Residential Location Decisions: Heterogeneity and the Trade-off between Location and
Housing Quality
DISSERTATION
Presented in Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy
in the Graduate School of The Ohio State University
By
Moon-Jeong Kim
Graduate Program in City and Regional Planning
The Ohio State University
2010
Dissertation Committee:
Hazel A. Morrow-Jones, Advisor
Jean-Michel Guldmann
Don Haurin
Copyright by
Moon-Jeong Kim
2010
Abstract
This dissertation is a socio-economic approach to the residential location model.
Heterogeneity of households’ residential location decisions and actual trade-offs made in
the housing market are explored. Specifically, this dissertation explores both
heterogeneous residential location decisions among different categories of households
and trade-offs between location and housing quality. It is assumed that social values are
reflected in locations, and locations with highly valued characteristics are preferred by
homebuyers, and that living in preferred locations means that the household has higher
social status. In order to live in preferred locations, households may have to make a tradeoff by giving up some housing quality. This research uses a repeat homebuyers’ dataset in
Franklin County, which is the central county in the greater Columbus, Ohio metropolitan
area. I utilize the two-stage nested logit model with interaction terms for different
household characteristics.
The estimation results provide a range of information about households’
residential location decisions. First, households with school-aged children are attracted to
locations with high school quality and high-income neighbors, while choosing older
houses (with more bedrooms). In other words, they make a trade-off by choosing older
houses—less expensive homes in the housing market—in order to live in these preferred
locations. Second, middle-income households with school-aged children are more likely
ii
to choose these same preferred locations, but they tend to choose older and smaller
houses with more rooms. As expected, their relatively limited incomes seem to stimulate
the trade-off between location and housing quality. They even accept higher crime rates
in their community choices. Third, households with householders who are 50 years old
and over prefer safer communities, indicating that safety is an important social value to
this group. In their dwelling choices, this group is more likely to choose multi-family
attached houses (e.g., condos, duplexes, and townhouses) with fewer bedrooms. This
group’s age-specific circumstances seem to affect their housing choices significantly.
The operationalization of the concept of social status with the status of locations
as preferred locations is one contribution of this work. The second contribution is that
this study broadens the perspective of the residential location modeling by providing a
variety of determinants associated with community and dwelling characteristics. The
utilization of the random utility theory—particularly the nested logit modeling—makes
the third contribution. I believe that this study will help extend the understanding of
actual determinants of residential location decisions in the U.S. housing market, and
improve the urban residential location theory.
iii
Dedication
This document is dedicated to my parents,
Byung Young Kim and Yusoon Oh.
iv
Acknowledgments
I would like to express my sincere thanks to people who have been with me and
have provided me with thoughtful support and encouragement during this long journey.
My special appreciation goes to my academic advisor, Dr. Hazel A. Morrow-Jones, for
her considerate support throughout my doctoral study at The Ohio State University. With
her constant encouragement and valuable academic advices, I have completed my
doctoral study. She is an insightful researcher and a decent professor that I could follow
with trust. I would also like to express my appreciation to my committee members. I give
my special thanks to Dr. Jean-Michel Guldmann for his thorough advice that improved
my dissertation, particularly the methodology. He has provided me with insightful
advices and special kindness all the time. I would also like to express my thanks to Dr.
Don Haurin for his valuable feedback and advices that made my dissertation more solid.
I am very grateful to Dr. Kenneth Pearlman for his support and generosity during
my doctoral study at Ohio State. He is a respectable professor that has provided doctoral
students, including me, with academic insight and personal kindness. I also express my
thanks to Dr. Byung Sun Chai and Dr. Tae Youn Jang for their academic and emotional
supports in South Korea.
I express my warm thanks to my Korean colleagues, Hee Jung Jun, Inkwon Park,
Young Kook Kim, and Jae Teuk Chin, for their friendship and support. They have made
v
my life at Ohio State meaningful and joyful. Also, I express my sincere thanks to my
church friends, including Juhee Park, Miryang Kim, and many others, for their constant
prayers and emotional support.
My special appreciation goes to my parents, Byung Young Kim and Yusoon Oh,
for their love and support. This dissertation is dedicated to them with love and respect. I
express my thanks to my sisters and brother-in-laws as well. They have always been my
supporters. I would also like to express my great thanks to my husband, Cheolho, and my
4 year-old daughter, Hajin, for their love, care, and endurance. They have brought
something special and precious—that cannot be measured—into my life. Finally and
most importantly, with my heart I would like to give my sincere appreciation to the Lord
who is perfect in everything.
vi
Vita
1997................................................................B.E. Architecture, Chonbuk National
University
2002................................................................M.S.P. Planning, University of Tennessee
2008................................................................M.CRP. City and Regional Planning, The
Ohio State University
2007 to present ..............................................Graduate Teaching Associate, Department
of City and Regional Planning, The Ohio
State University
Publications
Kim, Moon J., and Morrow-Jones, Hazel A. (2010). Intrametropolitan Residential
Mobility and Older Inner Suburbs: A Case Study of the Greater Columbus, Ohio
Metropolitan Area. Conditionally accepted in Housing Policy Debate.
Morrow-Jones, Hazel A., and Kim, Moon J. (2009). Determinants of Residential
Location Decisions among the Pre-Elderly. Journal of Transport and Land Use.
Vol. 2(1). 47-64.
Kim, Moon J., and Morrow-Jones, Hazel A. (2005). Current Determinants of Residential
Location Choices: An Empirical Study in the Greater Columbus Metropolitan
Area. In D. M. Levinson, and Krizek, Kevin J. (Ed.), Access to Destinations (pp.
149-170): Elsevier.
vii
Fields of Study
Major Field: City and Regional Planning
viii
Table of Contents
Abstract ............................................................................................................................... ii
Dedication .......................................................................................................................... iv
Acknowledgments............................................................................................................... v
Vita.................................................................................................................................... vii
Publications....................................................................................................................... vii
Fields of Study ................................................................................................................. viii
Table of Contents............................................................................................................... ix
List of Tables .................................................................................................................... xii
List of Figures .................................................................................................................. xiv
Chapter 1: Introduction ...................................................................................................... 1
Chapter 2: Literature Review.............................................................................................. 8
1. The Monocentric Model in Residential Location Decisions....................................... 8
2. Limitations: Commuting, Polycentricity, and Heterogeneity ................................... 10
3. Current Determinants in Residential Location Decisions ......................................... 17
4. Random Utility Model .............................................................................................. 22
Summary ....................................................................................................................... 27
ix
Chapter 3: Methodology ................................................................................................... 29
1. Social Values and Residential Location Decisions ................................................... 29
2. The Random Utility Model in Households’ Residential Location Choices .............. 35
2.1. Random Utility Functions and Residential Location Decisions......................... 36
2.2. Conditional Logit Model .................................................................................... 37
2.3. The Nested Logit Model..................................................................................... 38
3. Hypotheses ................................................................................................................ 41
Chapter 4: Data and Model Specifications ....................................................................... 47
1. Data ........................................................................................................................... 47
2. Data Description........................................................................................................ 48
2. 1. Community and Dwelling Attributes ................................................................ 49
2.2. Household Attributes .......................................................................................... 54
2.3. Descriptive Statistics by School District ............................................................ 55
3. Sampling Methodology ............................................................................................. 58
4. Model Specifications................................................................................................. 60
Chapter 5: Results and Discussion.................................................................................... 63
1. Estimation Results for Households with School-aged Children ............................... 64
2. Estimation Results for Households with Householders Who Are 50 Years Old and
Over............................................................................................................................... 69
x
3. Estimation Results for Households with School-aged Children at Different Income
Levels ............................................................................................................................ 73
3.1. Estimation Results for Middle-income Households with School-aged Children74
3.2. Comparison of Estimation Results for Households with School-aged Children at
Different Income Levels ............................................................................................ 80
4. Estimation Results for Households with Older householders at Different Income
Levels ............................................................................................................................ 88
5. Summary of the Estimation Results .......................................................................... 94
Chapter 6: Conclusion and Policy Implications................................................................ 96
References....................................................................................................................... 103
Appendix A: Constant Quality House Price Indices....................................................... 110
Appendix B: Descriptive Statistics of Data Sets............................................................. 112
Appendix C: Descriptive Statistics of the Models and Correct Model Specifications ... 113
Appendix D: Detailed Information of the Nested Logit Models .................................... 115
xi
List of Tables
Table 1. Categories of Households ................................................................................... 43
Table 2. Definitions and Sources of Variables ................................................................. 50
Table 3. Descriptive Statistics by School District ............................................................ 56
Table 4 Summary Statistics of Sampled Dwelling and Community Characteristics........ 60
Table 5. Estimates of the Utility Parameters for Households with School-aged Children65
Table 6. Estimates of the Utility Parameters for Households with Older Householders.. 70
Table 7. Estimates of the Utility Parameters for Middle-income Households with Schoolaged Children (compared to those for all households with school-aged children)........... 76
Table 8. Estimation Results of the Nested Logit Model of Households with School-aged
Children at Different Income Levels ................................................................................ 82
Table 9. Estimation Results of the Nested Logit Model for Households with Older
Householders at Different Income Levels ........................................................................ 90
Table 10. Constant-Quality House Price Index by Zip Code ......................................... 111
Table 11. Statistics of the Repeat Homebuyers’ Matched Dataset and the Survey Dataset
by School District ........................................................................................................... 112
Table 12. Descriptive Statistics of the Models and Model Specifications ..................... 113
Table 13. Descriptive Statistics of the Models with Two Kinds of Interaction Terms for
the Comparison of Households with Children at Different Income Levels.................... 114
xii
Table 14. Descriptive Statistics of the Models with Two Kinds of Interaction Terms for
the Comparison of Households with Older Householders at Different Income Levels . 114
Table 15. Estimates of Utility Parameters for Households with School-aged Children. 116
Table 16. Estimates of Utility Parameters for Households with Older Householders.... 117
Table 17. Estimates of Utility Parameters for Middle-income Households with Schoolaged Children .................................................................................................................. 118
Table 18. Estimates of Utility Parameters for Higher-income Households with Schoolaged Children .................................................................................................................. 119
Table 19. Estimates of Utility Parameters for Middle-income Households with Schoolaged Children .................................................................................................................. 121
Table 20. Estimates of Utility Parameters for Lower-income Households with Schoolaged Children .................................................................................................................. 123
Table 21. Estimates of Utility Parameters for Higher-income Households with
Householders Who Are 50 Years Old and Over............................................................. 125
Table 22. Estimates of Utility Parameters for Middle-income Households with
Householders Who are 50 Years Old and Over.............................................................. 127
xiii
List of Figures
Figure 1. Social Values and Households’ Residential Location Decisions ...................... 30
Figure 2. Trade-offs between Location and Housing Quality in Residential Location
Decisions........................................................................................................................... 33
Figure 3. Hierarchical Process of Residential Location Decisions................................... 41
Figure 4. Constant-Quality House Price Index by Zip Code and Local School District
Boundaries ...................................................................................................................... 110
xiv
Chapter 1: Introduction
The monocentric bid-rent model is the traditional residential location model in
urban economics. In its simplest form, as the distance from the CBD increase,
transportation costs increase and a household must spend more for commuting;
accordingly, the household bids less for land to keep its utility level and land rents
decrease (Alonso, 1964; Mills, 1967; Muth, 1969). In other words, households determine
their residential locations based on the trade-off between commuting cost and land rent.
The monocentric model has contributed significantly to the development of urban spatial
models since its development, thereby becoming the representative residential location
model.
The monocentric model, however, has been criticized due to both its theoretical
limitations and its limited applicability in the real world. First, the model has failed to
predict commuting distances correctly, although many studies have demonstrated the
existence of residential rent gradients (Anas, 1982; Hamilton, 1982). Actual commuting
distances are much greater than those estimated by the monocentric model in its extended
forms (Cropper and Gordon, 1991; Hamilton, 1982; Small and Song, 1992). Since the
monocentric bid-rent approach cannot successfully predict commuting, some researchers
have questioned whether commuting is a central determinant in residential location
models, arguing that commuting is a limited factor in explaining households’ residential
1
location decisions (Giuliano and Small, 1993; Kim and Morrow-Jones, 2005; Phe and
Wakely, 2000). Undoubtedly, the affordability of the automobile and dramatic
improvements in transportation systems have made commuting less important in
residential location decisions. Also, the introduction and popularity of the Internet have
changed the traditional concept of commuting because paid work does not necessarily
take place only in the physical environment of the employer (Phe and Wakely, 2000).
However, the findings about the importance of commuting in residential location models
are controversial, depending on the perspective of each study.
Secondly, there are theoretical limitations in the assumptions of the model itself.
According to Anas et al. (1998), a fundamental limitation is that the monocentric bid-rent
model is static; the model assumes a stationary state with durable housing and a quick
adjustment to equilibrium, both of which are not realistic. Muth (1985) also note that
some factors, such as dispersed employment and transportation improvements, can
transform the monocentric model in the real world. In fact, the urban structure has
become more polycentric, with the creation of “subcenters” in most U.S. metropolitan
areas. This change has created the need to modify the assumption of the monocentric
model.
Thirdly, the monocentric model tends to oversimplify households’ residential
location decisions. Anas et al. (1998) indicate that households’ varying preferences for
local amenities, different household characteristics, and unknown factors may explain
“excessive actual commuting,” and that heterogeneity is a critical factor in explaining
households’ residential location decisions. Modern, diverse lifestyles may mean that
2
individual preferences for a residence play a more important role than they did in the past.
The monocentric model is limited in explaining heterogeneous residential location
decisions among different categories of households. Although the monocentric model
was extended to include different household characteristics, such as income and family
size (see, for example, Wheaton, 1977), the standard model is too limited to investigate
these heterogeneity issues.
Many researchers have therefore argued that the standard monocentric model is
not applicable in reality, and that an alternative model must be developed (Anas, 1990;
Giuliano and Small, 1993; Phe and Wakely, 2000). However, although there are many
problems in the application of the monocentric bid-rent model, a concrete model that can
replace it has not yet been introduced and, accordingly, the monocentric model remains
representative (Balchin et al., 1995; Phe and Wakely, 2000).
Several studies have recently focused on other determinants of residential location
decisions, including school quality, housing preferences, neighborhood characteristics,
and other factors (Bayoh et al., 2006; Filion et al., 1999; Kim and Morrow-Jones, 2005;
OHRN., 1994). In a socio-economic approach, Phe and Wakely (2000) apply a society’s
value system—operating through what they call housing status—to the residential
location model, where housing status is defined as social desirability that a household
wants to obtain through its residence. This social desirability of a residence is based on
the values of the society, such as wealth, religion, education, and so on. Phe and Wakely
argue that households determine their residential locations by negotiating a trade-off
between housing status—expressed through residence in a desirable location—and
3
dwelling quality, while challenging the basic idea of the monocentric bid-rent model—the
trade-off between commuting cost and land rent. Although they study Vietnam, it is also
common to use one’s housing as a reflection of one’s status in the U.S. (Adams, 1984;
Maclennan, 1982; Rowles, 1993). Adams (1984) said that housing has hidden meanings,
such as “status, position, power, and personal identity,” (p.516) and Maclennan (1982)
also pointed out that social status plays a critical part in households’ residential location
decisions.
In order to study residential location decisions, I focus on the heterogeneity of
residential location decisions and the trade-offs associated with social status. Different
household characteristics generate different locational preferences, and these varying
preferences bring about heterogeneity in residential location decisions. This heterogeneity
has been ignored in the conventional monocentric model. Trade-offs between housing
status and dwelling quality are involved in these varying households’ residential location
decisions in the real housing market.
I operationalize the concept of housing status with measures of the status of a
location, because in the U.S., social status is generally associated with the location of a
house at least as much as it is with its quality. Characteristics such as good educational
systems and local history are valued in America, and these social values are reflected in
locations. Thus, specific locations such as good school districts and neighborhoods with
higher-income people are often preferred by homebuyers because of this perception, and
housing in these locations is relatively expensive. Living in these preferred locations may
mark higher social status.
4
In order to live in these good locations, households may have to make trade-offs
by giving up some level of housing quality. For example, when a household moves, it
examines several houses in different locations, and its final decision is made through a
trade-off, for example, choosing a smaller house in a very good school district or a
similarly priced, larger house in a poorer school district. If the household has school-aged
children, it may be more likely to choose a good school district and a smaller house as a
trade-off. Social values—education in this example—are already embedded in locations.
Social values are tied to social status, and good school districts provide
households with both educational benefits and a certain level of social status. Thus, Phe
and Wakely’s idea about the trade-off between housing status and housing quality can be
generalized to trade-offs between a preferred (desirable) location and housing quality.
Accordingly, I propose that households choose their residential locations by negotiating a
trade-off between a preferred location and housing quality. This approach is more
plausible in explaining households’ community and dwelling choices than that of the
conventional model explaining residential location decisions based on the trade-off
between commuting cost and land cost.
The first research question posed in this dissertation is how residential location
decisions differ between different categories of households. The second question is what
kinds of trade-offs between location and housing quality occur in each group’s residential
location decision; in other words, what features associated with housing quality are given
up, when choosing to live in highly preferred locations. I hypothesize that different
categories of households make different residential location decisions and have different
5
trade-offs between location and housing quality.
In exploring these questions, the random utility model, in the form of the nested
logit model, is used. This model considers a household’s residential location decision as a
probabilistic choice process among discrete alternatives. Locational equilibrium is
achieved through a probability distribution, rather than through household distribution in
space following the monocentric bid-rent model (Anas, 1990). In the nested logit model,
a variety of attributes related to community and dwelling are included, and these
variables allow for exploring preference variations and possible trade-offs between
location and housing quality. Based on the nested logit model, the decision-making
process is hierarchical: each household first selects a community, and then it chooses one
dwelling that maximizes the household’s utility. Under this hierarchical framework, a
community is chosen based on community characteristics, such as school quality,
property tax rate, and other socio-economic factors, and then a dwelling is chosen, given
the choice of a community. Household demographics are included as interaction terms in
the nested logit model, and this allows for exploring heterogeneous residential location
decisions based on different household characteristics.
This socioeconomic approach to residential location choices will improve our
understanding of actual residential location decisions and the trade-offs that homebuyers
make in the dynamic U.S. housing market. Thus, this study will be able to broaden the
perspective of residential location modeling by exploring various determinants in
households’ community and dwelling choices, heterogeneous residential location
decisions between different categories of households, and actual trade-offs between
6
location and housing quality. Furthermore, this research should help local policymakers
capitalize on their communities’ strengths to attract homebuyers. Therefore, this research
will help improve urban residential location theory and local housing policies.
The next chapter reviews the literature about the monocentric bid-rent model and
its limitations, recent studies on residential location decisions, and the random utility
model and its application to residential location modeling. Chapter 3 presents
methodology, including hypotheses, data, and model specifications. In Chapter 4, results
are presented. Conclusions are discussed in Chapter 5, along with policy implications.
7
Chapter 2: Literature Review
1. The Monocentric Model in Residential Location Decisions
According to Phe and Wakely (2000), since cities are mostly made up of housing,
the major theories of urban structure are residential location models, which are divided
into two main approaches: the market approach of urban economists and the non-market
approach of sociologists, geographers, and political scientists. In the market approach the
monocentric model (based on the concept of bid rent) has dominated urban spatial
models. The bid-rent is the maximum price for a unit of land that a household can pay at
a given utility level, and the land is sold to the highest bidder in a perfectly informed
market. Under the assumption that households are identical and mobility is costless,
households find residential locations that maximize their utility, creating equilibrium in
the overall market. Non-market approaches, however, are often based on the idea that
residential location patterns—land and house prices—are decided by monopolistic rent
rather than by market competition (Phe and Wakely, 2000).
In this section, the focus is on the market approach, namely the monocentric
model. In the literature, the terms “monocentric model” and “bid-rent model” are
frequently used interchangeably. The simple monocentric model—the standard model of
urban economics—assumes that in a city there is a single employment center, the central
business district (CBD), and that people commute from their residences to the CBD. The
8
concept of bid rent underlies the monocentric model: as distance from the center
increases, a household spends more for commuting and bids less for land at a given utility
level (Alonso, 1964; Mills, 1967; Muth, 1969). In other words, households determine
their residential locations by a trade-off based on commuting cost and land rent.
Historically, the bid-rent concept has its roots in von Thunen’s (1826) agricultural land
use model, which states that land rent varies with distance from a central marketplace.
Later, this concept was utilized in residential location models by Alonso, Mills, and Muth.
In the monocentric model, land rents decrease and transportation costs increase as the
distance from the CBD becomes greater. Thus, households who bid more for land reside
in areas closer to the CBD, and those who bid less choose to live in farther areas.
Furthermore, higher-income households tend to reside in areas farther from the urban
center because their need for housing services increases with income—that is, there is
income elasticity in the demand for housing.
After its development by Alonso, Mills, and Muth, the monocentric model was
generalized by the same authors and others (see, for example, Brueckner, 1987; Wheaton,
1974) and also extended to different types of households (e.g., income and family size)
(see, for example, Wheaton, 1977). Fujita’s (1989) work is a representative synthesis of
the monocentric approach, considering externalities such as local public goods and racial
prejudice. Based on the monocentric bid-rent concept, land rent gradients and density
gradients have been empirically tested, providing a large amount of empirical evidence.
There is also a large literature about urban density functions, showing that population
density becomes lower as distance from the CBD increases (Anas and Kim, 1992; Mills,
9
1972; Muth, 1969; Papageorgiou and Pines, 1989). Active research about density
gradients and whether the gradient has declined over time reflects the historical
background of post-war suburbanization. The influence of the monocentric model has
been significant in the development of urban spatial models. However, there are
limitations in this approach. Most importantly, Anas et al. (1998) indicate that a
fundamental limitation of the monocentric bid-rent model is that this model is static. That
is to say, the model assumes a stationary state with durable housing and a quick
adjustment to equilibrium, and both of the explanations are unrealistic. In the next section,
limitations of the monocentric model are discussed along with various changes in the
urban structure and the society that have influenced the monocentric model.
2. Limitations: Commuting, Polycentricity, and Heterogeneity
Criticism about the monocentric model starts with the difficulty in estimating
commuting costs in the model. Various changes over time have weakened the
applicability of the model and intensified the need to modify its assumptions. Among the
debates related to the model’s limitations, three aspects have been most critical: first,
commuting is not explained very well; second, the urban spatial structure has become
polycentric; and third, the monocentric model does not consider heterogeneity in
households’ residential location decisions. These three limitations are discussed below.
First, the standard monocentric model fails to estimate commuting distance and
time correctly. After the monocentric bid-rent approach was developed, only residential
rent gradients based on housing demand and utility maximization have been studied to a
10
great extent (Anas, 1982; Hamilton, 1982). However, commuting has been barely
anlyzed even though commuting cost is a central determinant in the standard monocentric
model. The lack of study about commuting, in contrast to a great deal of research about
residential rent gradients, has been raised and real commuting distances have been
compared to the predictions of the monocentric model by several authors (Cropper and
Gordon, 1991; Hamilton, 1982; Small and Song, 1992).
Hamilton (1982) appears to be the first to argue that the monocentric model
cannot predict commuting correctly. The commuting that Hamilton calculated with an
extended monocentric model with decentralized employment is 7 times greater than the
estimate from the standard monocentric model (Hamilton, 1982). Since commuting cost
explains the land rent gradients and density gradients in the standard model, this result
has generated significant discussions. Cropper and Gordon (1991) also show that actual
commuting is twice greater than the estimate of the monocentric model, even though their
model corrects for several factors, including two-worker families and actual employment
patterns. Small and Song (1992) also verify Hamilton’s argument that the standard
monocentric model cannot estimate commuting cost correctly. They find that actual
commuting in both time and distance is about three times greater than the estimate of the
standard model. Despite the standard model’s influence and achievements in urban
spatial modeling, commuting remains a critical weakness in the justification of the
monocentric model.
Furthermore, the idea that commuting is a central determinant in residential
location decisions has been challenged, and this debate is related to technological
11
improvements. For example, the popularity of the automobile and dramatic
improvements in transportation systems have made commuting less important in
residential location decisions. During the second half of the 20th century, transportation
improved dramatically, resulting in low transportation costs and shorter commuting times.
Thus, some researchers find that commuting time and distance are less important in
households’ residential location decisions (Giuliano and Small, 1993; Kim and MorrowJones, 2005; Phe and Wakely, 2000). For example, in a homeowners’ survey in the
greater Columbus metropolitan area in 1998, about 40% of the respondents stated that
distance to work was not important when choosing their new homes (Kim and MorrowJones, 2005). Several studies have also shown that commuting time utilities are negative
in residential location models (Levine, 1998; Weisbrod et al., 1980).
A new technology such as the Internet in recent years also strengthens these
arguments because this technology has changed the traditional concepts of work place
and commuting (i.e., paid work can now take place away from the employer’s location).
Transportation improvements have affected the urban spatial structure significantly
throughout history, and this new technology may have much greater effects on the
relationships between work places and residences in the future. However, many people
still consider commuting distance and time to be important in their residential location
decisions, depending on commuting means, gasoline price, etc (see, for example, Kim et
al., 2005).
Second, the change of the urban structure from a monocentric to a polycentric
city requires a modification of the assumptions of the standard monocentric model. It has
12
been already noted that non-CBD employment, nonresidential concentrations, and
transportation improvements can modify the conventional monocentric model (Muth,
1985). Among various changes during last half century, the polycentricity of the urban
spatial structure is the most notable change. The creation of “subcenters” characterized
by the concentration of employment activities has changed the American urban scene
considerably, indicating a change in the paradigm of urban spatial models. Many studies
have provided evidence that there are many subcenters in large U.S. metropolitan areas
(Cervero and Wu, 1998; Giuliano and Small, 1991; McMillen and McDonald, 1998).
Even “edge cities” have emerged with unique characteristics, such as huge concentrations
of office and retail space, and remote locations accessible only with automobiles
(Garreau, 1991). Many subcenters originate from older towns that urban expansion
forced to become incorporated cities with their own employment centers (Anas et al.,
1998). Also, newly developed suburbs are located around the outerbelts of older cities.
Instead of focusing on households’ residential location decisions, employment
and population densities, and land values are explored in the polycentric urban structure,
using the land rent and density gradients of the standard model. There are three functional
forms, depending on the assumptions, and these three models generalize the negative
exponential function of the monocentric model to the polycentric case (Heikkila et al.,
1989).1 One assumption is that each center has a declining bid-rent function for the
surrounding area, and that centers form separate zones in a region. The second
assumption—the opposite—is that each center is a complement in a region (part of a
1
The land rent and density gradient functions in the polycentric urban structure are described
primarily based on Anas et al. (1998)’s discussions (pp. 141-42).
13
region), and residents of a center are required to access to all other centers in the region.
The last assumption is an intermediate one that each center follows the second
assumption but a center’s influence declines as distance from the center becomes greater.
There are many studies that have used these model functions in order to study the
polycentricity of large U.S. metropolitan areas (see, for example, Gordon et al., 1986;
Griffith, 1981; Small and Song, 1994). These studies reveal that monocentric density
estimates do not fit very well, while also indicate that polycentricity is prominent in the
urban landscape, and thus, it should be taken into account in urban spatial modeling
(Anas et al., 1998). However, even though polycentricity is a very important urban
phenomenon, there are two aspects that should be noted. On the one hand, the CBD’s
influence is still significant to density and land values of surrounding areas. Anas et al.
(1998) explain that since the CBD is usually much larger in total employment and
employment concentration than the surrounding subcenters, its effects on density and
land values are greater than any other subcenters in a metropolitan region. On the other
hand, in terms of urban structure, Gordon and Richardson (1996) argue that even
polycentricity should not be discussed as the current urban structure anymore, because
dispersed employment patterns are more dominant than employment clusters in
subcenters and the CBD.
In the literature on polycentric urban structure, commuting is revisited. As
discussed previously, the land rent gradient based on the monocentric model fails to
explain actual commuting patterns. Even when density patterns are assumed to be
polycentric, this discrepancy is not eliminated (Giuliano and Small, 1993). Commuting
14
fails to be explained in the standard urban economics model—in both of the monocentric
and polycentric cases (Anas et al., 1998), even though it is a critical element in the tradeoff (along with land cost) in residential location decisions.
Third, the monocentric model tends to oversimplify households’ residential
location decisions. In other words, the standard monocentric model considers neither
households’ varying preferences (e.g., for locational amenities) nor heterogeneous
residential location decisions between different categories of households. Anas (1990)
indicate that ignoring households’ taste heterogeneity is the standard monocentric
model’s weakness, and that adding taste heterogeneity to the monocentric model leads to
greater decentralization.
Urban economists have questioned why commuting costs cannot be estimated
with the standard model, why people do not reduce commuting costs, or why commuting
is a minor factor in residential location decisions (Anas et al., 1998; Giuliano and Small,
1993). There are many plausible reasons. Anas et al. (1998) provide possible
explanations about ‘excessive’ actual commuting, including various household
preferences for local amenities, different household characteristics such as two-worker
households, segregation in the housing market, and other miscellaneous factors, such as
large moving costs. Also, aspects of suburban sprawl in the U.S. seem to involve
excessive commuting—valuing nature, farming heritage, “gentleman farmer” status, etc.
The monocentric model cannot fully consider these factors, even though “heterogeneity
of preferences and of job opportunities” is extremely important in residential location
decisions (Anas et al., 1998).
15
The monocentric bid-rent model has performed poorly in analyzing
heterogeneous residential location decisions among different categories of households. In
his original work, Alonso (1964) provided theoretical explanations for why households at
different income levels would differ in residential location decisions, either staying close
to the CBD or staying distant from the CBD. There have been some studies considering
different household demographics (see, for example, Wheaton, 1977) but the
monocentric bid-rent approach is far too limited to test heterogeneity of residential
location decisions.
The importance of allowing for preference variations in residential location
decisions and of considering heterogeneous residential location decisions depending on
different household characteristics seems to increase over time. During last half century,
society has changed considerably, and postmodernism underlies much of this change.2 In
the postmodernist society, diversity is an important value and people’s diverse lifestyles
may be its consequence, implying more variations in individual preferences when
choosing residences. Using activity-based travel modeling, Krizek and Waddell (2003)
study how households’ lifestyles are associated with travel patterns, activity participation,
vehicle ownership, and residential locations, and then identify nine different lifestyles
combined with households’ socioeconomic characteristics, such as household type,
2
Postmodernism has influenced the overall society originating from architecture to art,
philosophy, culture, and economy since the 1960s. Postmodernism can be illustrated as
complexity, ambiguity, diversity, high-technology, the globalization of capital, decentralized
society, and a push factor of urban restructuring.
16
presence of children, number of workers, and income.3 Their study demonstrates how
different preferences affect where people live and how they travel.
All of these problems have caused many researchers to argue that the standard
monocentric model is no longer applicable, and it should be replaced by an alternative
model (Giuliano and Small, 1993; Kim and Morrow-Jones, 2005; Phe and Wakely, 2000).
However, despite its many problems, a more solid model that can replace it has not yet
been introduced and, accordingly, the monocentric bid-rent model still remains a
representative urban model (Balchin et al., 1995; Phe and Wakely, 2000).
3. Current Determinants in Residential Location Decisions
Many recent studies have focused on aspects of residential location decisions
other than land costs and commuting costs: diverse household preferences and tastes,
changes in values over time, etc. For example, school quality is one of the priorities that
some households consider in choosing a residence, and many studies using the hedonic
price model show that high quality local schools are positively capitalized into property
values (Haurin and Brasington, 1996a, 1996b). There is also a large literature about the
capitalization of open space (e.g., parks) and farm land into property values, also using
the hedonic price model (see, for example, Geoghegan, 2002; Irwin, 2002; Johnston et al.,
2001; Ready et al., 1997). Other important factors in residential location decisions
3
They classify nine homogeneous groups with different lifestyles based on travel patterns,
activity frequencies, and residential location (urban form). Then, they examine co-variations
between each of these lifestyles and four kinds of households’ socioeconomic characteristics—
household type, presence of children, number of workers, and income. They combine each
lifestyle with households’ socioeconomic characteristics (e.g., retirees, urbanists with higher
income, suburban errand runners, family and activity oriented participants), demonstrating how
different dimensions interact.
17
include a variety of housing and neighborhood features (Filion et al., 1999; Kim and
Morrow-Jones, 2005; OHRN., 1994). Some earlier studies provide evidence that
variations in household demographics, preferences, and locational amenities diminish the
importance of commuting effects in urban spatial models (Giuliano, 1989; Wheaton,
1979). Also, Giuliano and Small (1993) find that commuting required by the actual
distribution of job and housing—the estimate using their polycentric model—is far less
than actual commuting in the Los Angeles region, and they suggest that factors such as
housing style and neighborhood characteristics may be more important in residential
location decisions in modern society.
Many studies have used survey data to examine a variety of important factors in
households’ residential location decisions. As discussed in the previous paragraph, school
quality is an important variable in households’ community and dwelling choices, and its
importance is consistent in many studies (Bayoh et al., 2006; Kim et al., 2005; Kim and
Morrow-Jones, 2005; Morrow-Jones, 2007; Morrow-Jones et al., 2004; OHRN., 1994).
Morrow-Jones (2007) finds that suburban homebuyers with school-aged children show
more interest in the academic quality of public schools and that they prefer newer houses.
Bayoh et al. (2006) also find that school quality affects households’ community choices
positively, and that it has the largest marginal effect in increasing households’
probabilities of choosing a central city rather than a suburban community. Their
argument is that improving school quality in a central city is the most effective policy to
attract homebuyers to the central city.
18
Filion et al. (1999) analyze people’s residential preferences in the Kitchener
Census Metropolitan Area in Canada, and show that place features (e.g., a nicer dwelling
and a better neighborhood) and proximity (e.g., a convenient location) are considered as
important reasons in moving decisions, while spatial factors, such as change in
employment location, are relatively less important.4 This implies that there is a decline in
the importance of accessibility to work place and a rise in that of place-specific factors
and proximity in residential location decisions (Filion et al., 1999). The Ohio Housing
Research Network (OHRN) (1994) studies major reasons for mobility in Ohio’s seven
major metropolitan areas, arguing that important factors that movers consider are
neighborhood safety, school quality, property values, the preference for a larger and
newer home, and so on. Also, Kim and Morrow-Jones (2005) provide a variety of
considerations in repeat homebuyers’ residential location decisions in central Ohio. Their
findings reveal that housing characteristics (floor plan, quality of construction, cost, etc.),
community characteristics (safety of the neighborhood and good investment or resale
value), and school quality (school reputation and quality of schools’ academic programs)
are considered to be important in choosing a new home. However, they also indicate that
accessibility considerations, including commuting distance to work place, are not
important in households’ decisions.
In contrast, some studies find that commuting is still important in households’
residential location decisions. While exploring trade-offs between access and space,
including dwelling quality, housing status, and amenity values, Kim et al. (2005) find that
4
Spatial factors include metropolitan-wide accessibility, place as home and neighborhood
features, and proximity as a possibility to reach activities (p.1318).
19
people prefer shorter commuting time, lower commuting cost, lower density, higher
quality of schools, and lower housing cost in Oxfordshire, U.K. Based on these findings,
they argue that commuting is still important in households’ residential location decisions.
These findings may result from the utilization of public transportation as a commuting
means and its price, depending on the distance between a residence and work place in an
area like the U.K. In their study about people’ preference for neotraditional
neighborhoods, Morrow-Jones et al. (2004) also find that shorter commutes are preferred
along with lower housing prices, lower density, more parks, and good schools, and that
higher density neotraditional neighborhoods are less preferred, holding other
characteristics constant.
In a socio-economic approach, Phe and Wakely (2000) apply the current value
system in society—what they called “housing status”—to the residential location model,
where housing status is defined as social desirability that a household wants to obtain or
express through its residence based on the values of the society, such as wealth, religion,
education, and so on. According to Phe and Wakely, households decide their residential
locations by “a trade-off between a desirable status and an acceptable level of dwelling
quality (p.19),” while indicating that the conventional trade-off theory fails to explain the
real housing market. In other words, the social status that people desire to obtain through
their residence plays a critical role in residential location decisions, and a household
spends more money for a unit of housing in order to live in a desirable location. A
household can spend less money by living in a less desirable location as well. In their
study of Hanoi, Vietnam, they identify local history as an important influence on
20
households’ perceptions about housing status, and that people were willing to pay more
for a unit of housing in a specific area consisting mostly of foreign offices and large
domestic firms. Phe and Wakely (2000) emphasize that the socio-economic approach can
explain gentrification and abandonment issues that cannot be explained in the standard
monocentric model.
Phe and Wakely’s socio-economic approach is a notable advance in
understanding households’ residential location decisions in a real housing market. Tradeoffs between housing status—expressed through a residence in a desirable location—and
dwelling quality are more plausible than the trade-off between commuting cost and land
rent in explaining households’ residential location decisions in reality. Although Phe and
Wakely studied Vietnam, it is also common to use one’s housing as a reflection of one’s
status in the U.S. (Adams, 1984; Maclennan, 1982; Rowles, 1993). In his article, The
Meaning of Housing in America, Adams (1984) points out that housing’s hidden
meanings include “status, position, power, and personal identity”, and Americans state
“who they are” through their housing (p.516-517). Morrow-Jones (1998) states that
American households use homeownership to achieve or mark “social mobility ” (p. 681).
Maclennan (1982) also indicates that social status is critical in households’ residential
location decisions.
In the U.S., social status is generally associated with the location of a house at
least as much as its size or quality, and thus, such locations as good school districts and
neighborhoods with a local history are highly preferred by homebuyers. Adams (1984)
shows a relationship between social status and the location of a house: when people buy a
21
house, they pay for a bundle of services provided by both the housing unit and the lot.
Particularly, the lot price comprises three elements—a location that determines
accessibility, the physical environment, and the social setting surrounding the lot. For the
social setting, he singles out neighbors, explaining that socially desirable neighbors who
have high status tend to increase house prices.
Capitalization of locational characteristics in house prices underlies the hedonic
price model, and studies about this capitalization make up a large literature.5 The location
of a house is very important in households’ residential location decisions. As MorrowJones (1998) explains, the location of one’s home—a good local school district—affects
the future of one’s children, given that a good education increases children’s success. The
location also determines the peer group that one’s children associate with, because
children with higher status are more likely to be in better school districts. The importance
of social status in households’ residential location decisions can be interpreted as the
importance of the location of the lot, given that social values are embedded in locations.
Phe and Wakely’s idea about the trade-off between housing status and housing quality
can be generalized to trade-offs between a preferred (desirable) location and housing
quality.
4. Random Utility Model
The standard urban spatial model—the monocentric bid-rent model—has
revealed its theoretical limitations and its limited applicability in the real housing market.
5
Since Rosen (1974) developed the hedonic price model, the model has received considerable
attention in its theory and empirical applications.
22
Recent studies have provided additional variables that are considered important in
households’ residential location decisions, but they are limited to describing households’
preferences in choosing their homes; they do not provide a strong theoretical model to
explain those preferences. As Anas (1990) noted, considering the heterogeneity of
household preferences is critical in residential location models, and residential location
decisions should be discussed, while including these various factors. The hedonic price
model provides estimations of those preferences by calculating the willingness to pay for
housing and neighborhood attributes. There is a large literature that shows positive effects
of school quality and environmental amenities on property values, but this approach does
not explain households’ decision-making processes for their residential locations or the
differences between different household types.
Random utility theory has several theoretical advantages over the bid-rent model.
For example, it allows for households’ preference variations, and a household’s decisionmaking process is regarded as a probabilistic choice process among discrete alternative
communities or residences. Anas (1990) explains that in the random utility framework
equilibrium is achieved by a probability distribution that indicates the odds that a
household chooses one location among discrete choices, different from the bid-rent
model that the locational equilibrium is explained by household distribution in space. In
random utility theory, a household is viewed as a utility maximizer—a utility maximizing
price taker—that chooses a residence among discrete alternatives, whereas in the bid-rent
model a household is viewed as a bidder.
23
In the random utility model, a variety of housing and community attributes are
included and can reveal households’ preferences in the residential location decisionmaking process. A household’s utility function is assumed to consist of measurable and
random components, and the random terms represent unknown dwelling and community
attributes and household characteristics, i.e., uncertainty in the decision-making process.
Various choices by households can only be explained by assuming that random terms
exist (Anas, 1982). Theoretically, this concept enables us to explore the heterogeneous
preferences of households that have different socioeconomic characteristics.
In its empirical applications, the multinomial logit model has been extensively
used in transportation studies, mainly to examine travel mode choices. Since theoretical
applications of the random utility concepts to households’ residential location decisions
by McFadden (1974, 1978) and Anas (1982), there have been empirical applications to
research about households’ community and housing choices as well (Bayoh et al., 2006;
Chattopadhyay, 2000; Lerman, 1977; Quigley, 1976, 1985, 1983).
The conditional logit model has been commonly used in location choice studies
(see, for example, Ellickson, 1981; Ellickson et al., 1977; Lerman, 1977; Nechyba and
Strauss, 1998; Quigley, 1976). Nechyba and Strauss (1998) study the impact of local
public services, other community characteristics, and ‘community entry prices’ on
households’ community choices. They find that all these variables explain individual
community choices, that public safety and educational quality are particularly important,
and that higher housing prices are less likely to attract households, holding everything
else constant. Using the hybrid conditional logit model, Bayoh et al. (2006) explore the
24
influence of local public goods in residential location decisions in Franklin county, which
is the central county of the greater Columbus, Ohio metropolitan area. Their findings
show that higher school quality had the largest positive effect on households’ community
choices, whereas higher crime rates and higher property taxes had negative effects.
In applications of the conditional logit model to households’ housing choices, the
number of alternative choices should be small in order to become empirically tractable.
Therefore, researchers tend to aggregate dwellings based on characteristics and make the
number of alternatives small (see, for example, Lerman, 1977; Quigley, 1976). Quigley
(1976) use 18 non-spatial choice sets based on housing types, and Lerman (1977)
constructed choice sets using a household’s income, driving license availability, and
automobile ownership. However, this arbitrary aggregation tends to be considered as a
weakness of the conditional logit model, along with its restrictive assumption of
‘independence of irrelevant alternatives’ (IIA). 6 Chattopadhyay (2000) explains that
estimates tend to have bias due to the arbitrary aggregation, and that the IIA assumption
cannot be tested in the conditional logit model.
The nested logit model is an extension of the conditional logit model, and the
approach has theoretical strength because it can test the IIA (Chattopadhyay, 2000). A
few researchers have applied the nested model to households’ residential location choices
in empirical studies, since McFadden (1978) introduced it. The nested logit model is
6
The conditional logit model assumes that random terms for each alternative are independently
and identically distributed according to the extreme value (Weibull) distribution. This assumption
is an important property, termed ‘independence of irrelevant alternatives’ (IIA), that the relative
odds for the choice of any two alternatives are independent of the attributes (Anas, 1982, pp.6065).
25
embedded in the idea that the decision-making process is a hierarchical choice process;
each household first selects a submarket in a deterministic manner, and then they choose
one dwelling that maximizes the household’s utility. Using the nested logit model,
Quigley (1985) studies renter households in the Pittsburgh metropolitan area in order to
obtain estimates of dwelling, neighborhood and public services attributes, including
accessibility features. He shows that renter households prefer a larger house, a
neighborhood with a shorter commuting time, and a town with lower school expenditures
and other public expenditures (outside the central city in the region). Chattopadhyay
(2000) studies the benefits of environmental amenities in residential location decisions
based on the nested logit model, comparing to the estimates obtained from the standard
hedonic model. In the model, he includes household demographics, such as race and
presence of children, as interaction terms, and finds that families with children prefer
houses with more rooms, less pollution, lesser property taxes, and better school facilities.
In order to overcome the estimation bias of the conditional logit model, both Quigley and
Chattopadhyay utilize McFadden’s (1978) sampling rule, whereby a researcher can create
a small subset for each household by selecting several dwellings at random. The nested
logit model is theoretically strong to estimate households’ preference variations,
heterogeneous residential location decisions, and even trade-offs between location and
housing quality. However, there have not been many empirical applications.
A nested logit approach that does not utilize both community and housing
attributes can, however, be found in many studies and this should be discussed separately
(see, for example, Kim et al., 2005; Quigley, 1976). Kim et al. (2005) study households’
26
intentions to move and community choices, and their nesting is constructed as follows: a
household first decides either to stay or to move, and then it chooses a residential location.
They treat all housing units within the same community as identical. Their findings show
that shorter commuting time, lower commuting cost, lower density, higher school quality,
and lower housing costs are important determinants of residential location decisions.
Summary
Many studies provide evidence that the monocentric bid-rent model cannot
explain commuting cost very well and commuting fails to prove its significance as a
central determinant in the standard residential location model. This does not mean that
commuting factors can be disregarded in a residential location model, because some
studies show that the influence of the CBD is still significant and commuting is important.
Polycentricity of the urban spatial structure and a variety of changes in technology and
values over time have created complexity and diversity in society and these changes seem
to influence households’ patterns of residential location as well. Thus, place-specific
characteristics and heterogeneous household preferences are too critical to exclude in
exploring determinants of residential location decisions. Most importantly, social status
may underlie households’ overall decisions about moving, neighborhood and housing
choices, and satisfaction. Examining the social status that a household can acquire
through its residence in a desirable location helps understand its decision-making process
in the housing market. Since social status is generally associated with the location of a
housing unit in the U.S., it is valuable to examine possible trade-offs that households
27
make by giving up some housing quality in order to live in a preferred location where
higher social status can be obtained.
The concept of the random utility model is useful to help disentangle the variety
of households’ residential location decisions, and the random elements of the model deal
with the unknown and unobservable factors. Particularly, the nested logit model is a
theoretically strong model that can include various factors that are considered important
in people’s neighborhood and residence choices. An empirical study using this model
will help us understand households’ residential location decisions in the real housing
market. This dissertation explores important determinants, heterogeneous residential
location decisions between different household characteristics, and trade-offs in
residential location decisions using the nested logit model.
28
Chapter 3: Methodology
1. Social Values and Residential Location Decisions
Phe and Wakely (2000)’s socio-economic approach provides insights into
residential location theory because their approach explains households’ residential
location decisions better than the monocentric bid-rent model. Although U.S. social
values are different from those of other countries, characteristics that are valued in the
U.S. affect households’ residential location decisions just as other countries’ values affect
decisions in those places. As many studies have shown, U.S. households move often and
consider neighborhood characteristics as well as housing characteristics when they decide
to move and choose a new house (Morrow-Jones, 2007).
Figure 1 delineates the residential location decision-making process. It also
illustrates the relationship between social values and preferred locations. The dotted box
in the figure surrounds the part of this process that will be studied in this dissertation. It
shows that household characteristics affect residential location decisions, that household
income is associated with housing affordability, and that trade-offs exist in residential
location decisions.
As can be seen in Figure 1, some valued characteristics in the U.S. include good
educational systems, accessibility, local history, social setting, and so on, and these social
values are reflected in preferred residential locations. Preferred locations, therefore,
29
Social Values
Preferred Location
-
- Good school districts
- Gentrified neighborhoods
- Neighborhoods with wealthy
neighbors
- Safe neighborhoods
- Areas accessible to
opportunities
Education
Local history
Social setting
Safety
Accessibility
Homebuyers
(Utility
Maximizers)
Income
(Affordability)
Different
Household
Characteristics
Trade-off (location
v. housing quality)
Living here means that they
have higher social status.
30
Higher (constant-quality)
House Price
Figure 1. Social Values and Households’ Residential Location Decisions
30
Residential
Location
Decisions
may include neighborhoods with good public schools, gentrified neighborhoods and wellmaintained older suburbs, neighborhoods with wealthy neighbors, and so on. Living in
these neighborhoods may mark higher social status as well as being a physical location. It
is common that U.S. households use their housing and neighborhoods as a reflection of
their status (Adams, 1984; Maclennan, 1982; Morrow-Jones, 1998; Rowles, 1993). Thus,
preferred locations tend to show relatively high real constant-quality house prices among
locations in a region.7
Households are utility maximizers subject to their budget constraints.
Demographic characteristics of a household—such as marriage status, presence of
children, etc.—affect residential location decisions directly because households with
different demographics tend to value different locations and housing characteristics,
thereby leading to different residential location choices. The budget constraint is closely
related to household income, and household income is a critical factor that determines
affordability—the level of housing a household can afford and the degree to which it can
achieve all the things it values in housing. Even though homebuyers may want to buy a
high quality house in a good neighborhood, they may not be able to purchase the best
house and the best neighborhood due to a variety of considerations, including the budget
constraint. Thus, some households make trade-offs between location and housing quality,
and after complex considerations they make their final residential location decisions
7
A constant-quality house is defined as “a unit where structural and land attributes, but not
community attributes, are held constant” (Haurin and Brasington, 1996b). Higher constant-quality
house price of a community means that people are willing to pay more to live in the community
because of certain characteristics of the community, separate from the characteristics of the
housing unit.
31
while maximizing their utility within their budget constraints. The final selection of a
house should be within a budget constraint that satisfies the household’s desires for a
combination of quality and location at the maximum possible utility.
Figure 2 depicts the concept of the relationships between housing quality and house price
for different residential locations. There are variations in the real constant-quality house
prices among the different locations. The constant-quality house prices—the prices of a
house with the same physical and land attributes but different community attributes—are
different among locations, with the house price rising as the area is more preferred by
people.8 A household has a budget constraint that determines a range of house prices it
can afford (between PA and PB). Also, it has a minimum housing quality that it needs
(HQA) and a maximum desired housing quality (HQB). In a highly preferred location,
there are fewer options the household can choose from and those options have relatively
lower housing quality (between HQA and HQA’). In a modestly preferred location, the
household has more options with better housing quality (to HQ A’’). In a less preferred
location, the housing quality could be much better with more housing options that the
household can purchase (to HQB). The household makes trade-offs between location and
housing quality, whether it chooses a lower-quality house in a highly preferred location or
a higher-quality house in a less preferred location. The household makes a final decision
among several alternatives while maximizing its utility.
8
Figure 4 and Table 10 in Appendix A show different constant-quality house price indices in
Franklin County, which is the central county of the greater Columbus, Ohio metropolitan area.
32
Housing Value
(Phh)
Highly Preferred Location
(High Ph)
Modestly Preferred Location
(Medium Ph)
PB
Less Preferred Location
(Low Ph)
PA
33
HQA HQA’
HQA’’
HQB
Housing Quality
Figure 2. Trade-offs between Location and Housing Quality in Residential Location Decisions
33
As a simple example, a middle-income class household with school-aged children
may value good schools. Suppose that its income allows for buying a house with the
value PB. In order to buy a house in a good school district, it may make a trade-off
between school district and housing quality, and it is more likely to maximize its utility
by choosing a good school district —in Figure 2, a highly preferred location—while
downsizing the house (lower than HQA’). Higher income enables a household to be
relatively free from these trade-offs, whereas lower income generates more trade-offs. As
household demographics vary, people value different characteristics of locations and
housing, and thus, trade-offs are different and may depend on household income as well.
In this study, housing quality is defined by the physical characteristics of housing,
such as the number of bedrooms, the age of the house, the square footage of the building,
and whether it is a single-family detached house or multi-family housing. A preferred
location is defined as a neighborhood or an area to which people are attracted by socioeconomic characteristics and reputation, and in which they expect an increase in property
values.
Renters are excluded from this research because of the limitation of the available
data set, but one possible scenario can be described briefly. Consider a household that is
strongly interested in living in a highly preferred location but cannot find housing it can
afford to buy at this location because of its budget constraint. The household could
choose to look for rental housing in the highly preferred location. Rental housing is
probably more expensive in more preferred locations as well, but may not require the
same level of resources (e.g., a downpayment or good credit history) as owning.
34
2. The Random Utility Model in Households’ Residential Location Choices
In reality, when households make a residential location decision, they consider
every factor simultaneously: whether they move or stay, the level of housing services,
housing tenure choice, and community choice. After various considerations and complex
trade-offs, households finally make a residential location decision and their choice
regarding community and housing tends to be greatly influenced by household
characteristics, such as age, income, marriage status, the presence of children, and so on.
Thus, a residential location model should generate the decision of moving from the
previous home and choosing the current home jointly and consider housing services,
community characteristics, and household characteristics all together (Bayoh et al., 2006;
Quigley, 1985; Rapaport, 1997).
However, estimation of a full model is impossible for many reasons (data
limitations not least among them) and most research is therefore conditional. Kim et al.
(2005) has recently studied households’ intentions to move and community choices using
a hierarchical nested logit model.9 Using a conditional logit model, Nechyba and Strauss
(1998) study the impact of local public services and other community characteristics on
households’ community choices. Bayoh et al. (2006) develop a hybrid conditional logit
model and study households who have decided to move while assuming housing services
as constant among communities to explore the influence of local public goods in
residential location decisions. Chattopadhyay (2000) use a nested logit model to estimate
the influence of environmental amenities in community and housing choices, and
9
They utilize the stated preference experiment, and say that there may be instrument bias in the
estimates because of that method.
35
compare the results with the estimation results of a hedonic model. These studies utilize
random utility functions, and the random utility model has the benefit of revealing
important determinants in residential location decisions.
I also adopt the random utility model to study households’ residential location
decision-making processes and trade-offs between location and housing quality. For the
analysis, a hierarchical nested logit model is used. The following three sections discuss (1)
random utility functions, (2) the logic of the conditional logit model, and (3) the nested
logit model.
2.1. Random Utility Functions and Residential Location Decisions
A household’s decision to choose a community and a residence is considered to
be a probabilistic discrete choice process, and random utility functions are its
mathematical foundation (Anas, 1982). Based on the standard random utility model, we
assume that there are a fixed number of submarkets, j = 1, … , J. Each alternative
submarket may be a local municipality, community or school district, and each one has a
unique bundle of public services and location characteristics (Bayoh et al., 2006). Each
submarket contains dwellings, whose characteristics include house price, geographic
accessibility, physical characteristics (e.g. age of the house, the number of rooms, the
house size or lot size, and structural type), and many other attributes.
The indirect utility function for a household i is

U jk  U X jk ,  jk

(1)
36
where Xjk, a vector of attributes for the kth dwelling in submarket j and  jk , the random
component of the utility for dwelling k in submarket j. The random term  jk represents
unknown dwelling and community attributes and varies from household to household.
The dispersed choices among households can only be explained by assuming that random
terms exist (Anas, 1982).
2.2. Conditional Logit Model10
The indirect utility function is assumed such that the measurable (Xjk) and random
(εjk) components are additively separable, and Equation (1) can be written as,
U jk  U X jk    jk .
(2)
U( ∙ ) measures the dependence of the strict utility on dwelling and submarket attributes.11
In the standard random utility model, a household i will choose a dwelling k in a
submarket j if the utility of choosing alternative (j, k), U jk , exceeds the utility of all other
alternatives. The probability that a specific household i will choose (j, k) is then given by

P jk = Prob U jk  U jk

for all  j, k   j, k  .
(3)
where P jk is the choice probability function for the alternative (j, k).
10
Anas (1982) called it the multinomial logit (MNL) model. Borooah (2002) defined individual
specific models as the multinomial logit, and choice specific models as the conditional logit. Thus,
I chose to call it the conditional logit model.
11
The nonrandom component of the utility is called strict utility, which can be used
interchangeably with identified, systematic, measurable, or common utility (Anas, 1982).
37
Under the assumption that the random utility terms for each alternative are
independently and identically distributed (IID) according to the extreme value (Weibull)
distribution, the probabilistic choice model can be written as,
Pjk 
e
J
U  X jk 
K
 e
U  X jk  
(4)
j1 k 1

with   

6  , where σ is the standard deviation of the distribution of each
alternative (Anas, 1982; McFadden, 1978). Equation (4) represents the conditional logit
form. The parameter λ is simply a scale factor for the systematic utility U( ∙ ), and is
absorbed into the definition of this utility. The parameters can be estimated by maximum
likelihood method. The conditional logit model has been used to explore the influence of
local public service levels in individual community choices (Bayoh et al., 2006; Nechyba
and Strauss, 1997).
2.3. The Nested Logit Model
Chattopadhyay (2000) states that the ‘independence of irrelevant alternatives’
(IIA), which is the major assumption of the conditional logit model, is not testable in that
model, but is so in the nested logit model. The nested logit model is embedded in the idea
that the decision-making process is a hierarchical choice process: each household first
selects a submarket in a deterministic manner, and then it chooses the one dwelling in
that market that maximizes its utility. The verification is as follows. The strict utility
function U( ∙ ) of Equation (2) can be expressed as the additively separable form
38
U (  )  1 U ( X j )  2 U ( X jk ) ,
(5)
where Xj is a vector of submarket attributes and Xjk is a vector of dwelling attributes. Let
V jk  U (  ) with λ = 1. Equation (4) can be expressed as a joint choice probability:
Pjk  Pj Pk j 
V jk
e
J
K
 e
.
(6)
V jk 
j1 k 1
The choice of dwelling, given the choice of submarket, and the choice of
submarket can be expressed as a conditional probability and a marginal probability,
respectively. The equations can be written with the inclusive value as
V 
Pk j 
e
Pj 
e
jk
e
J
(7)
Ij
V
j
e
(1 ) I j
V
j  (1

) I j

(8)
j1
where (1- δ) is a coefficient to be estimated 0    1 and the inclusive value is
expressed as
 K V 
I j  log  e jk  .
 k 1

(9)
The nested logit model is a special case of McFadden’s (1978) generalized
extreme value (GEV) model. The coefficient δ associated with the inclusive value can test
the property of the IIA (independence of irrelevant alternatives) (Chattopadhyay, 2000).
On the one hand, if δ = 0 then the model has the IIA property and the nested model
confirms that dwellings within the same submarket can be viewed as distinct alternatives.
39
It also implies that the probability equations collapse to the conditional logit expression,
and households’ choices are non-hierarchical. On the other hand, δ = 1 implies that
submarkets are distinct alternatives and dwellings within the same submarket are viewed
as similar. This means that households’ choices depend only on submarket characteristics.
In summary, under the hierarchical nested logit framework, a submarket is first chosen
based on the utility of community characteristics, such as school quality, property tax rate,
public service level, and so on, and then a dwelling is chosen, given the choice of
submarket.
Figure 3 shows a household’s residential location decisions following this
hierarchical process. Each household chooses a submarket first in a deterministic manner,
and then, within the submarket, it chooses a dwelling. In other words, suppose that a
household chooses submarket (S1) –one of the 2 available alternatives—and dwelling (D1)
within submarket (S1). It has two other alternatives within submarket (S1) and three other
alternatives within submarket (S2). The total number of rejected dwellings is 5. One
benefit of the nested logit model is that the coefficient of the inclusive value tests the IIA
property statistically. Also, the model reveals what kinds of attributes have stronger
influences on households’ community and housing choices. Furthermore, interaction
terms using household demographics will reveal differentiated residential location
decisions and the trade-offs made by different categories of households.
40
Choices
Households
S1
D1
D2
Submarket Choice
S2
D3
D4
D5
D6
Dwelling Choice
Figure 3. Hierarchical Process of Residential Location Decisions
3. Hypotheses
Based on the previous discussion, households’ residential location decisions are
explored using the random utility model, specifically the hierarchical nested logit model.
The model estimates the influence of characteristics of housing and community on
households’ location choices. As stated previously, this study explores heterogeneous
residential location decisions between different categories of households and trade-offs
between location and housing quality.
Household characteristics affect residential location decisions directly because
households with different demographics (e.g., marriage status, presence of school-aged
children, and presence of the elderly) desire and value different location and housing
characteristics, and thus, they will make different residential location decisions. In order
to explore heterogeneous residential location decisions by different categories of
41
households, I differentiate between what a household wants and what it can afford. On
the one hand, characteristics such as presence of children and age of the householder are
closely related to which characteristics of housing and neighborhood are more valued and
needed. For example, households with school-aged children may value good school
districts and need a house with more rooms as compared to those without children. In
order to live in a community with valued characteristics, a household may make a tradeoff between a preferred location and desired housing quality. Therefore, households with
school-aged children may choose a smaller house in a very high quality school district
rather than a similarly priced, larger house in a poorer school district.12 In this simple
example, the household trades off house size for living in a good school district.
On the other hand, the budget constraint associated with household income is
closely related to affordability: what (which level of housing and where) they can afford.
Higher-income households have more flexibility in spending, and thus, have a greater
range of housing and neighborhood choices and their trade-offs may not be significant.
However, middle-income households may have to make notable trade-offs between
location and housing quality by giving up a certain level of housing quality due to their
budget constraints. Special attention will be given to this middle-income group in terms
of trade-offs. Lower-income households may be severely constrained.
Therefore, I hypothesize that different categories of households will make
different residential location decisions and also different trade-offs between location and
housing quality. I start from households with different characteristics. For this study I
12
If they are higher-income households, they may choose a larger house in a relatively poor
school district but a nice neighborhood while sending their children to private schools.
42
select two distinct attributes among many possibilities: presence of school-aged children
and age of the householder (50 years old and over). I then examine each group based on
different income categories. Table 1 shows the categories of households that this study
will explore.13
Household
Income
Household
Characteristics
Higher Income
(Group 1)
Lower
Income
(Group 3)
(Group A-1)
(Group A-2)
Households with
school-aged children
in the middle-income
group
(Group A-3)
(Group B-1)
Older people in the
higher-income group
(Group B-2)
Older People in the
middle-income group
(Group B-3)
Presence of Children
(Group A)
Age of the householder, 50
years old and over
(Group B)
Middle Income
(Group 2)
Table 1. Categories of Households
1) Households with school-aged children (Group A)
Education is considered an important social value to households with school-aged
children, and thus, they are more likely to choose good public school districts, which
could include prestigious inner suburbs known for high public school quality in the
study area.14 Also, these households may consider socio-economic surroundings to be
important, and may prefer locations with higher median household incomes.
Compared to households without school-aged children, this group may have to buy
13
Note that this is not intended to be an exhaustive list of important characteristics.
14
Several inner suburbs of Columbus are famous for their good public schools. In addition to
high school quality, they are also considered prestigious neighborhoods.
43
relatively lower-quality houses, smaller, older houses, and/or multi-family attached
houses, in order to live in locations with especially high school quality.
2) Households with householders who are 50 years old and over (Group B)15
This group has age-specific characteristics that affect residential location decisions.
Morrow-Jones and Wenning (2005) indicate that a higher percentage of people move
down in housing price at age 50 (age bracket between 50 and 54) and over the age of
65 (age bracket between 65 and 69), probably due to marital break-up or child
launching at the earlier age, and health issues, loss of a spouse, or declining income at
age 65.16 Some are the elderly and retired, and their children are older and may either
have left their parents’ home or will leave soon. Thus, education becomes less
important as a social value to this group. Because of their age and the smaller number
of family members, they are more likely to choose houses appropriate for their age
and family stage; namely, houses with less rooms, smaller houses, or multi-family
attached houses rather than single-family detached houses, although these may not
necessarily be less expensive. Their decisions may be considered trade-offs or just
age-specific decisions.
15
The householder is not indicated in the survey, thus either the oldest male or the oldest female
is assumed to be the householder.
16
They categorize households into five-year age brackets using the age of the householder.
44
3) Households with school-aged children in different income categories
a. Higher-income households with school-aged children (Group A-1)
Since there are school-aged children in this group, they consider education as an
important social value and may prefer locations with good school quality.
However, the relatively high household income in this group enables them to
afford a highly-priced house in a good neighborhood rather than making a tradeoff. If they decide to send their children to private schools, good public school
quality may not matter to them anymore, although it may still affect the
investment value of the house.
These households have more flexibility in spending, and thus, in order to show
their social status, they may want to buy a very large home or to live in a
prestigious inner suburb.
b. Middle-income households with school-aged children (Group A-2)
This group is more likely to choose locations with good public school quality.
However, because of their budget constraints, they may have to make trade-offs in
order to live in good school districts. Thus, they are more likely to give up a
certain level of housing quality, such as house size and age of the house, as a
trade-off, including the choice of a multi-family attached house rather than a
single-family detached house. This study pays special attention to the trade-offs of
the middle-income households with school-aged children.
c. Lower-income households with school-aged children (Group A-3)
This group may not include many observations in the survey because their limited
45
income is more likely to prevent them from buying a house in a good school
district. Lower-income households with school-aged children are more likely to
rent a house in a good school district, but this study does not include renters.
4) Households with householders who are 50 years old and over in different income
categories
Higher-income households with older householders (Group B-1) may want to display
their achieved social status much more than the other groups. Local history may be an
important social value to them, and their spending flexibility may lead them to wellmaintained older suburbs or gentrified neighborhoods.
Middle-income households with older householders (Group B-2) are more likely to
choose houses appropriate for their age, such as smaller houses or multi-family
attached houses rather than single-family detached houses. There may not appear to
be any trade-off in their decisions, but age-specific considerations may be more
important.
Lower-income households with older householders (Group B-3) may consist of
retired people whose income is low but home equity is relatively high. Thus, they
may want to live in a house appropriate for their age (e.g., weakening health) in a nice
neighborhood. In terms of housing characteristics, they are more likely to choose
newer houses, smaller houses, and/or multi-family attached houses for easy
maintenance.
46
Chapter 4: Data and Model Specifications
1. Data
For this analysis, I use a deed transfer data set for the greater Columbus, Ohio
metropolitan area. All property sales in Ohio must have been filed, and the deed transfer records
have detailed property and mortgage information, along with buyer and seller names. The deed
transfers from October 2004 to April 2006 were matched based on buyer and seller name,
creating a data set of repeat homebuyers who sold and bought homes during the period.17
Using the matched data set, a repeat homebuyers’ survey was conducted by the Ohio
State University and the Center for Urban & Public Affairs at Wright State University in
2006. Only survey data for repeat homebuyers in Franklin County (the central county of
the area) were linked to the deed transfer records and used for the analysis. The deed
transfer records provide physical characteristics of the houses with addresses, which
made geocoding possible and allowed for the characteristics of each location to be added
to the file. The survey also provides households’ demographics. Four hundred eightyseven repeat homebuyer cases in 12 school districts in Franklin County were analyzed.18
Only repeat homebuyers’ data are used, excluding first-time homebuyers and
17
The matched buyer-seller data were provided by the Center for Urban and Regional Analysis
(http://cura.osu.edu).
18
Although 18 school districts are either fully or partially contained within Franklin County, 6
school districts (Canal Winchester, Hamilton, Licking Heights, Pickerlington, Reynoldsburg,
and Whitehall) are excluded due to small numbers of observations.
47
renters because of the limitations of the available data set. There are several benefits in
studying repeat homebuyers. They are familiar with the regional housing market and their
residential location decisions inform us more clearly about their trade-offs. Kim and
Morrow-Jones (2005) also explain that “repeat buyers’ movement patterns and attitudes
have an impact on others in the housing market as well, and their decisions have
important things to tell us about access and residential choices (p. 166).”
Franklin County is the central county of the greater Columbus, Ohio metropolitan
area. It has experienced significant urban sprawl, having been transformed into a
polycentric city over the past several decades. According to the U.S. Census Bureau, the
population of the metro area was 1,540,157 in 2000, ranking 33rd in population out of the
280 U.S. Metropolitan Statistical Areas, and almost 70% (1,068,978) of the metropolitan
population lived in Franklin County. Geographically, the central county covers most of its
suburban commuter shed. There are 45 local jurisdictions in Franklin County, including
the City of Columbus, which is the central city. In addition, there are 18 local school
districts and 48 zip codes either fully or partially contained within the county.
2. Data Description
As described in the hierarchical decision-making process of the nested logit
model, households first choose a community in a deterministic manner, and then, within
the community, they choose a dwelling. Bayoh et al. (2006) use local school districts as
communities in the hybrid conditional logit model, and Chattopadhyay (2000) uses
property tax rate and municipal spending per capita in defining city types in the nested
48
logit model.
In this study, I use local school districts as communities. Local school quality is
one of the most important factors in households’ residential location decisions, and local
school districts are closely related to property tax levels, which make up a large share of
household spending for housing. Figure 4 in Appendix A shows that constant-quality
house prices among zip codes within each school district are consistent in most of the
school districts except the Columbus school district. As discussed previously, some zip
code areas with higher constant-quality house prices are interpreted as highly preferred
locations by homebuyers who value some specific characteristics of the locations. The
price index ranges from -0.78727 to 0.50563 across zip codes (see Table 10 in Appendix
A). A price index 0.5056, for example, indicates that a house in this zip code area can be
sold at a 50.56% premium for the same-quality house in the reference zip code, 43201.
2. 1. Community and Dwelling Attributes
In defining community characteristics, variables related to local public services,
socio-economic characteristics, geographic accessibility, and other characteristics are
used. Definitions and sources of variables are described in Table 2. The local public
service variables include local property tax rates (LPTAXES), school district property tax
rates (SDPTAXES), and school performance index (SQUALITY). Local property tax
rates are the tax per thousand dollars of assessed value of the year 2005 assessed for
49
Variables
Dwelling Attributes
NROOMS
HAGE
HSIZE
Definitions
Sources
Total number of bedrooms
Age of the house (in years)
Total area of the house (in hundreds of
square feet)
Deed Transfer Data
Deed Transfer Data
Deed Transfer Data
DETACHED
If the house is detached = 1; if not = 0
Community Attributes
LPTAXES
Local property tax rates (2005)
SDPTAXES
School district property tax rates (2005)
Deed Transfer Data
SQUALITY*
School performance index (2005)
State of Ohio's
Department of Education
MINCOME*
Median household income (in thousands of
dollar)
Total crime per 1,000 population (2005)
US Census Bureau
Distance to the CBD from the centroid of
each school district (in tenths of a mile)
Constant-quality house price
GIS completed
CRIME*
DISTCBD*
CQPRICE
PRESUBURB*
If the neighborhood is one of prestigious
inner suburbs = 1; if not = 0
Franklin County Auditor
Ohio Department of
Taxation
FBI Uniform Crime
Report
Haurin and MorrowJones, 2005
Not Applicable
Household Attributes
INCOME
Total annual household income (Higher
income: if income is higher than $140,000
= 1, if not = 0; Middle income: if income is
between $60,001 and $140,000 = 1, if not
= 0; Lower income: if income is $60,000
and lower = 1, if not = 0)
2006 Homeowners
Survey
CHILDREN
If there are school-aged children = 1, if not
=0
2006 Homeowners
Survey
AGE
If the age of the householder is 50 years
old and over = 1, if not = 0
2006 Homeowners
Survey
Table 2. Definitions and Sources of Variables
Note: * indicates that the variables are related to social values in this study.
50
2006.19 School district property tax rates are total gross real property tax rate of the year
2005 assessed by school districts.20 The school performance index score is an (weighted)
average of test scores of all topics at every level, and data for the year 2005 are used.21
Socio-economic characteristics include the median household income (MINCOME) and
crime rates (CRIME).22 The median household income is the average median household
income between 2005 and 2007.23 The crime rate is the total number of violent and
property crimes per 1,000 population at the municipality level in 2005.24 An accessibilityrelated variable is the distance to the CBD (DISTCBD), measuring as the distance to the
central point of the zip code 43215 from the centroid of each school district.25 In addition,
19
The data were derived from tax rates provided by Franklin County Auditor.
http://www.co.franklin.oh.us/Auditor/ The tax rates assessed by the taxing district were
aggregated to the school district level.
20
The data were derived from property the tax statistics provided by the Ohio Department of
Taxation. http://tax.ohio.gov/
21
The data were derived from the interactive Report Card Home (ILRC) provided by State of
Ohio’s Department of Education. http://www.ode.state.oh.us
22
Race-related variables were not included in the model because the estimation procedure failed
to complete optimization. The percentage of white population and crime rates are highly
negatively correlated (correlation coefficient = -0.83620, p < 0.0001). Thus, it is assumed that the
crime variable contains race effects.
23
The data were derived from the 2005-2007 American Community Survey 3-Year Estimates
provided by the U.S. Census Bureau. The data are for areas with populations larger than 20,000
people, representing the average characteristics for the 3-year time period. Data for Bexley and
Grandview Heights school districts were not provided because of the population limitations, so
data were forecasted using the Census 2000 Summary File provided at the place level. First, the
municipal boundaries of Bexley and Grandview Heights at a municipality level are very similar to
those of the school districts. Second, the forecasting can be done based on the changes in Upper
Arlington because the communities are very similar in several characteristics: landlocked
geography, good school quality, higher percentage of white population, etc.
24
Crime data were derived from the FBI Uniform Crime report and were provided only
at the municipality level. Thus, the data used at the school district level are
approximations. http://www.fbi.gov/ucr/ucr.htm
25
The zip code, 43215, is comprised of major governmental and office buildings. Thus, the
51
there are other community variables such as the constant-quality house price (CQPRICE)
and whether the community is a prestigious inner suburb or not (PRESTIGIOUS). The
constant-quality house price is a computed (predicted) variable, not an observed real
house price.26 This variable is used to hold house price constant in the model. Depending
on interpretation, this variable can be used as a ‘community entry price,’ that is, one of
the community characteristics. Prestigious inners suburbs include Bexley, Grandview
Heights, Upper Arlington, and Worthington.27
In order to explore preferences for locations, some variables such as school
performance index (for education), median household income (for social setting), crime
(for safety), distance to the CBD (for accessibility), and whether the community is a
prestigious inner suburb (for local history) are taken into account. Education has been
repeatedly used to explain social values. The social setting surrounding one’s house is
central point of this zip code is considered the CBD in this study. In the case of the Columbus
school district, average distance to the CBD from the centroid of each zip code was used. The
data were calculated using GIS.
26
The constant-quality house price was obtained using a hedonic price model by zip codes. The
zip code-level house price indices were aggregated to the school district level, creating average
constant-quality house prices at the school district level. Boundaries between zip code areas and
school districts do not match, and thus, the centroid of each zip code was used to determine where
that zip code should be included.
27
Inner suburbs are those that were primarily developed after World War II, adjacent to central
cities. Anacker (2006) explains that these inner suburbs are surrounded by incorporated areas, and
thus, they cannot be expanded beyond their geographic boundaries. Based on these characteristics,
there are 5 inner suburbs in the Columbus area: Bexley, Grandview Heights, Upper Arlington,
Whitehall, and Worthington. Except Whitehall, the other four inner suburbs are known as
prestigious neighborhoods in the local area, because they provide high-quality public school
systems, and the majority of residents are white and high-income people. Their overall
characteristics are presented in Table 3. The different boundaries of the Worthington SD from the
city boundaries make it look like an outer suburb, but in this study, this community is considered
an inner suburb. The Repeat Homebuyers Survey does not provide any case for Whitehall, and
thus, this community is excluded in this study.
52
another important social value factor, and high-income neighbors mean social status in
itself. Having such neighbors suggests that one has achieved higher social status. Adams
(1984) has stated that socially desirable neighbors with high status increase housing
prices in neighborhoods. Safety is also one of the valued characteristics in our society,
and safe neighborhoods are always desired by people. Also, preference for areas with
higher accessibility is very common. The CBD provides many opportunities with high
accessibility, and the distance to the CBD has proved its importance, as land values are
higher in areas close to the CBD. The distance to the CBD is central to the monocentric
bid-rent model.
Lastly, certain prestigious inner suburbs have many attractions for homebuyers in
the Columbus area, and living in these neighborhoods is one mark of high social status in
this region. It is difficult to define and measure exactly what “prestige” means in the
context of a location. This variable is included in the model to see whether it captures
something unique in the local context. If this variable is statistically significant, it implies
that people may be attracted to these communities not only because of good schools,
high-income neighbors, and close locations to the CBD (variables that are also in the
model) but also because of some other factor that has not been measured. Accordingly,
good school districts, communities with higher median household incomes, safe
communities, areas close to the CBD, and prestigious inner suburbs are considered
preferred locations. As discussed earlier, different categories of households prefer
different community characteristics (and different housing characteristics), and, in order
to live in preferred locations, households will make trade-offs.
53
Dwelling attributes include the total number of bedrooms (NROOMS), the age of
the house (HAGE), the total area of the house (HSIZE), and whether the house is
detached or not (DETACHED). If the house is a single-family detached house, this
dummy variable takes a value of 1; if the house is a multi-family attached house, such as
a condo or a duplex, it takes a value of 0.
2.2. Household Attributes
The household attributes that are used as interaction terms include the total
annual household income, the presence of school-aged children, and the age of the
householder. The information for household demographics is derived from the 2006
Repeat Homebuyers Survey. In this survey, household income is classified into 11
categories, namely from $20,000 to more than $200,000, with a span of $20,000 for each
category. For this study, these categories are aggregated into three groups: higher, middle,
and lower incomes.28 The highest four categories 8 to 11 are considered higher income:
higher-income households are those who earn more than $140,000. Categories 4 to 8
(from $60,001 to $140,000) are considered middle income. Also, the lowest three
categories 1 to 3 are considered lower-income household group: lower-income
households are those who earn $60,000 or less. Dummy variables are associated to these
groups. The variable the presence of children is a dummy variable, and it is defined as 1
28
The mean value of this variable is 5.52, with a standard deviation of 2.64. Originally, categories
3 to 8 (from $40,001 to $160,000) were considered middle income. Higher-income households
were considered those who earn more than $160,000. Lower-income households were considered
those who earn $40,000 or less. However, that categorization created too few cases for higherincome and lower-income households—either with children or with older householders, and thus,
the categorization was revised.
54
if there is at least one child at age 5 to 18 in the household, and 0 if not. The variable the
age of the householder is defined as 1 if the age of the householder is 50 years old and
over, and 0 if it is not.
2.3. Descriptive Statistics by School District
Table 3 presents descriptive statistics by school district. Columbus is the central
city of the greater Columbus metropolitan area, and its characteristics include lower
school quality, lower median household income, lower percentage of whites, and higher
crimes, all of which result in the lowest constant-quality house price. However, cases in
the City of Columbus (124) make up 25% of the data set.
Four inner suburbs—Bexley, Grandview Heights, Upper Arlington, and
Worthington—are characterized by the highest school quality, higher local and school
district property tax rates, relatively higher median household income, a greater
percentage of whites, and high constant-quality house prices. The geographical locations
of the inner suburbs provide various benefits because they are all close to the CBD and
the Ohio State University, the largest university in the state and a major employer. These
locations display very high constant-quality house prices.
Mixed community characteristics characterize the outer suburbs. Dublin, Gahanna,
Hilliard, and Westerville are more recently developed suburbs since the 1990s, and are
considered either preferred or moderately-preferred communities. The New Albany
school district is unique because most of it was recently developed with highly
55
General
Location
Central City
Inner
Suburbs
Outer
Suburbs
56
Average
School Districts
Columbus
Bexley*
Grandview
Heights*
Upper Arlington
Worthington
Dublin
Gahanna Jefferson
Groveport Madison
Hilliard
New Albany-Plain
Southwestern
Westerville
Total
Number of
Number of
Cases
Households
Local
Property
Tax Rate
(2005)
School
School
Median
District
Percentage
Performance Household
Property
of White
Index
Income
Tax Rate
(%)
(2005)
($)
(2005)
124
7
192,133
4,705
103.09
134.74
66.47
108.45
73.7
101.8
34,859
70,200
59.15
92.45
8
2,953
129.95
101.28
103.3
54,328
95.92
55
29
41
32
9
89
13
49
31
(Total=487)
14,010
22,819
29,290
17,037
16,763
31,828
8,345
51,930
33,679
35,458
125.5
116.52
108.19
94.17
93.7
109.69
94.19
99.92
101.84
109.29
95.88
83.23
72.5
59.24
52.6
73.14
56.16
64.67
67.31
75.08
105.2
102.7
101.6
97.8
79.2
97.2
101.3
88.0
96.0
95.65
87,965
68,505
72,613
72,496
52,802
69,405
85,276
49,872
64,471
65,233
92.12
87.90
81.07
82.93
67.33
88.35
83.97
85.75
80.95
83.16
Continued
Table 3. Descriptive Statistics by School District
Note: * Data were obtained from the Census 2000 at the place level, and were forecasted based on changes in Upper Arlington SD.
56
Table 3 Continued
General
Location
Central City
Inner
Suburbs
Outer
Suburbs
57
Average
School Districts
Columbus
Bexley*
Grandview
Heights*
Upper Arlington
Worthington
Dublin
Gahanna Jefferson
Groveport Madison
Hilliard
New Albany-Plain
Southwestern
Westerville
Crime
Distance to
CBD
(miles)
Commuting
Time to
Work
(minutes)
ConstantQuality House
Price Index
124
7
82.50
40.43
4.5121
4.7315
20.10
17.40
-0.15596
0.21267
8
31.42
1.4919
16.90
0.46084
55
29
41
32
9
89
13
49
31
(Total=487)
13.90
30.13
16.99
28.35
35.61
30.76
17.81
35.62
28.40
32.66
4.8569
9.7547
10.7623
10.4266
10.8286
8.9835
13.9765
7.0438
10.6643
8.1694
18.40
19.70
20.90
21.20
22.70
21.50
23.80
21.60
21.10
20.44
0.38380
0.21775
0.25881
0.14953
-0.05182
0.07893
0.50563
0.07447
0.12167
0.18803
Number of
Cases
57
expensive homes targeted to wealthy families. The Groveport and Southwestern school
districts are outer suburbs, but their overall community characteristics are not very strong.
3. Sampling Methodology
This study adopts McFadden’s (1978) sampling rule: make a small subset for
each household by selecting dwellings at random from a large number of alternatives.
This subset is comprised of several dwellings, including the chosen dwelling unit. The
random sampling satisfies McFadden’s ‘uniform conditioning property’ and obtains
consistent estimates of parameters (Chattopadhyay, 2000; Quigley, 1985).29
As described in the Data section, the number of cases for the analysis is 487. In
the data set, there is a record of the dwelling and the community which each household
has moved to, providing the selected dwelling unit and the selected community. To do the
sampling, the repeat homebuyers’ matched data set is used. The total number of dwelling
units in this data set is 5,096. The matched data set provides alternative dwellings,
available in the market during the period from October 2004 to April 2006. The number
of dwellings available in each community (school district) is found in Table 4 in the
Appendix B.
The sampling procedure is as follows. In the first stage, in addition to the chosen
dwelling, two more dwellings that were rejected by the household are selected at random
29
One limitation of the conditional logit model in the application of households’ housing choices
is that the number of alternative choices should be small in order to become empirically tractable.
Therefore, researchers tend to aggregate dwellings based on characteristics and make the number
of alternatives small (Quigley, 1976; Lerman, 1977). Chattopadhyay (2000) explains that the
estimates tend to have bias due to arbitrary aggregation. McFadden’ suggested random sampling
can overcome this problem.
58
with equal probability from the community in which the household had actually chosen
its dwelling. In the second stage, besides the community where the chosen dwelling is
located, another community rejected by the household is selected at random from the set
of available alternative communities. Three more dwellings are selected at random from
this rejected community, with equal probability. Therefore, as can be seen, it is assumed
that each household chooses one dwelling out of six.
Table 4 presents summary statistics of the sampled dwellings and communities.
The second column represents the mean characteristics of the dwelling and community
chosen by the households. The third column indicates the mean characteristics of rejected
dwellings in the chosen community, (974 dwellings). The last column represents the
mean characteristics of the rejected dwellings in the rejected communities, (1,461
dwellings). The total number of observations for the analysis is then 2,922.
On average, households in the “chosen” data set tend to choose communities with
lower local property tax rates, lower school district property tax rates, lower school
quality, lower median household incomes, higher crimes, closer to the CBD, and lower
constant-quality house prices. Also, they are less likely to choose prestigious inner
suburbs. In terms of dwelling attributes, they are more likely to choose newer and bigger
houses with more rooms. They are more likely to choose single-family detached houses
within the selected communities. However, the dwellings in the rejected communities are
more likely to be single-family detached houses.
59
Chosen Dwelling
Rejected Dwellings
Mean (sd)
Mean (sd)
Rejected
Community
Rejected
Dwellings
Mean (sd)
3.28 (0.76)
31.57 (25.32)
1,945 (661)
0.67 (0.47)
3.20 (0.79)
33.88 (25.44)
1,805 (732)
0.65 (0.48)
3.24 (0.79)
34.23 (25.02)
1,903 (842)
0.68 (0.47)
107.56 (9.70)
72.56 (12.01)
91.80 (11.76)
61,154 (18,242)
40.91 (25.25)
7.56 (2.81)
0.1010 (0.1905)
0.20 (0.40)
487
107.56 (9.70)
72.56 (12.01)
91.80 (11.76)
61,154 (18,233)
40.91 (25.23)
7.56 (2.81)
0.1010 (0.1904)
0.20 (0.40)
974
109.71 (14.16)
75.57 (18.07)
96.23 (9.31)
68,929 (14,747)
31.49 (15.53)
8.28 (3.54)
0.2021 (0.1890)
0.36 (0.48)
1461
Chosen Community
Variables
Dwelling Attributes
NROOMS
HAGE
HSIZE
DETACHED
Community Attributes
LPTAXES
SDPTAXES
SQUALITY
MINCOME
CRIME
DISTCBD
CQPRICE
PRESUBURB
Number of Cases
Table 4 Summary Statistics of Sampled Dwelling and Community Characteristics
4. Model Specifications
The proposed model focuses on repeat homebuyers who have already sold their
previous house and purchased their current house are studied. The joint choice
probability of the nested logit mode is
Pjk  Pj Pk j 
V jk
e
J
K
 e
,
V jk 
j1 k 1
where Pjk is the probability of selecting the kth dwelling in the jth community. This is Eq.
(6) presented in the previous chapter. A household’s indirect utility function can be
written as
60


V jk    1r   11r HC1   12r HC 2 X 1 jr   ( 2 r   21r HC1   22r HC 2 ) X 2 jkr (10)
r
r
where X1 represents community attributes, X2 represents dwelling attributes, and HC1
and HC2 are household characteristics that are used as interaction terms. The first part of
Eq. (10) on the right-hand side represents community-specific attributes, and the second
part dwelling attributes. The α and θ values are unknown parameters that must be
estimated, and r denotes the rth dwelling attribute in the attribute vector X.
The nested logit model is a special case of McFadden’s (1978) generalized
extreme value (GEV) model, and is consistent with stochastic utility maximization
(Chattopadhyay, 2000). The nested logit model with a utility function of the form (6) can
be partitioned into the following two conditional probability components:


exp  2 r   21r HC1   22r HC X 2 jkr 
 r

Pk j  


exp I j


(11a)


exp   1r   11r HC1   12r HC 2 X 1 jr  1   I j 
 r
 (11b)
P j  


j exp r  1r  11r HC1  12r HC 2 X 1 jr  1   I j 




where Ij is the inclusive value and is written as



I j  log exp  2 r   21r HC1   22r HC2 X 2 jkr   .
 r

k


(11c)
The coefficient δ is the measure of similarity of the random utility at the dwelling
level in the jth community. If δ is equal to 0, then the model has the IIA property
(independence of irrelevant alternatives): namely, dwellings within the same community
61
are perceived as uncorrelated in their unobserved attributes, and thus, they are distinct
alternatives. It also implies that the probability relations lead to the conditional logit
model, and households’ choices of housing unit and submarket are simultaneous. If δ is
approximately one, dwellings within the same community are similar in unobserved
attributes, and thus, they are viewed as identical. That is to say, households’ choices
depend only on community characteristics. These interpretations are switched when the
coefficient of the inclusive value, 1- δ, is discussed. The parameters of the nested logit
model can be estimated by maximum likelihood.
62
Chapter 5: Results and Discussion
Estimation results for the nested logit models are presented and discussed in order
in this chapter. If the coefficient of the inclusive value lies between 0 and 1, then the
nested logit model is regarded as the correct model specification. As discussed previously,
if the coefficient of the inclusive value (1-δ) is close to 1, dwellings within the same
community are considered to be distinct alternatives, and the model satisfies the IIA
(independence of irrelevant alternatives) property. As explained in the previous chapter,
in this case households’ choice processes are simultaneous. Only estimation results of the
models in which the coefficients of the inclusive values lie between 0 and 1—mostly
close to 1—are reported in this dissertation.30
In the models, dwelling attributes in the first stage estimation include the total
number of bedrooms (NROOMS), the age of the house (HAGE), the total area of the
house (HSIZE), and whether the house is a single-family detached house (DETACHED).
Household characteristics are utilized as interaction terms with these dwelling attributes.
Community attributes in the second stage estimation consist of local property tax rates
(LPTAXES), school district property tax rates (SDPTAXES), school performance index
(SQUALITY), the median household income (MINCOME), crime rates (CRIME), the
distance to the CBD (DISTCBD), constant-quality house prices (CQPRICE), and whether
30
Table 12 in Appendix C shows the descriptive statistics and whether each modeling satisfies the
conditions for the correct model.
63
the community is a prestigious inner suburb (PRESUBURB). Again, household
characteristics are utilized as interaction terms with these community attributes.31
This dissertation aims to study heterogeneous residential location decisions
among different categories of households, and thus, estimation results are discussed
focusing on the variables’ interactions with household characteristics. Since the
hierarchical nesting strategy posits that a community is first chosen by a household, and
then a dwelling is chosen, estimation results for community variables are discussed first,
and then those of dwelling attributes. After that discussion, each group’s preferences for
locational characteristics are discussed in relation to the social values that are reflected in
locations, and each group’s trade-offs between location and housing quality are described.
1. Estimation Results for Households with School-aged Children
Table 5 reports the estimated coefficients for dwelling and community attributes
of the nested logit model for households with school-aged children.32 The coefficient of
the inclusive value is 0.9204, which is statistically significant at the 0.05 level.
Estimation results for all households—controlled by the presence of school-aged
children— are discussed very briefly before moving on to the discussion about estimation
results for households with school-aged children. School quality (SQUALITY) has a
positive effect on community choices, and the effect is statistically significant, while the
distance to the CBD (DISTCBD) and constant-quality house prices (CQPRICE) affect
31
The full model with all different household characteristics failed to complete optimization
(SAS warning message: QUANEW Optimization cannot be completed).
32
Table 15 in Appendix D shows detailed information on the estimation results.
64
their choices negatively. The estimation results suggest that people prefer good schools,
areas close to the CBD, and communities with lower entry prices, holding the others
constant.
Variables
NROOMS
NROOMS×C
HAGE
HAGE×C
HSIZE
HSIZE×C
DETACHED
DETACHED×C
LPTAXES
LPTAXES×C
SDPTAXES
SDPTAXES×C
SQUALITY
SQUALITY×C
MINCOME
MINCOME×C
CRIME
CRIME×C
DISTCBD
DISTCBD×C
CQPRICE
CQPRICE×C
PRESUBURB
PRESUBURB×C
INC
Estimates
-0.2916***
1.0236***
-0.0084**
0.0154**
0.0379***
-0.0151
0.1765
-0.0021
0.0397
0.4959***
-0.0776
-0.5475***
0.1275***
0.1792**
-0.0188
0.0651**
0.0099
0.0241
-0.0280***
-0.0405**
-4.9836***
-1.6284
-0.4853
1.0762
0.9204**
× indicates interaction terms with household characteristics (C:
Presence of children)
*** Significant at less than 0.01 level
** Significant at less than 0.05 level
* Significant at less than 0.1 level
Table 5. Estimates of the Utility Parameters for Households with School-aged Children
65
In dwelling attributes, house size (HSIZE) has a positive and significant effect on
dwelling choices. However, the number of bedrooms (NROOMS) and the age of the
house (HAGE) have negative and significant effects. That is to say, people are attracted
to bigger and newer houses with fewer bedrooms.
For households with school-aged children, local property tax rates (LPTAXES)
affect community choices positively, and the effect is statistically significant at less than
the 0.01 level.33 School district property tax rates (SDPTAXES) have a negative effect
on community choices with statistical significance at less than the 0.01 level. The school
district property tax rate variable has the expected negative sign, because people are
attracted to locations with lower school district property tax rates, holding the other
variables, including school quality, constant. As expected, school performance index
(SQUALITY) and the median household income (MINCOME) have positive effects on
this group’s community choices, and both of the variables are statistically significant at
less than the 0.05 level. The coefficient of the crime rate variable (CRIME) is positive,
but not significant. The distance to the CBD (DISTCBD) shows a negative sign, which is
significant at less than the 0.05 level. This implies that this group is more attracted to
communities close to the CBD, holding the other characteristics constant. Constantquality house prices (CQPRICE) have a negative effect on community choices, but the
effect is not statistically significant. Lastly, the prestigious inner suburb variable
33
Holding the others constant, the local property tax rate variable is expected to have a negative
sign, but this positive sign may result from omitted variables associated public services. More
than 8 explanatory variables for community attributes in the modeling result in failure to
complete optimization. Since the local property tax rate variable does not explain a preference for
locations associated with a social value, I accept this result as it is.
66
(PRESUBURB) has a positive effect, but the effect is statistically insignificant.
In dwelling attributes, the number of bedrooms (NROOMS) and the age of the
house (HAGE) affect this group’s dwelling choices positively, and the effects are highly
significant at less than the 0.01 level. The results indicate that households with schoolaged children tend to choose older houses with more bedrooms. The coefficients of the
variables, the total area of the house (HSIZE) and whether the house is a single-family
detached house (DETACHED), show negative signs, but both of the variables are
statistically insignificant.
In terms of preferred locations associated with social values, households with
school-aged children tend to choose good school districts and communities with higher
median household incomes. Since education is an important social value particularly to
families with children, public school quality is expected to affect this group’s residential
location decisions significantly, and it does. Also, high-income neighbors mean both an
educationally desirable setting and social status in itself, and thus, households with
school-aged children are attracted to locations with higher median household incomes.
In addition, the results suggest that this group is more likely to choose locations
closer to the CBD. Since central city neighborhoods close to the CBD usually do not have
good public schools, this result may be unexpected. However, holding every other
locational characteristic constant, it does make sense that people are more attracted to
communities close to the CBD. The result affirms the importance of proximity to the
CBD, which is a fundamentally important concept of the monocentric model. Thus,
choosing communities close to the CBD may not be the preference of individual
67
households with children but patterns of their choices holding the other characteristics
constant.
The effect of the prestigious inner suburb variable turns out to be statistically
insignificant, even though the coefficient of the variable is positive. As described
previously, these inner suburbs have exceptionally high-quality school systems, and thus,
they are highly preferred by families with children in the Columbus area. The estimation
result for this variable implies that households’ preference for prestigious inner suburbs
may be explained mostly with the three important aspects above: high school quality,
high-income neighbors, and proximity to the CBD. As can be seen in Table 3 in the
previous chapter, four inner suburban school districts (Bexley, Grandview Heights, Upper
Arlington, and Worthington) show the highest school performance indices, ranging from
101.6 to 105.2, among 12 school districts in this study. These four inner suburbs also
show relatively higher median household incomes. For example, the median household
income of Upper Arlington is $87,965, which is the highest among 12 communities.
Bexley and Worthington display higher median incomes than the average, even though
Grandview Heights’ median household income is lower than the average. Also, these
inner suburbs are very close to downtown Columbus, less than 5 miles from the centroids
of these school districts. The only exception is Worthington. Accordingly, it is not
surprising to see that the coefficient of the prestigious inner suburb variable is not
significant.
In terms of dwelling characteristics, households with school-aged children are
more likely to choose older houses with more bedrooms. Since these households have
68
children, they desire houses with more bedrooms because of the bigger family size.
However, choosing older houses may be interpreted as choosing lower-quality housing:
in general, older houses are more likely to be less expensive. Therefore, the results
suggest that households with school-aged children make a trade-off between location and
housing quality by choosing older houses in order to live in preferred locations such as
good school districts and communities with higher median household incomes. The
overall results support the hypothesized descriptions for this group.
2. Estimation Results for Households with Householders Who Are 50 Years Old and
Over
Table 6 shows the estimated coefficients of the nested logit model for households
with householders who are 50 years old and over. 34 The coefficient of the inclusive value
is 0.7850, which is statistically significant at less than the 0.01 level. In the model,
households with householders who are 50 years old and over is utilized as interaction
terms with community and dwelling attributes.
For all households controlled by the presence of older householders, many
community and dwelling attributes are statistically significant, whereas only a few
variables are significant for households with older householders. Only statistically
significant variables for all households are discussed very briefly, in order to focus on
community and dwelling choices of households with older householders.
34
Table 16 in Appendix D shows detailed information on the estimation results.
69
Variables
Estimates
NROOMS
NROOMS × Over50
HAGE
HAGE × Over50
HSIZE
HSIZE × Over50
DETACHED
DETACHED × Over50
LPTAXES
LPTAXES × Over50
SDPTAXES
SDPTAXES × Over50
SQUALITY
SQUALITY × Over50
MINCOME
MINCOME × Over50
CRIME
CRIME × Over50
DISTCBD
DISTCBD × Over50
CQPRICE
CQPRICE × Over50
PRESUBURB
PRESUBURB × Over50
INC
0.3843***
-1.0760***
-0.0017
-0.0095
0.0286**
0.0145
0.4828***
-0.6045**
0.1632**
0.0295
-0.2289***
-0.0042
0.2024***
-0.0924
0.0104
-0.0102
0.0307**
-0.0442*
-0.0378***
-0.0186
-5.2764***
0.1138
0.0988
-1.3167
0.7850***
× indicates interaction terms with household characteristics
(Over50: Age of the householder, 50 years old and over)
*** Significant at less than 0.01 level
** Significant at less than 0.05 level
* Significant at less than 0.1 level
Table 6. Estimates of the Utility Parameters for Households with Older Householders
The coefficient of local property tax rates (LPTAXES) is positive and statistically
significant, but that of school district property tax rates (SDPTAXES) is negative. School
performance index (SQUALITY) has a positive effect on community choices, and its
effect is statistically significant at less than the 0.01 level. Crime rates (CRIME) show a
70
positive and statistically significant sign. The distance to the CBD (DISTCBD) and
constant-quality house prices (CQPRICE) have negative and significant effects on
community choices. In dwelling attributes, the number of bedrooms (NROOMS), the
square footage of the house (HSIZE), and whether the house is a single-family detached
house (DETACHED) have positive and significant effects on dwelling choices.
For households with older householders, only the crime rate variable (CRIME) is
statistically significant at the 0.10 level. The higher the crime rate of a community is, the
less likely is that this group will choose to live in the community. Its statistical
significance is not high, but the result is critically important, because the coefficient of
the crime rate variable (CRIME) for all households—controlled by the presence of older
householders—is positive and statistically significant. This group must value safe-living
environments most among various locational characteristics.
Local property tax rates (LPTAXES) have a positive effect on this group’s
community choices, but the effect is statistically insignificant. School district property tax
rates (SDPTAXES) affect this group’s location decisions negatively, but again the effect
is not significant. As expected, school performance index (SQUALITY) shows a negative
sign, indicating that school quality is not important to this group. This variable for all
households shows a positive and statistically significant sign at less than the 0.01 level,
indicating that people prefer good school districts. The coefficient of median household
incomes (MINCOME) is negative, and that of the distance to the CBD (DISTCBD) is
negative, but again both of them are statistically insignificant. Constant-quality house
prices (CQPRICE) have a positive effect on their community choices, even though the
71
effect is not significant. The coefficient of this variable for all households is negative and
highly significant, suggesting that, in general, people are attracted to communities with
lower entry prices. The sign for choosing a prestigious inner suburb (PRESUBURB) is
negative. These inner suburbs are well known for high quality schools, but require high
school district property taxes, and these older householders may be less interested in
those. Living in a prestigious inner suburb also requires people to spend more time and
money on maintaining relatively old houses. The results indicate that households with
older householders are reluctant to pay these.
In terms of dwelling attributes, the number of bedrooms (NROOMS) has a
negative effect on dwelling choices, and the effect is highly significant at less than the
0.01 level. The coefficient of the age of the house (HAGE) is negative, but not significant.
The total area of the house (HSIZE) is positive, but without statistical significance. The
variable of whether the house is a single-family detached house (DETACHED) has a
negative effect on dwelling choices, and the effect is highly significant at the 0.05 level.
It is obvious that this older-age group prefers multi-family housing with fewer bedrooms.
These preferences for housing are contrast to those of all households who prefer bigger,
single-family detached houses with more bedrooms.
In their dwelling choices, households with older householders are more likely to
choose houses with fewer bedrooms, implying that their family size has decreased. This
group is also less likely to buy single-family detached houses: in other words, they prefer
to live in multi-family attached housing, including condos, duplexes, and townhouses.
This result suggests that their older age may make multi-family attached houses that
72
require less maintenance more attractive and appropriate. This group may have
experienced—or be experiencing—many kinds of changes in their lives. For example,
their children have left or are leaving their homes, they expect retirement sooner than
younger people, their health may be getting worse, and they may have lost their spouses.
These circumstances should affect this group’s housing choices, thereby choosing multifamily housing with fewer bedrooms.
Their preference for safer communities is distinctive, because this is the only
locational characteristic that shows statistical significance in this modeling. This result
demonstrates that safety is a critically important social value to this older-age group. As
hypothesized, they tend to choose their houses with fewer rooms perhaps due to their
decreased family size and their older age. In conclusion, the community and housing
choices made by households with householders who are 50 years old and over seem to
result from age-specific considerations rather than trade-offs. Although trade-offs
between a preferred location and housing quality are not discovered, it is apparent that
this older-age group has strong preferences for community and housing characteristics
appropriate for their age and family circumstances.
3. Estimation Results for Households with School-aged Children at Different Income
Levels
As hypothesized, different categories of households have different preferences in
their community and dwelling choices. The estimation results for households with
school-aged children reveal that this group makes a trade-off between a preferred location
73
and housing quality by choosing older houses that are relatively inexpensive, in order to
live in good school districts and communities with higher-income neighbors. Besides a
household’s demographic characteristics, a household’s income also influences its
residential location decision. Higher-income households’ flexible spending may make
their community and dwelling choices relatively wide-ranging, whereas lower-income
households are severely restricted in their choices. That is to say, a higher-income
household can purchase an expensive house located in a good neighborhood, but a lowerincome household’s choice is limited to a low-quality house in a poor neighborhood due
to its budget constraint. Middle-income households have less flexibility in their spending
than the higher-income group, but they can choose to live in preferred locations if they
decide to give up some housing quality. Thus, particular interest is given to this middleincome household group, because their budget constraints are expected to stimulate tradeoffs between location and housing quality. Since households with school-aged children
have shown strong locational preferences, it is interesting to discover how different
household incomes influence their community and dwelling choices. In this section,
community and dwelling choices of households with children at different income levels
are explored, focusing on middle-income households with school-aged children.
3.1. Estimation Results for Middle-income Households with School-aged Children
Among the nested logit models of households with children based on different
income levels, only the nested logit model for middle-income households with school-
74
aged children performs well.35 Thus, the estimation results for this group are reported in
Table 7.36 Middle-income households with school-aged children are those who earn
between $60,001 and $140,000, and have school-aged children in the household. The
coefficient of the inclusive value is 0.9850, which is very close to 1 with statistical
significance at less than the 0.05 level. For the comparison with all households with
school-aged children, the estimation results for households with children (from Table 5)
are presented in the last column.
Estimation results for all households—controlled by middle income with
children—are described very briefly only with statistically significant variables. They are
attracted to locations with lower school district property taxes, higher school quality,
closer to the CBD, and lower community-entry prices. In dwelling attributes, they prefer
newer and bigger houses. Discussions move on to middle-income households with
school-aged children comparing with all households with school-aged children.
All the coefficients of community and dwelling attributes for middle-income
households with children keep the same signs as those of the model for households with
school-aged children regardless of income. Also, all statistically significant coefficients
of community and dwelling variables for households with children remain the same in the
model for middle-income households with children as well. These results suggest that
this middle-income group is very similar to households with children in community and
35
The nested logit model for higher-income households with school-aged children fails to obtain
the correct model specification, in that the coefficient of the inclusive value (1-δ) is higher than
1.0. Also, in the model of lower-income households with children, that value lies between 0 and 1,
but it is not statistically significant.
36
Table 17 in Appendix D shows detailed information on the estimation results.
75
housing choices. In brief, they are attracted to good school districts and communities with
higher-income neighbors, and they tend to buy older houses with more bedrooms.
Variables
NROOMS
NROOMS×MC
HAGE
HAGE×MC
HSIZE
HSIZE×MC
DETACHED
DETACHED×MC
LPTAXES
LPTAXES×MC
SDPTAXES
SDPTAXES×MC
SQUALITY
SQUALITY×MC
MINCOME
MINCOME×MC
CRIME
CRIME×MC
DISTCBD
DISTCBD×MC
CQPRICE
CQPRICE×MC
PRESUBURB
PRESUBURB×MC
INC
Estimates of the
model with the
interaction term, MC
-0.1590
1.1589***
-0.0086***
0.0172*
0.0385***
-0.0728**
0.1976
-0.0187
0.0799
0.9814***
-0.1239*
-1.0631***
0.1184***
0.5113***
-0.0073
0.1321**
0.0059
0.1261***
-0.0347***
-0.0745**
-4.7008***
-5.623
-0.2915
1.5033
0.9850**
Estimates of the
model with the
interaction term, C
(from Table 5)
-0.2916***
1.0236***
-0.0084**
0.0154**
0.0379***
-0.0151
0.1765
-0.0021
0.0397
0.4959***
-0.0776
-0.5475***
0.1275***
0.1792**
-0.0188
0.0651**
0.0099
0.0241
-0.0280***
-0.0405**
-4.9836***
-1.6284
-0.4853
1.0762
0.9204**
× indicates interaction terms with household characteristics (MC: Middleincome households with children; C: Presence of children)
*** Significant at less than 0.01 level
** Significant at less than 0.05 level
* Significant at less than 0.1 level
Table 7. Estimates of the Utility Parameters for Middle-income Households with Schoolaged Children (compared to those for all households with school-aged children)
76
There are some differences between these two groups as well. Several variables in
the estimate results for middle-income households with children—for example, crime
rates in the community attributes and the total area of the house size in the dwelling
attributes—are statistically significant. Although these variables keep the same signs,
they are not statistically significant in the model for all households with children. As can
be seen, crime rates (CRIME) are statistically significant at less than the 0.01 level, and
have a positive effect on community choices. The result implies that middle-income
households with children show a tendency to choose communities with higher crime rates,
and this is unexpected and requires additional explanations later on. The total area of the
house (HSIZE) is statistically significant at the 0.05 level, and has a negative effect on
this group’s dwelling choices. This result indicates that middle-income households with
children are more likely to choose smaller houses.
Middle-income households with school-aged children reveal strong preferences
for locations with many statistically significant community attributes, and this preference
is very similar to all households with school-aged children. Preferred locational
characteristics of this group also resemble those of all households with school-aged
children, although the crime variable (CRIME) is statistically significant. Associated with
social values that are reflected in locations, education and high-status neighbors are
critical to this middle-income group with children, showing that they are more likely to
choose locations with good school quality and higher median household incomes.
77
This group’s preferences for good school districts and higher-income neighbors
are stronger than that of households with school-aged children regardless of income. The
variation of the coefficients of school performance index (SQUALITY) between all
households and middle-income households with children (0.1184 versus 0.5113) is
relatively big, compared to that variation between all households and households with
children (0. 1275 versus 0.1792). The variable interacting with middle income with
children (SQUALITY×MC) is statistically significant at the 0.01 level, whereas the
variable interacting with children (SQUALITY×C) is significant at the 0.05 level. The
coefficients of median household income (MINCOME) interacting with these terms also
show the same patterns. The variation of the coefficients between all households and
middle-income households with children (-0.0073 versus 0.1184) is much greater than
that between all households and households with children (-0.0188 versus 0.0651). These
results suggest that this middle-income group with children reveals a stronger tendency to
prefer good school districts and communities with high-income neighbors.
In terms of the positive and significant effect of the crime rates, there are two
possible scenarios associated with this middle-income group’s strong preference for
communities with high school quality and high-income neighbors. First, it may result
from the group’s budget constraint. For example, they cannot live in highly preferred
locations with all good characteristics such as good schools, high-status neighbors, and
safety. Therefore, middle-income households with school-aged children may accept
relatively high crime rates, in order to live in good school districts and communities with
higher median household incomes. Second, this middle-income group’s preference for
78
prestigious inner suburbs may be the explanation, because prestigious inner suburbs have
such characteristics as good schools and high-income neighbors, but relatively high crime
rates.
Table 3 in the previous chapter reveals that inner suburbs (except Upper Arlington)
tend to show relatively high crime rates probably because of their geographic locations.
They are nearby inner city neighborhoods in Columbus, of which the crime rate is the
highest among 12 communities in this study. Bexley and Worthington have high-quality
public schools and their median household incomes are high, and crime rates are
relatively high. Grandview Heights is one of the good school districts, showing the
second-highest school performance index, whereas its median household income is below
average with a higher crime rate. Upper Arlington is exceptional, displaying the highest
school performance index, the highest median household income, and the lowest crime
rate among 12 communities. Although the prestigious inner suburb variable interacting
with middle income with children (PRESUBURB×MC) is not statistically significant,
good schools and high-income neighbors, but higher crimes may indicate these inner
suburbs.
In terms of dwelling characteristics, middle-income households with school-aged
children tend to choose houses with more bedrooms but smaller and older houses. On the
one hand, because of the presence of children in the household, they have more family
members, and thus, they need to buy houses with more bedrooms. On the other hand,
they tend to choose smaller and older houses, which are less expensive in the housing
market. These results suggest that middle-income households with school-aged children
79
give up both the house size and the age of the house as a trade-off in order to live in good
school districts and communities with high-income neighbors. Their budget constraints
are likely to force this group to accept smaller houses and even higher crime rates in their
trade-offs, supporting the hypothesis that less flexibility in their budget may stimulate
their trade-offs.
3.2. Comparison of Estimation Results for Households with School-aged Children at
Different Income Levels
As stated previously, the models of higher-income and lower-income households
with children fail to perform well, thereby failing to explore how households with schoolaged children at different income levels differ in community and housing choices and
trade-offs. As an alternative approach that enables these different income groups to be
compared, the presence of householders who are 50 years old and over is additionally
included in each model as being utilized as interaction terms with community and
dwelling attributes. The models with two different characteristics of interaction terms
provide the correct model specifications, obtaining the correct coefficients of the
inclusive values, between 0 and 1, in all three models.37 The utilization of the presence of
older householders as interaction terms plays the role of producing correct model
specifications. This approach may be complicated in interpretations, but has a benefit that
estimation results for these different-income groups can be compared. Since this
approach aims to explore different community and housing choices among the three
37
Table 13 in Appendix C presents the descriptive statistics and whether each modeling satisfies
the conditions for the correct model.
80
groups, estimation results are discussed focusing on the variables’ interactions with
higher income, middle income, and lower income with children.
Table 8 reports the estimation results of the nested logit models. For all
households, overall estimation results are consistent in these three models. In general,
people are more likely to choose locations with higher local property tax rates, lower
school district property tax rates, higher school quality, higher crimes, closer to the CBD,
and lower community-entry prices: several variables are not statistically significant in the
model with middle income with children as interaction terms. In dwelling attributes,
people prefer bigger single-family detached houses with more bedrooms. In addition,
estimation results for households with older householders are generally consistent in
these three models as well: several variables show different signs in the model with
middle income with children as interaction terms from the other two. This older-age
group does not show any locational preferences, but they have preferences for multifamily attached housing with fewer rooms. The overall estimation results for households
with older householders in these models are almost the same as those of the modeling
that only the presence of older householders is utilized as interaction terms.38
The main purpose of the modeling displayed in Table 8 is to compare the
estimation results of the nested logit models for households with school-aged children
based on different income levels. The first two columns show the results for higher-
38
There are slight differences. For example, crime rates (CRIME) are not statically significant in
these models. The coefficients of constant-quality house prices (CQPRICE) are negative, whereas
this variable is positive in the previous model.
81
Estimates
Estimates
Estimates
82
Variables
(for higher
income)
Variables
(for middle
income)
Variables
NROOMS
NROOMS×HC
NROOMS×Over50
HAGE
HAGE×HC
HAGE×Over 50
HSIZE
HSIZE×HC
HSIZE×Over 50
DETACHED
DETACHED×HC
DETACHED×Over 50
LPTAXES
LPTAXES×HC
LPTAXES×Over 50
SDPTAXES
SDPTAXES×HC
SDPTAXES×Over 50
SQUALITY×HC
SQUALITY×Over 50
0.3440***
0.2158
-1.0866***
-0.0029
-0.0077
-0.0116
0.0177
0.1265***
0.0116
0.4555**
0.7043
-0.4821
0.1422*
0.0889
0.0334
-0.1997*
-0.1434
-0.0314
0.1424
-0.0280
NROOMS
NROOMS×MC
NROOMS×Over 50
HAGE
HAGE×MC
HAGE×Over 50
HSIZE
HSIZE×MC
HSIZE×Over 50
DETACHED
DETACHED×MC
DETACHED×Over 50
LPTAXES
LPTAXES×MC
LPTAXES×Over 50
SDPTAXES
SDPTAXES×MC
SDPTAXES×Over 50
SQUALITY×MC
SQUALITY×Over 50
0.2269*
1.0683***
-0.9826***
-0.0044
0.0158
-0.0105
0.0372***
-0.0809**
0.0072
0.5744***
-0.4697
-0.5677*
0.0221
1.0356***
0.1701
-0.0682
-1.1242***
-0.1663
0.5184***
0.0070
NROOMS
NROOMS×LC
NROOMS×Over 50
HAGE
HAGE×LC
HAGE×Over 50
HSIZE
HSIZE×LC
HSIZE×Over 50
DETACHED
DETACHED×LC
DETACHED×Over 50
LPTAXES
LPTAXES×LC
LPTAXES×Over 50
SDPTAXES
SDPTAXES×LC
SDPTAXES×Over 50
SQUALITY×LC
SQUALITY×Over 50
(for lower
income)
0.3350**
0.7996
-1.1759***
-0.0035
0.0188
-0.0122*
0.0322**
-0.1006**
0.0277
0.6371***
-1.5011**
-0.5837*
0.1469*
-0.0315
0.1071
-0.2202***
0.0009
-0.0929
-0.1359
-0.0480
Continued
Table 8. Estimation Results of the Nested Logit Model of Households with School-aged Children at Different Income Levels
82
Table 8 Continued
Variables
82
MINCOME
MINCOME×HC
MINCOME×Over 50
CRIME
CRIME×HC
CRIME×Over 50
DISTCBD
DISTCBD×HC
DISTCBD×Over 50
CQPRICE
CQPRICE×HC
CQPRICE×Over50
PRESUBURB
PRESUBURB×HC
PRESUBURB×Over 50
INC
Estimates
(for higher
income)
0.0072
-0.0162
-0.0151
0.0318**
0.0165
-0.0294
-0.0338***
-0.034
-0.0205
-5.0327***
4.9962
-1.0003
-0.0518
0.2791
-0.7261
0.9440***
Variables
MINCOME
MINCOME×MC
MINCOME×Over 50
CRIME
CRIME×MC
CRIME×Over 50
DISTCBD
DISTCBD×MC
DISTCBD×Over 50
CQPRICE
CQPRICE×MC
CQPRICE×Over50
PRESUBURB
PRESUBURB×MC
PRESUBURB×Over 50
INC
Estimates
(for middle
income)
-0.0097
0.1467**
0.0087
0.0093
0.1258**
-0.0134
-0.0247**
-0.0865***
-0.0334*
-4.5569***
-6.3017*
-0.3613
-0.1256
1.4647
-1.1706
0.9092***
Variables
MINCOME
MINCOME×LC
MINCOME×Over 50
CRIME
CRIME×LC
CRIME×Over 50
DISTCBD
DISTCBD×LC
DISTCBD×Over 50
CQPRICE
CQPRICE×LC
CQPRICE×Over50
PRESUBURB
PRESUBURB×LC
PRESUBURB×Over 50
INC
Estimates
(for lower
income)
0.0175
0.0288
-0.0109
0.0370***
-0.1174*
-0.0345
-0.0392***
-0.0319
-0.0260
-5.2098***
-9.6119
-0.0800
0.0859
-0.5713
-1.2906
0.5290**
× indicates interaction terms with household characteristics (HC: Higher-income households with children; MC: Middle-income
households with children; LC: Lower-income households with children; Over50: Age of the householder, 50 years old and over)
*** Significant at less than 0.01 level
** Significant at less than 0.05 level
* Significant at less than 0.1 level
83
income households with school-aged children who earn more than $140,001.39 The next
two columns display those for middle-income households with school-aged children who
earn between $60,001 and $140,000.40 The last two columns provide the estimation
results for lower-income households with children who earn $60,000 or less.41
Higher-income households with school-aged children do not show any
preference for locational characteristics, that is, no community attribute is statistically
significant. In terms of the signs of community attributes, local property tax rates
(LPTAXES) are positive, and school district property tax rates (SDPTAXES) are negative.
The school quality variable (SQUALITY) has a positive effect on this group’s
community choices. However, the coefficient of the median household income variable
(MINCOME) is negative, even though the effect is not significant. The crime variable
(CRIME) also shows a positive sign. Distance to the CBD (DISTCBD) is negative.
Constant quality house prices (CQPRICE) have a positive effect on their community
choices, even though the effect is not statistically significant as well. Lastly, the
prestigious inner suburb variable (PRESUBURB) shows a positive coefficient, but
insignificant.
In dwelling attributes, the signs of the variables, the number of bedrooms
(NROOM) and whether the house is a single-family detached house (DETACHED), are
positive. Also, the sign of the age of the house (HAGE) variable is negative. The
variables, however, are not statistically significant. Only the size of the house variable
39
Table 18 in Appendix D shows detailed information on the estimation results.
40
Table 19 in Appendix D shows detailed information on the estimation results.
41
Table 20 in Appendix D shows detailed information on the estimation results.
84
(HSIZE) is statistically significant at less than the 0.01 level with a positive effect on
their dwelling choices, indicating that higher-income households with school-aged
children tend to choose bigger houses.
Based on the results, higher-income households’ flexibility in spending seems to
enable them to purchase bigger houses. As hypothesized, large houses may be a means of
showing their social status. It is interesting that this group does not show any preference
for good school districts, even though there are school-aged children in the household:
the coefficient of school performance index (SQUALITY) is positive, but not statistically
significant. This result may be partly because they may send their children to private
schools rather than considering school quality of the location they live. In addition, the
positive sign of the constant-quality house prices (CQPRICE) for this group (statistically
insignificant though) is notable, because it contrasts to all the other groups. It suggests
that higher-income households with school-aged children may be attracted to
communities with higher entry prices, which mean some amenities—undiscovered in this
modeling—for higher-income people. New Albany with the highest constant-quality
house price in the Columbus area is a newly developed community with expensive homes
targeted at wealthy families. This community is comprised of large single-family
detached houses, whereas its school performance is relatively moderate. Thus, this
community may be one of this group’s preferred locations.
The estimation results for middle-income households with children are almost
the same as those in the previous model presented in Table 7. They reiterate that middleincome households with school-aged children are more likely to choose smaller houses in
85
order to live in good school districts and communities with higher median household
incomes. The constant-quality house price variable (CQPRICE) is statistically significant
at the 0.10 level, suggesting that this middle-income group is more likely to choose
communities with lower entry prices. The age of the house variable (HAGE) is no longer
statistically significant.
As expected, lower-income households with children show quite different
estimation results from the other two groups—higher income and middle income groups.
No community attribute is statistically significant except the crime variable (CRIME).
Local property tax rates (LPTAXES) show a negative sign, but school district property
tax rates (SDPTAXES) are positive. Even school performance index (SQUALITY) is
negative, indicating that community choices made by lower-income households with
school-aged children are not influenced by high school quality. Lower-income
households may not have an opportunity of entering good school districts because of their
budget constraints, even though they have school-aged children. The median household
income variable (MINCOME) shows a positive sign.
The coefficient of crime rates (CRIME) is negative and statistically significant at
the 0.10 level, indicating that lower-income households with children choose safer
communities, perhaps selecting safety over school quality when they cannot afford both.
Distance to the CBD (DISTCBD) is negative. As expected, the constant-quality house
price variable (CQPRICE) and the prestigious inner suburb variable (PRESUBURB) are
negative, showing that lower-income households do not choose (or cannot choose)
communities with higher entry prices or prestigious inner suburbs.
86
In dwelling attributes, the number of bedrooms (NROOM) and the age of the
house (HAGE) have positive effects on this lower-income group’s dwelling choices, but
both of them are not statistically significant. The coefficients of the variables, the total
area of the house (HSIZE) and whether the house is a single-family detached house
(DETACHED), are negative and statistically significant at less than the 0.05 level. That is
to say, lower-income households with school-aged children are more likely to choose
smaller multi-family attached houses, which are relatively inexpensive in the housing
market. Also, this choice may be necessary to live in safer neighborhoods.
It is notable that the signs of the community and dwelling attributes for lowerincome households with children are the opposites of those for higher-income households
except the number of room variable (NROOM), which is positive for the two groups, but
not statistically significant. Overall, these results suggest that this lower-income group
with children is severely constrained in their community and housing choices probably
because of their budget constraints, and thus, they are more likely to live in less preferred
locations. As hypothesized, their choices are limited to less expensive homes, smaller
multi-family attached houses, such as condos, duplexes, or townhouses. The results
reveal that highly preferred communities (e.g., good school districts) may not provide
enough affordable housing for lower-income households.
In conclusion, lower-income households tend to choose houses appropriate for
their limited household incomes rather than trade-offs. Even though they have schoolaged children, they do not have enough budget flexibility to purchase homes in good
school districts. Their preference for locational characteristics is not good schools but
87
safe neighborhoods. If they wanted to live in good school districts for an educational
purpose, they would have to become renters as a trade-off, but the cost of renting in those
places might also be prohibited.
4. Estimation Results for Households with Older householders at Different Income
Levels
All the nested logit models for households with householders who are 50 years
old and over based on different income levels failed to perform well.42 Similar to the
approach used for the comparison of the estimation results for households with schoolaged children at different income levels, the presence of school-aged children is
additionally included as an interaction term in each model as being utilized as interaction
terms with community and dwelling attributes. This approach enables higher-income and
middle-income households with older householders to be compared, providing the correct
model specifications.43 Lower-income households with older householders again failed to
provide a correct model specification: the coefficient of the inclusive value (1-δ) is higher
than 1.0. The utilization of the presence of school-aged children plays only the role of
producing correct model specifications. Therefore, estimation results are discussed
focusing on higher-income and middle-income households with older householders.
42
In the model of middle-income households with older householders, the coefficient of the
inclusive value lies between 0 and 1, but it is not statistically significant. For the other two groups,
the coefficients of the inclusive value (1-δ) are higher than 1.0.
43
Table 14 in Appendix C shows the descriptive statistics and whether each modeling satisfies the
conditions for the correct model.
88
Table 9 reports the estimation results of the nested logit models. For all
households, overall estimation results are consistent in these two models. In general,
people are attracted to good school districts, locations closer to the CBD, and
communities with lower entry prices. In dwelling attributes, people prefer newer and
bigger houses with more bedrooms and single-family detached houses in general: several
variables are not statistically significant. In addition, estimation results for households
with school-aged children are also consistent in these two models. Households with
children are more likely to choose locations with higher local property tax rates, lower
school district property tax rates, higher school quality, and higher median households
incomes. They also prefer older houses with more bedrooms. This group’s preferences in
these models are almost the same as those of the modeling that only the presence of
school-aged children is utilized as interaction terms.44
In Table 9, the first two columns represent the estimation results for higherincome households with older householders.45 The rest two columns display those for
middle-income households with older householders.46 The coefficients of the inclusive
values are 0.7613 and 0.6730, both of which are statistically significant at the 0.05 levels.
Households with older householders as a whole have not shown strong preference for
locations except attraction to safe communities. Thus, it is expected that different income
levels may not affect their locational preferences significantly.
44
There are slight differences in statistical significances.
45
Table 21 in Appendix D shows detailed information on the estimation results.
46
Table 22 in Appendix D shows detailed information on the estimation results.
89
Variables
Estimates (for
Variables
higher income)
NROOMS
NROOMS×C
NROOMS×H50
HAGE
HAGE×C
HAGE×H50
HSIZE
HSIZE×C
HSIZE×H50
DETACHED
DETACHED×C
DETACHED×H50
LDPTAXES
LPTAXES×C
LPTAXES×H50
SDPTAXES
SDPTAXES×C
SDPTAXES×H50
SQUALITY
SQUALITY×C
SQUALITY×H50
MINCOME
MINCOME×C
MINCOME×H50
CRIME
CRIME×C
CRIME×H50
DISTCBD
DISTCBD×C
DISTCBD×H50
-0.2809*
1.1704***
-0.4522
-0.0114***
0.0136*
0.0338**
0.0369***
-0.0317
0.0780*
0.2271
-0.0093
-0.2380
0.0620
0.4246**
0.0051
-0.1055
-0.4597***
-0.1156
0.1478***
0.1408
0.0864
-0.019
0.0561*
0.0461
0.0186
0.0169
-0.0576
-0.0295***
-0.0309
-0.0398
NROOMS
NROOMS×C
NROOMS×M50
HAGE
HAGE×C
HAGE×M50
HSIZE
HSIZE×C
HSIZE×M50
DETACHED
DETACHED×C
DETACHED×M50
LDPTAXES
LPTAXES×C
LPTAXES×M50
SDPTAXES
SDPTAXES×C
SDPTAXES×M50
SQUALITY
SQUALITY×C
SQUALITY×M50
MINCOME
MINCOME×C
MINCOME×M50
CRIME
CRIME×C
CRIME×M50
DISTCBD
DISTCBD×C
DISTCBD×M50
Estimates (for
middle income)
-0.1645
1.0265***
-0.7584**
-0.0071*
0.0125
-0.0163*
0.0303**
-0.0162
0.0364
0.3889**
-0.1362
-0.4391
0.0186
0.4881***
0.2952
-0.0512
-0.5402***
-0.3740
0.1126**
0.1713*
0.1897
-0.0112
0.0584*
-0.0161
0.0128
0.0209
0.0065
-0.0217**
-0.0437
-0.0605**
Continued
Table 9. Estimation Results of the Nested Logit Model for Households with Older
Householders at Different Income Levels
90
Table 9 Continued
Variables
Estimates (for
Variables
higher income)
Estimates (for
middle income)
CQPRICE
-4.9116***
CQPRICE
-4.7055***
CQPRICE×C
-1.1181
CQPRICE×C
-1.1811
CQPRICE×H50
-5.3848
CQPRICE×M50
-1.4491
PRESUBURB
-0.4008
PRESUBURB
-0.5521
PRESUBURB×C
0.9804
PRESUBURB×C
1.0793
PRESUBURB×H50
-0.2665
PRESUBURB×M50
0.3462
INC
0.7613**
INC
0.6730**
× indicates interaction terms with household characteristics (H50: Higher-income households
with householders who are 50 years old and over; M50: Middle-income households with
householders who are 50 years old and over; C: Presence of children)
*** Significant at less than 0.01 level
** Significant at less than 0.05 level
* Significant at less than 0.1 level
As can be seen, only several dwelling attributes are statistically significant,
implying that dwelling attributes are the main influences on these groups’ residential
location choices. This is consistent with the estimation results for all households with
older householders; recall that they preferred multi-family housing with fewer bedrooms,
probably because of age-specific considerations and family circumstances.
For higher-income households with older householders, none of the community
attributes is not statistically significant, implying that they do not have strong preference
for location. Each sign of the coefficients of community attributes shows that they are, if
any, attracted to preferred locations such as good schools, communities with higher
median household incomes, and safe communities: however, these variables are all
statistically insignificant. The households are discouraged in choosing communities with
higher entry prices and prestigious inner suburbs. These results do not support the
91
hypothesis that this higher-income group with older householders would consider local
history important, and thus, they would prefer well-maintained older suburbs.
In dwelling attributes, the coefficient of the number of room variable (NROOM)
is negative, but not significant. The coefficients of the variables, the age of the house
(HAGE) and the total area of the house (HSIZE,) are positive and significant at the 0.05
and 0.10 levels, respectively. The results indicate that higher-income households with
older householders are more likely to choose older houses, and they prefer bigger houses,
holding the other characteristics constant. The variable, whether the house is a singlefamily detached house (DETACHED), is negative, but not significant.
Their housing choices seem to result from their age-specific considerations, but
their preference for older houses cannot be explained clearly. Even though community
attributes are not statistically, the signs of these variables suggest that preferred locational
characteristics have positive effects on this group’s community choices, and it is believed
that their flexibility in spending because of their higher income enables them to buy
houses in good locations.
Middle-income households with older householders do not have strong
preferences for locations, and the effects of some community attributes resemble those of
higher-income households: for example, local property tax rates, school district property
tax rates, school performance index, and constant-quality house prices. However, the
median household income variable (MINCOME) is negative for this group, and the crime
rate variable (CRIME) is positive. The differences in these two attributes suggest that this
middle-income group may accept communities with lower median household incomes
92
and higher crime rates, though these are not statistically significant. Those choices are
different from higher-income households’ decisions, suggesting that their relatively
limited income between $60,001 and $140,000 may have caused that difference. The sign
of the prestigious inner suburb variable (PRESUBURB) is positive, implying that they
would choose prestigious inner suburbs, holding the other characteristics constant.
It is interesting that the distance to the CBD (DISTCBD) is statistically
significant at less than the 0.05 level, with a negative effect on community choices. This
result implies that they are more likely to choose locations closer to the CBD, holding the
other characteristics constant. The reason that this group prefers communities closer to
the CBD cannot be explained in this study, but there are some studies that older people
are more attracted to the availability of public transportation, or at least the convenience
of being near downtown.
In dwelling attributes, this group is more likely to choose houses with fewer
bedrooms and newer houses with statistical significances at less than the 0.05 and 0.10
levels, respectively. The coefficient of the total area of the house (HSIZE) is positive, but
not significant. Also, the coefficient of the variable whether the house is a single-family
detached house (DETACHED) is negative, but again statistically insignificant. The
results show that newer houses are important to middle-income households with older
householders. It is predictable for households with older householders to buy houses with
fewer bedrooms due to the decreased family size. Their preference for newer houses also
should be related to their older age, because they may be interested in easy maintenance,
as Morrow-Jones and Kim (2009) suggest.
93
In conclusion, households with older householders—either higher-income
households or middle-income households—tend to make housing choices based on agespecific considerations and family circumstances. Trade-offs between location and
housing quality are not revealed clearly in their residential location decisions. However,
signs of community attributes—statistically insignificant though—uncover that middleincome households may accept communities with relatively low-income neighbors and
high crime rates probably due to their constrained budget.
5. Summary of the Estimation Results
Different categories of households make different residential location decisions
and trade-offs between location and housing quality. Estimation results support the
importance of heterogeneity in residential location models, and provide evidence that
there are trade-offs between a preferred location and housing quality in households’
decisions. First, the presence of school-aged children influences the household’s
community and housing choices significantly. It is obvious that households with schoolaged children are attracted to good school districts and neighborhoods with high-status
neighbors. In order to live in these preferred locations, they choose older houses—
relatively inexpensive homes in the housing market—as a trade-off. Middle-income
households with school-aged children are particularly likely to downsize their houses
while choosing to live in good school districts and locations with higher median
household incomes. The results affirm that education is regarded as a critical social value
to households with children.
94
Secondly, households with older householders are more likely to choose safe
communities, and they prefer houses with fewer rooms and multi-family attached houses
(e.g. condos, duplexes, and townhouses). It is evident that safety is an important social
value to this group. Their preference for safe communities is not displayed in the
modeling for higher-income and middle-income households with older householders.
This may imply that safe-living environments are desired largely by lower-income
households with older householders, who may make up many retired people and the
elderly whose income is low, but home equity is relatively high. Even though this olderage group does not show strong preference for locational characteristics, the middleincome group with older householders has a tendency to choose communities with lower
median household incomes and higher crimes rates, and this tendency seems to be
associated with their limited income (budget constraints).
Housing choices made by households with older householders seem to result from
their age-specific considerations rather than trade-offs, and thus, their choices tend to
focus on housing characteristics appropriate for their relatively old age and the decreased
family size: that is, multi-family housing with fewer bedrooms. Depending on their
income levels, they show slightly different preferences for their housing as well.
95
Chapter 6: Conclusion and Policy Implications
Despite the significant contribution of the monocentric bid-rent model to the
development of urban spatial models, the model has shown several limitations. Among
the limitations, the monocentric model tends to oversimplify households’ residential
location decisions, and its trade-off assumption between commuting cost and land rent
does not explain actual individual households’ residential location decisions. Many recent
studies have provided various determinants of residential location decisions such as
school quality, local amenities, and various housing characteristics. Also, some
researchers have questioned whether commuting plays the central role in residential
location decisions, and if households determine their residential locations based on the
trade-off between commuting cost and land rent.
In a socio-economic approach, Phe and Wakely (2000) propose that households’
decisions are based on the trade-off between housing status and housing quality,
emphasizing social desirability that a household wants to achieve through its residence.
This social desirability is established by social values of the society, such as wealth,
ideology, religion, etc. Social status that households want to achieve through their
housing is an important aspect that should be considered in residential location models,
along with heterogeneity of households’ residential location decisions.
This dissertation is a socio-economic approach to the residential location model. I
96
have explored heterogeneity of households’ residential location decisions and trade-offs
that households make in their decisions in the actual housing market. Specifically, I have
explored heterogeneous residential location decisions among different categories of
households, and trade-offs between location and housing quality. I assume that social
values are reflected in locations and, in turn, highly valued locations become preferred
locations, and that living in preferred locations means that the household has higher
social status. Households make a trade-off in order to live in preferred locations, and in
this trade-off, households give up some housing quality. Phe and Wakely’s trade-off idea
is generalized to trade-offs between a preferred location and housing quality.
I used a repeat homebuyers’ dataset in Franklin County, which is the central
county in the greater Columbus, Ohio metropolitan area. The dataset provides physical
characteristics of the houses that each household sold and bought, addresses of the houses
that inform locations of the houses, and households’ demographics. I utilized the twostage nested logit model with interactions terms for different household characteristics,
and many models provided heterogeneous residential location decisions among different
categories of households. Since various community and dwelling attributes are included
in the nested logit model, trade-offs made by households in community and dwelling
choices could be explored.
The estimation results have provided a range of information about households’
residential location decisions in the actual housing market, supporting the initial
hypothesis that different categories of households will make different residential location
decisions and also different trade-offs between location and housing quality. First,
97
households with school-aged children was hypothesized that education and socioeconomic surroundings would be important to this group, that these households would
prefer good school districts and communities with higher median household incomes
because of these social values, and that they might choose relatively lower-quality houses
as a trade-off in order to live in these preferred locations. As expected, they are attracted
to locations with high school quality and high median household incomes, while
choosing older houses (with more bedrooms). In other words, they make a trade-off
between a preferred location and housing quality by choosing older houses—less
expensive homes in the housing market—in order to live in good school districts and
communities with high-income neighbors. These results confirm that education and highincome neighbors are important social values to households with school-aged children. In
terms of high-income neighbors, they have meanings such as an educationally desirable
setting and social status in itself. Therefore, households with school-aged children may
maximize their utility by living in good school districts and communities with high-status
neighbors, while giving up housing quality (the age of the house) as a trade-off.
Second, different household incomes are related to the flexibility in spending, and
thus, they affect community and housing choices. It was hypothesized that middleincome households would make a notable trade-off, whereas lower-income households
are severely restricted in housing choices. If middle-income households choose to live in
preferred locations expecting locational benefits, they have to give up some housing
quality because of their budget constraints: thus, special attention was given to this group.
It is not surprising that middle-income households with school-aged children prefer good
98
school districts and communities with higher median household incomes, and they
choose older and smaller houses as a trade-off. As expected, their relatively limited
incomes seem to stimulate the trade-off between a preferred location and housing quality.
They even accept higher crime rates in their community choices.
Third, households with householders who are 50 years old and over were
hypothesized that age-specific circumstances would affect their housing choices by and
large. Households with older householders are attracted to communities with lower crime
rates, which is their only locational preference. This result indicates that safety is an
important social value to this group, and that this older-age group prefers safer
communities. In their dwelling choices, this group is more likely to choose multi-family
attached houses (e.g., condos, duplexes, and townhouses) with fewer bedrooms. It is
unlikely that these households trade-off large single-family detached houses in order to
live in safer neighborhoods. Instead, as hypothesized, this group’s age-specific
circumstances seem to affect their housing choices significantly. That is to say, the
decreased number of family numbers and their older age encourage these households to
choose multi-family type houses with fewer bedrooms, which require less maintenance
and are appropriate for their smaller family size. In addition, middle-income households
with older householders are more likely to choose newer houses with fewer bedrooms.
Again, these newer houses should save their energy and money that are needed for
maintenance, perhaps freeing them for other activities. Overall, households with older
householders (including those at different income levels) do not have strong preference
for locations, and thus, a trade-off between location and housing quality is not obvious.
99
Their housing choices tend to be hugely influenced by their older age and smaller family
size.
This study provides substantial findings about individual households’ community
and housing choices and trade-offs between location and housing quality made in the
actual housing market. There are, however, several limitations in this empirical study.
First, the sample size for the analysis is relatively small. The total number of households
used for this study is 487, which is again the number of houses they finally chose. Each
household has 5 more alternatives for its housing choice, and thus, the total number of
observations is 2,922. In the process that categorizes these households into different
groups with different characteristics and incomes, the number of households for each
group becomes smaller, and this small number may lessen the sensitivity of the tests. In
addition, the modeling used for this study allows only for 8 different community
attributes for satisfied model specifications. This may result from this small sample size
as well. The second limitation is that the dwelling units used for the analysis are not
completely controlled by house prices. In order to relieve this issue, average constantquality house prices at the school district level are used in the modeling; however, this
approach may not correct this issue completely.
Despite its several limitations, this study provides many contributions. In this
study, I conceptualized preferred locations by assuming that social values are reflected in
locations, and that locations such as good school districts are often preferred by
homebuyers because of this perception. Living in these preferred locations may mark
higher social status. This operationalization of the concept of social status with the status
100
of locations as preferred locations is one contribution of this work. The second
contribution is that this study broadens the perspective of the residential location
modeling by providing a variety of determinants associated with community and
dwelling characteristics. Based on these determinants, this study has discovered
heterogeneity in household characteristics makes different residential location decisions
and different trade-offs between a preferred location and housing quality. Thus, this study
provides us with an example of the importance of the socio-economic approach to the
residential location model.
The utilization of the random utility theory—particularly the nested logit
modeling—makes the third contribution. Even though the conditional logit model has
been utilized in many housing choice studies, the nested logit model provides a few
empirical studies in literature probably because of its difficulty and complexity in
applications. The theoretical framework provides excellence including the capability of
testing the IIA property, but this method requires a great amount of work in manipulating
data for the empirical studies, such as random sampling. Therefore, the empirical study of
heterogeneous residential location decisions and the analysis of actual trade-offs between
location and housing quality provide a great contribution.
Lastly, the results may help local policymakers better understand and respond to
the desires of home buyers, providing direct policy implications. Communities may know
how to capitalize on their strengths for repeat homebuyers: for example, this study
reiterates the importance of school quality. Also, as the U.S. population is aging, demand
for multi-family housing will increase in the future housing market. These policy
101
implications provide the fourth contribution of this study. I believe that this study will
help extend the understanding of actual determinant of residential location decisions in
the U.S. housing market, and improve the urban residential location theory.
102
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Appendix A: Constant Quality House Price Indices
Figure 4. Constant-Quality House Price Index by Zip Code and Local School District
Boundaries
110
Constant-quality
House Price Indices
43054
0.50563
43221
0.48252
43212
0.46084
43214
0.44420
43215
0.43607
43202
0.38232
43016
0.28612
43220
0.28507
43085
0.24636
43017
0.23150
43209
0.21267
43235
0.18914
43081
0.16755
43230
0.14953
43110
0.11675
43119
0.08906
43026
0.07893
43231
0.07579
43123
0.05988
43068
0.02431
43229
0.01773
43206
-0.01642
43228
-0.03101
43125
-0.05182
43213
-0.07517
43224
-0.09212
43227
-0.11837
43204
-0.14332
43232
-0.14552
43207
-0.28804
43219
-0.29936
43223
-0.32083
43211
-0.39465
43205
-0.56078
43203
-0.71628
43222
-0.78727
Table 10. Constant-Quality House Price Index by Zip Code47
Note: The reference zip code is 43201, of which the house price index is therefore 0.
Zip Codes
47
The constant-quality house price indices at the zip-code level were provided by Professor
Donald Haurin and Hazel A. Morrow-Jones, who are in the Department of Economics and
Finance and in the Department of City and Regional Planning respectively at The Ohio State
University.
111
Appendix B: Descriptive Statistics of Data Sets
School District
(Community)
Columbus
Bexley
Grandview Heights
Upper Arlington
Worthington
Dublin
Gahanna-Jefferson
Groveport Madison
Hilliard
New Albany-Plain
Southwestern
Westerville
Total
Repeat Homebuyers'
Matched Dataset
Number of
Percentage
Dwellings
(%)
(A)
1619
31.77
134
2.63
46
0.90
342
6.71
383
7.52
434
8.52
287
5.63
124
2.43
661
12.97
125
2.45
603
11.83
338
6.63
5096
100.00
Survey Dataset
Number of Percentage
Cases (B)
(%)
124
7
8
55
29
41
32
9
89
13
49
31
487
25.46
1.44
1.64
11.29
5.95
8.42
6.57
1.85
18.28
2.67
10.06
6.37
100.00
B/A
(%)
7.66
5.22
17.39
16.08
7.57
9.45
11.15
7.26
13.46
10.40
8.13
9.17
9.56
Table 11. Statistics of the Repeat Homebuyers’ Matched Dataset and the Survey Dataset
by School District
112
Appendix C: Descriptive Statistics of the Models and Correct Model Specifications
Household Characteristics
Yes
No
Total
Model Specification
Number
of Cases (Table Reported)
School-aged children
138
340
478 Satisfied (Table 5)
Older householders
187
287
474 Satisfied (Table 6)
School-aged children
High-income
38
419
457 IV > 1.0
Middle-income
69
388
457 Satisfied (Table 7)
Low-income
25
432
457 IV: statistically insignificant
Older householders
High-income
25
429
454 IV > 1.0
Middle-income
82
372
454 IV: statistically insignificant
Low-income
67
387
454 IV > 1.0
Table 12. Descriptive Statistics of the Models and Model Specifications
Note: IV represents the coefficient of the inclusive value.
113
Household
Characteristics
Yes
Number of Cases
Older
OverHouselapped**
holders*
The
Rest
Model
Specification
Total (Table
Reported)
High-income with
38
(11)
253
475
children
Middle-income with
Satisfied
68
173
(7)
219
475
children
(Table 8)
Low-income with
25
(3)
258
475
children
Table 13. Descriptive Statistics of the Models with Two Kinds of Interaction Terms for
the Comparison of Households with Children at Different Income Levels
Note: * represents the number of households with older householders regardless of
income used in each model.
** represents the number of households with both demographics, school-aged children at
the different income level and older householders.
Household
Characteristics
Number of Cases
SchoolOverYes
aged
lapped**
Children*
The
Test
Model
Specification
Total (Table
Reported)
High-income with
25
(11)
308 475
older householders
Satisfied
(Table 9)
Middle-income with
82
131
(7)
247 475
older householders
Low-income with
66
(3)
259 475 IV > 1.0
older householders
Table 14. Descriptive Statistics of the Models with Two Kinds of Interaction Terms for
the Comparison of Households with Older Householders at Different Income Levels
Note: * represents the number of households with school-aged children regardless of
income in each model.
** represents the number of households with both demographics, older householders at
the different income level and school-aged children.
114
Appendix D: Detailed Information of the Nested Logit Models
115
Variables
NROOMS
NROOMS×C
HAGE
HAGE×C
HSIZE
HSIZE×C
DETACHED
DETACHED×C
LPTAXES
LPTAXES×C
SDPTAXES
SDPTAXES×C
SQUALITY
SQUALITY×C
MINCOME
MINCOME×C
CRIME
CRIME×C
DISTCBD
DISTCBD×C
CQPRICE
CQPRICE×C
PRESUBURB
PRESUBURB×C
INC
Estimate
-0.2916
1.0236
-0.0084
0.0154
0.0379
-0.0151
0.1765
-0.0021
0.0397
0.4959
-0.0776
-0.5475
0.1275
0.1792
-0.0188
0.0651
0.0099
0.0241
-0.0280
-0.0405
-4.9836
-1.6284
-0.4853
1.0762
0.9204
Standard
Error
0.1094
0.2419
0.0034
0.0074
0.0117
0.0219
0.1541
0.3032
0.0769
0.1647
0.0780
0.1734
0.0431
0.0875
0.0172
0.0315
0.0124
0.0243
0.0090
0.0187
1.3086
2.3191
0.4787
0.8002
0.3797
t Value
Pr > |t|
-2.67
4.23
-2.50
2.09
3.23
-0.69
1.15
-0.01
0.52
3.01
-0.99
-3.16
2.96
2.05
-1.10
2.07
0.80
0.99
-3.11
-2.16
-3.81
-0.70
-1.01
1.35
2.42
0.0077
<.0001
0.0123
0.0365
0.0012
0.4918
0.2518
0.9946
0.606
0.0026
0.3198
0.0016
0.0031
0.0407
0.2734
0.0385
0.4226
0.3218
0.0019
0.0309
0.0001
0.4826
0.3107
0.1786
0.0154
Notes: Number of observations =478, Number of cases = 2868; Log likelihood = -752.51040;
Number of iterations = 15, Optimization method = Newton-Raphson; Goodness of fit
(McFadden's likelihood ratio index) = 1- LogL /LogL0 = 0.5607.
Table 15. Estimates of Utility Parameters for Households with School-aged Children
Note: × indicates interaction terms with household characteristics (C: Presence of children)
116
Variables
NROOMS
NROOMS × Over50
HAGE
HAGE × Over50
HSIZE
HSIZE × Over50
DETACHED
DETACHED × Over50
LPTAXES
LPTAXES × Over50
SDPTAXES
SDPTAXES × Over50
SQUALITY
SQUALITY × Over50
MINCOME
MINCOME × Over50
CRIME
CRIME × Over50
DISTCBD
DISTCBD × Over50
CQPRICE
CQPRICE × Over50
PRESUBURB
PRESUBURB × Over50
INC
Estimate
0.3843
-1.0760
-0.0017
-0.0095
0.0286
0.0145
0.4828
-0.6045
0.1632
0.0295
-0.2289
-0.0042
0.2024
-0.0924
0.0104
-0.0102
0.0307
-0.0442
-0.0378
-0.0186
-5.2764
0.1138
0.0988
-1.3167
0.7850
Standard
Error
0.1234
0.2086
0.0039
0.0065
0.0125
0.0203
0.1816
0.2825
0.0781
0.1494
0.0795
0.1557
0.0445
0.0797
0.0170
0.0311
0.0124
0.0232
0.0093
0.0177
1.2769
2.3210
0.4421
0.9296
0.2759
t Value
Pr > |t|
3.11
-5.16
-0.43
-1.47
2.29
0.72
2.66
-2.14
2.09
0.20
-2.88
-0.03
4.54
-1.16
0.62
-0.33
2.47
-1.91
-4.09
-1.05
-4.13
0.05
0.22
-1.42
2.85
0.0018
<.0001
0.6679
0.1410
0.0220
0.4744
0.0078
0.0324
0.0367
0.8434
0.0040
0.9784
<.0001
0.2463
0.5384
0.7429
0.0135
0.0562
<.0001
0.2921
<.0001
0.9609
0.8232
0.1567
0.0044
Notes: Number of observations =474; Number of cases = 2844; Log likelihood = -737.39711;
Number of iterations = 16, Optimization method = Newton-Raphson; Goodness of fit
(McFadden's likelihood ratio index) = 1- LogL /LogL0 = 0.5659.
Table 16. Estimates of Utility Parameters for Households with Older Householders
Note: × indicates interaction terms with household characteristics (Over50: Age of the
householder, 50 years old and over)
117
Variables
NROOMS
NROOMS×MC
HAGE
HAGE×MC
HSIZE
HSIZE×MC
DETACHED
DETACHED×MC
LPTAXES
LPTAXES×MC
SDPTAXES
SDPTAXES×MC
SQUALITY
SQUALITY×MC
MINCOME
MINCOME×MC
CRIME
CRIME×MC
DISTCBD
DISTCBD×MC
CQPRICE
CQPRICE×MC
PRESUBURB
PRESUBURB×MC
INC
Estimate
-0.1590
1.1589
-0.0086
0.0172
0.0385
-0.0728
0.1976
-0.0187
0.0799
0.9814
-0.1239
-1.0631
0.1184
0.5113
-0.0073
0.1321
0.0059
0.1261
-0.0347
-0.0745
-4.7008
-5.6230
-0.2915
1.5033
0.9850
Standard
Error
0.1010
0.3321
0.0032
0.0105
0.0105
0.0337
0.1478
0.4141
0.0718
0.2983
0.0731
0.3164
0.0392
0.1628
0.0152
0.0543
0.0114
0.0486
0.0082
0.0331
1.1800
3.5420
0.4207
1.2227
0.4408
t Value
Pr > |t|
-1.57
3.49
-2.66
1.65
3.66
-2.16
1.34
-0.05
1.11
3.29
-1.70
-3.36
3.02
3.14
-0.48
2.43
0.51
2.60
-4.21
-2.25
-3.98
-1.59
-0.69
1.23
2.23
0.1155
0.0005
0.0078
0.0995
0.0003
0.0307
0.1813
0.9640
0.2657
0.0010
0.0898
0.0008
0.0025
0.0017
0.6316
0.0150
0.6077
0.0094
<.0001
0.0243
<.0001
0.1124
0.4884
0.2189
0.0254
Notes: Number of observations =457, Number of cases = 2742; Log likelihood = -724.09388;
Number of iterations = 16, Optimization method = Newton-Raphson; Goodness of fit
(McFadden's likelihood ratio index) = 1- LogL /LogL0 = 0.5607.
Table 17. Estimates of Utility Parameters for Middle-income Households with Schoolaged Children
Note: × indicates interaction terms with household characteristics (MC: Middle-income
households with school-aged children)
118
Variables
NROOMS
NROOMS×HC
NROOMS×Over50
HAGE
HAGE×HC
HAGE×Over 50
HSIZE
HSIZE×HC
HSIZE×Over 50
DETACHED
DETACHED×HC
DETACHED×Over 50
LPTAXES
LPTAXES×HC
LPTAXES×Over 50
SDPTAXES
SDPTAXES×HC
SDPTAXES×Over 50
SQUALITY
SQUALITY×HC
SQUALITY×Over 50
MINCOME
MINCOME×HC
MINCOME×Over 50
CRIME
CRIME×HC
CRIME×Over 50
DISTCBD
DISTCBD×HC
DISTCBD×Over 50
Standard
Error
0.1263
0.4467
0.2154
0.0040
0.0188
0.0067
0.0127
0.0404
0.0204
0.1879
0.6192
0.2936
0.0819
0.4449
0.1636
0.0825
0.4847
0.1702
0.0473
0.3266
0.0877
0.0181
0.0995
0.0337
0.0132
0.0819
0.0254
0.0098
0.0553
0.0194
Estimate
0.3440
0.2158
-1.0866
-0.0029
-0.0077
-0.0116
0.0177
0.1265
0.0116
0.4555
0.7043
-0.4821
0.1422
0.0889
0.0334
-0.1997
-0.1434
-0.0314
0.1870
0.1424
-0.0280
0.0072
-0.0162
-0.0151
0.0318
0.0165
-0.0294
-0.0338
-0.0340
-0.0205
t Value
2.72
0.48
-5.05
-0.74
-0.41
-1.73
1.39
3.13
0.57
2.42
1.14
-1.64
1.74
0.20
0.20
-2.42
-0.30
-0.18
3.95
0.44
-0.32
0.40
-0.16
-0.45
2.41
0.20
-1.16
-3.44
-0.61
-1.06
Pr > |t|
0.0065
0.6290
<.0001
0.4622
0.6815
0.0828
0.1631
0.0017
0.5681
0.0153
0.2553
0.1006
0.0824
0.8417
0.8383
0.0155
0.7674
0.8536
<.0001
0.6629
0.7496
0.6917
0.8708
0.6546
0.0159
0.8403
0.2472
0.0006
0.5388
0.2904
Continued
Table 18. Estimates of Utility Parameters for Higher-income Households with Schoolaged Children
Note: × indicates interaction terms with household characteristics (HC: Higher-income
households with children; Over50: Age of the householder, 50 years old and over)
119
Table 18 Continued
Variables
CQPRICE
CQPRICE×HC
CQPRICE×Over50
PRESUBURB
PRESUBURB×HC
PRESUBURB×Over 50
INC
Standard
Error
1.3490
6.7647
2.5970
0.4866
1.9299
0.9681
0.2848
Estimate
-5.0327
4.9962
-1.0003
-0.0518
0.2791
-0.7261
0.9440
t Value
Pr > |t|
-3.73
0.74
-0.39
-0.11
0.14
-0.75
3.31
0.0002
0.4602
0.7001
0.9152
0.8850
0.4532
0.0009
Notes: Number of observations =453, Number of cases = 2718; Log likelyhood = -684.28442;
Number of iterations = 17, Optimization method = Newton-Raphson; Goodness of fit
(McFadden's likelihood ratio index) = 1- LogL /LogL0 = 0.5785.
120
Variables
NROOMS
NROOMS×MC
NROOMS×Over 50
HAGE
HAGE×MC
HAGE×Over 50
HSIZE
HSIZE×MC
HSIZE×Over 50
DETACHED
DETACHED×MC
DETACHED×Over 50
LPTAXES
LPTAXES×MC
LPTAXES×Over 50
SDPTAXES
SDPTAXES×MC
SDPTAXES×Over 50
SQUALITY
SQUALITY×MC
SQUALITY×Over 50
MINCOME
MINCOME×MC
MINCOME×Over 50
CRIME
CRIME×MC
CRIME×Over 50
DISTCBD
DISTCBD×MC
DISTCBD×Over 50
Standard
Error
0.1295
0.3632
0.2152
0.0042
0.0110
0.0068
0.0136
0.0358
0.0207
0.2027
0.4381
0.2994
0.0864
0.3009
0.1649
0.0882
0.3193
0.1703
0.0489
0.1647
0.0874
0.0192
0.0570
0.0337
0.0139
0.0507
0.0259
0.0103
0.0333
0.0190
Estimate
0.2269
1.0683
-0.9826
-0.0044
0.0158
-0.0105
0.0372
-0.0809
0.0072
0.5744
-0.4697
-0.5677
0.0221
1.0356
0.1701
-0.0682
-1.1242
-0.1663
0.1197
0.5184
0.0070
-0.0097
0.1467
0.0087
0.0093
0.1258
-0.0134
-0.0247
-0.0865
-0.0334
t Value
1.75
2.94
-4.57
-1.05
1.44
-1.54
2.74
-2.26
0.35
2.83
-1.07
-1.90
0.26
3.44
1.03
-0.77
-3.52
-0.98
2.45
3.15
0.08
-0.50
2.57
0.26
0.67
2.48
-0.52
-2.40
-2.60
-1.75
Pr > |t|
0.0797
0.0033
<.0001
0.2959
0.1504
0.1224
0.0062
0.0237
0.7289
0.0046
0.2836
0.0580
0.7985
0.0006
0.3023
0.4394
0.0004
0.3288
0.0144
0.0017
0.9360
0.6158
0.0101
0.7965
0.5053
0.0132
0.6045
0.0165
0.0094
0.0798
Continued
Table 19. Estimates of Utility Parameters for Middle-income Households with Schoolaged Children
Note: × indicates interaction terms with household characteristics (MC: Middle-income
households with children; Over50: Age of the householder, 50 years old and over)
121
Table 19 Continued
Variables
CQPRICE
CQPRICE×MC
CQPRICE×Over50
PRESUBURB
PRESUBURB×MC
PRESUBURB×Over 50
INC
Standard
Error
1.5156
3.7026
2.5183
0.5217
1.2499
0.9911
0.2921
Estimate
-4.5569
-6.3017
-0.3613
-0.1256
1.4647
-1.1706
0.9092
t Value
Pr > |t|
-3.01
-1.70
-0.14
-0.24
1.17
-1.18
3.11
0.0026
0.0888
0.8859
0.8097
0.2413
0.2376
0.0019
Notes: Number of observations =453, Number of cases = 2718; Log likelyhood = -679.86448;
Number of iterations = 17, Optimization method = Newton-Raphson; Goodness of fit
(McFadden's likelihood ratio index) = 1- LogL /LogL0 = 0.5812.
122
Variables
NROOMS
NROOMS×LC
NROOMS×Over 50
HAGE
HAGE×LC
HAGE×Over 50
HSIZE
HSIZE×LC
HSIZE×Over 50
DETACHED
DETACHED×LC
DETACHED×Over 50
LPTAXES
LPTAXES×LC
LPTAXES×Over 50
SDPTAXES
SDPTAXES×LC
SDPTAXES×Over 50
SQUALITY
SQUALITY×LC
SQUALITY×Over 50
MINCOME
MINCOME×LC
MINCOME×Over 50
CRIME
CRIME×LC
CRIME×Over 50
DISTCBD
DISTCBD×LC
DISTCBD×Over 50
Estimate
0.3350
0.7996
-1.1759
-0.0035
0.0188
-0.0122
0.0322
-0.1006
0.0277
0.6371
-1.5011
-0.5837
0.1469
-0.0315
0.1071
-0.2202
0.0009
-0.0929
0.2134
-0.1359
-0.0480
0.0175
0.0288
-0.0109
0.0370
-0.1174
-0.0345
-0.0392
-0.0319
-0.0260
Standard
Error
0.1329
0.4909
0.2270
0.0044
0.0147
0.0071
0.0139
0.0450
0.0229
0.1966
0.6958
0.3036
0.0823
0.4225
0.1599
0.0837
0.4751
0.1658
0.0491
0.2132
0.0870
0.0176
0.1035
0.0319
0.0134
0.0669
0.0250
0.0099
0.0554
0.0188
t Value
Pr > |t|
2.52
1.63
-5.18
-0.79
1.28
-1.72
2.32
-2.24
1.21
3.24
-2.16
-1.92
1.78
-0.07
0.67
-2.63
0.00
-0.56
4.35
-0.64
-0.55
0.99
0.28
-0.34
2.76
-1.75
-1.38
-3.96
-0.58
-1.38
0.0117
0.1034
<.0001
0.4282
0.2013
0.0861
0.0204
0.0252
0.2248
0.0012
0.0310
0.0546
0.0744
0.9405
0.5030
0.0085
0.9985
0.5754
<.0001
0.5238
0.5809
0.3203
0.7808
0.7318
0.0057
0.0793
0.1666
<.0001
0.5653
0.1663
Continued
Table 20. Estimates of Utility Parameters for Lower-income Households with Schoolaged Children
Note: × indicates interaction terms with household characteristics (LC: Lower-income households
with children; Over50: Age of the householder, 50 years old and over)
123
Table 20 Continued
Variables
CQPRICE
CQPRICE×LC
CQPRICE×Over50
PRESUBURB
PRESUBURB×LC
PRESUBURB×Over 50
INC
Estimate
-5.2098
-9.6119
-0.0800
0.0859
-0.5713
-1.2906
0.5290
Standard
Error
1.3316
10.0638
2.3936
0.4583
2.5321
0.9462
0.2604
t Value
Pr > |t|
-3.91
-0.96
-0.03
0.19
-0.23
-1.36
2.03
<.0001
0.3395
0.9733
0.8512
0.8215
0.1726
0.0422
Notes: Number of observations =453, Number of cases = 2718; Log likelyhood = -694.88889;
Number of iterations = 19, Optimization method = Newton-Raphson; Goodness of fit
(McFadden's likelihood ratio index) = 1- LogL /LogL0 = 0.5719.
124
Variables
NROOMS
NROOMS×C
NROOMS×H50
HAGE
HAGE×C
HAGE×H50
HSIZE
HSIZE×C
HSIZE×H50
DETACHED
DETACHED×C
DETACHED×H50
LDPTAXES
LPTAXES×C
LPTAXES×H50
SDPTAXES
SDPTAXES×C
SDPTAXES×H50
SQUALITY
SQUALITY×C
SQUALITY×H50
MINCOME
MINCOME×C
MINCOME×H50
CRIME
CRIME×C
CRIME×H50
DISTCBD
DISTCBD×C
DISTCBD×H50
Standard
Error
0.1177
0.2559
0.4851
0.0037
0.0080
0.0164
0.0126
0.0240
0.0454
0.1663
0.3188
0.7170
0.0808
0.1673
0.5067
0.0816
0.1772
0.4983
0.0465
0.0906
0.2581
0.0183
0.0321
0.0836
0.0131
0.0250
0.0776
0.0097
0.0195
0.0468
Estimate
-0.2809
1.1704
-0.4522
-0.0114
0.0136
0.0338
0.0369
-0.0317
0.0780
0.2271
-0.0093
-0.2380
0.0620
0.4246
0.0051
-0.1055
-0.4597
-0.1156
0.1478
0.1408
0.0864
-0.0190
0.0561
0.0461
0.0186
0.0169
-0.0576
-0.0295
-0.0309
-0.0398
t Value
-2.39
4.57
-0.93
-3.09
1.70
2.06
2.93
-1.32
1.72
1.37
-0.03
-0.33
0.77
2.54
0.01
-1.29
-2.59
-0.23
3.18
1.55
0.33
-1.04
1.75
0.55
1.42
0.68
-0.74
-3.05
-1.58
-0.85
Pr > |t|
0.0170
<.0001
0.3513
0.0020
0.0898
0.0390
0.0034
0.1881
0.0860
0.1720
0.9768
0.7400
0.4428
0.0111
0.9920
0.1960
0.0095
0.8166
0.0015
0.1203
0.7379
0.2967
0.0804
0.5818
0.1565
0.4974
0.4580
0.0023
0.1131
0.3954
Continued
Table 21. Estimates of Utility Parameters for Higher-income Households with
Householders Who Are 50 Years Old and Over
Note: × indicates interaction terms with household characteristics (H50: Higher-income
households with householders who are 50 years old and over; C: Presence of children)
125
Table 21 Continued
Variables
CQPRICE
CQPRICE×C
CQPRICE×H50
PRESUBURB
PRESUBURB×C
PRESUBURB×H50
INC
Standard
Error
1.3623
2.3407
6.6885
0.4961
0.8197
2.4345
0.3639
Estimate
-4.9116
-1.1181
-5.3848
-0.4008
0.9804
-0.2665
0.7613
t Value
Pr > |t|
-3.61
-0.48
-0.81
-0.81
1.20
-0.11
2.09
0.0003
0.6329
0.4208
0.4192
0.2317
0.9128
0.0364
Notes: Number of observations =453, Number of cases = 2718; Log likelyhood = -705.64429;
Number of iterations = 18, Optimization method = Newton-Raphson; Goodness of fit
(McFadden's likelihood ratio index) = 1- LogL /LogL0 = 0.5653.
126
Variables
NROOMS
NROOMS×C
NROOMS×M50
HAGE
HAGE×C
HAGE×M50
HSIZE
HSIZE×C
HSIZE×M50
DETACHED
DETACHED×C
DETACHED×M50
LDPTAXES
LPTAXES×C
LPTAXES×M50
SDPTAXES
SDPTAXES×C
SDPTAXES×M50
SQUALITY
SQUALITY×C
SQUALITY×M50
MINCOME
MINCOME×C
MINCOME×M50
CRIME
CRIME×C
CRIME×M50
DISTCBD
DISTCBD×C
DISTCBD×M50
Standard
Error
0.1261
0.2525
0.3019
0.0039
0.0081
0.0097
0.0139
0.0234
0.0306
0.1848
0.3277
0.3973
0.0847
0.1679
0.2547
0.0851
0.1770
0.2750
0.0490
0.0897
0.1334
0.0190
0.0322
0.0504
0.0142
0.0252
0.0348
0.0101
0.0193
0.0294
Estimate
-0.1645
1.0265
-0.7584
-0.0071
0.0125
-0.0163
0.0303
-0.0162
0.0364
0.3889
-0.1362
-0.4391
0.0186
0.4881
0.2952
-0.0512
-0.5402
-0.3740
0.1126
0.1713
0.1897
-0.0112
0.0584
-0.0161
0.0128
0.0209
0.0065
-0.0217
-0.0437
-0.0605
t Value
-1.30
4.07
-2.51
-1.82
1.54
-1.68
2.18
-0.69
1.19
2.10
-0.42
-1.11
0.22
2.91
1.16
-0.60
-3.05
-1.36
2.30
1.91
1.42
-0.59
1.82
-0.32
0.90
0.83
0.19
-2.14
-2.27
-2.06
Pr > |t|
0.1921
<.0001
0.0120
0.0683
0.1244
0.0925
0.0291
0.4894
0.2336
0.0353
0.6777
0.2691
0.8261
0.0037
0.2464
0.5474
0.0023
0.1738
0.0214
0.0561
0.1550
0.5564
0.0694
0.7500
0.3674
0.4086
0.8526
0.0320
0.0233
0.0397
Continued
Table 22. Estimates of Utility Parameters for Middle-income Households with
Householders Who are 50 Years Old and Over
Note: × indicates interaction terms with household characteristics (M50: Middle-income
households with householders who are 50 years old and over; C: Presence of children)
127
Table 22 Continued
Variables
CQPRICE
CQPRICE×C
CQPRICE×M50
PRESUBURB
PRESUBURB×C
PRESUBURB×M50
INC
Standard
Error
1.4510
2.3288
3.3205
0.5427
0.8361
1.4149
0.3244
Estimate
-4.7055
-1.1811
-1.4491
-0.5521
1.0793
0.3462
0.6730
t Value
Pr > |t|
-3.24
-0.51
-0.44
-1.02
1.29
0.24
2.07
0.0012
0.6120
0.6625
0.3090
0.1967
0.8067
0.0381
Notes: Number of observations =453, Number of cases = 2718; Log likelyhood = -699.07151;
Number of iterations = 17, Optimization method = Newton-Raphson; Goodness of fit
(McFadden's likelihood ratio index) = 1- LogL /LogL0 = 0.5694.
128