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Intraurban variation in house price appreciation

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Intraurban variation in house price appreciation a case study, Jacksonville, Florida, 1980-1990
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Smersh, Greg T
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viii, 126 leaves : ill. ; 29 cm.

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Housing ( jstor )
Land use ( jstor )
Least squares ( jstor )
Market prices ( jstor )
Mathematical variables ( jstor )
Modeling ( jstor )
Polynomials ( jstor )
Price indices ( jstor )
Prices ( jstor )
Spatial models ( jstor )
Dissertations, Academic -- Geography -- UF
Geography thesis, Ph. D
City of Jacksonville ( local )
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bibliography ( marcgt )
non-fiction ( marcgt )

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Thesis (Ph. D.)--University of Florida, 1995.
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Includes bibliographical references (leaves 119-125).
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Typescript.
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Vita.
Statement of Responsibility:
by Greg T. Smersh.

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INTRAURBAN VARIATION IN
HOUSE PRICE APPRECIATION:
A CASE STUDY,
JACKSONVILLE, FLORIDA, 1980-1990














By

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)













ACKNOWLEDGMENTS


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.


111














TABLE OF CONTENTS



ACKNOWLEDGMENTS ......................................... iii


ABSTRACT ...................................... ........... vii


CHAPTERS

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








APPENDICES


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

By

Greg T. Smersh

August, 1995

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

considered naive.

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

vii








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.


viii













CHAPTER 1
INTRODUCTION


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)

level.

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








2

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.








3
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








4

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








5

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.













CHAPTER 2
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








7

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








8

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








9

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.
(pg. 300)

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.








10
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.








11
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.








13
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

employment centers.

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).








14
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








15
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








16

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.


Theoretical Summary


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.








19
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.








20
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

equation is



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,








21
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.


Multinodal Models


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








22
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

nodes.

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








23
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








24
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

negative externalities.

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

spatial context.

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

(1987) is


Pi = ,j k Ek Pjk [X,' Yik] + E,








25
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.


Accessibility Indices


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








26
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

urban landscape.

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.








27
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).








28
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.













CHAPTER 3
DATA


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.


Duval County,
Florida


Miles A re
--5 10--

Figure 3-1 Duval County and Study Area








30
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








31

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.


GIS Procedures


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.


Aggregation Techniques


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








32
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.


Geographic Aggregation


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








34

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.


Temporal Aggregation


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

geographic units.

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.












Repeat-Sales Data


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.













CHAPTER 4
METHODOLOGY


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)








37
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








38
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

Judge (1985).

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)








39
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.


Model Estimation


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

period.

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








40
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.

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,








41
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








42
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

MEAN
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








43
be held constant to observe the variation in price over time (i.e., appreciation) due

primarily to location in space.


Temporal Implications


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

are identified.

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








44
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

following equation:



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.








45
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),

is employed:



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

the equation.












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)

as follows:



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,








47
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
abnormal appreciation.


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
study area.

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

following chapter.













CHAPTER 5
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.


Model Specification


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








52

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.


The simultaneous-equations


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








53
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







54

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)








55
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








56
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








57

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.








58
Standardized housing characteristics of square footage, age, and lot size are calculated as

the combined average over time and space for all houses.


Price Equations


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.







60
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.












trice








1980 mLand
aI us Surface


Figure 5-2 Land Value Surface for 1980


Figure 5-3 Land Value Surface for 1982


19 2 Land
Value Surface






















1894 Land
VIllu Surface

Figure 5-4 Land Value Surface for 1984


Figure 5-5 Land Value Surface for 1986








1996 Land
alue Surface


Figure 5-5 Land Value Surface for 1986





























Figure 5-6 Land Value Surface for 1988


Figure 5-7 Land Value Surface for 1990








64

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

market.













CHAPTER 6
HOUSE PRICE APPRECIATION


Predicted 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

appreciation.


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








66

(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








67

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.








68
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








71
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.


Characteristic Effects


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.








73

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








74
(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








75

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.












Repeat-Sales Results


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.








80
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








81

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








82

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








83

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.













CHAPTER 7
CONCLUSION


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.








85

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








86
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

of land.

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








87
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.








88
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








89
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








91
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

price appreciation.














APPENDIX A
DATA PROCEDURES


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
51 Address1
52 Address2
53 City
54 State
55 Zip code




Full Text
72
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.
Characteristic Effects
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 + P, X; + E, and A, = ft, + E> P, + e,
where PJ5 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.


85
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


CHAPTER 5
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.
Model Specification
The aspatial or naive model is a standard, strictly cross-sectional hedonic price
equation of the following form:
P, = p0 + [i, SQFT, + p2 AGE¡ + P, LOT, + e,
50


45
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),
is employed:
A, = £j3£k3 Pik [X> Y,k] + e, (16)
where A, is the average annualized appreciation rate in grid cell i; (5jk denotes a vector of
coefficients of X,j and Yik, 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
the equation.


24
where Pu 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 Dit, time dummies with values
of 1 if the house sold in period t and 0 otherwise. Here, (3, denotes a vector of
coefficients on the spatial and aspatial plot-specific characteristics. As measures of
relative location, denotes a vector of coefficients of Rm, distances from positive and
negative externalities.
An expanded model considers the interactive effect between XJjt (zoning) and RlmI
(distance). Alternative functional forms in addition to the linear model were also
estimated including a log-linear transformation (of Pit), 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
spatial context.
TSA is a technique of fitting (absolute) spatial data by regressing the variable in
question (such as land value) on a p'h 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
(1987) is
P, = E/ Ekp pjk [X Y,k] + e,
(8)


63
Figure 5-6 Land Value Surface for 1988
Figure 5-7 Land Value Surface for 1990


113
Estimates for equation: PRICE88
Generalized least squares regression.
Observations
Mean of LHS
StdDev of resid
= 140
= 0.6098215E+05
= 0.5684023E+04
Weights
Std.Dev of LHS
Sum of squares
= ONE
= 0.2036022E+05
= 0.4264671E+10
R-squared
Durbin-Watson
RHO used for GLS
0.9215018E+00 Adjusted R-squared= 0.9173390E+00
2.0394957 Autocorrelation = -0.0197478
0.1516012
Variable
Coefficient
Std. Err
t-ratio
Prob|t|
Mean of X
Std.Dev.
SQFT88
32.480
1.782
18.231
0.00000
1473.2
303.40
AGE 8 8
-325.14
37.46
-8.679
0.00000
37.157
9.0110
LX88
-398.33
262.9
-1.515
0.12973
321.59
126.16
LY88
986.22
434.7
2.269
0.02327
186.06
71.668
LX288
20.907
10.67
1.960
0.05003
8005.2
3970.0
LY288
-70.243
29.02
-2.420
0.01550
2725.1
1486.7
LX2Y88
-1.8442
0.7305
-2.525
0.01158
115160
68486.
LXY288
3.0442
1.207
2.522
0.01167
67775.
43643.
Estimates for equation: PRICE90
Generalized least squares regression.
Observations
Mean of LHS
StdDev of resid
= 140
= 0.6266466E+05
= 0.5453471E+04
Weights
Std.Dev of LHS
Sum of squares
= ONE
= 0.2182196E+05
= 0.3925725E+10
R-squared
Durbin-Watson
RHO used for GLS
0.9370970E+00 Adjusted R-squared= 0.9337612E+00
1.9810445 Autocorrelation = 0.0094777
0.1111796
Variable
Coefficient
Std. Err
t-ratio
Prob|t|
Mean of X
Std.Dev.
SQFT90
30.931
1.806
17.123
0.00000
1478.5
322.25
AGE 90
-317.11
37.09
-8.549
0.00000
37.400
9.4700
LX90
-406.13
261.2
-1.555
0.11992
323.25
130.00
LY90
1031.1
435.9
2.365
0.01801
186.70
73.094
LX290
23.088
10.59
2.179
0.02930
8046.9
4027.8
LY290
-75.235
29.41
-2.558
0.01053
2729.2
1485.7
LX2Y90
-2.0700
0.7332
-2.823
0.00475
115590
68688.
LXY290
3.3354
1.222
2.729
0.00635
67894.
43554.



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/' r 81,9(56,7< 2) )/25,'$


13
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 vintagethe tendency in most U.S.
cities is for older, more obsolete housing units to be located closer to traditional central
employment centers.
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).


21
and 0 otherwise; and c, is the logarithm of the cumulative price index in period t. To
clarify, ct = ln(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.
Multinodal Models
To be relevant today, the monocentric model must be extended to represent the
modern 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


APPENDICES
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 .... Ill
I APPRECIATION MODELS 114
J REPEAT-SALES MODEL 117
REFERENCE LIST 119
BIOGRAPHICAL SKETCH 126
vi


94
Step 2:
Arrange all data in following format:
NAME:
ADDRESS:
CITY:
STATE:
ZIP:
PLUS4:
Parcel ID
Combine Address 1 and Address2 so that this field
contains a house number, directional prefix or suffix
if applicable, street name, and street type suffix. For
more accurate matching, this must be as complete as
possible.
City or town
Two letter state abbreviation
5 digit zip code (5 characters only)
4 additional digits (if available)
Step 3: Using a (GIS) address-matching procedure, determine latitude /
longitude coordinates.
Step 4: Based on the an origin at the southwest corner of the county,
convert latitude / longitude coordinates to Cartesian coordinates.
Procedure 4: Construct time period data sets
Step 1: Create separate data sets for biannual time periods (1979 and 1980,
1981 and 1982, etc.)
Step 2: Compound first year sales forward and discount second year sales
at urban appreciation rate based on month of sale. That is, all
1979 sales are compounded and all 1980 sales are discounted to
January 1, 1980.
Step 3: Using GIS, determine areal units which contain minimum number
of sales for each time period.
Step 4: Using a (GIS) point in polygon procedure, aggregate individual
property characteristics into areal units.


39
where SAP, is the spatial autoregressive price variable and cy 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 "Queens 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.
Model Estimation
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
period.
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


83
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.


101
2) Run do-loop that generates submarket dummies and regression:
35
gen a80
= 0
36
gen a81
= 0
37
gen a82
= 0
38
gen a83
= 0
39
gen a84
= 0
40
gen a85
= 0
41
gen a86
= 0
42
gen a87
= 0
43
gen a88
= 0
44
gen a89
= 0
45
gen a90
= 0
46
gen dummy =
0
47
replace
dummy
= 1 if disthigh < 1.0
48
replace
a80
=
yr80*dummy
49
replace
a81
=
yr81*dummy
50
replace
a82
=
yr82*dummy
51
replace
a83
=
yr83*dummy
52
replace
a84
=
yr84*dummy
53
replace
a85
=
yr85*dummy
54
replace
a86
=
yr86*dummy
55
replace
a87
=
yr87*dummy
56
replace
a88
=
yr88*dummy
57
replace
a89
=
yr89*dummy
58
replace
a90
=
yr90*dummy
59 regr lnpr yr81 yr82 yr83 yr84 yr85 yr86 yr87 yr88 yr89 yr90 a81 a82
a83 a84 a85 a86 a87 a88 a89 a90, noconstant
69 drop a80 a81 a82 a83 a84 a85 a86 a87 a88 a89 a90 dummy
The do-loop is run for multiple iterations. For each iteration, the increment of
disthigh (in line 47) is increased by 0.1 miles. The same procedure is done for distlow.
The distance at which the difference between market and submarket is greatest is
determined by (the statistical significance of) individual t-statistics of the submarket
dummies.


110
Estimates for equation: PRICE88
Ordinary least squares (OLS) regression.
Source | SS df MS Number of obs = 140
Model I
5.7388e+ll
8
7.1735e+10
Prob > F
= 0.0000
Residual |
4.3748e+09
132
33142101.0
R-square
= 0.9924
= 0.9920
Total
5.7826e+ll
140 4.
1304e+09
Root MSE
= 5756.9
price
Coef.
Std. Err
t
p>it|
[95% Conf.
Interval]
sqf t
33.38288
2.376855
14.045
0.000
28.68123
38.08454
age
-396.0799
45.427
-8.719
0.000
-485.939
-306.2208
lx
-874.6428
332.7011
-2.629
0.010
-1532.758
-216.5272
ly
1757.464
559.2833
3.142
0.002
651.1462
2863.782
1x2
39.36362
13.506
2.915
0.004
12.64741
66.07983
iy2
-114.4702
37.48219
-3.054
0.003
-188.6137
-40.32675
lx2y
-3.000065
.9294883
-3.228
0.002
-4.838684
-1.161445
lxy2
4.771301
1.544148
3.090
0.002
1.716824
7.825777
Estimates for equation: PRICE90
Ordinary least squares (OLS) regression.
Source
SS
df
MS
Number of obs
= 140
2^)11.48
Model
6.1193e+ll
8 7.
6491e+10
Prob > F
= 0.0000
Residual
4.0203e+09
132 30456710.7
R-square
= 0.9935
Adj R-square
Total
6.1595e+ll
140 4.
3997e+09
Root MSE
= 5518.8
price
Coef.
Std. Err
t
p>it|
[95% Conf.
Interval]
sqf t
31.2539
2.216352
14.102
0.000
26.86973
35.63806
age
-393.9619
43.2524
-9.108
0.000
-479.5194
-308.4043
lx
-776.0801
312.7203
-2.482
0.014
-1394.672
-157.4884
ly
1611.346
525.0574
3.069
0.003
572.7305
2649.961
1x2
37.37298
12.69001
2.945
0.004
12.27088
62.47507
iy2
-104.9904
35.40538
-2.965
0.004
-175.0257
-34.95503
lx2y
-2.911431
.8767774
-3.321
0.001
-4.645784
-1.177079
lxy2
4.473703
1.461916
3.060
0.003
1.581888
7.365517


103
Estimates for equation: PRICE84
Ordinary least squares (OLS) regression.
Source |
Number of obs =
140
Model
Residual
4.3738e+10
3.2742e+09
3
136
1.4579e+10
24075231.1
Prob > F
R-square
Adj R-square
Root MSE
= 0.0000
= 0.9304
= 0.9288
= 4906.7
Total
4.7012e+10
139
338213946
price
Coef.
Std.
Err
t
p>it|
[95% Conf.
Interval]
sqf t
38.99208
2.503488
15.575
0.000
34.04128
43.94288
age
-285.0002
51.1085
-5.576
0.000
-386.0704
-183.93
lot
1.096209
.1824752
6.007
0.000
.7353528
1.457064
_cons
-10474.21
3371.
866
-3.106
0.002
-17142.28
-3806.144
Estimates for equation: PRICE86
Ordinary least squares (OLS) regression.
Source |
df
Number of obs
136) =
140
851.87
Model
Residual
4.6953e+10
2.4987e+09
3 1.5651e+10
136 18372525.5
Prob > F
R-square
Adj R-square
Root MSE
= 0.0000
= 0.9495
= 0.9484
= 4286.3
Total
4.9452e+10
139 355766366
price
Coef.
Std. Err
t
p>it|
[95% Conf.
Interval]
sqft
36.877
2.057348
17.925
0.000
32.80847
40.94553
age
-272.4354
43.40968
-6.276
0.000
-358.2807
-186.5901
lot
1.531288
.1550505
9.876
0.000
1.224666
1.83791
_cons
-8313.186
2833.201
-2.934
0.004
-13916.01
-2710.358


xml version 1.0 encoding UTF-8
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INGEST IEID ERX4ZOA02_2YKQS4 INGEST_TIME 2013-01-23T15:15:47Z PACKAGE AA00012917_00001
AGREEMENT_INFO ACCOUNT UF PROJECT UFDC
FILES


58
Standardized housing characteristics of square footage, age, and lot size are calculated as
the combined average over time and space for all houses.
Price Equations
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.


91
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
price appreciation.


75
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. Johns River; these houses are located in Jacksonvilles
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 appreciationif they existwill be more obvious and not masked by variation in
housing attributes; this is discussed next.


This dissertation is dedicated to the memory of Martha E. Smersh (1925 -1987)


56
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) "Queens 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


20
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
(3)
where Pjt and P are the prices of repeat-sales transactions, with the initial sale at time x
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
(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
equation is
In (Pu / Pit) = £,T c, D + e
(5)
where Pit / P is the ratio of sales price for property i in time periods x and t; Dit is a
dummy variable which equals -1 at the time of initial sale, +1 at the time of second sale,


4
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


74
(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


79
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.


124
Palmquist, R.B., "Alternative Techniques for Developing Real Estate Price Indices,"
Review of Economics and Statistics, Volume 62, pp 442-480, (1980)
Parker, C., "Trend Surface and the Spatio-Temporal Analysis of Residential Land Use
Intensity and Household Housing Expenditure," Land Economics, Volume 57, pp 323-
337, (1981)
Rachlis, M.B. and A.M.J, Yezer, "Urban Location and Housing Price Appreciation,"
Papers of the Regional Science Association, Volume 57, pp 155-164, (1985)
Rosen, S., "Hedonic Prices and Implicit Markets: Product Differentiation in Pure
Competition," Journal of Political Economy, Volume 82, pp 34-55, (1974)
Smith, A., An Inquiry into the Nature and Causes of the Wealth of Nations, Clarendon
Press: Oxford, UK, (1776)
Thayer, M., H. Albers, and M. Rahmatian, The Benefits of Reducing Exposure to
Waste Disposal Sites: A Hedonic Housing Value Approach," Journal of Real Estate
Research, Volume 7, pp 265-282, (1992)
von Bohm-Bawerk, E., The Positive Theory of Capital, (1888), translated by Smart, W
Macmillan and Co.: London, UK, (1891)
von Thiinen, J.H., Den Isolierte Staadt, (1826), translated: The Isolated State by
Wartenberg, C.M., Permagon Press: New York, NY, (1966)
Waddell, Paul, Brian J.L. Berry and I. Hoch, "Housing Price Gradients: The Intersection
of Space and Built Form", Geographical Analysis, Vol. 25, pp 5-19, (1993a)
Waddell, P., B.J.L. Berry, and I. Hoch, "Residential Property Values in a Multinodal
Urban Area: New Evidence on the Implicit Price of Location," Journal of Real Estate
Finance and Economics, Volume 7, pp 117-141, (1993b)


APPENDIX H
INTERACTIVE MODEL WITH SIMULTANEOUS ESTIMATION
Estimates for equation: PRICE80
Generalized least squares regression.
Observations
Mean of LHS
StdDev of resid
R-squared
Durbin-Watson
RHO used for GLS
= 140
= 0.3914201E+05
= 0.3345748E+04
= 0.9382148E+00
= 2.0306799
= 0.1056754
Weights
Std.Dev of LHS
Sum of squares
Adjusted R-sq
Autocorrelation
= ONE
= 0.1350852E+05
= 0.1477612E+10
= 0.9349384E+00
= -0.0153399
Variable
Coefficient
Std. Err
t-ratio
Prob|t|
Mean of X
Std.Dev.
SQFT80
23.574
1.053
22.397
0.00000
1530.5
351.72
AGE 80
-186.30
21.13
-8.815
0.00000
38.414
8.9619
LX80
-168.63
145.0
-1.163
0.24490
328.19
132.63
LY80
478.11
238.7
2.003
0.04516
189.93
76.046
LX280
9.0441
5.876
1.539
0.12380
8170.6
4124.8
LY280
-43.551
15.92
-2.735
0.00623
2781.1
1555.0
LX2Y80
-0.93949
0.4013
-2.341
0.01923
117570
71045.
LXY280
1.9130
0.6615
2.892
0.00383
69171.
45347.
Estimates for equation: PRICE82
Generalized least squares regression.
Obs e rva tions
Mean of LHS
StdDev of resid
R-squared
Durbin-Watson
RHO used for GLS
= 140
= 0.4603644E+05
= 0.4629486E+04
= 0.9250365E+00
2.1125196
= 0.0739243
Weights
Std.Dev of LHS
Sum of squares
Adjusted R-sq
Autocorrelation
= ONE
= 0.1696932E+05
= 0.2829043E+10
= 0.9210612E+00
= -0.0562598
Variable
Coefficient
Std. Err
t-ratio
Prob|t|
Mean of X
Std.Dev.
SQFT82
26.482
1.235
21.447
0.00000
1524.5
338.46
AGE 8 2
-266.91
27.43
-9.730
0.00000
37.921
9.5096
LX82
-569.65
191.0
-2.983
0.00285
327.15
131.87
LY82
1206.1
318.8
3.783
0.00016
188.99
74.227
LX282
26.249
7.747
3.388
0.00070
8144.5
4111.8
LY282
-92.232
21.64
-4.262
0.00002
2762.7
1515.3
LX2Y82
-2.1938
0.5368
-4.087
0.00004
117030
70404.
LXY282
3.9552
0.8989
4.400
111
0.00001
68742.
44580.


INTRAURBAN VARIATION IN
HOUSE PRICE APPRECIATION:
A CASE STUDY,
JACKSONVILLE, FLORIDA, 1980-1990
By
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
1995


2
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 states largest
waterway. Jacksonville is one of the eastern seaboards busiest deep-water ports, serving
the U. S. Navy and merchant shipping. Jacksonville is also a major insurance and
banking center. Two interstate highways1-95 and I-10run 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 capita
personal income during the 1980s rose 90 percent in the state of Florida and over 94
percent in Duval county.


30
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 Revenues (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


115
Equation 3: Lot Size
Estimates for equation: APPR
Ordinary least squares regression.
Source
i
SS
df
MS
Number of obs
F ( 1, 138)
Prob > F
R-square
Adj R-square
Root MSE
= 140
= 32.47
= 0.0000
= 0.1905
= 0.1846
= .00576
Model
Residual
|
.001077214
.004577778
1
138
.001077214
.000033172
Total
1
.005654992
139
.000040683
appr
i
Coef.
Std.
Err.
t
p>it|
[95% Conf.
Interval]
lot
_cons
i
-.0006627
.0618792
.0001163
.0016312
-5.699
37.934
0.000
0.000
-.0008927
.0586538
-.0004328
.0651046
Equation 4: Square Footage, Age, and Lot Size
Estimates for equation: APPR
Ordinary least squares regression.
Source |
SS
df
MS
Number of obs
F ( 3, 136)
Prob > F
R-square
Adj R-square
Root MSE
=
140
Model I
Residual |
.001281086
.004373906
3
136
.000427029
.000032161
=
0.0000
0.2265
0.2095
.00567
Total |
.005654992
139
.000040683
=
appr
Coef.
Std. Err.
t
p>it|
[95% Conf.
Interval]
sqf t
.0000005
.0000030
0.170
0.865
-.0000055
.0000065
age
.0001476
.0000586
2.517
0.013
.0000317
.0002635
lot
-.0005848
.0002236
-2.616
0.010
-.0010270
-.0001427
_cons
.0544913
.0039129
13.926
0.000
.0467534
.0622292


66
(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


CHAPTER 6
HOUSE PRICE APPRECIATION
Predicted 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
appreciation.
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
65


37
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 SQFT¡, the mean structural square footage, AGE¡, the
mean building age, and LOT1; the mean lot size. Following from Jacksons (1979) model,
an interactive model that interacts lot size with a polynomial land price surface is derived:
(12)
where f¡j(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 Jacksons (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 Jacksons 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


22
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,T c, D + E> (3J X, + Emk K Dmi, + eit (6)
where Pit is the transaction price of property i at time t; ct denotes a vector of time
coefficients of Du, time dummies with values of 1 if the house sold in period t and 0
otherwise. Here, [1, denotes a vector of coefficients on the structural and locational
attributes, Xjit, 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, \r, denotes
a vector of coefficients of Dmi 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
nodes.
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


64
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 valueand 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
market.


81
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


57
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.


APPENDIX B
REGRESSION ASSUMPTIONS
Ordinary least squares (OLS) regression equations are used extensively in this
research. Multiple linear regression is a powerful tool that has some implicit assumptions
and potential problems; the econometric solutions to these problems can be quite
complicated. Basic (OLS) assumptions, diagnostics, and remedial measures are as
follows:
(1) Multicollinearity:
It is assumed that there is sufficient variation among the explanatory variables.
A symptom of multicollinearity is a high R-squared but low individual t-statistics. This
assumption can be checked by analyzing a correlation matrix of the explanatory variables.
If two variables are highly correlated, it is quite possible that one is a function of the
other (such as LOT_X and LOT_X2), and that one must be eliminated.
Often the most efficient solution is to use a stepwise regression. This enters
variables into the equation based on a critical F-value and allows those variables to stay
in the equation only if they maintain a critical F-value as other (significant) variables are
entered into the equation. The stepwise procedure is employed during the investigation
of spatial patterns of appreciation where appreciation rates are regressed on a polynomial
expansion of (X,Y) coordinates.
96


47
prompting an analysis of the extent of abnormal appreciation. A spline technique is
applied where multiple iterations of the model are ran 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.
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.
3)


116
Equation 5: Price
Estimates for equation: APPR
Ordinary least squares regression.
Source
I
SS
df
MS
Number of obs
F ( 1, 138)
Prob > F
R-square
Adj R-square
Root MSE
= 140
= 28.73
= 0.0000
= 0.1723
= 0.1663
= .00582
Model
Residual
j
.000974373
.004680619
1
138
.000974373
.000033918
Total
i
.005654992
139
.000040683
appr
I
Coef.
Std.
Err.
t
p>it|
[95% Conf.
Interval]
actp80
_cons

-.0000002
.0606788
.00000004
.00151360
-5.360
40.089
0.000
0.000
-.0000002 -
.0576860
-.00000012
.06367170
Equation 6: Polynomial Expansion of (X,Y) Coordinates
Estimates for equation: APPR
Ordinary least squares regression.
df
Number of obs =
140
Model
Residual
.005633974
.000021019
5 .001126795
134 1.5686e-07
Prob > F
R-square
Adj R-square
Root MSE
= 0.0000
= 0.9963
= 0.9961
= .0004
Total
.005654992
139 .000040683
appr
Coef.
Std. Err
t
p>it|
[95% Conf.
Interval]
X
-.0029955
.0001611
-18.598
0.000
-.0033141
-.0026770
y
.0044855
.0000733
61.225
0.000
.0043406
.0046304
x2
.0001794
.0000044
40.572
0.000
.0001707
.0001881
x2y
-.0000105
.0000001
-70.692
0.000
-.0000108
-.0000102
xy2
.0000014
.0000001
7.677
0.000
.0000010
.0000017
_cons
.0372827
.0018221
20.461
0.000
.0336789
.0408865


34
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.
Temporal Aggregation
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
geographic units.
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.


80
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 c, 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


62
Figure 5-4 Land Value Surface for 1984
Figure 5-5 Land Value Surface for 1986


89
price appreciation in the northeast. In fact, the increased access from the north side of
the St. Johns 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 corner 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.


APPENDIX J
REPEAT-SALES MODELS
Spline regression for: Northeast
Radial Area: 2.5 miles
(predicted negative abnormal appreciation)
Estimates for repeat-sales equation: lnpr
Ordinary least squares regression.
Source
ss
df
MS
Number of obs
= 3998
Model
194.557496
20 9.
72787478
Prob > F
= 0.0000
Residual
98.8168293
3978 .024840832
R-square
= 0.6632
Ad ^
R-square
Total
293.374325
3998 .073380271
Root MSE
= .15761
lnpr
Coef.
Std. Err
t
p>it|
[95% Conf.
Interval]
yr81
.0873677
.0095803
9.119
0.000
.0685848
.1061505
yr82
.1442588
.0092155
15.654
0.000
.1261912
.1623264
yr83
.2040763
.0085370
23.905
0.000
.1873391
.2208136
yr84
.2707677
.0087044
31.107
0.000
.2537023
.2878332
yr85
.3242259
.0084684
38.287
0.000
.3076231
.3408286
yr86
.3857562
.0082434
46.796
0.000
.3695946
.4019179
yr87
.4236192
.0085542
49.522
0.000
.4068482
.4403902
yr88
.4516835
.0087432
51.661
0.000
.4345420
.4688250
yr89
.4711132
.0091291
51.606
0.000
.4532151
.4890113
yr90
.4860392
.0088383
54.993
0.000
.4687112
.5033672
a81
-.0239935
.0326771
-0.734
0.463
-
.0880589
.0400719
a82
-.0329716
.0298553
-1.104
0.269
-
.0915047
.0255615
a83
-.0041118
.0288702
-0.142
0.887
-
.0607136
.0524900
a84
-.0320856
.0293899
-1.092
0.275
-
.0897063
.0255351
a85
-.0623629
.0296535
-2.103
0.036
-
.1205004
-.0042254
a86
-.0661533
.0277776
-2.382
0.017
-
.1206130
- .0116935
a87
-.0907208
.0292220
-3.105
0.002
-
.1480122
-.0334293
a88
-.1005559
.0305903
-3.287
0.001
-
.1605300
-.0405818
a89
-.1074609
.0297293
-3.615
0.000
-
.1657470
-.0491749
a90
-.095776
.0315633
-3.034
0.002
-
.1576578
-.0338941
117


104
Estimates for equation: PRICE88
Ordinary least squares (OLS) regression.
Source
ss
df
MS
Number of obs
= 140
Model
5.3359e+10
3
1.
7786e+10
Prob > F
= 0.0000
Residual
4.2623e+09
136
31340242.1
R-square
= 0.9260
Adj R-square
Total
5.7621e+10
139
414538598
Root MSE
= 5598.2
price
Coef.
Std.
Err
t
p>it|
[95% Conf.
Interval]
sqf t
44.31837
2.694156
16.450
0.000
38.99051
49.64622
age
-112.3605
55.81195
-2.013
0.046
-222.732
-1.989
lot
1.612671
.200135
8.058
0.000
1.216892
2.008451
_cons
-21502.39
3639
092
-5.909
0.000
-28698.91
-14305.86
Estimates for equation: PRICE90
Ordinary least squares (OLS) regression.
Source |
SS
df
MS
Model I
6.1406e+10
3
2.0469e+10
Residual |
4.7854e+09
136
35186917.6
Total |
6.6192e+10
139
476198059
Number of obs = 140
F( 3, 136) = 581.71
Prob > F = 0.0000
R-square = 0.9277
Adj R-square = 0.9261
Root MSE = 5931.9
price
Coef.
Std. Err.
t
p>it|
[95% Conf.
Interval]
sqf t
38.2844
2.853933
13.415
0.000
32.64058
43.92823
age
-170.962
55.8437
-3.061
0.003
-281.3963
-60.52773
lot
2.058979
.2100526
9.802
0.000
1.643588
2.474371
_cons
-14964.07
3694.981
-4.050
0.000
-22271.12
-7657.02


86
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
of land.
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


CHAPTER 3
DATA
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.
29


95
Procedure 5: Construct Repeat-Sales data set
Step 1:
Identify those properties which have sold at least twice in the 10
year study period (1979 1990), and delete all others.
Step 2:
Calculate time between sales (based on year and month of sale)
and delete all observations with a holding period of under one year.
Step 3:
Calculate annualized appreciation for each property. Then calculate
mean and standard deviation for annual appreciation and delete all
observations greater than or less than 2.5 standard deviations from
the mean.
Step 4:
Generate dummy variables for time of sale where D, = 1 if t is
most recent sale year, -1 if t is previous sale year, and 0 otherwise,
for all (t) time periods.
Note: During specific repeat-sales analyses, distances from predicted appreciation
maximum and minimum points to all houses will be calculated. Dummy variables for
location within a radial area of (predicted) abnormal appreciation (where D¡ = 1 if
property is located in a certain area, and 0 otherwise) will also be created.


CHAPTER 4
METHODOLOGY
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¡ = p, SQFT, + p2 AGE, + p3 LOT, + e, (11)
36


76
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¡ = Po + P, X1 + P2 Y, + p, X,2 + p4 X2Y, + p5 XY2 + 6,
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.


4
52
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. The simultaneous-equations
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


7
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 Thiinen (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 parcels 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 Thiinens (1826) original concept of an agricultural monocentric model was
generalized and applied to housing many years later by Alonso (1964). Models that


82
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.
NORTHWEST + MARKET NORTHEAST
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


CHAPTER 7
CONCLUSION
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.
84


43
be held constant to observe the variation in price over time (i.e., appreciation) due
primarily to location in space.
Temporal Implications
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
are identified.
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


TABLE OF CONTENTS
ACKNOWLEDGMENTS iii
ABSTRACT vii
CHAPTERS
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
iv


APPENDIX A
DATA PROCEDURES
The data for this study will come from the Florida Department of Revenues
(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:
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
51
Address 1
52
Address2
53
City
54
State
55
Zip code
92


CHAPTER 2
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
6


35
Repeat-Sales Data
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.


41
where Wy = Cy / T," Cy for connectivity matrix Cy where i and j are adjoining (Queens
case join) areas. The constant, 0, is assumed to equal 0 and p, 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


8
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


26
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
urban landscape.
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):
P, = Po + E,1 Pj Xj + (A,)L( + E, (9)
where price (in this case, census tract rent), P¡, is represented as a linear function of a
constant P0, a vector of variables which define structural and neighborhood characteristics
(Xj¡), and the quantity of land (L), as measured by lot size. The coefficients p; represent
a vector of structural and neighborhood characteristics, and (A) is the price of land as
a proxy for accessibility.


98
In this research, a major insight is that the (cross-sectional) data is time-series as
well. Individual equations are cross-sectional but these equations are run over multiple
time periods. Contemporaneous correlation (correlation at a given point in time but not
necessarily over time) in seemingly unrelated regression equations and a corrective
procedure are discussed in Appendix C.
(5) Spatial Autocorrelation:
Again, it is assumed that the regression error terms are random (not correlated).
This can be a problem in cross-sectional regression because variables are often correlated
to some degree with themselves over space. This can be tested with a variety of means
including Morans I and Daceys contiguity test. Here, a regression technique that is
discussed by Cliff and Ord (1973) is employed; this is shown on page 39. Spatial
autocorrelation is often the result of model misspecification; the interactive model that is
employed here is shown (see Table 5-7 on page 55) as a method of reducing spatially
autocorrelated error terms.


APPENDIX C
SEEMINGLY UNRELATED REGRESSION EQUATIONS
The seemingly unrelated regression equations (SUR) procedure simultaneously
estimates a set of equations in a manner that may reduce contemporaneous (at a given
point in time but not necessarily over time) correlation and improve the efficiency of the
model. Consider a simplified version of the strictly cross-sectional house price model
defined in equation 1 on page 17:
PRICE, = Pj Xj¡ + e¡
This model can be run separately for the six time periods (1980, 1982, 1984, 1986,
1988, 1990) in single estimation. Alternatively, the equations can be stacked and
estimated simultaneously:
PRICE80
X80 X82 X84 X86 X88 X90
p80
£80
PRICE82
X80 X82 X84 X86 X88 X90
p82
e82
PRICE84
=
X80 X82 X84 X86 X88 X90
P84
+
e84
PRICE86
X80 X82 X84 X86 X88 X90
P86
£86
PRICE88
X80 X82 X84 X86 X88 X90
P88
e88
PRICE90
X80 X82 X84 X86 X88 X90
P90
e90
If contemporaneous correlation does not exist, single estimation produces the best, linear,
unbiased estimate. However, if contemporaneous correlation does exist, SUR is a
superior estimation method. A generalized least squares (GLS) procedure is used to
produce a linear, unbiased estimate of P, with minimum variance.
99


93
Procedure 2: Construct initial data set
Step 1:
Identify those properties which are improved single family
detached units (D.O.R. Code = 1), and delete all others.
Step 2:
Identify those properties which have sold at least once in the 10
year study period (1979 1990), and delete all others.
Step 3:
Identify those properties which are owner occupied (by homestead
exemption) and delete all others.
Step 4:
Clean data set of apparent error, abnormal, and incomplete
observations:
A) Delete if land value < 1000.
B) Delete if assessed value < 1000.
C) Delete if year built < 1900.
D) Delete if total living area < 800.
E) Delete if total living area > 6000.
F) Delete if either sale price < 10,000
F) Delete if either sale price > 500,000
Step 5:
Generate price per square foot variable for each year and calculate
mean and standard deviation. Delete all observations greater than
or less than 2.5 standard deviations from their respective means.
Procedure 3: Clean address data for geo-coding
Step 1:
For ease of data manipulation in geo-coding it is easiest to split the
dataset into two files; the first containing property specifications,
prices, and dates (fields 04 to 29), and the second containing
address information (fields 51 to 55), with both using Parcel ID
(field 01) as the key field. Once geo-coded, the coordinate file can
be merged with the initial data set.


112
Estimates for equation: PRICE84
Generalized least squares regression.
Observations
Mean of LHS
StdDev of resid
R-squared
Durbin-Watson
RHO used for GLS
140
0.5153968E+05
0.4693314E+04
0.9344034E+00
2.0218867
0.0982745
Weights
Std.Dev of LHS
Sum of squares
Adjusted R-sq
Autocorrelation
ONE
0.1839059E+05
0.2907590E+10
0.9309248E+00
-0.0109433
Variable
Coefficient
Std. Err
t-ratio
Prob|t|
Mean of X
Std.Dev.
SQFT84
30.024
1.579
19.013
0.00000
1488.6
318.57
AGE 8 4
-317.08
30.02
-10.56
0.00000
37.736
8.7693
LX84
-499.74
199.8
-2.501
0.01240
326.29
130.91
LY84
1056.9
333.5
3.169
0.00153
187.99
71.158
LX284
24.951
8.186
3.048
0.00230
8128.3
4085.7
LY284
-80.874
22.46
-3.600
0.00032
2741.0
1445.6
LX2Y84
-2.1065
0.5685
-3.705
0.00021
116490
68663.
LXY284
3.6259
0.9403
3.856
0.00012
68221
42850.
Estimates for equation: PRICE86
Generalized least squares regression.
Observations
Mean of LHS
StdDev of resid
= 140
= 0.5631911E+05
= 0.3966479E+04
Weights
Std.Dev of LHS
Sum of squares
= ONE
= 0.1886177E+05
= 0.2076750E+10
R-squared
Durbin-Watson
RHO used for GLS
0.9554591E+00 Adjusted R-squared= 0.9530971E+00
1.9967455 Autocorrelation = 0.0016273
0.2111593
Variable
Coefficient
Std. Err
t-ratio
Prob|t|
Mean of X
Std.Dev.
SQFT86
31.377
1.329
23.614
0.00000
1475.5
316.48
AGE 8 6
-335.39
27.15
-12.35
0.00000
37.379
8.9695
LX86
-547.31
193.2
-2.833
0.00462
323.85
128.75
LY86
1128.5
319.5
3.532
0.00041
186.83
71.638
LX286
27.429
7.884
3.479
0.00050
8070.9
4039.9
LY286
-79.501
21.42
-3.711
0.00021
2731.3
1474.2
LX2Y86
-2.2152
0.5443
-4.070
0.00005
115900
68721.
LXY286
3.5491
0.8979
3.953
0.00008
68014
43428.


This dissertation was submitted to the Graduate Faculty of the Department of
Geography in the College of Liberal Arts and Sciences and to the Graduate School and was
accepted as partial fulfillment of the requirements for the degree of Doctor of Philosophy.
August, 1995
Dean, Graduate School


16
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.
Theoretical Summary
The contributions of economic theory to the perception of value conclude that
value is a market concept. Marshallian theory--the neoclassical approachintegrates 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.


51
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)
SQFTj 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, = P, SQFTj + p2 AGEj + E> P, [ LOTj fu(X,Y)] + e¡
Cartesian coordinates are the average X and Y coordinates. Because of
multicollinearity problems, the interactive terms of L_XYj, L_X3,, and L_X3¡ are dropped,
leaving the following interactive terms:
L_Xj the product of lot size times X
L_Yj the product of lot size times Y
L_X2¡ the product of lot size times X-squared
L_Y2j the product of lot size times Y-squared
L_X2Y¡ the product of lot size times X-squared times Y
the product of lot size times X times Y-squared
L_XY2¡


118
Spline regression for: Northwest
Radial Area: 3.5 miles
(predicted positive abnormal appreciation)
Estimates for repeat-sales equation: lnpr
Ordinary least squares regression.
Source
ss
df
MS
Number of obs
= 3998
Model
194.14049
20 9
.7070245
Prob > F
= 0.0000
Residual
99.2338349
3978
02494566
R-square
= 0.6618
Adj
= 0.6600
Total
293.374325
3998 .073380271
Root MSE
= .15794
lnpr
Coef.
Std. Err
t
p>lt|
[95% Conf.
Interval]
yr81
.0850951
.0095056
8.952
0.000
.0664588
.1037314
yr82
.1408195
.0090679
15.530
0.000
.1230414
.1585976
yr83
.1996303
.0084210
23.706
0.000
.1831205
.2161402
yr84
.266552
.0086028
30.984
0.000
.2496857
.2834183
yr85
.3156139
.0083710
37.703
0.000
.2992021
.3320257
yr86
.3747102
.0081496
45.979
0.000
.3587325
.3906880
yr87
.4133248
.0084459
48.938
0.000
.3967660
.4298836
yr88
.4369203
.0086881
50.289
0.000
.4198866
.4539539
yr89
.4582962
.0090260
50.775
0.000
.4406002
.4759923
yr90
.4769421
.0087934
54.239
0.000
.4597021
.4941821
a81
.0278783
.0367651
0.758
0.448
-
.0442018
.0999584
a82
.0228317
.0368016
0.620
0.535
-
.0493201
.0949834
a83
.0646941
.0348268
1.858
0.063
-
.0035860
.1329741
a84
.0472541
.0349200
1.353
0.176
-
.0212087
.1157169
a85
.070106
.0351375
1.995
0.046
.0012169
.1389952
a86
.0968098
.0329693
2.936
0.003
.0321716
.1614481
a87
.0658732
.0351438
1.874
0.061
-
.0030284
.1347748
a88
.1042177
.0345235
3.019
0.003
.0365323
.1719032
a89
.0716731
.0351065
2.042
0.041
.0028446
.1405016
a90
.0498854
.0346776
1.439
0.150
-
.0181022
.117873


REFERENCE LIST
Alonso, W., Location and Land Use, Harvard University Press: Cambridge, MA, (1964)
Anderson, R.J., and T.D. Croker, "Air Pollution and Residential Property Values,"
Urban Studies, Volume 8, pp 171-180, (1971)
Archer W.R., D.H. Gatzlaff, and D.C. Ling, "Measuring the Importance of Location on
House Price Appreciation," forthcoming in Journal of Urban Economics, (1995)
Asabere, P.K. and B. Harvey, "Factors Influencing the Value of Urban Land: Evidence
from Halifax-Dartmouth, Canada," AREUEA Journal, Volume 13, pp 361-377, (1985)
Bailey, M.J., R.F, Muth, and H.O. Norse, "A Regression Method for Real Estate Price
Index Construction," Journal of the American Statistical Association, Volume 58, pp
933-942, (1963)
Balkin, S. and J.F. McDonald, "The Market for Streetcrime: An Economic Analysis of
Victims-Offender Interaction," Journal of Urban Economics, Volume 10, pp 390-405,
(1981)
Ball, M.J., "Recent Empirical Work on the Determinants of Relative House Prices,"
Urban Studies, Volume 10, pp 213-231, (1973)
Berry, B.J.L., "Ghetto Expansion and Single-Family Housing Prices: Chicago, 1968-
1972," Journal of Urban Economics, Volume 3, pp 397-423, (1976)
Berry, B.J.L., and R. Bednarz, "The Disbenefits of Neighborhood and Environment to
Urban Property," Geographic Humanism, Analysis and Social Action, Ann Arbor, MI,
Geographical Publication #17, pp 111-148, (1977)
119


55
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


90
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. Brighams 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


23
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 = 5)1
r¡t
c, D + E> Pj Xji( + Emk K R, + e
(V)


71
the St. Johns 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 Brighams (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.


12
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 Quigleys (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.


49
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
study area.
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
following chapter.


31
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.
GIS Procedures
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 comer of the county.
GIS is also used to determine optimal areal 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.
Aggregation Techniques
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


APPENDIX E
NAIVE MODEL WITH SINGLE ESTIMATION
Estimates for equation: PRICE80
Ordinary least squares (OLS) regression.
Source |
SS
df
MS
Number of obs =
F( 3, 136) =
140
584.96
Model I
2.3540e+10
3
7.8468e+09
Prob > F =
0.0000
Residual |
1.8243e+09
136
13414177.2
R-square =
Adj R-square =
0.9281
0.9265
Total |
2.5365e+10
139
182480121
Root MSE =
3662.5
price
Coef.
Std. Err.
t
p>lt|
[95% Conf.
Interval]
sqft
25.1585
1.546941
16.263
0.000
22.09933
28.21767
age
-220.9296
37.48812
-5.893
0.000
-295.0647
-146.7946
lot
.8618326
.1254159
6.872
0.000
.6138151
1.10985
_cons
-2528.425
2354.768
-1.074
0.285
-7185.121
2128.271
Estimates for equation: PRICE82
Ordinary least squares (OLS) regression.
Source |
SS
df
MS
Number of obs =
F ( 3, 136) =
Prob > F =
R-square =
Adj R-square =
Root MSE =
140
495.69
0.0000
0.9162
Model I
Residual |
3.6672e+10
3.3538e+09
3
136
1.2224e+10
24660576.1
Total |
4.0026e+10
139
287957928
4965.9
price
Coef.
Std. Err.
t
p>it|
[95% Conf.
Interval]
sqft
32.06302
2.077704
15.432
0.000
27.95423
36.17181
age
-248.4908
47.87897
-5.190
0.000
-343.1743
-153.8072
lot
1.163501
.1635127
7.116
0.000
.8401446
1.486857
_cons
-9101.557
3129.29
-2.909
0.004
-15289.92
-2913.196
102


42
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
MEAN
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


68
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.


4 METHODOLOGY 36
Hedonic Price Equations 36
Naive versus Interactive Model 36
Single versus Simultaneous Estimation 37
Spatial Autoregressive Variable 38
Model 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
Model 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
v


9
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 citys past development upon current conditions, and
the preferences of different households for housing in different locations.
(pg. 300)
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.


121
Dubin, Robin A., "Spatial Autocorrelation and Neighborhood Quality," Regional Science
and Urban Economics, Volume 22, pp 433-452, (1992)
Fik, T. J., E. J. Malecki, and R. G, Amey, "Trouble in Paradise? Employment Trends and
Forecasts for a Service-Oriented Economy," Economic Development Quarterly, Volume
7, Number 4, pp 358-372, (1993)
Gatzlaff, D.H., and D.C. Ling, "Measuring Changes in Local House Prices: An Empirical
Investigation of Alternative Methodologies," Journal of Urban Economics, Volume 35,
pp 221-244, (1994)
Getis, A., "Second-Order Analysis of Point Patterns: The Case of Chicago as a
Multicenter Urban Region," The Professional Geographer, Volume 35, pp 73-80,
(1983)
Gillard, Q., "The Effect of Environmental Amenities on House Values: The Example of
a View Lot," Professional Geographer, Volume 33, pp 216-220, (1981)
Goodman, A.C., "Hedonic Prices, Price Indices, and Housing Markets," Journal of Urban
Economics, Volume 5, pp 471-484, (1978)
Green, D.L., "Urban Subcenters: Recent Trends in Urban Spatial Structure," Growth and
Change, Volume 11, pp 29-40, (1980)
Hall, R.E., "The Measurement of Quality Change From Vintage Price Data," in
Griliches, Z. (ed.) Price Index and Quality Change, Cambridge: Cambridge, MA,
(1971)
Halvorsen, R. and H.O. Pollakowski "Choice of Functional Form for Hedonic Price
Equations," Journal of Urban Economics, \olume 10, pp 37-49, (1981)
Haurin, D.R., and P.H. Hendershott, "House Price Indices: Issues and Results," AREUEA
Journal, Volume 19, pp 259-269, (1991)


40
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.
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 [ Ej" Wlj ej + Mi
(14)


123
Knos, D. S., "The Distribution of Land Values in Topeka, Kansas, in Spatial Analysis,
edited by B. J. L. Berry and D. F. Marble, Prentice Hall: Englewood Cliffs, NJ, (1968)
Krumbein, W.C. and F.A. Graybill, An Introduction to Statistical Modeling in Geology,
McGraw-Hill: New York, NY, (1965)
Lancaster, K., "A New Approach to Consumer Theory", Journal of Political Economy,
Volume 74, pp 132-157, (1966)
Li, M.M., and Brown, H.J., "Micro-Neighborhood Externalities and Hedonic Housing
Prices," Land Economics, Volume 56, pp 125-141, (1980)
Linneman, A., "Some Empirical Results on the Nature of the Hedonic Price Function for
the Urban Housing Market, Journal of Urban Economics, Volume 8, pp 47-68, (1980)
Linneman, A., "The Demand for Residence Site Characteristics," Journal of Urban
Economics, Volume 9, pp 129-148, (1981)
Little, J.T., "Residential Preferences, Neighborhood Filtering, and Neighborhood
Change," Journal of Urban Economics, Volume 3, pp 68-81, (1976)
Marshall, A., Principles of Economics, 8th ed., Macmillan and Co.: London, UK, (1920)
Mills, E.S., Studies in the Structure of the Urban Economy, John Hopkins Press:
Baltimore, MD, (1972)
Muth, R.F., Cities and Housing, Chicago University Press: Chicago, IL, (1969)
Muth, R. F., "Numerical Solution of Urban Residential Land Use Models," Journal of
Urban Economics, Volume 2, pp 307-332, (1975)


APPENDIX G
INTERACTIVE MODEL WITH SINGLE ESTIMATION
Estimates for equation: PRICE80
Ordinary least squares (OLS) regression.
Source 1
SS
df
MS
Number of obs
=
140
F ( 8, 132)
2640.24
Model I
2.3837e+ll
8
2.9796e+10
Prob > F
=
0.0000
Residual |
1.4897e+09
132
11285378.8
R-square
=
0.9938
Adj R-square
0.9934
Total |
2.3986e+ll
140
1.7133e+09
Root MSE
=
3359.4
price
Coef.
Std. Err.
t
p>it|
[95% Conf.
Interval]
sqf t
24.07798
1.261379
19.089
0.000
21.58285
26.57311
age
-217.9145
24.07348
-9.052
0.000
-265.5342
-170.2948
lx
-546.3024
185.8211
-2.940
0.004
-913.8749
-178.7299
ly
1090.404
308.183
3.538
0.000
480.7878
1700.021
1x2
24.17981
7.52863
3.212
0.002
9.28744
39.07219
ly2
-81.21345
20.50251
-3.961
0.000
-121.7694
-40.65745
lx2y
-1.928417
.5126379
-3.762
0.000
-2.942465
-.9143682
lxy2
3.439166
.8439294
4.075
0.000
1.76979
5.108542
Estimates for equation: PRICE82
Ordinary least squares (OLS) regression.
Source
SS
df
MS
Number of obs
= 140
Model
3.3385e+ll
8 4.
L732e+10
Prob > F
= 0.0000
Residual
2.8837e+09
132 21845951.9
R-square
= 0.9914
Adj R-square
Total
3.3674e+ll
140 2.
4053e+09
Root MSE
= 4674.0
price
Coef.
Std. Err
t
p>it|
[95% Conf.
Interval]
sqf t
27.69811
1.693468
16.356
0.000
24.34826
31.04795
age
-333.625
33.76213
-9.882
0.000
-400.4098
-266.8401
lx
-966.0692
256.572
-3.765
0.000
-1473.594
-458.5444
ly
1829.804
430.3064
4.252
0.000
978.615
2680.992
1x2
41.93702
10.38598
4.038
0.000
21.39252
62.48151
iy2
-127.9116
28.90292
-4.426
0.000
-185.0844
-70.73879
lx2y
-3.175686
.7137249
-4.449
0.000
-4.587505
-1.763868
lxy2
5.386727
1.18835
4.533
0.000
3.036052
7.737401
108


109
Estimates for equation: PRICE84
Ordinary least squares (OLS) regression.
Source | SS df MS Number of obs = 140
Model I
4.1599e+ll
8
5.1998e+10
Prob > F
= 0.0000
Residual |
2.9125e+09
132
22064153.1
R-square
= 0.9930
+_
= 0.9926
Total
4.1890e+ll
140 2.
9921e+09
Root MSE
= 4697.2
price
Coef.
Std. Err
t
p>it|
[95% Conf.
Interval]
sqf t
31.18561
2.05336
15.188
0.000
27.12386
35.24736
age
-385.1117
35.8829
-10.732
0.000
-456.0916
-314.1318
lx
-956.0176
266.306
-3.590
0.000
-1482.797
-429.238
iy
1795.145
449.081
3.997
0.000
906.8185
2683.472
1x2
42.46633
10.82194
3.924
0.000
21.05945
63.8732
iy2
-122.9602
29.99816
-4.099
0.000
-182.2996
-63.62091
lx2y
-3.195662
.7454879
-4.287
0.000
-4.670311
-1.721014
lxy2
5.253959
1.235059
4.254
0.000
2.810891
7.697027
Estimates for equation: PRICE86
Ordinary least squares (OLS) regression.
Source
SS
df
MS
Number of obs
= 140
Model
4.9133e+ll
8 6.
1416e+10
Prob > F
= 0.0000
Residual
2.1841e+09
132 16546212.7
R-square
= 0.9956
Adj R-square
= 0.9953
Total
4.9351e+ll
140 3.
5251e+09
Root MSE
= 4067.7
price
Coef.
Std. Err
t
p>it|
[95% Conf.
Interval]
sqf t
32.00891
1.666486
19.207
0.000
28.71244
35.30538
age
-391.3471
32.52526
-12.032
0.000
-455.6853
-327.009
lx
-729.6795
236.5278
-3.085
0.002
-1197.555
-261.8042
iy
1420.61
399.9107
3.552
0.000
629.5471
2211.673
1x2
34.00906
9.629595
3.532
0.000
14.96077
53.05735
iy2
-92.92281
27.09196
-3.430
0.000
-146.5134
-39.33224
lx2y
-2.575662
.6685466
-3.853
0.000
-3.898113
-1.253211
lxy2
4.00718
1.11872
3.582
0.000
1.794241
6.22012


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.
viii


53
materials than the other mode! 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


BIOGRAPHICAL SKETCH
Greg T. Smersh is the son of Dr. Jerome F. Smersh and Martha E. Smersh and
was raised in Seattle, Washington. He graduated from the University of Washington in
1981 with a Bachelor of Science in Building Construction and from Western Washington
University in 1984 with a masters in business administration. From 1978 to 1983, Greg
worked as a general contractor for Smersh Brothers Construction and from 1984 to 1990
as a securities analyst for the firms of Shearson Lehman Brothers and Cable, Howse, and
Ragen. He is currently completing his Ph.D. in geography at the University of Florida
and conducting research that focuses on the spatial aspects of both residential and
commercial real estate.
126


48
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
abnormal appreciation.
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.


17
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 twicethe 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.


60
Additionally, these appreciation rates will be analyzed as a function of location and used
to create an appreciation rate surface map.
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.


10
The interest in applying these methods to housing markets evolved from
Lancasters (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.


32
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.
Geographic Aggregation
A number of preliminary tests using third and fourth order expansions of Jacksons
(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.


122
Harrison, D and D. Rubinfeld, "Hedonic Housing Prices and the Demand for Clean Air,"
Journal of Environmental Economics and Management, Volume 5, pp 81-102, (1978)
Heikkila, E., P. Gordon, J.I. Kim, R.B. Peiser, and H.W. Richardson, "What Happened
to the CBD-Distance Gradient?: Land Values in a Polycentric City", Environment and
Planning A, Vol. 21, pp 221-232, (1989)
Hembd, J., and C.L. Infanger, "Application of Trend Surface Analysis to a Rural Housing
Market," Land Economics, Volume 57, pp 303-322, (1981)
Hendershott, P.H., and T. Thibodeau, "The Relationship Between Median and Constant
Quality House Prices: Implications for Setting FHA Loan Limits," AREUEA Journal,
Volume 18, pp 323-334, (1990)
Henderson, J.V., Economic Theory and the Cities, Academic Press: New York, NY,
(1977)
Jackson, J. R. "Intraurban Variation in the Price of Housing," Journal of Urban
Economics, Volume 6, pp 464-479, (1979)
Johnson, M. S. and W. R. Ragas "CBD Land Values and Multiple Externalities," Land
Economics, Volume 63, pp 337-347, (1987)
Judge, G. G., The Theory and Practice of Econometrics, Wiley: New York, NY, (1985)
Kain, J.F. and J.M. Quigley, "Measuring the Value of Housing Quality," Journal of the
American Statistical Association, Volume 65, pp 532-548, (1970)
Keil, K.A. and R.T. Carson, "An Examination of Systematic Differences in the
Appreciation of Individual Housing Units," Journal of Real Estate Research, Volume
5, pp 301-318, (1990)


107
Estimates for equation: PRICE88
Generalized least squares regression.
Observations
Mean of LHS
StdDev of resid
140
0.6098215E+05
0.5757802E+04
Weights
Std.Dev of LHS
Sum of squares
ONE
0.2036022E+05
0.4508711E+10
R-squared
Durbin-Watson
RHO used for GLS
0.9194507E+00 Adjusted R-sq
1.9208018 Autocorrelation
0.0965382
0.9176739E+00
0.0395991
Variable Coefficient Std. Err t-ratio Prob|t| Mean of X Std.Dev.
Constant -8872.4
SQFT88 36.333
AGE88 -203.52
LOT88 1802.4
3217. -2.758 0.00581
2.058 17.657 0.00000
50.50 -4.030 0.00006
163.2 11.047 0.00000
1473.2 303.40
37.157 9.0110
13.251 4.1226
Estimates for equation: PRICE90
Generalized least squares regression.
Observations
Mean of LHS
StdDev of resid
R-squared
Durbin-Watson
RHO used for GLS
140
0.6266466E+05
0.5947792E+04
0.9251766E+00
1.9902306
0.1471694
Weights
Std.Dev of LHS
Slim of squares
Adjusted R-sq
Autocorrelation
ONE
0.2182196E+05
0.4811167E+10
0.9235261E+00
0.0048847
Variable Coefficient Std. Err t-ratio Prob|t| Mean of X Std.Dev.
Constant
-5780.2
3371.
-1.714
0.08645
SQFT90
31.794
2.357
13.486
0.00000
1478.5
322.25
AGE90
-219.37
52.51
-4.177
0.00003
37.400
9.4700
LOT90
2225.9
184.2
12.085
0.00000
13.317
4.3716


11
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 sites 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,


106
Estimates for equation: PRICE84
Generalized least squares regression.
Observations
Mean of LHS
StdDev of resid
R-squared
Durbin-Watson
RHO used for GLS
140
0.5153968E+05
0.5114155E+04
0.9221122E+00
2.0183873
0.0856988
Weights
Std.Dev of LHS
Sum of squares
Adjusted R-sq
Autocorrelation
ONE
0.1839059E+05
0.3557024E+10
0.9203941E+00
-0.0091936
Variable Coefficient Std. Err t-ratio Prob|t| Mean of X Std.Dev
Constant 1651.9
SQFT84 30.322
AGE84 -370.37
LOT84 1393.5
2902.
1.931
45.74
148.3
0.569
15.707
-8.098
9.394
0.56921
0.00000
0.00000
0.00000
1488.6 318.57
37.736 8.7693
13.435 4.3446
Estimates for equation: PRICE86
Generalized least squares regression.
Observations
Mean of LHS
StdDev of resid
R-squared
Durbin-Watson
RHO used for GLS
= 140
= 0.5631911E+05
= 0.4418812E+04
= 0.9447211E+00
= 1.9649866
= 0.1426210
Weights
Std.Dev of LHS
Sum of squares
Adjusted R-sq
Autocorrelation
= ONE
= 0.1886177E+05
= 0.2655522E+10
= 0.9435017E+00
= 0.0175067
Variable Coefficient Std. Err
Constant 2072.0 2552.
SQFT86 30.584 1.628
AGE86 -351.93 40.46
LOT86 1671.3 131.9
t-ratio Prob|t| Mean of X Std.Dev.
0.812 0.41684
18.781 0.00000
-8.698 0.00000
12.671 0.00000
1475.5
37.379
13.324
316.48
8.9695
4.1964


87
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 mnimas
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.


67
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.


14
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
housings 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


APPENDIX D
SPLINE REGRESSION PROCEDURE
A computer program has been created to run the spline regression for the repeat-
sales technique. The data consist of last sale price (lprice), prior sale price (pprice), last
sale year (lyr), prior sale year (pyr), distance from point of appreciation maximum
(disthigh), and distance from appreciation minimum (distlow).
1) Create logged price ratio and (market) dummy variables:
01 gen lnpr = In(lprice/pprice)
02 gen yr80 = 0
03
replace yr80
=
1
if
lyr
==
1980
04
replace yr80
=
-1
if
pyr
==
1980
05
gen yr81 = 0
06
replace yr81
=
1
if
lyr
==
1981
07
replace yr81
=
-1
if
pyr
==
1981
08
gen yr82 = 0
09
replace yr82
=
1
if
lyr
==
1982
10
replace yr82
=
-1
if
pyr
==
1982
11
gen yr83 = 0
12
replace yr83
=
1
if
lyr
==
1983
13
replace yr83
=
-1
if
pyr
==
1983
14
gen yr84 = 0
15
replace yr84
=
1
if
lyr
==
1984
16
replace yr84
=
-1
if
pyr
==
1984
17
gen yr85 = 0
18
replace yr85
=
1
if
lyr
==
1985
19
replace yr85
=
-1
if
pyr
==
1985
20
gen yr86 = 0
21
replace yr86
=
1
if
lyr
==
1986
22
replace yr86
=
-1
if
pyr
==
1986
23
gen yr87 = 0
24
replace yr87
=
1
if
lyr
==
1987
25
replace yr87
=
-1
if
pyr
==
1987
26
gen yr88 = 0
27
replace yr88
=
1
if
lyr
==
1988
28
replace yr88
=
-1
if
pyr
==
1988
29
gen yr89 = 0
30
replace yr89
=
1
if
lyr
==
1989
31
replace yr89
=
-1
if
pyr
==
1989
32
gen yr90 = 0
33
replace yr90
=
1
if
lyr
==
1990
34
replace yr90
=
-1
if
pyr
==
1990
100


120
Brigham, E.F., "The Determinants of Residential Land Values, Land Economics,
Volume 41, pp 325-334, (1965)
Case, K.E., "The Market for Single-Family Homes in the Boston Area," New England
Economic Review, (May/June), pp 38-48, (1986)
Case, K.E., and R.J. Shiller, "Prices of Single-Family Homes since 1970: New Indexes
for Four Cities," New England Economic Review, (Sept/Oct), pp 45-56, (1987)
Case, K.E., and R.J. Shiller, "The Efficiency of the Market for Single-Family Homes,"
The American Economic Review, Volume 79, pp 125-137, (1989)
Case, K.E., and R.J. Shiller, "A Decade of Boom and Bust in the Prices of Single-Family
Homes; Boston and Los Angeles, 1983 to 1993," New England Economic Review,
March/April, pp 40-51, (1994)
Chicoine, D.L., "Farmland Values at the Urban Fringe: An Analysis of Sale Prices,"
Land Economics, Volume 57, pp 353-362, (1981)
Chorley, R.J., and P. Haggett, "Trend Surface Mapping in Geographical Research,"
Transactions and Papers of the Institute of British Geographers, Publication 37, pp 47-
67, (1965)
Clapp, J.M., and C. Giaccotto, "Estimating Price Indices for Residential Properties: A
Comparison of Repeat Sales and Assessed Value Methods," Journal of the American
Statistical Association, Volume 87, pp 300-306, (1991)
Cliff, A. and J. Ord, Spatial Autocorrelation, Pion: London, UK, (1973)
deLeeuw, F. and R. J. Struyk, The Web of Urban Housing, The Urban Institute:
Washington, D. C., (1975)


88
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 corner 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 comer 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 comer 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


46
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)
as follows:
In (P / P) = £,T c, D,, + £,T c, D + eu (17)
where Dit 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 c, is the logarithm of any additional (positive or negative) cumulative
appreciation due to being in an abnormal appreciation "submarket."
Areas of predicted abnormal appreciation may be indicated by the interactive
model. Spatial patterns of appreciation may also be indicated by the TSA model,


APPENDIX I
APPRECIATION MODELS
Equation 1: Square Footage
Estimates for equation: APPR
Ordinary least squares regression.
Source
I
SS
df MS
Number of obs
F ( 1, 138)
Prob > F
R-square
Adj R-square
Root MSE
= 140
= 22.62
= 0.0000
= 0.1408
= 0.1346
= .00593
Model
Residual
|
.000796239
.004858753
1 .000796239
138 .000035208
Total
1
.005654992
139 .000040683
appr
I
Coef.
Std. Err. t
p>it|
[95% Conf.
Interval]
sqft
_cons
i
-.0000078
.0646419
.0000016 -4.756
.0024974 25.883
0.000
0.000
-.000011
.0597037
-.0000045
.0695801
Equation 2: Age
Estimates for equation: APPR
Ordinary least squares regression.
Source
1
SS
df MS
Number of obs
F ( 1, 138)
Prob > F
R-square
Adj R-square
Root MSE
= 140
= 17.16
= 0.0000
= 0.1106
= 0.1042
= .00604
Model
Residual
.000625507
.005029485
1 .000625507
138 .000036446
Total
i
.005654992
139 .000040683
appr
i
Coef.
Std. Err. t
p>it|
[95% Conf.
Interval]
age
_cons
1
.0002407
.0439209
.0000581 4.143
.0022518 19.505
0.000
0.000
.0001258
.0394683
.0003556
.0483734
114


28
However, Jacksons 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 Jacksons (1979)
polynomial expression of land prices that seems the most promising for the examination
of spatial variation in house price appreciation. Jacksons 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.


25
where P¡ is the price per square foot of property i; Pjk denotes a vector of coefficients of
Xy and Ylk, Cartesian coordinates of the properties in the sample and j + k < p, where the
model is a p"1 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.
Accessibility Indices
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


61
Figure 5-2 Land Value Surface for 1980
Figure 5-3 Land Value Surface for 1982


CHAPTER 1
INTRODUCTION
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)
level.
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
1


5
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.


I certify that I have read this study and that in my opinion it conforms to acceptable
standards of scholarly presentation and is fully adequate, in scope and quality, as a
dissertation for the degree of Doctor of Philosophy.
Timothy J. Fik, Chairman
Associate Professor of Geography
I certify that I have read this study and that in my opinion it conforms to acceptable
standards of scholarly presentation and is fully adequate, in scope and quality, as a
dissertation for the degree of Doctor of Philosophy. \
Edward J. Malecki
Professor of Geography
I certify that I have read this study and that in my opinion it conforms to acceptable
standards of scholarly presentation and is fully adequate, in scope and quality, as a
dissertation for the degree of Doctor of Philosophy. sj
Peter R. Waylen ^
Associate ProfessoroFGeography
I certify that I have read this study and that in my opinion it conforms to acceptable
standards of scholarly presentation and is fully adequate, in scope and quality, as a
dissertation for the degree of Doctor of Philosophy.
(Q,
John R. Dunkle
Professor of Geography
I certify that I have read this study and that in my opinion it conforms to acceptable
standards of scholarly presentation and is fully adequate, in scope and quality, as a
dissertation for the degree of Doctor of Philosophy.
oiirl P T inn '
David C. Ling
Associate Professor of finance.
Insurance, and Real Estate


78
Repeat-Sales Results
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 (P,, / Pit) = E,T c, Dit + EtT e, Dlt + e
where the coefficient estimate £, 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.


125
Weicher, J., and R. Zerbst, "The Externalities of Neighborhood Parks: An Empirical
Investigation," Land Economics, Volume 49, pp 99-105, (1973)
Zellner, A., Readings in Economic Statistics and Econometrics, Little, Brown: Boston,
(1968)


73
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.
COEFF.
UNIVAR.
T-STAT.
MULTIVAR.
COEFF.
MULTIVAR.
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


54
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)


44
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
following equation:
A, = p, SQFT, + P2 AGE, + P3 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.


27
The theoretical accessibility function A = f(Xj,Yk) denotes the level of accessibility
at location (Xj,Yk) using Cartesian coordinates Xj 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, = E,p Ekp a* [XJ Y|k] + r, (10)
where r¡ is a remainder and j + k < p. Although equation (9) is written in pth 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).


33
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


18
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. = P + E,k Pi Xj, + e, (1)
where P¡ is the transaction price of property i, i = 1 to n observations, and Pj denotes a
vector of coefficients, j = 1 to k, on the structural and locational attributes, Xj¡, which
could include square footage, age, lot size, and various neighborhood characteristics. The
coefficient p0 is an intercept term and £, 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.


70
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


ACKNOWLEDGMENTS
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.


77
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 comer 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.


3
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


97
(2) Linearity of functional form:
It is assumed that the relationship between dependent and independent variables
is linear. It is quite possible that the relationship between price and square footage could
be nonlinear; as square footage increases so does price, but at a decreasing rate. This is
best analyzed by plotting the variables in question. Here, the relationship between price
and square footage (and age) is assumed to be linear while the relationship between price
and location is specified as a polynomial function.
(3) Heteroscedasticity:
It is assumed that the regression variance is constant. However, with cross-
sectional data, it is not unusual to find an increasing variance. As price increases over
space, its variance might also increase. A plot of the residuals provides the easiest
verification; alternatively, the Goldfeld-Quant, Park, or Glejser tests can be performed.
In cross sectional studies, the appearance of homoscedastic errors may actually be
spatially autocorrelated errors.
(4) Serial Autocorrelation:
It is assumed that the regression error terms are random (not correlated).
However, this can be a problem in time-series regression because variables are often
correlated to some degree with themselves over time. This is commonly checked by
testing the Durbin-Watson statistic.


APPENDIX F
NAIVE MODEL WITH SIMULTANEOUS ESTIMATION
Estimates for equation: PRICE80
Generalized least squares (GLS) regression.
Observations
Mean of LHS
StdDev of resid
R-squared
Durbin-Watson
RHO used for GLS
140
0.3914201E+05
0.3744895E+04
0.9225936E+00
2.0689386
0.0865833
Weights
Std.Dev of LHS
Sum of squares
Adjusted R-sq
ONE
0.1350852E+05
0.1907297E+10
0.920886E+00
Autocorrelation = -0.0344693
Variable
Coefficient
Std. Err
t-ratio
Prob|t|
Mean of X
Std.Dev
Constant
4487.1
2116.
2.121
0.03396
SQFT80
21.978
1.248
17.614
0.00000
1530.5
351.72
AGE 80
-282.78
34.27
-8.252
0.00000
38.414
8.9619
LOT 80
878.37
106.6
8.241
0.00000
13.523
4.4084
Estimates for equation: PRICE82
Generalized least squares (GLS) regression.
Observations
Mean of LHS
StdDev of resid
R-squared
Durbin-Watson
RHO used for GLS
* 140
* 0.4603644E+05
= 0.5198864E+04
= 0.9054632E+00
= 1.9339435
= -0.0076121
Weights
Std.Dev of LHS
Sum of squares
Adjusted R-sq
Autocorrelation
= ONE
= 0.1696932E+05
= 0.3675834E+10
= 0.9033778E+00
= 0.0330283
Variable Coefficient Std. Err t-ratio Prob|t| Mean of X Std.Dev.
Constant
2806.1
2593.
1.082
0.27912
SQFT82
26.379
1.517
17.395
0.00000
1524.5
338.46
AGE 8 2
-344.11
40.71
-8.453
0.00000
37.921
9.5096
LOT 8 2
1191.7
125.9
9.466
0.00000
13.478
4.3766
105


15
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


59
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.


LD
1780
1995
/$*3 7
UNIVERSITY OF FLORIDA
3 1262 08554 9243


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
By
Greg T. Smersh
August, 1995
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 depreciationthe effect
of age on a structurecan be assumed to be spatially constant. However, the assumption
that intraurban land prices, or changes in those prices, are spatially constant may be
considered naive.
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
vii


19
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 = £> ft In Xju + E,T c, D + 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 ft indicates a vector of coefficients on the structural and
locational attributes. Here, c, denotes a vector of time coefficients on Dit, time dummies
with values of 1 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.


69
Predicted House Price Appreciation
(in Standard Deviations)
APPRECIATION
-1 to 41
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.


38
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
Judge (1985).
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/ Cjj pJ / E; c8
(13)