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INTRAURBAN VARIATION IN
HOUSE PRICE APPRECIATION:
A CASE STUDY,
JACKSONVILLE, FLORIDA, 1980-1990
GREG T. SMERSH
A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY
UNIVERSITY OF FLORIDA
This dissertation is dedicated to the memory of Martha E. Smersh (1925 -1987)
A great deal of gratitude is due to all committee members for their generous help
and support. More than anyone, Dr. Timothy Fik has offered countless hours of advice
and direction and has given a substantial amount of inspiration to this work. Dr. David
Ling has also provided much support and motivation. Additionally, other committee
members, Dr. Edward Malecki, Dr. Peter Waylen, and Dr. John Dunkle, have offered
helpful guidance and suggestions; their help and encouragement is most appreciated.
TABLE OF CONTENTS
ACKNOWLEDGMENTS ......................................... iii
ABSTRACT ...................................... ........... vii
1 INTRODUCTION ...... ................................. 1
2 REVIEW OF THE LITERATURE ............................. 6
Review of Theory and Modeling ................... ..... 6
Land Value Theory ............................. 6
Monocentric City Models .................... ..... 7
Hedonic House Price Models ..................... 9
House Price Appreciation ......................... 13
Theoretical Summary ......................... 16
Review of Alternative Methodologies ................... 17
Price Equations and Indices ....................... 17
Hedonic Price Index Estimation ............... 18
The Repeat-Sales Technique ................. 19
Multinodal Models ............................. 21
Trend Surface Analysis ...................... 24
Accessibility Indices ............................ 25
Price Model Summary ........................ 28
3 DATA .............. ...... ............... ........... 29
Source and Scope of the Data ................. ......... 29
GIS Procedures ......................... ........... 31
Aggregation Techniques ............................... 31
Geographic Aggregation ......................... 32
Temporal Aggregation ........................... 34
Repeat-Sales Data ................. ................ 35
4 METHODOLOGY ........................................ 36
Hedonic Price Equations .............................. 36
Naive versus Interactive Model ..................... 36
Single versus Simultaneous Estimation ............... 37
Spatial Autoregressive Variable ................... 38
M odel Estimation .................. ..... ........... 39
Component Prices of Structure and Land .............. 39
Consideration of Spatial Autocorrelation .............. 40
Spatial Variation in the Price of Land ................ 41
Predicting Price and Appreciation ........................ 41
Standard Housing Prices ......................... 42
Temporal Implications ........................... 43
Patterns of Appreciation ............................... 44
Tests Using Repeat-Sales ............................. 46
Methodology Summary .............................. 47
5 PRICE EQUATION RESULTS ............................... 50
Price Model Comparison .............................. 50
M odel Specification ............................ 50
Structural Unit Prices ........................... 52
Land Unit Prices .............................. 55
Spatial Autoregressive Variable ................. 56
Spatial Dependence of Error Terms .................. 57
Model Estimation and Prediction ......................... 57
Price Equations .............................. 58
Land Value Prediction ........................... 59
6 HOUSE PRICE APPRECIATION ............................ .65
Predicted Appreciation ................................ 65
Temporal Implications of the Price Model ............. 65
House Price Appreciation ......................... 68
Appreciation Equation Results .......................... 72
Characteristic Effects ............. .............. 72
Effects of Price ............................... 73
Spatial Patterns of Appreciation .................... 76
Repeat-Sales Results ................................. 78
7 CONCLUSION .......................................... 84
House Price and Appreciation .. ...... ... ........ .. 84
Appreciation in Jacksonville ............................ 88
Directions for Further Research .......................... 90
A DATA PROCEDURES .................. ................. 92
B REGRESSION ASSUMPTIONS .............................. 96
C SEEMINGLY UNRELATED REGRESSION EQUATIONS ........... 99
D SPLINE REGRESSION PROCEDURE ........................ 100
E NAIVE MODEL WITH SINGLE ESTIMATION ................. 102
F NAIVE MODEL WITH SIMULTANEOUS ESTIMATION .......... 105
G INTERACTIVE MODEL WITH SINGLE ESTIMATION ........... 108
H INTERACTIVE MODEL WITH SIMULTANEOUS ESTIMATION .... 111
I APPRECIATION MODELS ................................ 114
J REPEAT-SALES MODEL ................................ 117
REFERENCE LIST ................................ .... ...... 119
BIOGRAPHICAL SKETCH ................................ 126
Abstract of Dissertation Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Doctor of Philosophy
INTRAURBAN VARIATION IN
HOUSE PRICE APPRECIATION:
A CASE STUDY,
JACKSONVILLE, FLORIDA, 1980-1990
Greg T. Smersh
Chairperson: Timothy J. Fik
Major Department: Geography
Classic land use and location theory suggest that residential property values in an
urban area and the temporal changes in those values will vary spatially. However, there
is a lack of research that defines how location affects land and housing prices and
virtually no investigation of the spatial variation in house price appreciation.
Within an urban area, it is reasonable to assume that structural prices are spatially
constant, at least from a cost perspective. Similarly, economic depreciation--the effect
of age on a structure--can be assumed to be spatially constant. However, the assumption
that intraurban land prices, or changes in those prices, are spatially constant may be
This study investigates the Jacksonville, Florida, housing market from 1980 to
1990. Two hedonic housing price models are compared: a "naive" aspatial model and a
spatial model that includes location as an "interactive" component. The latter framework
incorporates a theoretical accessibility function that denotes the unit price of land at
different locations in space. As a general specification, a polynomial expansion of the
function f(X,Y) over a Cartesian (X,Y) coordinate system is employed. According to this
specification, prices of structural characteristics are considered spatially constant while
the price of land is allowed to vary spatially. The naive and interactive models are
estimated for both single and multiple time periods. With respect to coefficient
estimation and spatially dependent error terms, the interactive, simultaneously estimated
model is shown to be the superior specification.
Differences (percentage change) between price model equations for adjacent time
periods are used to predict house price appreciation over space using a standard bundle
of housing characteristics. Appreciation is then evaluated as a function of housing
characteristics and location. While housing characteristics seem to have a negligible
effect on appreciation, a definite spatial pattern emerges; this supports the notion that
location plays an important role in house price appreciation. A repeat-sales methodology
is employed to verify the existence of the implied positive and negative abnormal
appreciation. In addition, the methodology estimates the geographic extent (radial
distance from a maximum or minimum) of aberrant appreciation.
The importance of location as a determinant of property values has long been
recognized in the theoretical literature on urban property valuation. Indeed, much
theoretical and empirical work has been done studying the spatial variation of land and
housing prices in the urban economics, geography, and real estate literatures. Similarly,
the price appreciation (or returns) of real property with respect to time (but not space) has
been examined in the economics, finance, and real estate literatures. However, there has
been very little investigation of the spatial variation in house price appreciation.
House price appreciation is important to U.S. homeowners whose wealth is
typically dominated by home equity. If appreciation varies spatially, as some theories
suggest, then certainly such knowledge should be of interest to owners of both owner-
occupied and renter-occupied (investment) housing. A more complete understanding of
house price appreciation over space is also of importance to home mortgage investors and
property accessors. Additionally, studies of the intraurban house price appreciation may
be of interest to those who formulate housing policy, at least on a local (city or county)
The primary focus of this research is an investigation of alternative methodologies
that could certainly be applied to any urban housing market, and more broadly, to any
real estate (such as commercial) market. As an empirical case study however, this
research explores house price transactions in the geographical study site of Jacksonville,
Florida during the time period of 1980 to 1990.
Jacksonville is located in northeast Florida on the Atlantic Ocean and encompasses
all of Duval county, thus making city and county one and the same. Duval county and
the urban area of Jacksonville are divided by the St. Johns River, the state's largest
waterway. Jacksonville is one of the eastern seaboard's busiest deep-water ports, serving
the U. S. Navy and merchant shipping. Jacksonville is also a major insurance and
banking center. Two interstate highways--I-95 and I-10--run through downtown, linking
Jacksonville to Los Angeles on the east-west axis, and to Maine and Miami on the north-
south axis. Within an eight-hour drive on these highways live over 30 million people.
In the past 50 years, the state of Florida has seen tremendous growth, from a
population of under 2 million in 1940 to nearly 13 million in 1990. During the 1980s,
Florida saw a 30 percent increase in population, the second-highest increase of all states
in the United States (Fik, Malecki, and Amey, 1993). Jacksonville (Duval county) has
a 1990 population of approximately 672,900 people, up 18.5 percent from a 1980
population of 567,600 people.
During the 1980s, total employment in Florida rose over 40 percent, the highest
percentage increase of all states in the United States. However, manufacturing
employment in Florida increased only 16 percent during the same time period; in Duval
county, manufacturing employment increased a mere 6.7 percent. However, per capital
personal income during the 1980s rose 90 percent in the state of Florida and over 94
percent in Duval county.
Nationally, the median price of a single-family home rose from $62,200 to
$95,500 in 1990, a 53.5 percent increase. In Duval county, house prices are much less
than the national median but prices increased more during the 1980s. The median price
of a single-family house in Duval county rose from $39,200 in 1980 to $62,700 in 1990,
an increase of 60 percent. During this time period, interest rates on a 30-year fixed rate
conventional mortgage fell rose from 13.77 percent in 1980 to a high of 16.63 percent in
1981 and then steadily fell to a low of 10.13 percent in 1990.
The national economy saw strong growth in the 1980s; gross domestic product
(GDP) rose over 100 percent from 2.7 trillion in 1980 to 5.5 trillion in 1990. In response
to this and the dramatic drop in both inflation and interest rates, the value of the U. S.
securities market tripled between 1980 and 1990. It is important to point out, however,
that these changes in the state and national economies would not be expected to have any
influence on the intraurban variation of house prices in Jacksonville. Even local changes
in population and employment, to the extent that they are spatially uniform, would not
necessarily be expected to affect house prices.
Land use and location theory suggest that residential property values in an urban
area will vary spatially and that intraurban variation of house price appreciation is also
to be expected. Such theories are discussed in chapter 2, in a review of the literature.
However, there is a lack of research that properly defines the extent to which location
affects housing prices within the urban area and virtually no investigation of the spatial
variation in house price appreciation. As the urban land and housing markets are so
diverse and heterogeneous, the study of price variation over both time and space is a
difficult task. A review of various modeling methodologies and various specifications of
location in house price models is also discussed in chapter 2.
Additional information on Jacksonville and the data employed in this research are
discussed in chapter 3 while the methodologies employed in this investigation are
discussed in chapter 4. This research first explores linear regression methods to measure
the spatial variation of intraurban house prices. As casual observation indicates, the price
of land varies spatially; the specification of land prices as spatially constant in a model
may be considered, therefore, "naive." A naive model is compared to an alternative
model which holds structural characteristics spatially constant but allows the price of land
to vary spatially. Specifically, the alternative model incorporates a polynomial expansion
of (X,Y) coordinates as a measure of the value of location (the unit value of land) at
different locations in space and hence is presented as an "interactive" model. The naive
and interactive models are estimated for single time periods and simultaneously over time
utilizing single-equation and simultaneous-equation techniques. The objective of this
investigation is to determine which model is best suited to separate the value of land from
the value of the structure.
Results of the estimated house price models are then discussed in chapter 5. Here,
the superior model specification is identified and used to predict land price surfaces. The
price model uses a standard bundle of housing characteristics to predict prices for
different time periods.
Chapter 6 discusses appreciation results. From the price equations, changes in the
prices of land and structure are analyzed. Appreciation of structural characteristics is
compared to the appreciation of land alone and a composite price index of land and
structure is compared to other price indices.
Areas of predicted "abnormal" appreciation are then identified. Abnormal
appreciation is defined here as appreciation above or below two standard deviations from
the mean rate of appreciation in the market. The existence of abnormal appreciation does
not necessarily imply a spatial pattern; that consideration is next investigated by analyzing
appreciation as a function of housing (structural) characteristics and location.
A repeat-sales technique is used to verify the existence of abnormal appreciation.
Employing a spline regression procedure, the repeat-sales model is used to estimate the
radial distances at which houses within exhibit the greatest difference in appreciation from
the rest of the market. A summary and conclusion is presented in chapter 7.
REVIEW OF THE LITERATURE
Review of Theory and Modeling
In this section, value theory and its unique application to land and housing is
reviewed. Theoretical bases of the hedonic approach to modeling house values are also
discussed. Finally, the theoretical aspects of house price appreciation, including the
implications from value theory, are reviewed.
Land Value Theory
The value of a particular good, including land, is explained in various
microeconomic value theories. Classical economists, such as Adam Smith (1776), viewed
land value as a function of labor (as a factor of production) and recognized the income
to land as a residual effect. As materials costs were fixed, labor was the integral
component of production, and it was the cost of labor that determined the value of
production. The labor cost premise was carried over to explain land income and value
since land was considered a factor of production. However, the other factors of
production, labor and capital, were mobile and could flow to locations that might provide
greater returns. Therefore, labor had precedence over land for achieving a return, and
land was considered to be price-determined by labor. The greater the marginal
productivity of a parcel of land, the greater the residual it provided to owners. This
residual has been referred to as "surplus rent."
The German economist, Johann Heinrich von Thtinen (1826), made a major
contribution to land value theory by adding the element of location to marginal
productivity. Von Thiinen was concerned with the arrangement of different agricultural
uses around a single market center. He theorized that the pattern of land use which
developed was the result of different transportation costs (for each crop) and the intensity
with which it was grown. He developed the concept of rent gradients for different
agricultural land uses where rent is a function of the yield (or profitability) of a land
parcel and, more importantly, the parcel's distance from the market.
Whereas classical theory places its emphasis on the cost of production (supply),
marginal utility theory focuses on utility (demand). According to marginal utility
theorists such as von Bohm-Bawerk (1888), the utility produced by the last unit of an
economic good determines its value. Value is determined without consideration for costs
of production; the short-run resolutions of marginal utility alone govern the theory.
Alfred Marshall (1920) combined classical theory with marginal utility theory in his
neoclassical market equilibrium theory, emphasizing that the interaction of both of these
forces is important in the determination of value.
Monocentric City Models
Von Thinen's (1826) original concept of an agricultural monocentric model was
generalized and applied to housing many years later by Alonso (1964). Models that
assume a monocentric city represent a unique branch of microeconomic theory; these
models expand consumer behavior theory to incorporate the consumption of land and
locational preference. The spatial factor complicates neoclassical economic theory
because households must locate in only one location and no two households can occupy
the same location. To simplify this problem, monocentric models assume that all
employment is centrally located, that locational choice depends only on commuting costs
and land consumption, and that housing capital is infinitely divisible and mobile.
Alonso (1964) assumed production and consumption decisions determined land
consumption by households. In his model, the direct household preference for land
determines residential density. Muth (1968), and later Mills, (1972) expanded the
monocentric model to incorporate housing. In the Muth-Mills model, consumer utility
depends on the consumption of other goods and an aggregate commodity, "housing." In
the Muth-Mills approach, residential density is determined by the production function for
housing. The major predictions of the monocentric models are that residential densities
decline (at a decreasing rate) with distance from the central business district (CBD) and
that house prices also decline with distance at a decreasing rate.
The basic assumptions of monocentric city models are unrealistic. In particular,
housing capital is lumpy in size and nontransportable and locational decision making is
not typically based on a trade-off between land consumption and commuting costs.
Furthermore, while the form of many urban areas has tended towards a pattern of central
employment in the past, the general pattern of urban employment in the contemporary city
is much more dispersed. Few metropolitan areas have a single dominant node such as
the CBD, service employment is widely dispersed and there has been a decentralization
of office and industrial establishments as well.
Despite questionable assumptions, many insights into urban housing markets have
been derived from the works of Alonso, Muth, and Mills. The most intriguing
observation is that housing and accessibility are jointly purchased. As Muth (1968) notes,
until quite recently, most writings on urban residential land and housing
markets tended to neglect accessibility. They emphasized instead the
dynamic effects of a city's past development upon current conditions, and
the preferences of different households for housing in different locations.
The classical literature suggests that increases in the centrality (accessibility) of
a parcel of land will generally lead to an increase in value. In other words, accessibility
advantages due to location are capitalized in the price of housing.
Hedonic House Price Models
New modeling approaches were developed in the 1960s as a method to better
understand the relationship between housing market prices and the components of
"housing services" imbedded within them; these became known as "hedonic" models. A
simplification of the heterogeneous aspects of urban housing stock was first accomplished
by couching the demand for housing in terms of these housing services or "bundles" of
housing attributes to estimate implicit characteristic prices. In this perspective, housing
value is viewed as a bundle of (utility producing) services offered by a combination of
structural and locational characteristics, the component prices of which are never directly
observed in property transactions.
The interest in applying these methods to housing markets evolved from
Lancaster's (1966) consumer theory of differentiated products; this theory proposed that
all households have demands for underlying characteristics (inherent in all traded
commodities) and that households combine these characteristics to produce "satisfactions."
Focusing on the use of multi-variate models, hedonic studies aimed at uncovering
consumer preferences for (structural) housing characteristics.
The hedonic (or preference) approach was also applied to estimating the effect of
location and the impact of accessibility (primarily to employment centers), environmental
amenities, and externalities. Such models employed distance gradients (such as miles
from the CBD or an externality), gravity model expressions of accessibility, or dummy
variables (for location in specific areas). The advantage of the hedonic approach is that
it allows for the estimation of coefficients for each characteristic holding the effect of all
others constant. Detailed discussions of the mechanics of hedonic price models are
offered by Rosen (1974) and Little (1976).
Theory suggests that the value of land is a phenomenon that results from the
forces of supply and demand. In turn, supply and demand are the market effects of the
relative scarcity and utility associated with urban land. Transaction prices reflect supply
and demand conditions and the outcome of a market-clearing process by which
households of various incomes arrange themselves by geographic location and type of
housing stock. Thus, the estimation of implicit prices represents not demand but rather
an estimate of the (upper) bid-rent function of different buyers for particular housing
components and the (lower) offer function of different sellers.
In an early regression model, Brigham (1965) sought to ascertain determinants of
residential land value. This study utilized data on land value gradients (measured in price
per square foot) along three vectors which extended from the city (CBD) center of Los
Angeles to Los Angeles County boundaries. Brigham suggested that land value was a
function of a site's accessibility, amenity level, topography, and certain historical factors
that affect its utilization. As Brigham observes,
urban land has a value over and above its value in rural uses because it
affords relatively easy access to various necessary or desirable activities.
If transportation were instantaneous and costless, then the urban population
could spread out over all usable and all land prices would be reduced to
their approximate value in the best alternative use. (pg. 326)
Brigham created an accessibility potential variable that measured the accessibility
potential of each site to multiple workplaces; other variables included distance to the
CBD, an amenity variable (average neighborhood house price), and a topography dummy
variable. Regression equations were fitted to spatial moving averages of the value per
square foot for single family properties on each vector. The data were smoothed in this
manner to remove as much spurious variation as possible and to allow the investigation
of general, not local, variations in land values. This empirical investigation provided
strong statistical evidence to support the concept of property values as a function of
structural and neighborhood characteristics and accessibility to employment.
Other researchers have measured accessibility in similar ways. An investigation
of land values in Topeka, Kansas by Knos (1968) compared linear and nonlinear gradients
(of distance to the CBD) to a generalized (population potential) accessibility index, also
derived from a gravity model. Alone, the index was only marginally significant; however,
its combination with distance gradients provided a highly significant model. With regard
to the importance of (CBD) workplace accessibility, the empirical evidence is somewhat
mixed. In Kain and Quigley's (1970) study of the St. Louis housing market, the inclusion
of a distance variable (in miles from the CBD) was found to be statistically insignificant.
However, the works of Brigham (1965) and Knos (1968) suggest that such a finding may
simply be the result of model misspecification.
Other early developments in hedonic price models tended to view property price
solely as an additive property of hedonic characteristics (Berry, 1976, and Linneman,
1980, and 1981). Berry (1976) and Berry and Bednarz (1977), investigated price
differences in ethnically distinct housing markets in Chicago. These analyses sought to
study market segmentation based on race and income; specifically, they concluded that
single-family housing prices in Black and Hispanic neighborhoods were significantly less
than in White neighborhoods.
Henderson (1977) suggests that the external benefits or costs of particular land
uses or urban activities will be capitalized into property values. With regard to such
"externalities" or spillover effects, analyses of hedonic prices have provided direct
evidence of residential blight (Kain and Quigley, 1970); air pollution (Anderson and
Croker, 1971; Harrison and Rubinfeld, 1978); closeness to appealing amenities (Weicher
and Zerbst, 1973); neighborhood characteristics (Berry and Bednarz, 1977); proximity to
non-residential land use (Li and Brown, 1980); nearness to a potentially dangerous land
use (Balkin and McDonald, 1981); environmental amenities (Gillard, 1981) and proximity
to waste disposal (Thayer et al., 1992), among others.
While the estimated coefficients of such measures in hedonic regression are
usually significant, Ball (1973) notes that the independent effect of distance (or
generalized accessibility) is often rather small. In part, this may simply reflect the
negative covariance between accessibility and housing vintage--the tendency in most U.S.
cities is for older, more obsolete housing units to be located closer to traditional central
Hedonic regression models have often included neighborhood externalities with
dummy variables (for location in specific zones) or distance gradients. However, such
models have generally underspecified the locational characteristics of housing as they
have not included the influences of all urban nodes (employment centers, schools,
shopping centers, etc.), axes (highways and major arterials), and externalities (parks,
landfills, airports, etc.).
House Price Appreciation
Several theories suggest that the temporal change or appreciation in house prices
(ex-ante) will vary within an urban area. First, Muth (1975) has demonstrated that rising
real income and population have caused net (implicit) rental income (and therefore
housing prices) to increase faster at the city fringe than at the city center. Second,
various studies of house prices and rental income indicate that housing depreciates at a
decreasing rate with the age of the unit. All else the same, this should produce varying
rates of appreciation among submarkets as the vintage of the housing stock is not uniform
across the metropolitan area (Archer, Gatzlaff, and Ling, 1995).
Further, deLeeuw and Struyk (1975) demonstrate a "filtering model" which
indicates that larger houses will experience more rapid price appreciation. The demand
for housing has been shown to be income elastic and therefore, rising real income in an
urban area tends to generate an increased demand for larger houses and a corresponding
decrease in demand for smaller, less functional houses. Housing unit size clearly exhibits
spatial variation although such variation is more likely to be scattered and have less of
a spatial pattern than housing age or lot size.
Finally, the theoretical models of land price may indicate foundations for theories
of land price appreciation. The theoretical and empirical literatures suggest that increases
in accessibility will lead to increases in property value. If accessibility is interpreted in
a general connotation of the word (accessibility to work, accessibility to shopping,
accessibility to crime, accessibility to appealing amenities, etc.), then, in aggregate,
accessibility defines the location of a specific site. Any changes in accessibility benefits
(or dis-benefits) may be due literally to increased access (a new road) or simply an
increase/decrease in an activity (shopping, crime). Thus, theory may imply that such
changes in accessibility advantages over time will be reflected in changes in price.
In addition to the ex-ante effects of perimeter location, house age, and house size,
ex-post appreciation may also be affected by unanticipated changes in the value of
housing's physical or locational characteristics. For example, localized storm damage
may result in significant price changes; such unanticipated exogenous "shocks" may
increase or decrease prices dramatically, especially over short time periods. The effects
of other events such as the construction of a new highway or shopping mall may be
significant over longer time periods; such events may be seen as significantly changing
accessibility benefits in an urban area.
The limited empirical evidence available does suggest that house price appreciation
is affected by location within the urban area. Using hedonic techniques and five
metropolitan areas, Rachlis and Yezer (1985) find that the rate of change in house prices
is statistically related to location characteristics of housing. As their measures of location,
Rachlis and Yezer (1985) used distance to the CBD, distance to a high income
neighborhood, and distance to a minority neighborhood. Keil and Carson (1990) find a
statistically significant difference in appreciation between incorporated and non-
incorporated locations within a metropolitan area.
Defining neighborhoods by zip codes, Case and Shiller (1994) find that property
values in Boston and Los Angeles appreciate at similar rates when the metropolitan area
as a whole is performing well. However, they find substantially more dispersion in
appreciation when the metropolitan area is experiencing price declines.
Using a repeat-sales methodology in a cross sectional study of Miami census tract
groups over a 22-year time period, Archer, Gatzlaff, and Ling (1995) seek to determine
if there is significant locational variation in house price appreciation and find that over
half of the 79 tract groups show statistically significant abnormal (annual) appreciation.
The repeat-sales methodology uses only houses which have sold twice during a specific
time period to generate an overall price index or sets of indices for different areas. Their
procedure generates a pair of indices that compare each tract group to the combination
of all other tract groups; the process is repeated for all 79 tract groups. Abnormal
appreciation is defined (for a census tract group) as a rate of appreciation that is
significantly different from the rest of the market. However, tract group location explains
only 12 percent of the variation in appreciation that is unexplained by market-wide price
movements. Abnormal appreciation here appears to be dominated by influences at the
individual house level or perhaps an alternative (i.e., smaller) geographic level.
The contributions of economic theory to the perception of value conclude that
value is a market concept. Marshallian theory--the neoclassical approach--integrates all
other relevant theories into the supply-demand model. Supply and demand are the market
effects of the relative scarcity and utility associated with a particular good.
Land as an economic good complicates neoclassical economic theory because
households must locate in only one location and no two households can occupy the same
location. Theoretical models, such as the monocentric city models of Alonso, Muth, and
Mills must therefore impose strict assumptions to simplify the situation. While these
assumptions are quite unrealistic, many insights about the interrelationships of urban
housing markets have come from the observation that housing and location are a
composite or "bundled" good.
Hedonic models seek to uncover consumer preference (or utility) for different
components of housing which are never directly observed in actual property transactions.
Hedonic models can be used to differentiate various housing characteristics, including
location. A review of alternative methodologies is provided in the following section.
Review of Alternative Methodologies
The previous section discusses hedonic models as a methodology for separating
the value of various housing characteristics. Typically, spatial effects are derived from
hedonic models at a given point in time, while temporal effects are estimated using either
hedonic or repeat-sales methods that may include various measures of location. This
section first discusses the use of rudimentary hedonic equations for price indices and the
derivation of the repeat-sales technique. The remainder of the chapter discusses methods
for incorporating various measures of location in more complex hedonic equations.
Price Equations and Indices
The basic hedonic house price model regresses transaction price on structural
characteristics (such as square footage and age), land characteristics (such as lot size),
and locational (or neighborhood) characteristics. This approach can be used to generate
a temporal price index in several ways. Alternatively, house price indices can be
generated using data on only those houses which sold twice--the repeat-sales technique.
The advantage of the repeat-sales technique is that it avoids the temporal variation
in characteristic prices manifest in hedonic estimation; significant variation in these prices
may bias index results. This technique is derived as the difference between two hedonic
equations for different time periods; constant quality (no change in housing attributes over
time) is assumed and so hedonic variables drop out of the estimating equation, leaving
only time as an explanatory variable.
Hedonic Price Index Estimation
Generating the hedonic index requires a sample of house sales from multiple time
periods. Transaction prices are regressed on structural and locational characteristics.
Once the hedonic equation has been estimated, it can be used to produce a price index.
There are two major models: "strictly cross-sectional" and "explicit time-variable."
In the strictly cross-sectional model of house prices, the implicit characteristic
prices are estimated in a separate hedonic regression for each time period, thereby
allowing the implicit characteristic prices to vary over time. A model of the following
type is common (e.g., Berry, 1976):
P, = 0o + ipj X, + E, (1)
where P, is the transaction price of property i, i = I to n observations, and Pj denotes a
vector of coefficients, j = 1 to k, on the structural and locational attributes, X,, which
could include square footage, age, lot size, and various neighborhood characteristics. The
coefficient j0 is an intercept term and Ei is a random, normal, independent error term.
Price indices are then predicted for each period by applying the estimated implicit
prices to a standardized bundle of housing attributes. This model is often used in a single
time period when measuring spatial effects. With time held constant, location in space
can be measured in a more distinct manner; the simultaneous estimation of price over
both time and space is more complicated.
The explicit time-variable approach includes time as an independent dichotomous
variable; the following is a popular functional form (e.g., Clapp and Giaccotto, 1991):
In P,, = EJk 0 In Xji, + Et c, Di, + E, (2)
where "In" denotes natural logarithm, P, is the transaction price of property i at time t,
t = 1 to T time periods, and Pj indicates a vector of coefficients on the structural and
locational attributes. Here, c, denotes a vector of time coefficients on Di, time dummies
with values of I if the house sold in period t and 0 otherwise. From this equation, the
anti-logarithm (e") of the coefficient c,, scaled by 100, then becomes a (cumulative) price
appreciation index. This model is discussed by Clapp and Giaccotto (1991) and Gatzlaff
and Ling (1994). Potential problems associated with the hedonic technique, including
model misspecification, sample selectivity and the choice of functional form, as
discussed by Palmquist (1980) and Halvorsen and Pollakowski (1981). These problems
can be partially overcome by employing the repeat-sales technique.
The Repeat-Sales Technique
The repeat-sales technique allows for the estimation of intertemporal market price
indices for "quality-adjusted" or standardized properties. The origins of this technique
can be traced back to the work of Bailey, Muth, and Norse (1963) and are discussed by
Hall (1971), Palmquist (1980), Case (1986), and Gatzlaff and Ling (1994). This
technique is a modification of the explicit time variable approach that uses a chain of
overlapping time periods to predict cumulative appreciation rates for specific time periods.
More precisely, the repeat-sales model is the difference between the log of a "second"
sale model and the log of a "first" sale model. From equation (2) then
In P,, In P,, = (3k PlnXit, + Er ct) (L PlnXji, + Er c.D) + ej, (3)
where Pi, and P,, are the prices of repeat-sales transactions, with the initial sale at time T
and the second sale at time t for t = 1 to T time periods. If housing quality is constant,
(the implicit assumption in the repeat-sales technique) then structural and locational
variables cancel out and the difference between the two prices is solely a function of the
intervening time period. Under this condition, equation (3) reduces to
In P,, In P, = ET c, Di, E1T C Di, + eit (4)
To execute this procedure, the dependent variable is the log of the price ratio generated
from a property having sold twice. The log of the price ratio is then regressed on a set
of dummy variables, one for each period in the study. The repeat-sales estimating
In (Pi, / Pi,) = ET c, Dil +ei, (5)
where Pi, I P,, is the ratio of sales price for property i in time periods T and t; D,, is a
dummy variable which equals -1 at the time of initial sale, +1 at the time of second sale,
and 0 otherwise; and c, is the logarithm of the cumulative price index in period t. To
clarify, ct = In(l + A,), where A, is the cumulative appreciation rate for year t.
The repeat-sales model avoids many of the problems associated with hedonic
models, but is subject to several criticisms. Case and Shiller (1987) and Haurin and
Hendershott (1991) note that the sample may not be representative of the housing stock,
upgrading of the property may be ignored, and attribute prices may change over time.
Given the somewhat restrictive functional form of the basic repeat-sales model,
any measures of location must properly be included as interactive (as opposed to additive)
terms; the inclusion of one location (dummy) variable will double the number of
estimated coefficients. With respect to the generation of temporal indices, Gatzlaff and
Ling (1994) find that the "strictly cross-sectional" models and "explicit time-variable"
hedonic models with limited variables of square footage, age, and lot size produce indices
similar to those estimated with repeat-sales.
To be relevant today, the monocentric model must be extended to represent the
modem urban setting and recent research has sought to incorporate additional measures
of location within a multinodal context. This results in multiple price gradients and may
undermine the significance of the CBD as a single influence. Heikkila et al. (1989)
present a model of residential land values which explicitly incorporates distance from
multiple employment centers. The conclusion of this study of housing in Los Angeles
County is that the CBD price gradient becomes statistically insignificant once distances
to employment centers are included. This finding contradicts one of the principle features
of the monocentric model.
Point pattern analyses by Green (1980) and Getis (1983) influenced the hedonic
price models of Waddell, Berry, and Hoch (1993), which explicitly incorporate distance
from multiple market (or employment) centers. Their investigation of the Dallas housing
market examined the implicit price of relative location over discrete measures of distance
(rather than continuous gradients) in a multi-nodal area.
Waddell, Berry, and Hoch included both temporal and spatial effects but did not
allow measurement of an interactive effect; the model form extends from equation (2):
In P,, = E, c, D,, + Ek P, Xit + .m' X, Dm, + Eit (6)
where Pit is the transaction price of property i at time t; c, denotes a vector of time
coefficients of Di, time dummies with values of 1 if the house sold in period t and 0
otherwise. Here, f, denotes a vector of coefficients on the structural and locational
attributes, X,,, such as age of construction, wall type, log of living area, and percent of
land in census tract for various land uses. As measures of relative location, denotes
a vector of coefficients of Dm,, dummy variables based on distance intervals of less than
one mile, one to two miles, two to five miles, and five to ten miles from major urban
Although equation (6) allows for the creation of a house price index that includes
spatial effects, it specifies space as discrete rather than continuous and assumes that time
and space have additive effects on property price because both space and time are
represented with dummy variables. The model is easy to interpret; however it does not
consider any interactive effects of space and time. Therefore, the model does not
properly measure price appreciation over space.
Heikkila et al. (1989) and Waddell, Berry, and Hoch (1993a, 1993b) incorporate
such explanatory variables as accessibility to suburban employment centers, expressways,
and other nodes and axes of influence. Waddell, Berry, and Hoch (1993a) find that,
the emergence of new nodes of regional significance has created house
price gradients that far overshadow any residual gradient with respect to
the CBD. Moreover, the raw price gradients surrounding these new nodes
are almost completely explained by structural and neighborhood variables,
indicating the degree to which the physical stock and the form of
neighborhood externalities have been reshaped in response to these
emergent spheres of influence. In older established areas of the city it has
been much more difficult to adjust the housing stock, and both
depreciation and negative externalities far outweigh residual price-distance
gradients. (pg. 15)
Although empirical evidence has supported the theory that the land value gradient
declines with increasing distance from central points within an urban area, it is the work
of Johnson and Ragas (1987) that examines the spatial influence of externalities within
the CBD. They contend that it is centrality (accessibility in general) and multiple
externalities that influence land values. Johnson and Ragas (1987) develop a model for
undeveloped urban land and explore various model specifications and functional forms
using data from New Orleans. From equation (1), but including time and distance
variables, Johnson and Ragas estimate
P,, = ET c, Di, + k p3 Xi,, + Em- k ,,, +t it
where P,t is the transaction price per square foot of property i at time t, i = 1 to n, and
t = 1 to T; and c, denotes a vector of time coefficients of D,, time dummies with values
of 1 if the house sold in period t and 0 otherwise. Here, Pj denotes a vector of
coefficients on the spatial and aspatial plot-specific characteristics. As measures of
relative location, denotes a vector of coefficients of R,,, distances from positive and
An expanded model considers the interactive effect between Xji (zoning) and R,,
(distance). Alternative functional forms in addition to the linear model were also
estimated including a log-linear transformation (of Pi,), and a Box-Cox transformation.
Trend Surface Analysis
Johnson and Ragas (1987) then compare their (price gradient) models to trend
surface analysis (TSA) models. They find that the TSA models better predicts land prices
(based on values of R2). TSA offers a way to measure price variations in a purely
TSA is a technique of fitting (absolute) spatial data by regressing the variable in
question (such as land value) on a pth order polynomial expansion of the Cartesian
coordinates for each data value (Hembd and Infanger, 1981; Parker, 1981). The general
form of the absolute location or trend surface (TSA) model used by Johnson and Ragas
Pi = ,j k Ek Pjk [X,' Yik] + E,
where P, is the price per square foot of property i; Pjk denotes a vector of coefficients of
X,, and Y,, Cartesian coordinates of the properties in the sample and j + k < p, where the
model is a p* order polynomial.
Trend surface mapping has traditionally been used in engineering and the
geological sciences (Krumbein and Graybill, 1965). TSA applications to geographical
research are presented by Chorley and Haggett (1965). Although the TSA price equation
lacks any explanatory meaning and the only way to demonstrate model results is visually-
-the comparison of this pure spatial model to graphic displays of other (behavioral)
hedonic models can provide valuable insight.
A trend surface analysis of property values throughout an urban area demonstrates
how urban spatial structure affects (localized) price gradients. TSA not only identifies
prominent nodes on the landscape, it also shows the value at those nodes, the slope of the
price (value) gradient, and thus the effect of proximity to a node. However, the trend
surfaces would be expected to vary tremendously for different land uses. For example,
the demand for accessibility to retail sites is much better defined than the demand for
accessibility to (from) residential sites. The spatial variation in house prices is often so
great that the observation of spatial patterns in individual prices is difficult and areal
aggregation may become necessary.
The models of Alonso (1964), Muth (1969), and Mills (1972) suggest that
increases in the accessibility of a parcel of land in an urban area will generally lead to
an increase in the value of that parcel. The hypothesis that accessibility plays a
prominent role in the determination of house price and house price appreciation suggests
that researchers would be intent on determining if spatial variations are observable.
However, there is a lack of research that properly defines relative location (or a general
accessibility index) in such a manner as to capture all of the multinodal features of the
Despite the importance of location, few hedonic price equations have been
constructed to include more sophisticated measures of accessibility; a notable exception
was the contribution of Jackson (1979). In a study of the Milwaukee housing market,
Jackson uses house rents from the U. S. Census Bureau for one time period at the (census
tract) geographic level to derive a continuous measure of house price (rents) over space.
What is most significant about this model is its capacity to isolate the influence of
location or accessibility in general on the price of housing in the following form,
extending from equation (1):
Pi = io + Ejk P1 Xj + QD (A,)L, + Ei (9)
where price (in this case, census tract rent), P,, is represented as a linear function of a
constant Po, a vector of variables which define structural and neighborhood characteristics
(Xi), and the quantity of land (L), as measured by lot size. The coefficients P, represent
a vector of structural and neighborhood characteristics, and O(A) is the price of land as
a proxy for accessibility.
The theoretical accessibility function A = f(Xj,Yk) denotes the level of accessibility
at location (X,,Yk) using Cartesian coordinates X, and Yk. If the function f were known,
the level of accessibility at a given location could be evaluated with respect to the spatial
distribution of all prominent nodes (employment centers, retail shopping outlets, schools,
etc.) As a general specification, Jackson (1979) employed a Taylor series expansion of
the function f(X,Y) about the midpoint of a Cartesian coordinate system, yielding:
A, = jP E' a [Xi, Yik] + r, (10)
where r, is a remainder and j + k < p. Although equation (9) is written in p" order
polynomial form, a remainder exists to account for the inexactness of the transformation
at order p. Equation (9) is a representation of a double power series formula, equation
(8), that is widely used in trend surface analysis. Substituting equation (10) into equation
(9), the underlying dependence of land value on accessibility produces "a double power
series representation of land price." According to this model specification, hedonic prices
of structural and neighborhood characteristics are considered spatially constant while the
price of land varies spatially as a result of demand for more accessible sites. This model
formulation "is consistent with theories of urban land value which hold that accessibility
advantages are capitalized in the land price." (Jackson, 1979, pg. 467)
An OLS assumption that has a high potential to be violated and yet often goes
unchecked in hedonic price equations which incorporate measures of location is that error
terms are not spatially correlated; this problem is discussed by Cliff and Ord (1973).
However, Jackson's methodology for incorporating accessibility was also shown as a way
in which to reduce the likelihood of encountering estimation problems caused by spatially
dependent (autocorrelated) error terms.
Price Model Summary
From the alternative model specifications reviewed here, it is Jackson's (1979)
polynomial expression of land prices that seems the most promising for the examination
of spatial variation in house price appreciation. Jackson's work is the foundation for this
research; however, in this research there are significant differences. Jackson used census
tract rents for one time period while this investigation uses actual house sales (aggregated
at a much smaller geographic level) to estimate house price equations for multiple time
periods. These data are discussed in more detail in the following chapter while specific
methodologies are discussed in chapter 4.
Source and Scope of the Data
This research analyzes the Jacksonville, Florida housing market. With regard to
boundaries, the city of Jacksonville is synonymous with Duval County. As this study is
concerned with urban housing, a 154-square-mile study area (see Figure 3-1) is defined.
Miles A re
Figure 3-1 Duval County and Study Area
This (11 mile by 14 mile) study area contains what could be characterized as an urban
density of housing. It is physically bounded to the west by Interstate 295 and to the north
by the St. Johns River and is logically bounded in all directions by a paucity of housing.
The study area and major urban nodes and axes are shown in Figure 3-2.
Figure 3-2 Study Area and Major Nodes and Axes
The data come from the Florida Department of Revenue's (DOR) property tax
records. These data are compiled each year by the DOR and maintained as a multi-tape
database which includes information on every parcel in the state of Florida. These data
include square footage, age, lot size, last sales price and date, and previous sales price and
date. To adjust for any mispricing (due to improvements, family sales, etc.) the data have
been carefully cleaned; detailed procurement, cleaning, and manipulation procedures are
presented in Appendix A.
The data span the years 1979 to 1990 and are aggregated temporally into biannual
time periods. Within the 154-square-mile study area, there are an average of 1,928 sales
per biannual time period or a total of 11,570 sales over the entire 12 year period. Of
these, there are 3,998 houses which sold twice and are used in the repeat-sales analysis.
Using a geographic information system (GIS) address matching procedure, all
properties are geo-coded. This process searches a street database and interpolates a
(latitude / longitude) point based on the house number contained within the range for its
block. Latitude / longitude coordinates are then converted into Cartesian coordinates with
an origin at the southwest corer of the county.
GIS is also used to determine optimal area units (described below) and, using a
point in polygon procedure, aggregate individual property characteristics into the specified
areal units. Finally, once points of maximum (minimum) appreciation are identified, GIS
is used to calculate distances from every house to those points; this is for use in the
repeat-sales spline regression.
The data are aggregated both geographically and temporally. The rational for
geographic aggregation is that too much "noise" exists at the individual house level; that
is, there is excess variation in house price beyond that which can be explained by square
footage, age, and lot size. The rational for temporal aggregation is, first, that there are
only minor price changes over space on an annual basis and, second, that temporal
aggregation allows geographic aggregation at a smaller geographic level.
A number of preliminary tests using third and fourth order expansions of Jackson's
(equation 9) model are performed to determine an optimal aggregation technique. Using
individual sales, about half of the interactive terms are significant but the overall
explanatory power of the model is lower (R2 statistics of approximately 0.80) than
expected. This is likely due to unobservable differences such as maintenance, overall
quality, and amenities in individual houses.
Aggregation at the census tract level is too broad; the explanatory power of the
model is improved (R2 statistics of around 0.85) but few interactive terms are statistically
significant. Aggregation at the census block group level produces better results (R2
statistics nearing 0.90 with over half of the interactive terms significant) but the number
of house sales vary tremendously between block groups.
A spatial moving average (using 1 mile radial areas at 1 mile increments) is also
created; this produces superior results (R2 statistics over 0.90 with most of the interactive
terms highly significant). However, this method is rejected because of the double
counting of house sales. Finally, a 140 cell grid (see Figure 3-3) system that seeks to
minimize the variation in number of sales between geographic units is partitioned.
Figure 3-3 Study Area Grid System
This system is based on a grid of quarter sections where a section equals one
square mile. Quarter sections are joined in such a manner that each unit contains as
nearly an equal number of sales for each time period; there are an average of 14 sales per
areal unit and a minimum of 4 sales per areal unit for each time period. This model has
good explanatory power (R2 statistics of 0.94 to 0.96) and many of the interactive terms
are highly significant. It is the preferable method because it allows the greatest number
of geographic units with the most evenly aggregated number of house sales. This grid
system reflects a more even spatial distribution of house sales.
In aggregating the data, the mean is taken for the variables of price, square
footage, age, and lot size for each grid cell for each time period. The (X,Y) coordinates
for each cell are not the cell centroid but, rather, the mean (X,Y) coordinate for all houses
(regardless of year of sale) in that grid cell. These coordinates are then used in the
interactive terms for all time periods.
The data are aggregated temporally into biannual time periods to allow geographic
aggregation within a greater number of (smaller) grid cells. Additionally, it is observed
that there is a relatively minor change (about 5 percent) in prices on an annual basis.
However, strong motivation exists for the adjustment (compounding forward or
discounting back) of house prices. Because models seek to estimate price changes over
both time and space, a greater possibility exists for bias (due to time of sale) between
A price index is created for the entire study area using average house sales; this
index is nearly identical to indices created with hedonic regression and repeat-sales.
These annual urban appreciation rates are used to adjust actual sales prices on a monthly
basis. For example, time period "1980" contains 1979 sales which are compounded
forward to the midpoint of the 24-month period and 1980 sales which are discounted back
to the midpoint. That is, for time period 1980, individual sale prices are compounded /
discounted to January 1, 1980 using the price index. In this fashion, data sets are created
for the 6 biannual time periods, 1980 through 1990. These data sets will be used to
estimate six strictly cross-sectional hedonic models; the equations are then used to predict
appreciation rates over space.
Data used in the repeat-sales technique are individual houses which sold twice;
these data thus preserve information that is lost in aggregation. The spatial distribution
of these (3998) data points is shown in Figure 3-4.
Figure 3-4 Spatial Distribution of Repeat Sales Observations
This data set is used to test the existence of any predicted abnormal appreciation.
Additionally, it is used to estimate the radial extent of any abnormal appreciation; the
methodology is discussed in the following chapter.
Hedonic Price Equations
A hedonic regression model that allows land prices to vary spatially is not only
intuitively appealing, but may provide more accurate structural and locational coefficient
estimates. Additionally, simultaneous-equation estimation may be preferable to single-
equation estimation as contemporaneous correlation may be present in the error structure
of the models. Regression assumptions are discussed in Appendix B.
Using the data discussed in the prior chapter, four model specifications are tested.
These are the naive model with single-equation estimation; the naive model with
simultaneous-equations estimation; the interactive model with single-equation estimation;
and the interactive model with simultaneous-equations estimation.
Naive versus Interactive Model
Models that incorporate the price of land as either spatially variant or aspatial are
compared here; the aspatial or "naive" model is the standard hedonic price equation
defined in equation (1):
P, = 0, SQFT, + 2, AGE, + 3, LOT, + e, (11)
where P, is the mean transaction price of all houses in grid cell i, i = 1 to 140, and
estimated as a linear function of SQFTi, the mean structural square footage, AGE,, the
mean building age, and LOT,, the mean lot size. Following from Jackson's (1979) model,
an interactive model that interacts lot size with a polynomial land price surface is derived:
P, = P3 SQFT, + P2 AGE, + Ejk P3 [ LOT, f,(X,Y)] + Ei (12)
where fi(X,Y), j = 1 to k, is a polynomial expansion of (X, Y) coordinates. According
to this model specification, the structural characteristics of square footage and age are
considered spatially constant while lot size interacts with the polynomial terms, allowing
the price of land to vary spatially.
The primary advantages of this specification over Jackson's (1979) model are: the
use of actual sales data; multiple time periods; aggregation at much smaller geographic
units; and the origin of the Cartesian coordinate system. Although Jackson's use of an
origin at the data (X,Y) median allows interactive coefficients to be interpreted as partial
derivatives, there is no theoretical justification for his "double power series" representation
of price that this method manifests. Based upon preliminary tests of both methodologies,
an origin outside of the data set seems to offer more reasonable results and is used here.
Single versus Simultaneous Estimation
Separate estimation of the interactive model for each of the six time periods
produces many coefficient estimates on square footage, age, and the interactive terms that
exhibit relatively strong temporal patterns. These temporal patterns suggest a spatial
pattern of house price appreciation. If this is so, the data should be regarded not only as
cross-sectional but as time-series as well. This implies that error terms in equations for
different time periods may be autocorrelated at a given point in time but not necessarily
correlated over time. This is known as contemporaneous correlation and is discussed by
One method of combining cross-sectional and time-series data effectively "stacks"
the regression equations and estimates model coefficients (for all time periods)
simultaneously via a generalized least squares (GLS) technique. The possible gain in the
efficiency of the model obtained by simultaneously estimating price equations for all time
periods led Zellner (1968) to assign the title "a set of seemingly unrelated regression
equations." Seemingly unrelated regression (SUR) estimation is employed for both the
naive and interactive price models. A more technical description of the seemingly
unrelated regression procedure is presented in Appendix C.
Spatial Autoregressive Variable
The interactive model will estimate an overall assessment of the intraurban
variation in land price. To examine more "localized" effects, a spatial autoregressive
price variable is created. This is an average of price in all contiguous grid cells; the
variable is defined as follows:
SAP = [ E c, PJ / E ci (13)
where SAP, is the spatial autoregressive price variable and c, is a binary connectivity
matrix that denotes the connectivity of each cell with all other cells. The matrix is based
on what Cliff and Ord (1973) refer to as a "Queen's case" (edge-to-edge and vertex-to-
vertex) set of joins. This variable is created for each time period and tested as an
additional variable in the interactive models.
The results of the four model specifications are compared with respect to
coefficient estimation and spatially dependent error terms. Based on these criteria, the
"superior" model specification is selected.
Component Prices of Structure and Land
The estimated coefficient price for square footage represents the unit price of
structural components; over time, this coefficient should more or less emulate a general
construction price index. Because the cost of materials to construct a house will generally
rise over time in an approximation of such an index. Estimated coefficient prices on
square footage are compared to the Producer Price Index (PPI) for construction materials,
a national index. These coefficients would be expected to be positive and can directly
be interpreted as the price per square foot to construct a new house in the expressed time
The implicit price for age represents a measure of depreciation. This coefficient
would be expected to be negative and to remain fairly constant over time. However, as
the age variable in this data set is calculated as age in 1995 rather than age in the year
of sale, the coefficient on age should become slightly more negative with each successive
The coefficient on lot size represents the unit price of land. These are estimated
directly for the naive models and expected to be positive. For the interactive models,
these terms are not directly interpretable although, based upon predicted prices, an overall
(urban) estimate of price per square foot of land for each time period can be derived.
Unlike coefficient estimates for structural square footage and age, however, there are no
obvious expectations as to how the unit price of land should behave over time.
It is unclear how the pattern of these coefficients over time will vary between each
of the four models. However, the extent to which the temporal patterns of these
coefficient estimates follow the above expectations will be the primary criterion for
determining the superior model specification.
Consideration of Spatial Autocorrelation
A model specification that produces the best linear unbiased estimate assumes that
error terms are not correlated; however, in the case of these cross-sectional price
equations, the existence of spatial autocorrelation should be a distinct concern. Various
methods are available for testing the spatial dependence of error terms. Here, a regression
technique that is discussed by Cliff and Ord (1973) is employed:
Ei = 0 + p [ wj eij + K,
where wij = c, I/ j" ci for connectivity matrix cil where i and j are adjoining (Queen's
case join) areas. The constant, 0, is assumed to equal 0 and I, is a normal, random, and
independent error term. Statistical tests which reject (the null hypothesis that) p = 0
indicate that correlation exists. Tests are performed for each time period in each model.
Spatial Variation in the Price of Land
Spatial variation in the price of land is designated only in the interactive models
and is represented by a third order polynomial surface. While this may seem a rather
rudimentary measure, the objective here is to capture a broad measure of the spatial
variation in house prices over the urban landscape.
In an urban housing market, the demand for accessibility (to employment,
shopping, schools, etc.) is extremely heterogeneous. This makes the evaluation of a land
price surface enigmatic and constrains estimation to the simple third order surface that is
employed here. However, this specification of land price should be sufficient to represent
major spatial patterns in price and to observe changes in those patterns over time.
Interactive model coefficients represent the interaction of lot size with the various
polynomial forms of (X,Y) coordinates. While these interactive coefficient estimates are
not directly interpretable, they can be used to "predict" 3-dimensional land price surfaces.
Predicting Price and Appreciation
Approximate achievement of model expectations defined above along with
diminished spatial dependence of the error terms will identify the superior model
specification and estimation method. That model specification is used to predict prices
for each time period; predicted prices are then used to calculate appreciation rates.
Appreciation is calculated as the average annualized change in price between (two-year)
time periods and is therefore expressed as an average annualized rate.
Standard Housing Prices
House prices are predicted using a standard bundle of square footage, age, and lot
size. These standard characteristics are simultaneously averaged over the urban area and
over the different time periods and are shown in Table 4-1.
Table 4-1 Standardized Housing Characteristics
Structural Square Footage (SQFT) 1488
Age of Structure (AGE) 37.51
Square Footage of Land (LOT) 13,360
The interactive house price equation predicts house prices at different points in
(X,Y) space; these price (trend) surfaces are demonstrated visually with 3-dimensional
maps for each time period. Using the standard bundle, housing characteristics are held
constant over space and, therefore, the house price surface at any point in time will
replicate the land price surface.
Actual housing prices are likely to vary widely over the urban area. Because this
model allows prices to be separated for land and structure, structural characteristics can
be held constant to observe the variation in price over time (i.e., appreciation) due
primarily to location in space.
The superior model is then used to reveal the separation of appreciation into
structural and locational elements. Land prices are averaged over space so that overall
(temporal) structural appreciation can be compared to the overall temporal appreciation
of land alone. The total "composite" (land plus structure) cumulative appreciation rate
is then calculated; this (hedonic composite) index should approximate a cumulative
appreciation rate derived from alternative methodologies such as an average price index
or repeat-sales price index.
Finally, the model is used to predict (standard) house prices for the 140 points in
space and, from those prices, infer average annualized rates of appreciation. A two-year
appreciation rate is calculated between each time period; an average is then taken of those
rates and annualized for all 140 points. Then, areas of predicted abnormal appreciation
This specification allows the observation of appreciation due solely to location, an
approach that would not be possible with models that do not fully incorporate location.
This may reveal appreciation characteristics that would be otherwise masked by the
spatial or non-spatial variation in other housing attributes. The mixture of house size, age
of structure, and lot size differs across the urban area and actual appreciation would be
expected to be more erratic than predicted (constant quality) appreciation due to variation
in demand for non-locational attributes. Theory would suggest that age and lot size show
more explicit spatial patterns while house size is more likely to be scattered and have less
of a spatial pattern. While these characteristics may influence appreciation, this
methodology predicts for the (constant quality) standard bundle and therefore measures
the effects of "pure" spatial influences due only to location.
Patterns of Appreciation
Using the hedonic model with predicted appreciation as the dependent variable,
both structural and spatial patterns of house price appreciation are investigated. First,
structural characteristics are investigated. The work of deLeeuw and Struyk (1975)
suggests that larger and newer houses will experience more rapid price appreciation; the
(null) hypothesis that size and age do not influence appreciation will be tested with the
A, = p3 SQFT, + 32 AGEi + 13 LOT, + e, (15)
where the average annualized appreciation rate A, is expressed as a linear function of
SQFT,, the mean structural square footage, AGE,, the mean age of the structure, and
LOT,, the mean lot size. Appreciation rates are regressed on these variables individually
and in the multivariate equation above. The effect of house price (in 1980) is also
investigated. As house price is assumed to be a linear function of square footage, age,
and lot size, it is analyzed alone.
The existence of any abnormal appreciation may indicate that there is spatial
variation in appreciation but it does not necessarily indicate any spatial pattern. Variation
in appreciation may be explained not just by location but by demand for specific types
of housing. However, with the predictive model, spatial patterns in appreciation may be
more evident due to standard (constant quality across space) housing.
Regressing predicted appreciation on a polynomial expansion of (X,Y) coordinates
will provide a test of the (null) hypothesis that no spatial pattern of house price
appreciation exists. A third-order polynomial expansion of the TSA model, equation (8),
A, = Ej3'k3 pjk [X, Yik] + Ei (16)
where A, is the average annualized appreciation rate in grid cell i; p~k, denotes a vector of
coefficients of Xi, and Yi, Cartesian coordinates of the grid cells and j + k < 3, where the
model is a third order polynomial.
Although the coefficients in this equation lack any explanatory meaning, high
statistical significance (of the coefficients) would indicate that spatial patterns do exist.
Spatial patterns could be expected as A, represents the average percentage difference
between polynomial smoothed functions using a standard bundle of housing
characteristics. The trend surface (TSA) equation is best represented visually; using
computer graphics software, a 3-dimensional "appreciation" surface is created by graphing
Tests Using Repeat-Sales
Variation in appreciation due to location in space may be suggested by differences
in the (interactive) hedonic model while spatial patterns may be implied by the TSA
appreciation equation above. To verify the existence of any predicted abnormal
appreciation, additional analyses are performed using the repeat-sales technique. These
will test for any significant difference in price appreciation based upon individual houses
which have sold twice.
The implicit assumption in the repeat-sales approach is that the quality of these
houses has remained constant over time. Following Archer, Gatzlaff, and Ling (1995),
the repeat-sales equation here estimates a dual index in an extension from equation (5)
In (Pi, / Pi,) = E,' c, Dit + t' bt it + e,, (17)
where bit is a dummy variable which equals -1 at the time of initial sale or +1 at the time
of second sale if the property is in an area of (predicted) abnormal appreciation, and 0
otherwise. Now, c, is the logarithm of the cumulative price index in period t for the
general market and e, is the logarithm of any additional (positive or negative) cumulative
appreciation due to being in an abnormal appreciation submarkett."
Areas of predicted abnormal appreciation may be indicated by the interactive
model. Spatial patterns of appreciation may also be indicated by the TSA model,
prompting an analysis of the extent of abnormal appreciation. A spline technique is
applied where multiple iterations of the model are run to estimate the distance effects of
any abnormal appreciation.
The spline regression is a methodology which tests many (radial) distances to
determine a "threshold" distance at which the difference between two areas is most
pronounced. Here, distance intervals of 0.10 miles will be tested. The computer program
for running the spline regression is included in Appendix D. The optimum model, based
on coefficient t-statistics, will converge on a radial distance that contains a minimum
number of observations and captures the greatest difference (in appreciation) between
market and submarket. Repeat-sales tests based on individual sale transactions that verify
the location of abnormal appreciation would strongly support the relevance of the
interactive model. Indeed, the corroboration of model results at the individual house level
with those from a generalized price model would have significant implications.
Methodology Summary and Assumptions
This methodology is based on the work of Jackson (1979) with substantial
expansion. The methodology can be summarized in an 8-step procedure as follows:
1) Estimate the four model specifications, compare coefficient estimates, and identify
the superior model specification to use for all prediction.
2) Predict and visually demonstrate land value surfaces.
3) Compare the appreciation of structural characteristics to the (spatially averaged)
appreciation of land. Additionally, compare a composite price index (of land and
structure) to other temporal price indices.
4) From the equations, calculate house price appreciation over space and identify
areas of predicted abnormal appreciation.
5) Analyze appreciation as a function of housing (structural) characteristics as well
as price (in 1980).
6) Analyze appreciation as a function of location, and visually demonstrate spatial
patterns of appreciation.
7) Estimate the radial distances (about maximum and minimum points of predicted
appreciation) at which houses within exhibit the greatest difference in appreciation
from the rest of the market.
8) Test for statistically significant differences (between market and submarket) and
visually graph a temporal price index for the market and any submarkets of
Results for steps 1 and 2 are discussed in the following chapter. There, the
superior model specification and estimation method is identified and used to predict land
price surfaces. Results for the remaining steps are discussed in chapter 6.
This methodology has some limitations and also makes some explicit assumptions
as to simplify the procedures and more easily interpret the results. Some basic
definitions, limitations and assumptions are summarized as follows:
1) In this research the word "appreciation" can, as in the urban economics literature,
refer to either appreciation (rising prices) or depreciation (falling prices). In
Jacksonville during the 1980s, house prices were generally rising; however, the
methodologies specified here can accommodate (and accordingly measure) both
rising and falling prices.
2) The definition "abnormal appreciation" refers to prices that are rising at an
appreciation rate that is above (positive abnormal) or below (negative abnormal)
the average rate of appreciation. For the hedonic models, this is defined as 2
standard deviations from the mean, i.e., significant at the 0.05 level, assuming a
normal distribution of appreciation rates. For the repeat-sales model, this is
defined as statistically different from the market at the 0.05 significance level.
3) Prices are expressed in nominal dollars. Although prices are compounded forward
(or discounted back) to the midpoint of the 24-month period using an urban house
price index, there is no adjustment to real dollars. For the study of spatial
variation in price appreciation, the use of real or nominal dollars is irrelevant.
4) The limitation of the study area to a 154-square-mile area has potential boundary
problems in that major urban nodes or other important influences may be located
just outside the study area. However, the polynomial expression of land price
should reflect the influence of any external effects that are located outside the
5) The structural variables of square footage and age are somewhat limited but they
are the only structural variables available in the (Florida DOR) data set. However,
as other studies have shown, these variables are the most important and are
sufficient for the generation of hedonic indices (Gatzlaff and Ling, 1994).
6) The polynomial expression is rather limiting in its ability to estimate spatial
variation in the price of land. Jackson (1979) employed a fourth-order model;
preliminary tests of the data here suggest that only a third-order model will work
well in all time periods. However, this expression should be sufficient to capture
significant variation in house prices.
7) Many alternative functional forms of the estimating equation are available,
including log-linear, semi-log, and Box-Cox transformation. However, preliminary
tests suggest that such functional forms do not offer significant improvement over
the linear/polynomial form that is specified here.
Additional definitions, limitations and assumptions are discussed elsewhere in the
text where appropriate. For example, linear regression assumptions are discussed in
Appendix B. Alternative solutions and suggestions are offered in chapter 7 under
"Directions for Further Research." Results for the price equations are examined in the
PRICE EQUATION RESULTS
Price Model Comparison
Price equations are estimated for six different time periods using both single
period estimation and simultaneous, seemingly unrelated, regression (SUR) estimation for
both the naive and interactive models. Four model specifications are defined as follows:
1) naive, single-equation estimation (NSE)
2) naive, seemingly unrelated, regression estimation (NSUR)
3) interactive, single-equation estimation (ISE)
4) interactive, seemingly unrelated, regression estimation (ISUR)
These model specifications and estimation methods are compared with respect to
coefficient estimates of structural (unit) prices and land (unit) prices, as well as spatially
dependent error terms. The superior model specification will be used for prediction.
The aspatial or naive model is a standard, strictly cross-sectional hedonic price
equation of the following form:
P, = Po + Pi SQFTi + P2 AGE, + 33 LOT, + ei
Naive model variables are described as follows:
P, the mean of actual transaction prices that have been compounded forward
or discounted back to January 1 of the time period year at the overall
urban rate of appreciation (each time period contains sales from two years)
SQFI, the mean structural square footage for the given time period
AGE, the mean (1995) building age for the given time period
LOT, the mean lot size for the given time period
This model specification is used in both the single-equation estimation (NSE) and
simultaneous-equation estimation (NSUR) naive models. The spatial or interactive model
interacts lot size with a polynomial expansion of (X, Y) coordinates as follows:
P, = i, SQFT, + ,2 AGE, + E, P3 [ LOT, fJ(X,Y)] + E
Cartesian coordinates are the average X and Y coordinates. Because of
multicollinearity problems, the interactive terms of L_XY,, L_X3i, and L_X3, are dropped,
leaving the following interactive terms:
L_X, the product of lot size times X
L_Yi the product of lot size times Y
L_X2, the product of lot size times X-squared
L_Y2, the product of lot size times Y-squared
L_X2Y the product of lot size times X-squared times Y
L_XY2 the product of lot size times X times Y-squared
This (third order) model specification is used in both the single-equation (ISE) and
simultaneous-estimation (ISUR) interactive models. Alternative functional (logarithmic)
forms are tested for single-equation estimation models but offer no significant
improvement. The linear model also provides more directly interpretable results.
Structural Unit Prices
Structural prices (per square foot) are assumed to be spatially constant in all
models. However, estimated prices vary significantly between model specifications. The
coefficients on square footage (in dollars) are shown in Table 5-1; these are all significant
at the 0.001 level or better. Complete results are presented in Appendices E through H.
Table 5-1 Coefficients on Square Footage of Structure
NSE NSUR ISE ISUR
1980 25.16 21.98 24.08 23.57
1982 32.06 26.38 27.70 26.48
1984 38.99 30.32 31.18 30.02
1986 36.88 30.58 32.01 31.38
1988 44.32 36.33 33.38 32.48
1990 38.28 31.79 31.25 30.93
These coefficients can directly be interpreted as the price per square foot to
construct a new house in the expressed time period.
estimation of the interactive model (ISUR) predicts a temporal index (based on estimated
coefficients) that are more similar to the Producer Price Index (PPI) for construction
materials than the other model specifications. Square footage price coefficients for all
model specifications (from Table 5-1) are converted to indices. All estimated coefficient
prices are divided by the 1980 coefficient price; this generates cumulative indices that are
set to value of 1 in 1980. In Table 5-2, these are compared to the PPI index which is
adjusted (to value of 1 in 1980) in the same manner. The correlation coefficients between
these model coefficients and the PPI index are then shown in Table 5-3.
Table 5-2 Indices for Square Footage and Producer Price Index
NSE NSUR ISE ISUR PPI
1980 1.000 1.000 1.000 1.000 1.000
1982 1.274 1.200 1.150 1.123 1.095
1984 1.550 1.379 1.295 1.274 1.156
1986 1.466 1.391 1.329 1.331 1.184
1988 1.762 1.653 1.386 1.378 1.272
1990 1.521 1.446 1.298 1.312 1.346
Table 5-3 Correlation of Coefficients with Producer Price Index
NSE NSUR ISE ISUR
PP INDEX 0.835 0.875 0.850 0.881
The ISUR model specification predicts a temporal index (of coefficient
prices on square footage) that most closely emulates the Producer Price Index for
construction materials. These two indices demonstrate roughly the same cumulative
appreciation (31 and 34 percent) in 1990. Additionally, the simultaneously estimated
interactive model is most highly correlated with the Producer Price Index for construction
materials between 1980 and 1990.
Structural depreciation is estimated using the average age of houses; this variable
is also assumed to be spatially constant. Again, estimation of coefficient prices varies
between models as shown in Table 5-4; these coefficients represent dollars of depreciation
for each additional year of house age and are all significant at the 0.001 level or better.
Table 5-4 Coefficients on Age of Structure
NSE NSUR ISE ISUR
1980 -220.92 -282.78 -217.91 -186.30
1982 -248.49 -344.11 -333.62 -266.91
1984 -285.00 -370.37 -385.11 -317.08
1986 -272.43 -351.93 -391.35 -335.39
1988 -112.36 -203.52 -396.08 -325.14
1990 -170.96 -219.37 -393.96 -317.11
The ISUR model specification predicts a temporal progression of coefficients that
is more systematic than the other models. Specifically, this follows the expectation that,
because the age variable in this data set is calculated as age in 1995 rather than age in
the year of sale, the coefficient on age should become slightly more negative with each
successive time period.
These coefficients can directly be interpreted as the amount of physical
depreciation that occurred (on average) in the specific time period. To be expressed as
a percentage, construction costs (square footage coefficients times average square footage)
are subtracted from house (structure only) prices predicted by the simultaneous-equations
estimation of the interactive model. This yields a cumulative physical depreciation
estimate of approximately 14 percent.
Land Unit Prices
Land prices (per square foot) are assumed to be spatially constant in the naive
models but are allowed to vary spatially in the interactive models. Estimation of
coefficient prices varies somewhat between model specifications and estimation methods;
these are shown (in dollars per square foot) below in Table 5-5.
Table 5-5 Coefficients on Square Footage of Land
NSE NSUR ISE' ISUR*
1980 0.862 0.878 0.780 0.730
1982 1.163 1.192 1.232 1.151
1984 1.096 1.393 1.480 1.382
1986 1.531 1.671 1.804 1.690
1988 1.613 1.802 2.047 1.917
1990 2.059 2.226 2.382 2.174
* implied spatial average (not actual) coefficient
The coefficients shown above for the interactive models are calculated by
predicting the land value at the (140) points in space and taking a spatial average. While
these averages are in line with naive model results temporally, the focus of the
investigation here is the variation of land values over space. Significant spatial variation
is found to exist; Table 5-6 demonstrates the variation (standard deviation and range) in
land price (in dollars per square foot) over the (n = 140) grid cell space.
Table 5-6 Summary Statistics for Land Unit Prices over Space
MEAN STD. DEV. MINIMUM MAXIMUM
1980 0.730 0.121 0.163 1.032
1982 1.151 0.143 0.232 1.568
1984 1.382 0.130 0.712 1.799
1986 1.690 0.117 1.313 2.031
1988 1.917 0.130 1.516 2.148
1990 2.174 0.174 1.646 2.648
Spatial Autoregressive Variable
The interactive model will estimate an overall assessment of the intraurban
variation in land price. To examine more "localized" effects, a spatial autoregressive
price variable has been created; this variable is an average of price in all contiguous grid
cells based upon the Cliff and Ord (1973) "Queen's case" (edge-to-edge and vertex-to-
vertex) set of joins.
The spatial autoregressive variable is tested as an additional variable in the
interactive models. Alone, this variable is statistically significant. However, when it is
included as an additional variable along with square footage, age, and the interactive
terms, it becomes insignificant in all years. This suggests that the interactive models,
with their third-order polynomial expression of land prices, are sufficiently explaining the
spatial variation in house prices--or at least the spatial variation that can be estimated
from the data available.
Spatial Dependence of Error Terms
Various methods are available for testing the spatial dependence of error terms;
here, a regression technique is employed. Tests are performed for each time period in
each model; t-statistics are presented in Table 5-7 where the critical value of t at the 0.05
significance level using a two-tail test is 1.98. These results demonstrate the ability of
the ISUR model specification to reduce spatially autocorrelated error terms.
Table 5-7 t-statistics on Tests for Spatial Dependence
NSE NSUR ISE ISUR
1980 3.982 4.746 2.837 2.487
1982 2.562 4.979 1.978 0.751
1984 4.827 5.244 4.095 2.247
1986 5.885 7.116 4.477 2.625
1988 4.316 5.959 4.502 2.703
1990 5.430 6.061 3.172 1.977
Model Estimation and Prediction
The ISUR model specification is chosen as the best overall model and is used to
predict house price variation over space. House prices are predicted for each time period
by applying the estimated implicit prices to a standardized bundle of housing attributes.
Standardized housing characteristics of square footage, age, and lot size are calculated as
the combined average over time and space for all houses.
The ISUR model specification produces simultaneous-equations estimation of
structural and (interactive) locational model coefficients for all time periods. Structural
coefficients are significant at the 0.001 level while interactive coefficients are nearly all
significant at the 0.05 level; estimates are shown below in Table 5-8.
Table 5-8 ISUR Equation Coefficients
1980 1982 1984 1986 1988 1990
SQFT 23.57 26.48 30.02 31.38 32.48 30.93
AGE -186.30 -266.91 -317.08 -335.39 -325.14 -317.11
L_X -168.63 -569.65 -499.74 -547.31 -398.33 -406.13
L_Y 478.1 1206.1 1056.9 1128.5 986.22 1031.1
L_X2 9.04 26.25 24.95 27.43 20.91 23.09
L_Y2 -43.55 -92.32 -80.87 -79.50 -70.24 -75.24
L_X2Y -0.939 -2.194 -2.106 -2.215 -1.844 -2.070
L_XY2 1.913 3.955 3.626 3.549 3.044 3.335
Most obvious about the interactive coefficient estimates is their temporal pattern,
that is, the coefficients demonstrate a non-random pattern over time. This strongly
suggests that intraurban variation in the appreciation of urban land may be likely to have
a spatial pattern.
Land Value Prediction
Intraurban variation in house price that is captured in the price equations can be
demonstrated visually. The interactive coefficients can be multiplied by the appropriate
(X,Y) coordinate expansion to predict a set of Z values that are associated with each
(X,Y) point in space. Surface maps are created to demonstrate the spatial variation in
urban land values. For the predictive (standard bundle) model, housing characteristics are
held constant over time and space and therefore the house price surface would be
identical to the land price surface; all Z values are simply shifted upwards by the value
of a standard house.
The three dimensional land value surfaces are created using an 80 X 100 line grid
to represent the 11 mile by 14 mile (154-square-mile) urban area. Therefore, the grid
lines are spaced at approximately 0.14 miles. Input data for the construction of the
surface maps consist of the 140 (X,Y) grid cell coordinates and their associated Z values,
the predicted land values at those points. The surface maps are generated using a
kreiging process which interpolates a smoothed set of Z values over space based on the
uneven distribution of (X,Y) points.
While a series of land value surfaces may suggest a spatial pattern of appreciation,
the equations for these surfaces will be combined to specifically calculate predicted
appreciation rates over space in the following chapter. Specifically, appreciation will be
calculated as the average annualized percentage difference between time periods. Areas
of abnormal (greater or less than two standard deviations from the mean) will be depicted.
Additionally, these appreciation rates will be analyzed as a function of location and used
to create an appreciation rate surface map.
/ Orthographic View Angle
Figure 5-1 Angle of View for Surface Maps
Land value surface maps are created for all time periods, 1980 through 1990, and
show the predicted price surface. The orthographic projection angle is shown above in
Figure 5-1; this is a 225 degree rotation about the Z-axis with a tilt of 30 degrees. These
maps view the study area from the southwest comer looking towards the northeast and
are shown in Figures 5-2 through 5-7.
aI us Surface
Figure 5-2 Land Value Surface for 1980
Figure 5-3 Land Value Surface for 1982
19 2 Land
Figure 5-4 Land Value Surface for 1984
Figure 5-5 Land Value Surface for 1986
Figure 5-5 Land Value Surface for 1986
Figure 5-6 Land Value Surface for 1988
Figure 5-7 Land Value Surface for 1990
The third-order polynomial surfaces derived from the price equations and shown
in Figures 5-2 to 5-7 capture only an abstract representation of the urban dynamics that
occurred during this time span. The maps show the price surface--the spatial variation
from the minimum to maximum value--and they would look identical for predicted land
values only or for predicted values of land and housing. These land price surface maps
demonstrate an obvious temporal pattern of above average price increase in the northwest
and below average price increase in the northeast.
In the following chapter, the price equations are used to compare changes in the
prices of structural characteristics to changes in the (spatially averaged) price of land.
The price equations are then used to determine house price appreciation over space and
identify areas of abnormal appreciation. Appreciation is next analyzed as a function of
housing (structural) characteristics and location. Finally, the repeat-sales technique is
used to verify the existence of abnormal appreciation and estimate the radial distances at
which houses within exhibit the greatest difference in appreciation from the rest of the
HOUSE PRICE APPRECIATION
The preceding chapter identifies the interactive model with simultaneous-equations
estimation (ISUR) as the superior model specification with which to predict prices for
each time period. In this chapter, prices are determined for land and structure separately
so that the appreciation of each can be observed. The composite of locational and
structural appreciation over time is then compared to alternative house price indices.
These predicted prices are then used to calculate appreciation rates where
appreciation is calculated as the average change in price between time periods and is
therefore expressed as an average annualized (two-year) rate. Areas of implied (positive
or negative) abnormal appreciation are identified where abnormal appreciation is defined
as appreciation above or below two standard deviations from the mean rate of
Temporal Implications of the Price Model
Total prices for house, land, and their composite are predicted for a standardized
urban house that has a living area of 1488 square feet, age of 37.5 years, and lot size of
13,360 square feet. To investigate temporal effects, predicted land prices are averaged
(over space) for each time period; this is accomplished by predicting land prices for all
(X,Y) coordinates with the standard lot size and taking an average. Total prices of land,
structure, and their composite are shown in Table 6-1. These prices, in dollars, for house
(structural characteristics), land (location), and their composite are then all divided by
their 1980 price and expressed as indices in Table 6-2.
Table 6-1 Estimated Total Prices
AVERAGE AVERAGE STANDARD
HOUSE LAND' COMPOSITE' DEVIATION
1980 28922 10123 39045 12780
1982 30250 15712 45963 15377
1984 32727 18694 51421 16967
1986 33761 22471 56232 17711
1988 35770 25310 61080 18020
1990 33872 28889 62760 19845
* Average for urban area
Table 6-2 House Price Component Indices
HOUSE LAND COMPOSITE
1980 1.000 1.000 1.000
1982 1.046 1.552 1.177
1984 1.132 1.847 1.317
1986 1.167 2.220 1.440
1988 1.237 2.500 1.564
1990 1.171 2.854 1.607
The composite index is based on predicted total prices and reveals the proportions
of total price due to structure and land. For this time span, approximately 74 percent of
total value is attributable to the structure while 26 percent is attributable to land; these are
averages for the urban area. Additionally, intraurban price indices could be calculated
based on the predicting equations for specific (X,Y) coordinates.
The composite price index predicted by the ISUR model specification, with land
values averaged over the urban area, is equivalent to a standard cross-sectional hedonic
index. This index is compared to an average house price index (based on all sales) and
repeat-sales index (based on houses which sold twice) for the same (1980-1990) time
period in the 154-square-mile urban area. These indices are shown in Table 6-3.
Table 6-3 Alternative House Price Indices
AVERAGE PRICE HEDONIC (ISUR) REPEAT-SALES
1980 1.000 1.000 1.000
1982 1.166 1.177 1.150
1984 1.268 1.317 1.303
1986 1.414 1.440 1.462
1988 1.462 1.564 1.550
1990 1.528 1.607 1.601
The hedonic ISUR index is generated from aggregated biannual sales data. The
average price index and repeat-sales index, however, are based on single year sales; only
the alternate (even-numbered) years are shown above. Regardless, the hedonic index is
similar to the average price index and nearly identical to the repeat-sales index.
The interactive model with simultaneous-equations estimation (ISUR) is shown to
be a superior specification and methodology because coefficient estimates are more fitted
to theoretical expectations. More importantly, the ISUR model specification convincingly
produces a methodology for separating house price from land price and therefore allows
the appreciation of those two components to be observed independently.
The hedonic ISUR (composite) index in Tables 6-2 and 6-3 indicates a cumulative
appreciation rate of 60 percent, approximately 5 percent annualized; this is based on
prices that are averaged over space. These predicted price indices suggest that structural
appreciation (rise in cost of construction less physical depreciation) averaged about 1.6
percent annually while land appreciation averaged approximately 11 percent.
On a cross-sectional basis, the composite price appreciation average is 5.3 percent
annualized with a standard deviation of about 0.5 percent. This is the average of
appreciation rates for different points in space; cross-sectional variation in appreciation
is the central focus of this investigation.
House Price Appreciation
The model is used to predict house prices for (the 140) points in space and, from
those prices, to infer average annualized rates of appreciation. House price appreciation
is predicted using a standard bundle of housing characteristics. These standardized
characteristics are the average for the urban area over all time periods. The standard
house has a living area of 1488 square feet, age of 37.5 years, and lot size of 13,360
square feet. Predicted appreciation is shown in Figure 6-1.
Figure 6-1 Predicted House Price Appreciation
Figure 6-1 shows predicted appreciation in standard deviations where appreciation
is approximately normally distributed. The average appreciation rate is 5.3 percent with
a standard deviation of 0.5 percent. Abnormal positive appreciation is defined as over
6.3 percent (2 standard deviations above the mean) while abnormal negative appreciation
is defined as under 4.3 percent (2 standard deviations below the mean). An area of
predicted abnormal positive appreciation is apparent in the northwest comer of the study
area while an area of abnormal negative appreciation is evident in the northeast.
Figure 6-2 Urban Axes and Areas of Abnormal Appreciation
Figure 6-2 shows the areas of predicted abnormal appreciation in the northwest
(positive) and the northeast (negative) along with major urban axes. Urban axes increase
accessibility to certain areas--in the 1980s, areas in the proximity of 1-295, in the
northwest, and the Dames Point Bridge, in the northeast, realized a change in accessibility
benefits from the construction of these axes. Households in the northwest receive the
benefit of increased accessibility to the Jacksonville International Airport, other interstates,
and the urban center (via 1-10). However, households in the northeast receive a negligible
or even negative benefit due to the Dames Point Bridge. Changes in accessibility benefits
there (access to the urban center) are realized more by households on the north side of
the St. John's River; the south side may have experienced only more congestion and
perhaps more crime, an accessibility dis-benefit.
However, as other work has strongly suggested, it is not highway access alone that
increases the demand for individual sites. For example, in Brigham's (1965)
investigation, an accessibility potential (to employment) variable is considered in addition
to distance gradients alone. The locations of those places being accessed (i.e.,
employment centers, schools, shopping centers, etc.) are, therefore, important in such
house price models.
This model specification avoids the need to know the locations of important nodes;
by specifying the price of land as a polynomial expression, all external effects are
implicitly included in the price of housing. Housing characteristics, however, may have
an effect on appreciation. Averages of housing characteristics are shown in Table 6-4.
Table 6-4 Housing Characteristic Averages for Areas of Abnormal Appreciation
NORTHWEST MARKET NORTHEAST
1980 PRICE 28435 39400 48230
SQUARE FOOTAGE 1220 1488 1705
AGE 37.98 37.49 29.97
LOT SIZE 8612 13360 15462
There are significant differences between housing characteristics in the northwest
and northeast and the overall market. In the following section, housing characteristics are
analyzed as potential explanatory factors of house price appreciation.
Appreciation Equation Results
A hedonic model with appreciation as the dependent variable is used to
investigate both structural and spatial patterns of house price appreciation. Variation in
appreciation may be attributable to housing characteristics of square footage, age, and lot
size, location in space, or their combination. Because appreciation is calculated as the
average percentage change in predicted prices using standard characteristics and a
polynomial expression of land price, spatial patterns may be anticipated.
The effect of structural and lot size characteristics is investigated by regressing
appreciation on actual characteristics for the 140 points in space. The variables are
analyzed individually and together as follows:
A, = Po + Pi X, + e, and Ai = o + Ek p, X, + e,
where pj, 1 to k, represent the characteristic prices of square footage, age and lot size.
Square footage and lot size (in thousands of square feet) are found to have had a
negative influence on appreciation while age appears to have had a positive influence.
These effects are observed in both a univariate and multivariate regression equations. In
the multivariate equation, square footage becomes statistically insignificant, due most
likely to its relatively high correlation (r = 0.85) with lot size.
Coefficient estimates for all characteristics are extremely small; large unit changes
would have negligible effects on appreciation. Additionally, R-squared statistics on these
equations are small, ranging between 0.10 and 0.20. So, while these characteristics may
have a small significant effect, they explain very little of the variation in appreciation.
Table 6-5 shows basic results (coefficients and associated t-statistics) of the individual
(univariate) and joint (multivariate) regressions; full results are given in Appendix I.
Table 6-5 Effects of Structural and Lot Size Characteristics on Appreciation
UNIVAR. UNIVAR. MULTIVAR. MULTIVAR.
COEFF. T-STAT. COEFF. T-STAT.
SQFT -.0000078 -4.756 .0000005 0.170
AGE .0002407 4.143 .0001476 2.517
LOT -.0006627 -5.699 -.0005848 -2.616
These statistics suggest that smaller and older houses experience greater price
appreciation; a finding which contradicts the work of deLeeuw and Struyk (1975).
However, these results, along with results from the price model strongly suggest that it
is the demand for accessibility (location) rather than the demand for specific types of
housing that is the primary driver of intraurban house price appreciation.
Effects of Price
The above results suggest that, while the relationships between house price
appreciation and housing characteristics are statistically significant, estimated coefficients
(interpretable as the increase in appreciation for a one unit change in the characteristic)
are very small and have a negligible effect. Housing markets may be segmented by size
or age, but also by price. Indeed, house price has been shown to be a linear function of
house size, age, and lot size. As a basis for market segmentation, price is intuitively
appealing because it is the basis for demand. Households with different income levels
are limited, at least on the upper end, to the range of house prices they can afford.
Figure 6-3 Spatial Variation in House Price
The spatial distribution of (1980) house price is shown in Figure 6-3. Most
noticeably, the more expensive houses tend to be located along the eastern and
southwestern shores of the St. John's River; these houses are located in Jacksonville's
more exclusive residential neighborhoods. They also tend to be larger; house price is
highly correlated (r = 0.935) with house size. To test the effects of price on appreciation,
appreciation rates are regressed on (1980) house prices for the 140 grid cells. Table 6-6
shows basic statistical results.
Table 6-6 Statistics for the Regression of Appreciation on Price
COEFFICIENT STD. ERR. T-STATISTIC
PRICE80 -.00000019 .000000036 -5.360
Price is significant but its effect is small; the coefficient above suggests that for
a thousand dollar increase in price, appreciation will decrease by only 0.02 percent. Such
market segmentation should not be ignored however. Variation in the demand (over
different price levels) for housing may influence appreciation and cloud studies seeking
to determine if such variation is explainable.
However, to investigate spatial patterns of appreciation, housing characteristics
such as price (or size) are not considered; appreciation rates are based on the predictive
(standard bundle) model where all houses are assumed identical. Thus, spatial patterns
of land appreciation--if they exist--will be more obvious and not masked by variation in
housing attributes; this is discussed next.
Spatial Patterns of Appreciation
To investigate the variation in appreciation due to location in space, appreciation
rates are regressed on a polynomial expansion of (X,Y) coordinates. A stepwise
procedure (see Appendix B) selects the most significant variables and drops those which
are likely to cause multicollinearity. The best fitting (TSA) equation is as follows:
A, = 0 + 0 + Xi + Yi + P Xi2 + p4 X2Y + p3 XYi + e,
Although the TSA equation lacks any explanatory meaning with regard to direct
interpretation of the coefficients, high statistical significance would indicate that spatial
patterns do exist. Table 6-7 shows t-statistics; full results are given in Appendix I.
Table 6-7 t-statistics for the TSA Appreciation Model
X Y X2 X2Y XY2
T-STATISTIC -18.598 61.225 40.572 -70.692 7.677
The high statistical significance of the coefficients indicate that spatial patterns
indeed exist; the critical value of t at the 0.05 (two-tail) significance level is 1.98. The
adjusted R-squared statistic is 0.996, indicating that the overall explanatory power of the
model is exceptional. However, TSA equations are best demonstrated visually; the
estimated equation is graphed in Figure 6-4.
Figure 6-4 Trend Surface Analysis of Appreciation
The appreciation equation exhibits a spatial pattern that agrees with prior
observation; abnormal positive appreciation is evident in the northwest corer of the study
area while an area of abnormal negative appreciation is obvious in the northeast.
Additionally, significant appreciation can be observed in the southeast, although this has
not been identified as "abnormal." Most importantly, however, is the manifestation of a
very distinct spatial pattern of appreciation.
This manner of calculation makes suggested abnormal appreciation suspect;
predicted appreciation is the average of differences between smoothed polynomial
functions that themselves are based on averages of actual house prices. However, repeat-
sales at the individual house level can be used to test these indications.
To test for the existence of the predicted patterns of positive and negative
abnormal appreciation, additional analyses are performed using the repeat-sales technique.
These tests will identify any significant difference (between the urban market area and
a locational submarket area) in price appreciation based upon individual houses which
have sold twice. The estimating equation is as follows:
In (Pit / Pi) = ET' c, D," + ET t l, + Eit
where the coefficient estimate e, is the logarithm of any additional (positive or negative)
cumulative appreciation due to being in a specific submarket.
Of the 11,570 sales which were aggregated over both space and time, there are
3,998 houses which sold twice. Not only is the data set significantly different, but the
repeat-sales technique is an entirely different methodology; the model provides the
advantage of using full information of the individual observation, thus enabling the
observation of locational effects on appreciation at the individual house level.
Verification of abnormal appreciation using the repeat-sales technique would
strongly support the validity of the simultaneously estimated interactive hedonic model
and the TSA appreciation model. Where the interactive model predicts appreciation from
the "differences" in generalized price surfaces, the repeat-sales model is based upon the
appreciation of houses in the overall market and specific submarket areas.
Figure 6-5 Radial Areas of Abnormal Appreciation
Because spatial patterns of appreciation are evident in the TSA model, a spline
regression procedure is employed to estimate the distance effects of any abnormal
appreciation. In the spline regression, multiple iterations of the model are run to
determine the radial distance (about the maximum and minimum appreciation values) at
which appreciation is most different between market and submarket. For the northwest
(predicted positive abnormal), the radius is 4.4 miles while for the northeast (predicted
negative abnormal), the radius is 2.0 miles. These radial areas identified by the spline
regression are shown in Figure 6-5, above.
The repeat-sales model is used as a test of differences between the specific
submarket and the overall market. Submarket appreciation is considered "abnormal" if
a statistically significant difference exists between the two. The standard statistical
hypothesis that each e, equals zero is evaluated. However, the (null) hypothesis must be
rejected for several years to assume any pattern of abnormal appreciation. More
importantly, the pattern of cumulative appreciation differences should increase (decrease)
over time to support the perception of aberrant appreciation.
The 4.4 mile radial area in the northwest is constrained by the study area
boundary. This is a 31.3 square mile area that contains 185 observed repeat-sales. Table
6-8 demonstrates that appreciation in the northeast is significantly more than the rest of
the market; the critical value of t at the (one-tail) 0.05 significance level is 1.64.
Table 6-8 Submarket Appreciation in the Northwest
COEFF. T-STAT. INDEX MARKET DIFF.
1980 ------ ------ 1.000 1.000 0.000
1981 0.028 0.758 1.120 1.089 0.031
1982 0.023 0.620 1.178 1.151 0.027
1983 0.065 1.858 1.303 1.221 0.082
1984 0.047 1.353 1.369 1.305 0.063
1985 0.070 1.995 1.471 1.371 0.100
1986 0.097 2.936 1.602 1.455 0.148
1987 0.066 1.874 1.615 1.512 0.103
1988 0.104 3.019 1.718 1.548 0.170
1989 0.072 2.042 1.699 1.581 0.118
1990 0.050 1.439 1.694 1.611 0.082
In the northwest, abnormal positive appreciation is evident in all years with an
average annual difference of 9.2 percent. It is statistically significant in 6 years at the
0.05 significance level using a one-tail test. The pattern of annual differences in
appreciation is rather erratic; annual appreciation can be inferred from the difference
column in Table 6-8. This index, along with the indices for the market and the northeast
are graphically illustrated in Figure 6-6. As can be observed there and above, the
cumulative difference follows a steadily increasing pattern between 1982 and 1988.
The 2.0 mile radial area in the northeast is constrained by the St. Johns River and
the study area boundary. This is a 6.4 square mile area that contains 470 observed
repeat-sales. Table 6-9 shows that appreciation in the northeast is significantly less than
the rest of the market; again, the critical value of t at the 0.05 significance level is 1.64.
Table 6-9 Submarket Appreciation in the Northeast
COEFF. T-STAT. INDEX MARKET DIFF.
1980 ------- ------- 1.000 1.000 0.000
1981 -0.024 -0.734 1.065 1.091 -0.026
1982 -0.033 -1.104 1.118 1.155 -0.037
1983 -0.004 -0.142 1.221 1.226 -0.005
1984 -0.032 -1.092 1.270 1.311 -0.041
1985 -0.062 -2.103 1.299 1.383 -0.084
1986 -0.066 -2.382 1.377 1.471 -0.094
1987 -0.091 -3.105 1.395 1.527 -0.132
1988 -0.101 -3.287 1.421 1.571 -0.150
1989 -0.107 -3.615 1.439 1.602 -0.163
1990 -0.096 -3.034 1.477 1.626 -0.148
In the northeast, abnormal negative appreciation is apparent in all years with an
average annual difference of -8.8 percent. It is statistically significant at the 0.05 level
in six years. As demonstrated in Table 6-9 above and illustrated in Figure 6-6 below, the
cumulative difference grew consistently larger between 1984 and 1989.
Figure 6-6 Market and Submarket Price Indices
The graphed indices in Figure 6-6 display a strong negative deviance from the
market in the northeast and a less consistent, but statistically significant, positive deviance
from the market in the northwest. Complete regression results for the northwest and
10 1B81 1982 1883 1984 1985 1988 1997 19
0 NORTHWEST + MARKET 0 NORTHEAST
northeast areas are presented in Appendix J These results strongly support the
conclusions from the predictions of price and appreciation (from the hedonic,
simultaneously estimated, interactive model).
The areas of predicted abnormal appreciation (based on standard deviations from
the mean rate of appreciation) are similar to the radial distances estimated by the spline
regression. In part, the "optimal" radial distance is a function of the number of houses
contained within it; the submarket must contain a minimum number of observations (at
least 100 of the 3998 total observations) but not so many as to lessen differences with the
rest of the market. Thus, the sparsely developed northwest is designated a larger (4.4
mile) radius while the more densely developed northeast has a smaller (2.0 mile) radius.
Abnormal appreciation has been identified by a generalized model using a
rudimentary third-order polynomial expression of land price and aggregate data. The
validity of the implications (with regards to spatial variation in house price appreciation)
of this model is confirmed by an alternative model (repeat-sales) that specifies
appreciation as a function of time alone and uses individual sales observations. A
conclusion and summary of these findings follows in the succeeding chapter.
House Price and Appreciation
From the Brigham (1965) macro-analysis of Los Angeles County (4120 square
miles) to the Johnson and Ragas (1987) micro-analysis of a 1.38 square mile area in New
Orleans, empirical investigation has found strong support for the hypothesis that location
(or accessibility) advantages are captured in the land price. However, house price models
discussed in the literature today typically underspecifiy the characteristics of location. In
the hedonic or repeat-sales equation, areal differentiation using dummy variables can be
used to specify areal units such as census tracts; this is only a discrete measure of
location that disregards potential boundary problems and provides no measure of any
spatial pattern. Hedonic models may include distance gradients to capture distance decay
effects (a spatial pattern) but, like the areal differentiation approach, can capture only
limited aspects of location.
Even multinodal models cannot fully define the properties of location as an
indeterminable number of ever changing externalities exist on the urban landscape. Such
models are appropriate for analyses of particular locational effects but fail to capture the
aggregate effect of location on the price of housing. Location as a "service bundle" is
distinct; each site is unique with respect to its access to the urban environment.
The simultaneous-equations estimation of the interactive model provides a
methodology to fully capture the effect of spatial variation in a hedonic model, at least
on a broad level. While the third-order polynomial specification limits estimation to a
very generalized land value surface, it is sufficient for the purposes of this study. Indeed,
demand for accessibility in the urban housing market is so heterogeneous that the third-
order specification is the only functional form that works well over many time periods
and for that reason is selected here. For other land uses, such as office or retail, demand
for accessibility may be expected to be more consistent, and thus, the use of higher order
functions more appropriate.
Another important observation of the ISUR model specification is that house price
information can be regarded not only as cross-sectional but as time-series as well. The
simultaneous-equations estimation of house price equations using the SUR procedure is
shown to provide a significant gain in the efficiency of the hedonic model. This model
specification produces more reliable coefficient prices (of square footage and age) and
reduces both contemporaneous and spatial autocorrelation of the error terms.
The ability of this model to predict intraurban house prices may also prove
beneficial for other uses such as the setting of mortgage loan limits. The simultaneously
estimated interactive hedonic model may provide a methodology more reliable than those
(median and constant quality) discussed by Hendershott and Thibodeau (1990); the model
has definite advantages with respect to the generation of submarket indices.
However, the major contribution of this model is its ability to reveal the separation
of appreciation into structural and locational components. The fundamental deduction
here is that structural appreciation is due predominately to the rising cost of building
materials (less physical depreciation), thus implying that the majority of all differences
in real appreciation are due to changes in the relative values of location. This perception
agrees with the classical economic ideology that property values are the residual effect
By holding structural characteristics spatially constant and using a standard bundle
of characteristics, the model allows the observation of appreciation due solely to location.
While implicit characteristic prices on square footage and age vary over time, they remain
consistent spatially. It is important to realize that such an investigation could not be
properly conducted with models that do not fully incorporate location in this manner.
This approach also reveals appreciation characteristics that may otherwise be
masked by the variation in other housing attributes; with the predictive model, spatial
patterns in appreciation are more evident. Variation in appreciation may be explained not
just by location but also by demand for specific types and prices of housing. House
price, house size, the age of the structure, and other housing characteristics vary across
the urban area and actual appreciation may be expected to be more erratic than the
predicted (constant quality) appreciation due to variation in demand for non-locational
attributes. Thus, methodologies that do not incorporate measures of location in such a
manner may lack the ability to uncover various idiosyncrasies of house price appreciation.
The fundamental deduction of this investigation is that house price appreciation
varies over the urban area in a spatially and temporally consistent manner. Such variation
is due to the underlying aggregate demand for accessibility benefits; these benefits change
in spatial patterns over time. In an urban housing market, the concept of accessibility is
quite ambiguous; it differs for different households. The model specification used here
captures only an abstract representation of the urban dynamics that occurred during this
time span. This (third-order) function can identify only one absolute maximum and one
absolute minimum point of appreciation; in actuality, many relative maximas and minimas
may be expected.
This research finds no support for theoretical (ex-ante) appreciation expectations
with regards to perimeter location, house age, or house size; to the contrary, it is found
that smaller (and older) houses tended to appreciate more, but only negligibly so. Rather,
it is found that house price appreciation is primarily affected by location and the changes
in accessibility benefits at different locations; these benefits are priced by the market for
residential housing. The changes in accessibility benefits are likely due to new urban
nodes and axes or the changing influences of existing nodes and axes. The findings here
support price appreciation implications from price theory: accessibility benefits are
capitalized in the price and therefore, relative changes in accessibility benefits affect the
level of change (appreciation) in price.
The primary contribution of this analysis is a methodology which reveals the
appreciation maximum and minimum and determines the distance from those points at
which appreciation (for the submarket within that radial area) is most different from
appreciation for the rest of the market. While this captures the spatial pattern of
appreciation and identifies abnormal appreciation in a very general manner, findings are
substantiated by the evidence from repeat-sales.
The repeat-sales model provides strong support for the simultaneously estimated
interactive model and its ability to predict areas of abnormal appreciation. The
simultaneously estimated interactive hedonic model aggregates data both spatially and
temporally and is smoothed over space by its polynomial functional form. The repeat-
sales methodology, on the other hand, preserves full information of the individual house
sale by combining sales data over different holding periods to estimate an annual index
or sets of intraurban indices.
Appreciation in Jacksonville
This research has found that definite spatial pattern of house appreciation were
apparent in Jacksonville during the 1980s. Abnormal positive appreciation was estimated
in the northwest corer of the study area. This above-average appreciation is most easily
explained by the urban axis, 1-295, which was completed in the early 1980s and increased
accessibility in the northwest. Households in the northwest received the accessibility
benefits of increased access to the Jacksonville International Airport and other interstates,
as well as improved access to the urban center.
Abnormal negative appreciation was estimated in the northeast corer of the study
area. This below-average appreciation is most easily explained by another urban axis, the
Dames Point Bridge, but for different reasons. Although construction was not completed
until the late 1980s, commercial activity increased in the northeast corer of the study
area in anticipation of the new bridge. This commercial activity and the additional
congestion that it brought to the area was most likely a principal reason for lower house
price appreciation in the northeast. In fact, the increased access from the north side of
the St. John's river and the increased commercial activity have been major factors in
making this area the highest crime district in Jacksonville.
The price surfaces in Figures 5-2 through 5-7 and the appreciation surface in
Figure 6-4 also identify an emerging urban node in the southeast corer of the study area
although this area was not identified as having "abnormal" appreciation. During the
1980s, the Southpoint Business Park and Mayo Clinic were constructed; as employment
nodes, these appear (at least visually) to have had an impact on housing prices.
For Jacksonville, housing characteristics were statistically significant factors or
house price appreciation, as was house price (in 1980). However, coefficients were very
small and these factors appear to have had a negligible effect. It is quite conceivable that
there was a greater demand for lower-priced housing in Jacksonville in the 1980s and it
is unknown what other factors may have influence housing prices in Jacksonville.
The conclusion from this investigation of house price appreciation in Jacksonville
is that housing characteristics, including price, have little effect on appreciation. Rather,
it is the changes in accessibility benefits that appear to be the fundamental cause. The
works of Brigham (1965), Jackson (1979), Johnson and Ragas (1987), and others have
strongly suggested that land prices are a function of accessibility. This research suggests
that spatial variation in house price appreciation is essentially due to changes in
accessibility, the result of the changing influence of nodes and axes that are integral parts
of the ever-changing urban spatial structure.
Directions for Further Research
Much room remains for improvements on and extensions of the methods used
here. The size of the study area is a primary interest, especially regarding the application
of polynomial expressions of land price. Smaller areas may accommodate higher-order
polynomial functions as evidenced by the Johnson and Ragas (1987) sixth-order function
that was applied to a 1.38 square mile area. The defined (154-square-mile) study area
that is used here is not expected to pose specific boundary problems as the polynomial
expression should theoretically capture the external effects of any influences that are
inside or outside the study area. However, it may prove interesting to investigate the
application of different (third-order and higher) polynomial functions to a larger areas
such as the entire county.
Spatial aggregation is another area of interest. Statistically, more observations
(and thus more degrees of freedom) are desirable and will produce stronger results. The
140-grid-cell aggregation technique that was used here produced better results than
aggregation at the census tract or census block group level. The notion of a spatial
moving average is also intriguing; such an approach was justified by Brigham (1965) as
a way to remove as much spurious variation (in house price) as possible and allow the
investigation of general (rather than local) variations in land values. Brigham's moving
average was one-dimensional (along a vector), but a two-dimensional moving average
could be applied utilizing GIS. This technique was rejected here because of the double
counting of some sales. However, to the extent that such double counting is random, this
technique could be justified and would result in a larger number of observations. In any
aggregation technique, the number of individual houses being aggregated is also a concern
and may influence results.
The structural characteristics of square footage and age were held spatially
constant here with reasonable justification. However, the built form of housing may have
spatial effects; these could be investigated by specifying square footage as spatially
variant. Alternative functional forms could also be further investigated.
This research provides a rudimentary methodology for continuing investigations
of intraurban variation in house price appreciation. The existence of abnormal
appreciation however, does not imply overall abnormal returns. The total return on an
asset is its appreciation (or capital gain) plus its rent (or dividend) yield. Thus, the
relationship of house price appreciation with implicit house rents is an area for
investigation. Additionally, the relationship with various measures of risk (including
variance of appreciation and number of sales) remains an interesting research area.
This research fills a niche in the housing literature. The principal contribution is
a methodology for investigating house price appreciation in a manner that fully
incorporates location and separates the value due to location from the value due to
structural characteristics. As suggested above, there is much room for further addition
to and expansion of this work. Expanding on implications from the house price literature,
this research also provides support for theoretical axioms of spatial variation in house
The data for this study will come from the Florida Department of Revenue's
(DOR) multi-tape database of county property tax records.
Procedure 1: Export DOR data
Read in data tapes to files extracting the following data in DOS (ASCII) format:
Field No. Field Label
01 Parcel ID
04 D.O.R. Land Use Code
06 Total just value
07 Total assessed value
10 Land value
11 Land units code
12 Number of land units
15 Year improvement built
16 Total living area
21 Most recent sale price
22 Most recent sale date
28 Previous sale price
29 Previous sale date
42 Homestead exemption
55 Zip code
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