued by

the city at $42,000, more than 18 times their selling price (MacDonald, 2013).

59

Anecdotal

evidence suggests that properties not selling during the housing crisis are also over-assessed.

60

One hypothesis for the observed level of assessment inaccuracy in Detroit is that
assessors have attempted to avoid large losses in the tax base.

61

From city data on sales prices

and assessed values, if assessments were 50 percent of market value as reflected in actual sales
prices, tax revenue from residential properties sold in 2009 would drop from $18.4 million to
less than $4.2 million. This represents a decrease in average property taxes from $2,100 to
$480.

62

Assuming this estimated decrease is indicative of all residential properties (not strictly

those selling in 2009), the pressure to keep assessments artificially high is understandable. In
addition to the decline in property values, problems generating property-tax revenue in Detroit

58

A number of articles in The Detroit News were recently devoted to these concerns. The
following link provides a series of articles on Detroit property taxes and assessment practices:
http://www.detroitnews.com/article/99999999/METRO/130221002andtemplate=THEMEandthe
me=METRO-DETROIT-TAXES
59

Other examples of over-assessment include: houses selling for $12,500 are valued at $62,000
and properties less than $100 are valued at nearly $46,000 by the City.
60

Bill McCarthy, a Detroit resident, lived in his home since 1985 and had his $38,594
assessment decreased to $8,500; however, this decrease came only after appealing to the
Michigan Tax Tribunal when the Detroit Board of Review refused to change the assessment.
This changed his annual tax bill from $3,000 to $800 (MacDonald, 2013).

61

DeCesare and Ruddock (1998) state that assessed values may contain errors caused by
political decisions to intentionally override market values.
62

This estimate was calculated using the sample of properties used in this study (i.e., residential
properties sold in 2009). Current tax revenues are calculated by multiplying the State Equalized
Value (SEV) by the millage rate each property is subject to, whereas estimated tax revenues are
calculated by multiplying half the property’s sale price by the millage rate.
113

are exacerbated by the continued exodus of residents, as well as an exceptionally high propertytax delinquency rate.

63

A second possible reason for the observed level of assessment

inaccuracy in Detroit is that limited resources and staffing have hindered the ability of assessors
to make the proper adjustments to assessed values. Recently, budget cuts decreased the
assessment division’s staff from 90 employees in the late 1990s to 36 in 2012. As stated by
Detroit’s Chief Assessor, Linda Bade, these “...workers do their best under tough conditions”
(MacDonald, 2013). A final possible explanation for the observed level of assessment
inaccuracy is the subjectivity of the valuation process (DeCesare and Ruddock, 1998). That is,
assessors may be assessing properties using standard procedures; however, because the
valuations are based on limited comparables, the results are not truly representative of market
conditions.

64

The purpose of this chapter is to examine assessment regressivity in an eroded housing
market. This study makes two key contributions to the existing literature: 1) I examine the effect
of assessment practices on the vertical and horizontal inequities in a collapsed real-estate market;
and 2) I use quantile regression techniques to assess inequity. Standard regression analysis has
been the traditional tool for measuring vertical and horizontal inequities resulting from
assessment practices; however, standard regressions are not well suited to evaluate inequity

63

The 2010 Census estimates a population of 713,777, which is down from 951,270 in 2000 and
1.85 million at its peak in 1950 (U.S. Census). Regarding tax delinquency, about 47 percent of
property owners did not pay their 2011 tax bills – leaving nearly $246.5 million in uncollected
taxes and fees (MacDonald, 2013).
64

As anecdotal evidence of handpicking optimal sales in Detroit, the most recent sales study
undertaken by the assessment division included only 684 sales (or 5.6 percent) of the city's
12,118 home sales from October 2011, to September 2012. This is a much lower percentage
than other cities surrounding Detroit: Hazel Park, Pontiac, and Ferndale had assessments based
on 15, 16.5, and 30 percent of sales, respectively (MacDonald, 2013).
114

because of their reliance on central tendencies. As I discuss in detail later, the quantile
regression technique reveals how assessment practices affect the entire distribution of assessment
ratios, making this approach ideal for examining equity issues. The quantile regression approach
also reveals the sources of the average effect observed in standard regression analysis – whether
the effect is the result of a location shift (i.e., a change in the mean value), a scale shift (i.e., a
change in the variance), or both. Understanding the degree of the inequities may provide an
additional incentive to conduct a formal reassessment of properties to create a more coherent and
equitable property tax.

65

6.2 Methods and Data
6.2.1 Assessment Ratio and Equity
An assessment ratio is defined as the assessed value divided by the market value. While
market values are associated with ideal conditions (Clapp, 1990), sales prices have traditionally
been used as a proxy for market values, since they are observable and readily available
(McMillen and Weber, 2008). Furthermore, using the sales price in place of market value is
acceptable in this study given the nature of Michigan assessment practices; assessments are to be
completed using sale-price data from the previous year. To further ensure that sales prices are an
appropriate proxy for market values, I restrict the examination of 2010 assessment ratios using
data for properties sold in the previous year.
Concerning assessment equity, DeCesare and Ruddock (1998) provide the following
definition: “The degree to which assessment bears a consistent relationship to market value for

65

Assessment practices in Detroit are currently under review by a private firm hired by the State
Tax Commission. Their evaluation will determine whether assessment practices are within State
guidelines and whether a citywide reassessment will be undertaken. For details, see:
http://www.detroitnews.com/article/20130409/POLITICS02/304090341/1022/POLITICS/Michi
gan-s-tax-board-investigate-whether-Detroit-overtaxing-property-owners.
115

all properties at the assessment date.” Perfect equity is exhibited when the ratio is constant
regardless of the property value (Paglin and Fogarty, 1972).
6.2.2 Vertical Equity
Vertical inequity results when there are systematic differences in assessment ratios
among properties of different values. These differences are considered regressive (progressive)
when high-value (low-value) properties are assessed at lower rates than low-value (high-value)
properties (DeCesare and Ruddock, 1998). As previously highlighted, traditional assessment
equity research contains numerous specifications for detecting vertical inequity; Table 6.1
provides a summary of the various tests used by researchers to measure vertical inequity.
An important issue in the literature is the validity of models examining equity using two
variables. As noted by DeCesare and Ruddock (1998), a simple bivariate model may result in
omitted variable bias because assessments are likely influenced by other factors.

66

In the

regression results presented later, I present the results from both the traditional bivariate models,
and from multivariate models including property and location characteristics.

66

McMillen and Weber (2008) also suggest the inclusion of additional variables is important for
measuring vertical equity.
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Table 6.1 Tests for Vertical Inequity in Property Tax Assessments
Null Hypothesis Evidence of
Model
Source
(no inequity)
Regressivity
Paglin and
β0 = 0
β0 > 0
AV = β 0 + β1SP + ε
Fogarty (1972)
β1 = 1
β1 < 1
ln AV = β 0 + β1 ln SP + ε
Cheng (1974)
β1 = 0
β1 < 0
AV /SP = β 0 + β1SP + ε
IAAO (1978)
Kochin and
β1 = 1
β1 > 1
ln SP = β 0 + β1 ln AV + ε
Parks (1982)
β0 > 0 ,
β0 = β2 = 0
Bell (1984)
AV = β 0 + β1SP + β 2 SP 2 + ε
β2 < 0
AV = β 00 + β10 SP + β 01Low + β 02 High
+β11LowSP + β12 HighSP + ε

β 00 = β 01 = β 02 = 0

β 00 > 0 *

Sunderman et
al. (1990)

ln SP = β 0 + β1 ln AV + ε
β1 = 1
β1 > 1
Clapp (1990)
ln AV = b0 + b1Z + u
Notes:
AV = Assessed value
SP = Market value (measured by sales price)
Low = Indicator variable equal to one if the sale price is in the lower knot, zero otherwise
High = Indicator variable equal to one if the sale price is in the upper knot, zero otherwise
Z
= -1 if AV and SP rank in the bottom third of the data; +1 if AV and SP rank in the top
third of the data; zero otherwise
* β 00 > 0 indicates regressive for middle price range. Low and High measure whether the
intercepts for these groups are different from the middle group

6.2.3 Horizontal Equity
Horizontal inequity is defined as the systematic difference in assessment ratios among
properties with similar market values and characteristics. In addition to the increasing awareness
of assessor bias in favor of higher-valued properties, there is an expectation that assessors may
consistently under- or over-assess properties with certain characteristics. Horizontal inequity in
assessment practices has historically been concerned with these ‘other variables’. DeCesare and
Ruddock (1998) recommend including a range of explanatory variables in vertical equity
models. Most assessment ratio studies examining horizontal equity use the following model:

117

[6.1]

SEV /P = α 0 + α i X + u

(Berry and Bednarz, 1975)

where X is a vector of property and location characteristics. The null hypothesis to test
horizontal equity is H0 : α i = 0. Consider the following example: if X represents a geographic
location and the coefficient is positive and statistically significant, then the assessment ratio is
higher for properties in location X compared to similar properties in other areas (Cornia and
Slade, 2005). To measure horizontal equity properly, I must: 1) include sales price in X from
equation [6.1] above (Goolsby, 1997; McMillen and Weber, 2008); 2) split the data into
subsamples based on sales price (Cornia and Slade, 2005); or 3) split the data into subsamples
based on assessed values (Allen and Dare, 2002).
An alternative method for measuring horizontal inequity was introduced by Allen and
Dare (2002):
[6.2]

(SEV /P) − (SEV /P) = γ 0 + γ i X + v

(Allen and Dare, 2002)

where (SEV /P) is the mean assessment ratio in the jurisdiction and X is a vector of property and
location characteristics. The null hypothesis to test horizontal equity is H0: γ i = 0, and rejection
of the null hypothesis indicates there is horizontal inequity within the sample. A negative
(positive) and statistically significant coefficient indicates decreasing (increasing) assessment
error with an increase in the independent variable. For example, a positive coefficient for age of
the house indicates older houses face increased assessment error – an indication that assessing
older houses is a more difficult task (Allen and Dare, 2002).
Although there is no standardized list of variables to include in X, the variables often
cited can be separated into three groups: 1) property characteristics, 2) neighborhood
characteristics, and 3) homeowner characteristics. The property characteristics included in most

118

studies of horizontal inequity include age of the house (in decades), living area, and lot size.
However, the list of neighborhood characteristics varies substantially. Berry and Bednarz (1975)
argue the inclusion of neighborhood characteristics is important because there are significant
variations in assessment ratios for single-family homes among neighborhoods within major
cities. To address this issue, I include a set of neighborhood indicator variables.

67

Finally,

homeowner characteristics considered in previous studies and implemented in the present
analysis include an indicator variable identifying in-state vs. out-of-state residents, and indicator
variable identifying whether the property is the property owner’s primary residence.
6.2.4 Quantile Regression Analysis
While measuring inequity “on average” provides a good initial assessment, observing the
mean effect yields a limited perspective of how assessment practices affect the location and
shape of distributions (Buchinsky, 1994). As in Chapter 5, I implement a quantile regression
model (QRM) to determine how the conditional distribution of assessment ratios varies given the
covariates. In the context of assessment ratios, the quantile regression approach provides a more
complete evaluation of equity because it shows whether the assessment practices creates a
progressive, regressive, or non-linear ratios across property values. As the example in section
5.2.3 highlighted, quantile regressions enable one to examine changes in the distribution of the
dependent variable because QRM allows the distribution of the dependent variable to differ from
the covariate’s underlying density.

67

Other neighborhood variables implemented in the past include: per-capita income by census
tract (Ross, 2011 and 2012), number of sales in the neighborhood (Allen and Dare, 2002;
McMillen and Weber, 2008; Ross, 2012), unemployment rate (Ross, 2011), and the proportion of
commercial or industrial properties in the area (Ross, 2011). However, adding these variables to
the neighborhood indicator variables already included adds little to the model.
119

By using quantile regression techniques, the analysis presented in this chapter offers a
clear evaluation of: 1) the extent of assessment regressivity (i.e., vertical inequity); 2) the
variation in assessments within property-value groups (i.e., horizontal inequity); and 3) the
distributional effects of property, location, and homeowner characteristics on horizontal equity.
6.2.5 Data and Descriptive Statistics
The City of Detroit’s Assessment Division provided parcel-level information for this
research. Relevant information provided for each parcel in the City includes: 2010 assessed
values (SEV), last sale date, last sale price, property characteristics, and homeowner
characteristics. The full dataset includes information for 11,175 improved, single-family, taxable
properties that sold in 2009. Upon examining the data, three remaining issues required attention:
1) a number of properties were bundled and sold as single transactions; 2) some properties had a
sale price or assessed value equal to zero; and 3) a number of properties were owned by banks or
other lending institutions. Bundled properties were excluded because the price of any single
property within the bundle cannot be determined. Properties with a sale price or assessed value
equal to zero were excluded because there is no known reason, other than error, for why a
property would have zero value.

68

Bank-owned properties were excluded for three reasons: 1)

these likely represent “distressed” sales; 2) it is reasonable to expect that many of the bankowned properties have fallen into disrepair, especially with the surge in foreclosures in recent

68

There are 125 properties with a sales price equal to zero, and 199 properties with an assessed
value equal to zero. These zero-value properties are spread throughout the City of Detroit; 42 of
the 54 neighborhoods have at least one property with a sales price equal to zero, and 38
neighborhoods have at least one property with an assessed value equal to zero.
120

years;

69

and 3) banks may have an incentive to overstate the value of foreclosed property.

70

Combined, these criteria eliminate 2,095 observations from the sample and a total of 9,080
properties remain.

71

Finally, the International Association of Assessing Officers (IAAO, 2010) recommends
trimming the sample of statistical outliers. The IAAO defines an outlier as an assessment ratio
outside 1.5 multiplied by the interquartile range (IQR), where the IQR is the difference between
the first and third quartiles. Furthermore, the IAAO (2010) notes that a distribution of ratios is
often skewed to the right and suggests using the logarithmic transformation of assessment ratios
to identify additional low and fewer high ratios as outliers. Table 6.2 shows the relevant
statistics for trimming outliers using the logarithmic transformation. The lower bound for
trimming is the first quartile minus 1.5 times the IQR, and the upper bound is the third quartile
plus 1.5 times the IQR. The critical values for trimming are [-0.582, 4.578]. Following
McMillen (2013), observations with sales prices below the 1st percentile or above the 99th

69

Without proper maintenance, foreclosed houses often suffer disrepair due to the weather (e.g.,
lack of heat in the winter) and are prone to vandalism (either by the homeowner being foreclosed
on taking all they can, or intruders stealing copper piping and other metals to trade for cash).
70

A comparison between bank-owned properties and the rest of the dataset highlights this
concern. The average sales price of the 1,162 bank-owned properties is $106,000 while the
average sales price of the remaining properties is $13,000. Banks’ reluctance to record a loss
seems to far outweigh (2) above.

71

There are two limitations in my analysis related to the dataset. First, I am unable to exclude
all non-arms-length transactions because I am not able to identify the previous property owner.
The property may have been owned by a bank (foreclosed property) or a family member,
therefore some prices may be lower than they would be if they were arms-length transactions.
Second, I am unable to measure the “true cost” of properties purchased with tax delinquencies.
As an example, a property may have sold for $20,000, but the previous owner could have owed
$4,000 in back-taxes. Therefore, the “true cost” (or true sale price) is $24,000. Again, some sale
prices may be lower as a result. Overall, I anticipate the number of properties matching one of
these two criteria to be small and have little influence on the conclusion.
121

percentile have also been eliminated. Combined, these criteria trim 430 observations
(approximately 4.74 percent) from the sample.

72

Table 6.2 Outlier Trimming
log(Assessment Ratio)
-0.750

Sales Price
$
1

th

1.353
1.988
2.643

$ 3,498
$ 7,500
$15,000

th

10.545
-0.582
4.578

$93,812
$
1
$93,812

st

1 Percentile
25 Percentile
Median
th
75 Percentile
99 Percentile
Lower Bound for Trimming
Upper Bound for Trimming

In total, there are 8,650 observations in the final dataset. Summary statistics for the
variables used in the analysis are presented in Table 6.3, and detailed definitions for these
variables are provided in Appendix 6.A. Table 6.3 includes summary statistics for the full
sample, as well as for five sub-groups based on the sales price.
From Table 6.3, the average assessment ratio is 11.87, but note there are substantial
differences across subsamples. Property owners with the lowest valued properties have a much
higher average assessment ratio, and the assessment ratio declines as property values increase.
Interestingly, the average assessment ratio is greater than one, regardless of the sales price
quintile. These summary statistics provide initial evidence that properties are being overassessed (on average). Observing systematic over-assessments is very rare: I found only one
assessment ratio study where over-assessment was documented. In particular, Oldman and

72

Regressions including these outliers yield similar results. In fact, the regressions I present are
more conservative estimates.
122

Aaron (1965) discovered properties in Boston with assessment ratios greater than one; however,
this result was true for only a few “questionable sales” that were not single-family properties.
Table 6.3 Summary Statistics

Variable
Assessment Ratio
SEV (x2)
Sale Price
House Age
Living Area
Lot Size
MI Resident
PRE
District 1
District 2
District 3
District 4
District 5
District 6
District 7
District 8
District 9
District 10
# of Obs.

74

Quintile 1
Full Sample
Mean Std. Dev. Mean Std. Dev.
11.87
14.08
30.43
19.51
56,119
22,707
41,229
16,137
12,667
15,370
1,711
797.3
6.666
1.357
6.970
1.425
1,131
499.7
1,091
514.3
830.7
200.3
804.2
195.3
0.856
0.351
0.790
0.408
0.355
0.478
0.204
0.403
0.090
0.287
0.152
0.359
0.166
0.372
0.201
0.401
0.083
0.276
0.081
0.274
0.010
0.101
0.018
0.132
0.074
0.261
0.044
0.205
0.054
0.227
0.094
0.292
0.198
0.398
0.182
0.386
0.137
0.344
0.116
0.320
0.127
0.333
0.087
0.282
0.060
0.237
0.025
0.156
8,650
1,929

73

73

Quintile 2
Mean Std. Dev.
11.57
4.315
49,996
17,442
4,413
705.4
6.678
1.318
1,068
476.2
816.2
185.9
0.902
0.297
0.331
0.471
0.099
0.298
0.204
0.403
0.074
0.262
0.012
0.108
0.065
0.247
0.069
0.254
0.223
0.417
0.106
0.308
0.118
0.323
0.029
0.169
1,531

"Questionable sales" are properties for which the Metropolitan Mortgage Bureau of Boston
had reason to doubt the accuracy of information obtained from the Registry of Deeds.
74
Although I would expect the statutory assessment ratio to equal 0.50 given the relationship
between assessments and sales prices, I multiply the assessment portion of the ratio by two so the
ratio may be compared with previous assessment ratio studies. Multiplying the assessed values
by two leads to the expectation of assessment ratios equal (or close) to one.
123

Table 6.3 (cont’d)
Variable
Assessment Ratio
SEV (x2)
Sale Price
House Age
Living Area
Lot Size
MI Resident
PRE
District 1
District 2
District 3
District 4
District 5
District 6
District 7
District 8
District 9
District 10
# of Obs.

Quintile 3
Quintile 4
Mean Std. Dev. Mean Std. Dev.
7.749
2.564
5.095
1.795
57,724
17,982
65,308
21,057
7,577
1,152
13,177
2,438
6.586
1.269
6.475
1.316
1,094
470.4
1,168
492.6
825.5
182.0
847.8
195.5
0.876
0.329
0.890
0.313
0.362
0.481
0.418
0.493
0.075
0.263
0.052
0.222
0.186
0.390
0.124
0.329
0.076
0.264
0.086
0.280
0.007
0.086
0.006
0.075
0.073
0.260
0.099
0.299
0.039
0.193
0.026
0.159
0.207
0.405
0.201
0.401
0.125
0.331
0.162
0.369
0.159
0.366
0.153
0.360
0.053
0.223
0.092
0.289
1,748
1,770

Quintile 5
Mean Std. Dev.
2.202
1.344
67,501
27,752
37,645
19,006
6.588
1.385
1,235
521.5
862.2
233.4
0.833
0.374
0.475
0.500
0.069
0.253
0.115
0.320
0.099
0.299
0.009
0.094
0.089
0.284
0.042
0.200
0.181
0.385
0.177
0.382
0.118
0.323
0.101
0.302
1,672

Two additional observations from Table 6.3 are worth noting: 1) despite large differences
in assessment ratios across property values, property characteristics are very similar; and 2) the
number of property owners claiming the property as their principal residence increases as the
sales price increases.
6.3 Empirical Analysis
6.3.1 Traditional IAAO Measure of Regressivity
Although the mean provides an initial look at assessment regressivity, two simple
techniques for evaluating assessment uniformity are recommended by the IAAO. Table 6.4
presents these traditional statistics for the full sample, as well as for five sub-groups.

124

Table 6.4 Traditional Assessment Performance Measures

Price-Related Differential (PRD)
Coefficient of Dispersion (COD)

Full Sample
2.68
109.56

1
1.26
58.95

Sales Price Quintile
2
3
4
1.02
1.02
1.03
28.90
25.47
27.39

5
1.23
57.88

The price-related differential (PRD), a descriptive statistic, is the primary statistic
recommended by the IAAO for evaluating the extent of assessment regressivity.

75

IAAO

standards call for the PRD to be between 0.98 and 1.03; differentials above 1.03 indicate
assessment regressivity and differentials below 0.98 indicate progressivity. Examining the PRD
for full-sample, the value far exceeds the IAAO’s upper limit of 1.03. Examining the
differentials calculated for each sales price quintile, all quintiles show some level of regressivity
(PRD>1); however, only the first and fifth quintile (i.e., lowest and highest valued properties,
respectively) exceed the upper limit defined by the IAAO.
The second measure recommended by the IAAO is the coefficient of dispersion
(COD).

76

The COD measures assessment variability and assessments are considered uniform if

the COD is between 5 and 15 for single-family residential properties (IAAO, 2010). With a
value of 109.55, Detroit’s COD indicates variability greatly exceeding IAAO’s acceptable range
(i.e., very low uniformity). Therefore, a traditional assessment ratio study implies both
regressivity and variability of Detroit’s assessment ratios far exceeding the standards set forth by
the IAAO. Breaking the traditional analysis into sale price quintiles, each quintile exhibits
75

The PRD is calculated by dividing the arithmetic mean by the value-weighted mean (IAAO,
2010).

76

According to IAAO (2010), the COD is calculated by the following steps: 1) subtract the
median from each assessment ratio, 2) take the absolute value of calculated differences, 3) sum
the absolute values, 4) divide by the number of ratios, 5) divide by the median, and 6) multiply
by 100.
125

variability exceeding IAAO standards, whereas only the lowest and highest valued properties
exceed IAAO standards of regressivity.
6.3.2 Vertical Inequity: Traditional Statistical Analysis
A more formal IAAO-recommended procedure to measure assessment regressivity is
regression analysis. Following the traditional regression methods presented above (Table 6.1),
Table 6.5 presents the regression results examining vertical inequity in Detroit. Although most
traditional models use a bivariate approach, DeCesare and Ruddock (1998) note differences in
assessment levels can only be “properly identified when other attributes that influence this
relationship are clearly represented in the model.” Therefore, column (3) of Table 6.5 presents
multivariate regression results using the variables previously discussed. The conclusions of the
bivariate and multivariate models bear strong similarities; assessment regressivity is generally
observed across all methods with the exception of the Kochin and Parks (1982) model. Finding
progressivity using the Kochin and Parks model is a common finding in the literature since the
model is biased towards progressivity (Clapp, 1990). Clapp (1990) claims to correct this bias in
his model; as the results from the Clapp model show, regressivity is observed when the Kochin
and Parks bias is corrected.

126

Table 6.5 Traditional Results for Vertical Inequity
Model

AV = β 0 + β1SP + ε
ln AV = β 0 + β1 ln SP + ε
AV /SP = β 0 + β1SP + ε
ln SP = β 0 + β1 ln AV + ε

AV = β 0 + β1SP + β 2 SP 2 + ε
AV = β 00 + β10 SP + β 01Low + β 02 High
+β11LowSP + β12 HighSP + ε

β 0 or β1

β 0 or β1

(bivariate)
50,603***
(282.02)
0.1739***
(0.0047)
-0.0004***
(9.97e-06)
0.9323***
(0.0234)
$44,597***
(361.75)
-0.00001***
(7.07e-07)

(multivariate)
35,465***
(3,919.5)
0.1041***
(0.0040)
-0.0004***
(9.52e-06)
0.8407***
(0.0301)
31,608***
(3,939.7)
-8.35e-06***
(5.45e-07)

42,850***
34,819***
66,725***

30,596***
28,156**
46,686***

Conclusion
Regressive
Regressive
Regressive
Progressive
Regressive at an
accelerating rate

Regressive

ln SP = β 0 + β1 ln AV + ε
2.4529***
3.3303***
Regressive
(0.0360)
(0.0710)
ln AV = b0 + b1Z + u
Notes: Standard errors are in parentheses and regressions are corrected for
heteroskedasticity. Asterisks denote significance at the 1% (***), 5% (**), and 10% (*)
levels.

To examine assessment regressivity in Detroit thoroughly, I must also analyze the degree
of regressivity. Following McMillen (2011), I examine the variability of assessments in Detroit
by estimating the functions from the IAAO regressions.

77

The estimated functions are

presented in Figure 6.1. The straight line in the figure is the estimation from a simple linear
regression, and the curved line is from a nonlinear estimation (locally weighted regression). As
shown in Figure 6.1, both approaches indicate falling assessment ratios with increasing sales
prices (i.e., regressivity exists). While the linear model shows the average slope across

77

I focus on the IAAO (1978) model for the remainder of this section, due to its widespread use
and ease of interpretation. Most studies generally focus on the IAAO model and/or the model of
Paglin and Fogarty (1972), or some variant (i.e., Cheng, 1974; Bell, 1984).
127

observations, the nonlinear estimation indicates assessment ratios are extremely high at very low
sales prices with the ratio appearing horizontal for properties greater than $30,000. Figure 6.2
provides a closer examination of the nonlinear regression estimates for properties worth more
than $30,000; the assessment ratios continue to decrease as property values increase – properties
worth more than $70,000 begin to see average assessment ratios equal to one. Furthermore,
properties worth more than $70,000 have ratios half the ratio of properties worth $30,000$40,000 and substantially smaller than the ratios of properties worth less than $10,000.
Figure 6.1 Regression Estimates

128

Figure 6.2 Nonlinear Regression Estimates for Sales > $30,000

6.3.3 Vertical Inequity: Quantile Regression Analysis
While the standard regression analysis undertaken thus far is useful for showing
assessment ratios in Detroit vary with sales prices (in a regressive way), standard regressions do
not address the degree of assessment ratio variability at different sales prices (McMillen, 2011).
I now turn to the quantile regression approach, which allows me to examine how the full
distribution of assessment ratios varies by sales price.
The standard quantile regression estimates for the bivariate IAAO model are presented in
Table 6.6, and the quantile regression coefficients for quantiles ranging from p = 0.02, 0.03, ...,
129

0.98 are presented in Appendix 6.B.

78

Consistent with the OLS results, the estimates presented

in Table 6.6 imply assessment ratios are lower for more expensive properties. Focusing on the
coefficients for Sales Price across quantiles, the slope is much steeper at the 90 percent quantile
than at the 10 percent quantile – indicating assessment ratios converge as property sale prices
increase (i.e., the distribution’s variance decreases).
Table 6.6 Quantile Regression Results for Vertical Inequity
Quantile
50%
90%
90% - 10%
10.753*** 30.622***
24.792***
Constant
(0.074)
(0.816)
(0.757)
-0.0003*** -0.0004*** -0.0002***
Sales Price
(3.71e-06)
(0.00004)
(0.00002)
# of Obs.
8,650
Notes: Standard errors are in parentheses and the standard errors for the last
column are from 100 bootstrap replications. Asterisks denote significance at the
1% (***), 5% (**), and 10% (*) levels.
Independent Variable

10%
5.830***
(0.074)
-0.0002***
(3.70e-06)

To examine whether the assessment ratio’s variance decreases as the price of property
increases (i.e., scale shift), consider the difference between coefficient estimates across quantiles.
The difference between the 10 percent and 90 percent quantiles is presented in the last column of
Table 6.6. The difference is statistically significant; that is, the distribution of assessment ratios
narrows as the sales price increases.
While examining the changes in the assessment ratio’s variance is relatively
straightforward, the results presented in Table 6.6 require some additional explanation.
Interpretation of the quantile regression estimates is perhaps most easily understood with
graphical illustrations of how the distribution changes as an explanatory variable takes on
different values. Figure 6.3 presents the predicted values from a nonlinear quantile regression of
78

Quantile regression estimates for Sales Price are similar in the multivariate model. These
results are highlighted in Table 8.
130

assessment ratios on sales prices. The results suggest assessment ratios are relatively high at all
quantiles for low prices, with high variability displayed such that there is a large spread between
the 10 and 90 percent quantile lines. As the sale price increases beyond $30,000, the regression
lines appear horizontal and the variability disappears. A closer examination is offered in Figures
6.4 through 6.7; both the assessment ratios and their variability continue to decrease as the sales
price increases. An alternative method of showing these results is to graph the estimated
conditional density functions of assessment ratios. Figure 6.8 presents the estimated conditional
density functions of assessment ratios for properties in the first, third, and fifth sales price
quintiles. Assessment ratios are tightly clustered around one for high-value properties (quintile
5). However, the distribution shifts to the right and has a much greater variance as the sales price
decreases. Figure 6.8 also highlights that the traditional results were derived from both a scale
and location shift. Together, Figures 6.3 through 6.8 provides a clear evaluation of the degree of
inequity resulting from assessment practices.

131

Figure 6.3 Nonlinear Quantile Regression Results

132

Figure 6.4 Nonlinear Quantile Regression Results: $0 to $5,000

133

Figure 6.5 Nonlinear Quantile Regression Results: $5,000 to $30,000

134

Figure 6.6 Nonlinear Quantile Regression Results: $30,000 to $60,000

135

Figure 6.7 Nonlinear Quantile Regression Results: $60,000 to $90,000

136

Figure 6.8: Conditional Quantile Distributions, by Sale Price Quintiles

6.3.4 Horizontal Inequity: Traditional Statistical Analysis
Table 6.7 provides the traditional horizontal equity results. Consider first the results of
property characteristics. The coefficient on House Age is positive and statistically significant,
the coefficient on Living Area is negative and statistically significant (column (2)), and the
coefficient on Lot Size is statistically insignificant. Interpreting the results from column (1),
older houses have higher assessment ratios, all else equal. From column (2), older houses have
increased assessment error and larger houses experience decreased assessment error. These

137

results indicate that assessing older houses is a more difficult task and assessing larger houses is
easier. It is reasonable to expect that assessors have a more difficult time assessing older houses,
since the variation in property conditions is likely much larger relative to newer houses.
Concerning the plausibility of the coefficient for living area in the column (2), there is a greater
number of large houses in the data, relative to small houses. This provides assessors more
observations from which to make the assessment, all else equal.

79

Consider next the effects of homeowner characteristics on horizontal equity. The
coefficients on MI Resident and PRE are negative and statistically significant. This indicates that
those who live in Michigan, but not necessarily on the property, have lower assessment ratios
and smaller assessment errors than non-Michigan property owners. In addition, those claiming
the house as their principal residence (PRE) have lower assessment ratios and smaller assessment
errors, relative to those not living on the property. One possible explanation for these results is
that while Detroit assessors seek to mitigate tax base erosion by over-assessing properties, they
also seek to minimize community backlash and tax appeals. With these goals in mind, assessors
may follow Michigan law more closely for those most familiar with Michigan’s property tax law
(i.e., Michigan residents), and value property closer to the market for those most familiar with
current market conditions (i.e., Detroit residents). In addition, the availability of each type of
property owner to make an appeal to the Board of Review may also influence these results.

79

I examined the relative number of small versus big houses by comparing the number of
properties lower than one standard deviation from the mean Living Area with the number of
properties greater than one standard deviation.
138

Table 6.7 Traditional Results for Horizontal Inequity
Berry and Bednarz
Allen and Dare
Independent Variable
(1975)
(2002)
19.2562***
9.4177***
Constant
(1.3422)
(1.1357)
-0.0004***
-0.00002***
Sale Price
(9.58e-06)
(5.72e-06)
0.4502***
0.6944***
House Age
(0.1429)
(0.1209)
0.0002
-0.0011***
Living Area
(0.0004)
(0.0003)
-0.0007
0.0011
Lot Size
(0.0009)
(0.0008)
-3.1483***
-2.9221***
MI Resident
(0.5043)
(0.4338)
-1.9140***
-1.6447***
PRE
(0.2496)
(0.2094)
0.6699
-0.5853
District 2
(0.6304)
(0.5418)
-2.2243***
-1.4108**
District 3
(0.7040)
(0.5887)
-4.6086***
-0.5618
District 4
(1.7556)
(1.3847)
-6.6642***
-1.6848***
District 5
(0.7249)
(0.5980)
-1.0994
-0.8787
District 6
(0.9119)
(0.7776)
-2.0639***
-1.8861***
District 7
(0.5752)
(0.4847)
-0.8046
-0.9845*
District 8
(0.6191)
(0.5246)
-3.1283***
-2.6460***
District 9
(0.6054)
(0.5101)
-4.0245***
-2.2526***
District 10
(0.6542)
(0.5393)
# of Obs.
8,650
R-squared
0.223
0.033
Notes: Standard errors are in parentheses and regressions are
corrected for heteroskedasticity. Asterisks denote significance at
the 1% (***), 5% (**), and 10% (*) levels.

139

Finally, consider the effects of the neighborhood on assessment ratios. The coefficients
on District 3, District 4, District 5, District 7, District 8, District 9 and District 10 are all
negative and statistically significant.

80

These results indicate assessment practices are not

uniform across the city. Similar properties in different parts of the city have lower assessment
ratios, or experience decreased assessment error.

81

6.3.5 Horizontal Inequity: Quantile Regression Analysis
There are two primary approaches for examining horizontal equity. The first is a literal
examination of horizontal equity, as defined by Sirmans, Gatzlaff, and Macpherson (2008): “like
properties having the same market values are assessed differently. That is, horizontal inequity
can be examined by analyzing the distribution of assessment ratios within property-value groups,
holding other factors constant. To do this, I once again consider the assessment ratio
distributions previously highlighted in Figure 6.8; however, I now want to focus on the variation
within individual property-value distributions rather than on the difference between groups.
Figure 6.8 shows substantial inequity among low-value properties (large variance), some lowvalue properties have assessment ratios close to one, while other low-value properties have ratios
greater than thirty.
Following the more traditional approach for examining horizontal inequity, I use quantile
regression techniques determine whether the results from the standard regression analysis are
derived from a location shift (mean), scale shift (variance), or both. Quantile regression
estimates for the horizontal equity model are presented in Table 6.8, and the quantile regression
80

District 1 is the omitted category. Thus, these Districts have lower assessment ratios than
District 1, whereas Districts 2 and 6 are not significantly different than District 1.
81

Following Goolsby (1997), I also considered the log-log specification of the traditional
approach and the results did not change.
140

coefficients for quantiles ranging from p = 0.02, 0.03, ..., 0.98 are presented in Appendix 6.C.
These results highlight the limitations of traditional regression analysis, since traditional
approaches do not identify the variation across quantiles. Focusing on the coefficients for House
Age, the slope is negative at the 10 percent quantile and positive at the 90 percent quantile – an
indication that age affects assessment ratios across the distribution differently and assessment
ratios are diverging (i.e., the distribution’s variance increases) as the age of the house increases.
To examine whether the assessment ratio’s variance decreases as the property
characteristics change (i.e., a scale shift), the difference between coefficient estimates across
quantiles is tested; this difference is presented in the last column of Table 6.8. As discussed
earlier, examining the changes in the assessment ratio’s variance is relatively straightforward, but
the quantile regression estimates in Table 6.8 are perhaps most easily understood with graphical
illustrations of how the distribution changes as an explanatory variable takes on different values.
These results are presented in Figures 6.9 through 6.16.

141

Table 6.8 Quantile Regression Results for Horizontal Inequity
Quantile
Independent Variable
10%
50%
90%
90% - 10%
7.8570*** 12.0601*** 40.5374***
32.6804***
Constant
(0.3834)
(0.6021)
(4.5188)
(3.7514)
-0.0002*** -0.0003***
-0.0003***
-0.0002***
Sales Price
(2.77e-06)
(4.35e-06)
(0.00003)
(0.00001)
-0.3647***
0.0195
1.4607***
1.8254***
House Age
(0.0406)
(0.0638)
(0.4789)
(0.3703)
0.0006***
0.0010***
-0.0019
-0.0024**
Living Area
(0.0001)
(0.0002)
(0.0016)
(0.0010)
-0.0006**
-0.0008*
-0.0022
-0.0017
Lot Size
(0.0003)
(0.0005)
(0.0034)
(0.0024)
0.2266*
-0.8582***
-8.7964***
-9.0230***
MI Resident
(0.1231)
(0.1933)
(1.4507)
(2.2038)
0.2021**
-0.2677*
-6.3468***
-6.5489***
PRE
(0.0913)
(0.1433)
(1.0754)
(0.8231)
1.2089***
0.6439**
-1.7769
-2.9858
District 2
(0.1706)
(0.2678)
(2.0101)
(2.0427)
0.3996**
-1.3169***
-7.0202***
-7.4198***
District 3
(0.2015)
(0.3165)
(2.3752)
(2.4499)
-2.1746*** -3.6773***
-8.7414*
-6.5668
District 4
(0.4441)
(0.6973)
(5.2336)
(5.8645)
-0.7646*** -4.2822*** -17.4850*** -16.7204***
District 5
(0.2169)
(0.3406)
(2.5564)
(1.9693)
0.1358
-0.3569
-3.6313
-3.767
District 6
(0.2433)
(0.3820)
(2.8670)
(2.9628)
0.6443*** -1.0197***
-8.8688***
-9.5131***
District 7
(0.1663)
(0.2611)
(1.9597)
(1.7461)
0.7947***
-0.6072**
-6.4476***
-7.2422***
District 8
(0.1784)
(0.2802)
(2.1028)
(1.9880)
0.7580*** -1.4353*** -10.9468*** -11.7048***
District 9
(0.1805)
(0.2835)
(2.1275)
(1.9795)
0.7741*** -2.0576*** -13.0811*** -13.8552***
District 10
(0.2220)
(0.3487)
(2.6168)
(1.9038)
# of Obs.
8,650
Notes: Standard errors are in parentheses and the standard errors for the last column
are from 100 bootstrap replications. Asterisks denote significance at the 1% (***),
5% (**), and 10% (*) levels.

142

The quantile regression results offer a much richer evaluation than the traditional
regression analysis. Regarding property characteristics, while the mean results for House Age
show increasing assessment ratios for older houses, the quantile regression results demonstrate
the mean effect is the result of increased variance (i.e., the scale shift is greater than the location
shift). As shown in Figure 6.9, the peak of the assessment-ratio distribution for older houses is to
the left of the peak for newer properties, but note that the variance is also much larger for older
houses. There was no difference in the assessment ratios across house size (column (1) of Table
6.7); however, the quantile regression results indicate the variance decreases (i.e., assessments
become more uniform) for larger properties. This is consistent with the conclusion drawn from
the Allen and Dare model (column (2) of Table 6.7) – there is “decreased assessment error” for
larger properties. Finally, Figure 6.11 shows Lot Size has no effect on mean assessment ratios
(consistent with the standard regression results), and no change in the variance (consistent with
the quantile results).
Recall that the traditional models reveal lower assessment ratios, as well as decreased
assessment errors, for Michigan residents and those occupying the property as their primary
residence (PRE). In the quantile regressions, the estimated conditional density functions of
assessment ratios (Figures 6.12 and 6.13) show the mean effects are derived mainly by a scale
change (i.e., decreasing variance). Last, only districts four and five appear to experience location
shifts (i.e., mean shifts), leading to the mean effects drawn above (District 5 also undergoing a
scale shift), whereas all the other effects derived above were the result of scale shifts.

143

Figure 6.9 Quantile Distributions: House Age

144

Figure 6.10 Quantile Distributions: Living Area

145

Figure 6.11 Quantile Distributions: Lot Size

146

Figure 6.12 Quantile Distributions: MI Resident

147

Figure 6.13 Quantile Distributions: PRE

148

Figure 6.14 Quantile Distributions: Districts 1 through 4

149

Figure 6.15 Quantile Distributions: Districts 5 through 7

150

Figure 6.16 Quantile Distributions: Districts 8 through 10

6.4 Property Tax Implications
Vertical and horizontal assessment inequity has important implications for individual
property tax bills that can be illustrated with a simplified example of residential tax payments in
Detroit. If Detroit assessors were to assess properties strictly at 50 percent of the market value of
property, a $1,700 property would be assessed at $850, and a $37,000 property would be
assessed at $18,500 (Table 6.9). Based on these assessments and the full millage rate of
residential properties in Detroit, the estimated tax bill of the $1,700 property would be $72 and
151

the tax bill of the $37,000 property would be $1,562 – each would pay an amount proportionate
to the market value of the property (4.22 percent).
Table 6.9 Assessment Equity
Quintile 1
$1,700
0.50
$850
0.08444
$72

Average Market Value
Assessment Rate (50%)
Assessed Value
Full Millage Rate
Estimated Tax Bill

Quintile 5
$37,000
0.50
$18,500
0.08444
$1,562

Table 6.10 illustrates vertical inequity by comparing assessed values and estimated tax
bills using the assessment ratios highlighted in Figure 6.8 (i.e., assessments are regressive and
more variable for lower-valued properties). The estimated assessment ratios for the lowest
valued properties (Quintile 1) range from 4 to 28, whereas the range for the highest valued
properties is only 0.5 to 5. Although tax payments for low-value property owners will generally
be lower than the tax payments for high-value property owners, the effective tax rates of lowvalue property owners are much higher.

82

Only a small number of high-value properties are

subject to effective tax rates greater than low-value properties.

82

For purposes of this chapter, effective tax rates equal the tax payment divided by the market
value of property (i.e., sale price). Although the standard approach for measuring effective tax
rates requires dividing the tax payment by the assessed value, this would simply yield the millage
rate in my numerical example. Furthermore, calculating the effective tax rate as I have done here
offers a “true effective tax rate.” That is, the rate the owner pays rather than what they would
expect to pay if their assessment reflected the sales price of their property.
152

Table 6.10 Vertical and Horizontal Inequity
Average Market Value
Assessment Rate
Assessed Value
Full Millage Rate
Estimated Tax Bill
Effective Tax Rate

4
$6,800
$574
33.78%

Quintile 1
$1,700
16
28
$27,200
$47,600
0.08444
$2,297
$4,019
135.10% 236.43%

0.5
$18,500
$1,562
4.22%

Quintile 5
$37,000
2
5
$74,000
$185,000
0.08444
$6,249
$15,621
16.89%
42.22%

In addition to the inequity between property-value groups, there are also substantial
inequities within property-value groups. As discussed earlier, there are two approaches to
measuring horizontal inequity: 1) examine tax-payment differences within property-value groups
(Table 6.10), and 2) examine tax-payment differences based on property characteristics (Table
6.11). Table 6.10 shows that actual tax payments vary dramatically for otherwise identical
homes – from $570 to $4,020 for the lowest valued properties and from $1,560 to $15,620 for
the highest valued properties. In other words, a homeowner may receive a tax bill 7 to 10 times
higher than his/her neighbor, even if both property owners paid the same price for their property.
Finally, Table 6.11 examines horizontal inequity based on the age of the house. Using
assessment rates from Figure 6.9 and estimating the tax bills based on these rates, older houses
have lower assessment rates, on average, but are subject to more variable rates – with some
properties experiencing higher rates than newer houses.
Table 6.11 Horizontal Inequity (Market Value = $13,000)
House Age (in decades)
11
0
Assessment Rate
5
24
9
19
Assessed Value
$65,000 $312,000 $117,000 $247,000
Full Millage Rate
0.08444
0.08444
Estimated Tax Bill
$5,489 $26,345
$9,879
$20,857
Effective Tax Rate
42.22% 202.66% 76.00%
160.44%

153

6.5 Conclusions
This study offers an evaluation of the vertical and horizontal inequity created by
assessment practices during a period of disequilibrium such as the one created by the recent
housing crisis. Using parcel-level data from the City of Detroit, I use traditional IAAO
measures, regression analysis, and quantile regression techniques to assess the degree of
assessment inequity across Detroit property owners. By all measures, assessment practices are
vertically inequitable (i.e., regressive). The IAAO and traditional regression approaches
highlight regressivity; however, additional insight is gained by using quantile regression
analysis. Specifically, the variability of assessment ratios decreases as the price of properties
increase, offering a clear illustration of how assessment practices violate vertical equity. In
addition, my analysis shows how assessment practices generate significant horizontal inequity:
properties of similar value and characteristics face substantial differences in assessment ratios
and tax payments.
As a final note, this analysis is not equivalent to an actual appraisal study. There are a
number of possible explanations for the differences between this evaluation and actual
assessments. The City’s assessments are based on a much smaller number of comparable
sales.

83

My comparison is based on aggregate data, rather than the evaluation of individual

properties. The City may employ one of the other accepted approaches to property valuation,
such as the cost approach or income capitalization method. I must also note the State Tax
Commission provides oversight of assessments in Detroit, as with all local jurisdictions in
Michigan. Assessments are reviewed and approved at both the county and State level.
Nevertheless, this evaluation highlights the substantial differences existing between actual
83

As previously noted, the most recent sales study included only 684 sales (or 5.6 percent) of
the city's 12,118 home sales from October 2011, to September 2012.
154

selling prices and assessed values. At a minimum, this analysis suggests the City of Detroit is
likely to continue receiving a large number of property tax assessment appeals.

84

84

Again, the Michigan Tax Tribunal handled 3,015 residential cases from Detroit last year
alone.
155

APPENDICES

156

Appendix 6.A
Table 6.12 Variable Definitions
Variable
Assessment Ratio

Definition
SEV (x2) divided by Sale Price.

SEV (x2)

The 2010 state equalized value (or assessed value) of the property,
multiplied by two to be comparable to the sale price.

Sale Price

The 2009 sale price of the property.

House Age

Age of the residential structure, estimated as a continuous variable with
each successive number representing an additional decade.

Living Area

Size of the residential structure (square feet).

Lot Size

Size of the property associated with the residential structure (acres).

MI Resident

Indicator variable to distinguish whether the property owner lives in
Michigan (1= property owner lives in Michigan, and 0 otherwise).

PRE

Indicator variable to distinguish whether the property owner lives in the
property and claims the property as their principal residence (1= property
owner claims the property as their principal residence, and 0 otherwise).

157

Appendix 6.B
Figure 6.17 Standard Quantile Coefficient Estimates: Vertical Equity

158

Figure 6.17 (cont’d)

159

Appendix 6.C
Figure 6.18 Standard Quantile Coefficient Estimates: Horizontal Equity

160

Figure 6.18 (cont’d)

161

Figure 6.18 (cont’d)

162

Figure 6.18 (cont’d)

163

Figure 6.18 (cont’d)

164

Figure 6.18 (cont’d)

165

Figure 6.18 (cont’d)

166

CHAPTER 7
Conclusion

In this dissertation I examine the effects of Michigan’s assessment growth limit and
assessment practices on property tax equity. In the first essay, I use survey data to evaluate the
distributional consequences of the taxable value cap in the property tax in Michigan, as well as
the changes to these distributional effects following the housing market crisis. I demonstrate the
link between the taxable value cap and a substantial redistribution of property tax payments.
Specifically, estimates from 2008 indicate that homeowners who have lived in their home since
1994 (or earlier) faced effective property tax rates roughly 19 percent less than the effective rates
faced by new homebuyers, all else equal, and the effect increased to 23 percent in high-growth
areas. The overall benefit of homeowners living in their home since 1994 (or earlier) was
reduced in 2012. Specifically, the effective tax rate of long-time homeowners (i.e., those owning
their home since 1994 or before) was about 16 percent less than the effective rate faced by new
homebuyers, all else equal. However, the benefit received by those in high-growth areas
increased to 34 percent. I also find that after the housing market crisis, older homeowners enjoy
a tax benefit over younger homeowners. Finally, I document a regressive relationship between
income and effective tax rates: All else equal, high-income homeowners have lower effective
property tax rates, relative to low-income homeowners (with the 2008 data also showing middleincome homeowners benefitting).
In the second essay, I use tax data to offer a new evaluation of the degree of inequity
created by Michigan’s assessment growth limit. Using parcel-level data from the City of Detroit,
quantile regression analysis is used to assess the degree of horizontal and vertical inequity
created across homeowners. The evaluation of horizontal equity indicates that those who have
167

lived in their homes since 1994 or earlier, face effective property tax rates between 19 and 52
percent lower than the effective rates faced by new homebuyers, all else equal. These rates are
even lower for properties qualifying for the Neighborhood Enterprise Zones program. The
evaluation of vertical inequity indicates that properties nearly half as valuable may pay as much
as 8 percent more in taxes as a result of the taxable value cap. Perhaps more importantly, the
analysis reveals how the assessment growth cap leads to non-linearities in effective tax rates
across property-value groups. One could make arguments for more or less progressivity in
effective tax rates across the property-value groups, but it is more difficult to justify a non-linear
tax burden distribution. Using quantile regression techniques, I highlight that Michigan’s
assessment growth limit has created non-uniform changes to the distribution of effective tax
rates; effective tax rates in some property-value groups become more variable and others less – a
result both unknown and difficult to predict without quantile regression techniques. Finally, an
important implication of my analysis is that inefficiencies are created from the cap. These
concerns are validated in this chapter as I measure the extent to which the cap limits mobility,
thereby creating a “lock-in” effect. Overall, property tenure increases by nine years for those
fully benefitting from the assessment growth limit; however, the effect on tenure varies
substantially across different valued properties (from 0 to 16 years).
In the last essay, I offer an evaluation of vertical and horizontal inequity created by
assessment practices during a period of disequilibrium such as the one created by the recent
housing crisis. Using parcel-level data from the City of Detroit, I use traditional IAAO
measures, regression analysis, and quantile regression techniques to assess the degree of
assessment inequity across Detroit property owners. By all measures, assessment practices are
vertically inequitable (i.e., regressive). In addition, my analysis shows how assessment practices

168

generate significant horizontal inequity: properties of similar value and characteristics face
substantial differences in assessment ratios and tax payments.
There are several policy implications that stem from this dissertation. First, my findings
highlight that assessment growth limits in Michigan have created large inequities within property
value groups, across property value groups, and among homeowners of different ages and
incomes. Second, these inequities have remained present through the housing market crisis.
Together, these findings provide a more complete understanding of the effects of assessment
growth limits and should provide policymakers with the impetus to consider systemic changes
toward a more coherent, efficient, and equitable property tax system. Finally, the findings from
my third chapter highlight assessment practices in Detroit have created regressive assessments
and varying tax payments within and among property value groups. Although this may be the
attempt of assessors to avoid a complete erosion of the tax base, it is important to understand the
degree of the created inequities to provide an additional incentive to conduct a formal
reassessment of properties to, once again, create a more coherent and equitable property tax.
In addition to these policy implications, this dissertation offers two notable contributions
to the literature. First, I examine the effect of assessment policies and practices on tax payments
in a real-estate market substantially affected by the housing crisis. Specifically, I show how the
effects of assessment growth limits change as a result of the crisis and provide insight on
persistent inequities in a collapsed real-estate market. Second, I use quantile regression
techniques to assess inequity. Standard regression analysis has been the traditional tool for
measuring vertical and horizontal inequities; however, standard regressions are not well suited to
evaluate inequity because of their reliance on central tendencies. As highlighted, the quantile
regression technique reveals how entire distributions are affected, illustrating how useful this

169

approach is for examining equity issues. The quantile regression approach also reveals the
sources of the average effect observed in standard regression analysis – whether the effect is the
result of a location shift (i.e., a change in the mean value), a scale shift (i.e., a change in the
variance), or both.

170

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