FINAL
L REPO
ORT
Estim
mating
g Lake Amennity Values ffor
Reside
R
ential Houses
H
s on G
Grand L
Lake oo’ the
Cheerokeees
SUBMIT
TTED TO:
Grand Riiver Dam Auuthority
PREPAR
RED BY:
Monika Ghimire,
G
Ph..D.
Tracy A. Boyer, Ph.D
D.
Dave Shiideler, Ph.D..
Max Mellstrom, Ph.D
D.
Departmeent of Agricuultural Econnomics
Oklahom
ma State Univversity
January, 2017
1
Contents
Introduction ..................................................................................................................................... 3
Economic Valuation........................................................................................................................ 4
Matched Pair Method ...................................................................................................................... 5
Study Area ................................................................................................................................... 5
Eufaula Lake ............................................................................................................................ 5
Grand Lake .............................................................................................................................. 6
Data ............................................................................................................................................. 7
Methodology ............................................................................................................................... 8
Descriptive Statistics ................................................................................................................... 9
Results and Discussion .............................................................................................................. 13
Hedonic Valuation Method ........................................................................................................... 16
Data Preparation ........................................................................................................................ 17
Descriptive Statistics ................................................................................................................. 18
Econometric Model ................................................................................................................... 20
Results and Discussions ............................................................................................................ 22
Conclusions ................................................................................................................................... 29
References ..................................................................................................................................... 30
2
Introduction
Grand Lake o’ the Cherokees is the third largest reservoir in Oklahoma, encompassing
46,500 surface acres of water and 1,300 miles of shoreline (GRDA, 2008). Grand Lake is
situated in northeastern Oklahoma in four counties: Delaware, Ottawa, Craig, and Mayes. The
lake is a major destination for outdoor recreation and second homes. Marinas, lakeshore parks,
public boat launches, and thousands of private docks provide access to the lake. Over one million
visits are made to the lake’s commercial and public access points annually. Grand Lake is also
significant in that it is the only reservoir in Oklahoma where private residential and commercial
entities can own property at the shoreline. Grand Lake is managed by the Grand River Dam
Authority (GRDA), a state agency created by the Oklahoma Legislature in 1935 to be a
"conservation and reclamation district for the waters of the Grand River.” GRDA develops and
manages public recreation on Grand Lake including shoreline and surface water use with
cooperation with state agencies and local communities. GRDA provides land and access for the
operation of state and municipal parks on the lake. GRDA completed a shoreline development
inventory in 2006, which documented private facilities such as boat docks and ramps.
Owning land with waterfront or water views is highly desirable because of the scenic and
recreational amenities provided by water. Hence, prices for land with access to these amenities
tend to be higher than for other lands. Studies have shown that land values around Grand Lake
are greater than elsewhere in the state (GRDA, 2008). Agricultural land values in Mayes,
Delaware, and Ottawa Counties have increased by 58%, 28% and 25%, respectively during the
period of 2004-2006 to 2013-2015 (Doye, 2017). However, no studies disaggregate the values
for specific lake amenities for residential houses in the region.
This study estimates the value of water-related amenities including view, lake access and
proximity, lake frontage, and dock capacity to residential properties around Grand Lake. We
used two different methods, matched pair and hedonic price methods, to evaluate the value of
water-related amenities. The matched pair method was used to identify the general value of
amenities and locational advantages attributable to the lake relative to a benchmark. We matched
residential properties in the Grand Lake region to similar properties in the Eufaula Lake region
and attributed sales price differences to the added value of Grand Lake. The hedonic price
method was used to value individual amenities for Grand Lake properties, including distance of a
house from the lake, dock availability, and lake frontage.
3
Economic Valuation
There are two basic types of environmental and natural resource values. Use values are
based on the actual use of a good or service produced by the environment. This includes both
extractive and non-extractive uses requiring physical activity. Non-use values are values not
associated with the physical use of an environmental good or service. Non-use values are also
known as “existence values,” because it is an individual’s mere awareness that the good exists
that creates value. Environmental and natural resources often support multiple types of value.
Economic valuation measures one or more types of these values. Total economic value is the
sum of all relevant use and non-use vales for a resource. For water resources, use values include
the value of drinking water, water for manufacturing, and water-based recreation, among other
uses. Water for drinking and manufacturing are types of extractive use, while water for
recreation is a non-extractive use. There may also be non-use values for water. For example, a
person may get value from the knowledge that a resource like Grand Lake exists, and are willing
to pay some amount to protect it.
This study focuses exclusively on use values associated with the lake for private property
owners. Price premiums for land with lake amenities, such as water frontage, are measurable in
the same manner that a realtor or assessor would estimate the value added to a home from
increased square footage or additional bedrooms. However, we use statistical rather than
heuristic methods to estimate this value. Individual lake amenities to residential homes are
valued using the hedonic method (Freeman, 2003), and the overall value of Grand Lake relative
to another lake in Oklahoma is valued using the matched pair method.
To achieve the goal of estimating the value of lake amenities to Grand Lake in this study,
the research team in the Department of Agricultural Economics presented the following research
plan.
1. To estimate the value of water-related amenities such as view, lake access, lake frontage,
and docking capacity to residential homeowners around Grand Lake using hedonic price
analysis.
2. To calculate the economic impact of lakefront property on Grand Lake by estimating the
contribution of such property to the tax bases in the region.
3. To collect GIS data needed for economic impact study simulation for watershed land
management.
4
Matched Pair Method
Matched pair methods are used to evaluate the effect of a treatment by comparing a
treated unit with a non-treated unit. Matching is necessary because the treatment is conducted
outside of a laboratory setting, and treatment is non-random. The matched pair method pairs up
one treated unit with a non-treated unit (or possibly several non-treated units) that has similar
observable characteristics. Conceptually, if the pairs are identical for every characteristic except
the treated status, then difference in the outcome variable of interest can be attributable to the
treatment. In our study, the treatment is waterfront access on Grand Lake and the outcome of
interest is property value.
Matches are assigned based on propensity scores, which could be thought of as an index
value to summarize the observable characteristics of each property in the study. Propensity score
matching (PSM) was developed by Rosenbaum and Rubin (1983). Since then, research using
propensity score analysis has grown exponentially (Holland, 1986; Rubin, 1974; Sobel, 1996;
Winship and Morgan, 1999). Economists regularly use PSM to identify the effects of variables
on economic outcomes in non-randomized settings, including the effect of water amenities on
residential home values (Abbot and Klaiber, 2013). In this study, we use PSM to pair properties
on Grand Lake to properties on Eufaula Lake. This comparison provides a measure of the value
of a house in the Grand Lake region relative to other lake-focused regions. Eufaula is chosen
because it is the only lake in Oklahoma besides Grand Lake with private lake frontage
ownership. While property on or near water is generally worth more than other property, our
approach demonstrates that Grand Lake is a uniquely valuable lake in the region.
Study Area
Eufaula Lake
Eufaula Lake is the largest man-made lake in Oklahoma with a surface area of 102,000
acres, volume of 3,798,000 acre feet and 600 miles of shoreline (O'Dell, 2016). It is located in
southeast Oklahoma on the Canadian River, 27 miles upstream from its confluence with the
Arkansas River, near the town of Eufaula. The lake covers parts of McIntosh, Pittsburg, Haskell,
and Okmulgee counties. Its mean elevation is 585 feet above sea level. The lake was constructed
to provide flood control, hydroelectricity, water supply, navigation and recreation. Eufaula Lake
is 128 miles and 84 miles away from Oklahoma City and Tulsa, respectively (Fig. 1). Lake
5
Eufaula is
i a recreatio
onal destination for peop
ple from all oover Oklahom
ma and draw
ws anglers frrom
across the United Staates for fishin
ng tournameents. Other aactivities at E
Eufaula Lakee include
boating, swimming, hiking,
h
hunting, golfing,, and horseb ack riding.
Grand Lake
L
Grand
G
Lake o'
o the Cherok
kees is situatted in northeeast Oklahom
ma and is thee third largesst
lake in Oklahoma
O
wiith a surface area of 46,5
500, volume of 1,515,4166 acre feet aand 1,300 miiles
of shoreline (GRDA,, 2008). It is settled in th
he foothills oof the Ozark Mountain R
Range. Grannd
d
and mostly rocky. The
T average depth is 36.33 feet, with a mean elevvation of 7455 feet
Lake is deep
above seaa level. Thee lake coverss parts of Deelaware, Ottaawa, Craig, aand Mayes ccounties. Graand
Lake is 170
1 miles and 69 miles away
a
from Oklahoma
O
Ci ty and Tulsaa, respectively (Fig 1). B
Both
Grand Laake and Eufaaula Lake arre several hours from Okklahoma Cityy and about one hour froom
Tulsa. Liike Eufaula, Grand Lakee is a major recreation
r
deestination in the region, aas well as ann
importan
nt lake for sp
port fishing to
ournaments.. Other activvities at Grannd Lake incluude boating,,
swimmin
ng, hiking, an
nd using offf-road vehicles.
o Grand and
d Eufaula Laakes in Oklahhoma.
Figure. 1. Location of
6
Data
We obtained data on residential sales transactions (MLS data) from 2013 to 2015 in the
Grand Lake and Eufaula Lake regions from databases of the Northeastern Real Estate Board and
Southeastern Real Estate Board of Oklahoma. Pre-2013 transactions are not included because
these data were not available for the Eufaula Lake region. The household transaction data
included household characteristics such as house age, lot size, garage capacity, house stories,
total beds, total baths, house square footage, year sold, existence of dock and pool, and water
frontage. After eliminating missing and some extreme values, a total of 170 house transactions
at Grand Lake and 835 house transactions at Eufaula Lake were available to conduct the
propensity score matching analysis (Table 1).
Table 1. Number of waterfront and non-waterfront houses sold in Grand Lake and Eufaula
region from 2013 to 2015.
Grand Lake
Eufaula
Waterfront
Non-Waterfront
Waterfront
Non-Waterfront
2013
22
36
2
94
2014
9
19
5
333
2015
31
53
3
398
62
108
10
825
Year
Total
Most of the houses sold in both lake regions did not have waterfront, but a greater
proportion of waterfront houses were sold in the Grand Lake region compared to the Eufaula
Lake region (Fig.2 and 3). On Grand Lake, residential houses can be located adjacent to the
shoreline, which gives it a locational advantage for residential houses and may explain why there
were more transactions of waterfront houses on Grand Lake compared to Lake Eufaula.
We obtained spatial data layers for Eufaula Lake and Grand Lake from Geospatial
Gateway (Geospatial Gateway, 2016) and GRDA, respectively. The locational advantage of
being adjacent to a lake or in a neighborhood with water access is well established in economic
research (Walsh, 2009). Based on the spatial extent of water amenity values established in prior
research, we conducted the propensity score matching analysis for houses within a 5 mile buffer
7
of both lakes. The buffer was delimited using ArcMap 2013. The house characteristics used to
match Grand Lake properties with Eufaula Lake properties are listed in Table 2.
Methodology
The propensity score is defined by Rosenbaum and Rubin (1983) as the probability of
treatment assignment conditional on observed baseline variables. In randomized experiments, the
results in two treatment groups may often be directly compared because their units should be
similar on average. In nonrandomized experiments, such direct comparisons may be misleading,
because the units exposed to one treatment could differ systematically from the units not exposed
to the treatment. Thus, propensity scores can be used to group treated units with similar control
units so that direct comparisons are more meaningful. Conditional on the propensity score, the
distribution of measured baseline variables is similar between treated and untreated units.
First, we define the Grand Lake residential sales as the treatment group and Eufaula Lake
residential sales as the control (untreated) group. The variables used to match the properties from
Grand Lake to Eufaula Lake were house age, lot size, garage capacity, house stories, total bed,
total bath, house square footage, year house sold, existence of dock and pool, and water
frontage.i The logit model was used to estimate the probability of treatment status based on these
variables. Using the probabilities as propensity scores, home sales in the Grand Lake region were
matched with sales in the Eufaula Lake region with similar propensity scores. The difference
between these two groups provides an estimate of the average value of a residential property in
the Grand Lake region relative to Eufaula Lake.
Properties were matched based on the nearest neighbor technique. The twelve variables
used to estimate the propensity score provided the best balance between the treatment and
controls groups. The variables that yielded lowest bias were selected for propensity score
matching analysis. The nearest neighbor technique pairs a treated unit with an untreated unit that
has the closest distance between their propensity scores. We trimmed the sample of matched
pairs so that all matches had a propensity score difference within a defined caliper band. The
caliper matching assigns the maximum allowable difference in propensity score between the
treated case and the control case. Based on the distribution of the propensity score of the control
observations, we used a caliper of 0.02 (a difference of 0.02 in propensity scores between the
treated and control cases). With caliper matching, the treated units that do not have good
8
matches (i.e., are within the range of a caliper) with the control observations are dropped from
the matching analysis. We performed matching with replacement. This means that after a control
observation is used as a match, it is put back into the sample and can be used more than once to
match other treated observations. Each treated case is used only once, but the same control case
may be used several times, if it is the closest match for many different treatment cases.
We used the psmatch2 command in Stata for the propensity matching analysis and, after
matching, the pstest command in Stata to test the balance of the variables. To assess balance,
Table 4 presents the bias and the mean differences between the treated and control units in the
matched sample.
Descriptive Statistics
Descriptive statistics of the PSM sample are provided in Table 2. The average sale price
for houses in the Eufaula Lake region is lower compared to the Grand Lake region. On average,
houses are older and located on bigger lot sizes in the Eufaula Lake region compared to the
Grand Lake region. In both regions, more houses were sold in 2015 than in 2013 and 2014. The
average levels for lot size, incidence of central air conditioning, number of stories, total
bedrooms, and total baths were similar for properties between the two lakes. However,
significant differences were found in dock presence and waterfront homes sold between two
lakes. The Eufaula Lake region had only 4% of sales with docks, while 24% of houses in the
Grand Lake region had docks. Similarly, only 1% of houses sold were waterfront houses in
Eufaula Lake region, while in Grand Lake region 36% of houses sold were waterfront houses.
There was a significant difference in the percentage of houses using city water between the
Grand Lake and Eufaula Lake regions: 65% of houses around Grand Lake compared to only
45% of houses around Eufaula Lake. The difference in shoreline frontage between Grand Lake
and Eufaula Lake homes could explain the large gap in sales prices between the two regions.
9
Averagee house salle price forr waterfron
nt houses in
n Grand L
Lake
vs. Eu
ufaula Lak
ke
$350,000
$324,4552
House sold price
$300,000
$251,2677
$250,000
$224,265
$200,000
$149,667
7
$150,000
$96,135
$
$100,000
$85,020
$50,000
$0
2013
3
Year
20114
Grand Lake
22015
Eufaulaa Lake
Figure 2.. Average ho
ouse sale pricce for waterffront housess in Grand Lake vs Eufauula Lake from
2013 to 2015.
2
Average non-- waterfron
nt house sa le price in Grand Lak
ke vs.
Eufaula
E
Laake
$14
40,000
House sold Price
$12
20,000
$109
9,411
$118,674
$103,059
$114,779
$102,7300
$10
00,000
$81,379
$8
80,000
$6
60,000
$4
40,000
$2
20,000
$0
2013
20144
Year
Grand LLake
2015
Eufaulla lake
Figure 3.. Average ho
ouse sale pricce for non-w
waterfront hoouses in Grannd Lake vs E
Eufaula Lakke
from 201
13 to 2015.
10
Table 2. Descriptive Statistics for Grand Lake vs Eufaula Lake Residential Sales (2013-2015)
Eufaula Lake
Variable
Grand Lake
Mean
Std. Dev.
Mean
Std. Dev.
$114,825.80
$101,670.6
$171,020.70
$157,906.20
Age of building
34.72
22.37
31.56
20.23
Lot size (Acres)
5.97
23.72
5.81
15.96
Percentage of house sold in 2015
0.49
0.64
Percentage of house sold in 2014
0.40
0.16
Percentage of house sold in 2013
0.11
0.20
Percentage of house with central air conditioning
0.79
0.85
Percentage of house with dock
0.04
0.24
Percentage of house with pool
0.03
0.02
Number of stories
1.12
0.32
1.29
.521
Total bath
1.99
0.61
2.20
.829
Total bed
2.94
0.67
3.12
.816
1,587.53
532
1,833.21
786.15
Average sold price
House square footage (sq.ft.)
Percentage of houses with city water source
0.40
0.65
Percentage of houses with community water source
0.38
0.20
Percentage of homeowner houses
0.01
0.36
Number of observations
835
170
11
Table 3. Estimated coefficient for the propensity score logit regression.
Variables
Coefficients
Std. Err.
Age of building
0.0229
0.0323
Lot size (Acres)
0.0278
0.0203
-0.0006
0.0008
Cubed age of building
0.0000
0.0000
Squared lot size (acres)
-0.0002
0.0002
House sold in 2014
-1.2806***
0.2730
Squared age of building
House sold in 2013
0.3048
0.2720
Central air conditioning
0.1204
0.2915
Dock
0.5991
0.4424
House with pool
-0.4083
0.6923
Total bath
-0.0540
0.2411
Total bed
0.1453
0.2045
House square footage
0.0001
0.0003
City water
1.5592***
0.3304
Community water
Homeowner houses
Constant
-0.0138
0.3629
3.7570***
0.4372
-3.4623***
0.7204
12
Table 4. Results of PSM balance testing.
Variable
Mean Treated
Mean Control
%bias
p-value
Age of Building
31.70
29.31
11.2
0.33
Lot size (Acres)
4.985
5.58
-3
0.74
1435.10
1370.80
3.5
0.77
Cubed age of building
80128
84031
-2.4
0.84
Squared lot size (Acres)
232.48
338.53
-2.3
0.56
House sold in 2014
0.16
0.16
-1.5
0.89
House sold in 2013
0.18
0.24
-14.1
0.27
Central air conditioning
0.85
0.86
0
1
Dock
0.22
0.22
0
1
Pool
0.01
0.02
-4.1
0.65
Total Bath
2.17
2.05
17
0.12
Total Bed
3.11
2.99
15.7
0.14
House square footage
1815
1698.30
17.4
0.13
City water
0.68
0.69
-1.3
0.90
Community water
0.18
0.19
-1.4
0.89
Waterfront houses
0.33
0.33
0
1
Number of observations
170
835
Squared age of building
Results and Discussion
The results of the propensity score matching are provided in Table 4. After balancing
propensity score matches, the average treatment effect is computed as the average difference in
the sale price between the treatment and control units across the matched pairs. Table 5 includes
the estimated average treatment effects for all houses, non-waterfront houses and houses sold in
2013, 2014, and 2015. The average treatment effect for the waterfront houses was not estimable
because of the small number of waterfront house sales in the Eufaula Lake region (control group)
relative to the Grand Lake region (treatment group).
13
The average value of a house in the Grand Lake was significantly greater than the
average value of a house in the Eufaula Lake region. The average treatment effect is $47,850 for
all houses (Table 5). This means that, on an average, house in the Grand Lake region are valued
$47,850 more compared to houses in Eufaula Lake region. By individual year, the average
treatment effect for 2013 was significantly higher in Grand Lake compared to Eufaula Lake.
However, the average treatment effects for 2014 and 2015 were not significantly different
between Grand Lake and Eufaula Lake. For the non-waterfront houses, the average value of
being in the Grand Lake region was lower than being in the Eufaula Lake region. This result
shows that house values around Grand Lake are higher mostly due to the value of waterfront
properties. Non-waterfront houses on Eufaula Lake are valued on average $24,438 more than
similar houses around Grand Lake.
14
Table 5. Average value of being on Grand Lake vs. Eufaula Lake
Yearly
All Houses
z-stat
Non-waterfront
z-stat
Average value of being in
$168,230
$95,651
Grand Lake region
Average value of being in
$120,380
$120,089
Eufaula Lake region
Average difference (Grand
$47,850 2.54**
$-24,438 -1.82*
Lake vs Eufaula Lake)
** and * represents statistical significance at 5% and 10% levels, respectively
2013
z-stat
2014
z-stat
2015
$168,102
$81,621
$166,364
$93,114
$90,276
$136,821
$74,988
1.99**
-$8,655
-0.44
z-stat
$29,543
1.01
15
Hedonic Valuation Method
Quality-differentiated goods, including residential properties, can be valued using
hedonic methods. An individual’s willingness to pay for a good varies systematically with the
characteristics of a good. Thus, willingness to pay is naturally higher for goods of better quality
or that come with added features. For residential properties, willingness to pay and, therefore,
sales price depend on market characteristics such as the size and age of the structure, as well as
non-market characteristics such as the quality of nearby environmental amenities. Hedonic
methods provide an estimate of the value of each individual characteristic using statistical
techniques (Pendleton and Mendelsohn, 1998; Faux and Perry, 1999; Wilson and Carpenter,
1999).
Hedonic methods are widely used in economics to value residential property
characteristics. Since the method was first applied by Rosen (1974), it has become the most
common approach for valuing goods and services. It is widely used to value non-marketed
environmental amenities (Benson et al., 1998; Freeman, 2003; Lansford and Jones, 1995; Mahan
et al., 2000). However, few published hedonic studies report on the values of lake amenities such
water frontage, dock access, and distance to the water.
The value of residential property characteristics can “spill over” across properties. This
means that the characteristics (and value) of one home can influence the characteristics (and
value) of surrounding homes. Spillover effects occur because people prefer living closer to nicer
and higher valued houses, which can create a positive feedback loop that pushes house prices up
in desirable neighborhoods. Hedonic methods applied to property values can account for the
influence of these spillover effects using statistical techniques that incorporate spatial
dependencies. The spatial lag and spatial error models are the two most frequently used models
in the literature. Although modeling spatial dependencies in the hedonic valuation literature has
been popular in recent decades (Pace and Gilley, 1997; Basu and Thibodeau, 1998; Paterson and
Boyle, 2002; Wilhelmsson, 2002; Kim et al., 2003) only a few studies have incorporated spatial
dependencies in estimating the value of lake amenities (Ara et al., 2006; Walsh et al., 2011; Frey
et al., 2013).
Spatial dependencies can also be attributed to important characteristics that are difficult
to observe or include in the statistical model. Similar builders/building techniques, neighborhood
attributes, and other omitted variables can be sources of apparent spatial dependence. Thus, an
16
important feature of this study is incorporating spatial dependence to determine the values of
lake amenities to residential houses in Grand Lake region.
Data Preparation
Household transaction data (Multiple Listing Service) for the hedonic valuation study
was obtained from the Northeastern Real State Board of Oklahoma. These data contain house
sales price and characteristics such as the number of bedrooms, number of bathrooms, parcel
size, and house age. Single and multi-family residential property sales within 5 miles of the
Grand Lake region in Oklahoma for the period of 2000-2015 were used for the hedonic valuation
analysis. GRDA was the source of several layers of GIS maps, such as Grand Lake base map,
flood zone layers, and elevation files for the Grand River Basin. The property shape files for the
individual counties were obtained from the county assessors of the individual counties.
Each sale was matched with its property shape file based on the reported house address.
For the properties with missing and incorrect addressees, the longitude, latitude and legal
description were used to match a sale with the property shape file. LIDAR elevation files with a
10 meter resolution were used to compute the elevation and slope of each parcel near the
centroid. The longitude and latitude of the centroid of each parcel was calculated in ArcMap and
was used to define the location of individual properties and to calculate variables such as
distance to the lake. The Euclidean distance from the centroid of the parcels to the lake was used
as the distance measure. The location of properties sold from 2000- 2015 in Grand Lake region is
provided in Figure 4.
17
Figure 4.. Location off sold residen
ntial homes from 2000 tto 2015 withhin five miles of Grand L
Lake.
Descriptive Statisttics
After
A
cleaning
g the data, a total of 3,96
67 complete household ttransactions were used too
estimate the hedonic pricing mod
del. Summarry statistics ffor the depenndent and inndependent
variabless for all housses, waterfro
ont, and non--waterfront hhouses is preesented in Taable 6.
Significaant differencees in charactteristics acro
oss these cateegories weree observed ffor the follow
wing
variabless: sale price, house age, availability
a
of
o docks, houuse square ffootage, city water, and
septic sew
wer. Waterfrront houses are
a more exp
pensive and larger. Out of allsales, 62% of the
waterfron
nt houses in our sales daata are in Gro
ove school ddistrict, whilee 39% of noon-waterfront
houses in
n our sales data are in thee Grove scho
ool district. Seventy ninee percent off waterfront
houses haave septic seewer, but only 39% of th
he non-waterrfront houses have septicc sewer. The
average house
h
sale prrice of a watterfront housse is more thhan double thhe average ssold price off a
non-wateerfront housee (Fig. 5). Th
he waterfron
nt house pricce has been iincreasing ovver time from
m
2000 to 2015
2
except for a sudden
n decline in 2013.
2
18
Table 6. Descriptive statistics of the variable for all, waterfront, and non-waterfront house sales (2000-2015, N=3967)
All Houses
Variables
House sold price
Lot size
Max elevation (meter)
Distance (meter)
House age (years)
Air conditioning
Basement
Days on market
Dock
Water frontage
Garage capacity
Electric heating
Grove vs other school district
Septic vs city sewer
Stories
Total bathroom
House area (square foot)
City water
Community water
Other water source (well)
Flood insurance
Mean
$166,625.30
1.23
243.56
1,138.08
26.04
0.80
0.13
171.54
0.32
0.34
1.42
0.42
0.46
0.53
1.21
2.01
1,727.19
0.68
0.22
0.10
0.08
Std. Dev.
$145,979.50
3.96
11.24
1,637.53
19.78
152.37
0.95
0.45
0.77
746.01
Waterfront Houses
Non-waterfront Houses
Mean
Mean
Std. Dev
$275,872.10
1.18
240.10
180.56
20.06
0.86
0.27
192.09
0.61
$183,928.60
4.25
10.49
567.95
14.41
1.48
0.57
0.62
0.79
1.40
2.32
2,022.57
0.52
0.33
0.15
0.10
1.05
163.36
0.55
0.86
926.04
Std. Dev
$110,459.10
1.26
245.34
1,630.37
29.12
0.77
0.06
160.98
0.16
$74,763.97
3.81
11.20
1,783.50
21.40
1.39
0.34
0.38
0.39
1.11
1.85
1,575.32
0.77
0.17
0.09
0.07
0.90
145.30
0.34
0.67
578.01
19
All homes
Waterfront
Nonwaterfront
Average House Sold Price ($)
$320,000
$280,000
$240,000
$200,000
$160,000
$120,000
$80,000
$40,000
$0
Year
Figure 5. Average residential sale prices for all houses, waterfront houses, and non-waterfront
houses (2000 -2015).
Econometric Model
Hedonic valuation model assigns values to different home characteristics and the lake
amenities variables such as lake proximity, water frontage, docking, and lake view separately.
Hedonic valuation model was specified as property prices are a function of the property
characteristics and lake amenities, and other variables as follows.
where,
is a dependent variable which represents property prices,
is the vector of independent
variables which include property characteristics, lake amenities and so on (Table 6),
is the
vector of intercept shifts that correspond to attributes measured using dummy variables in , and
is identically and independently distributed error term.
There have been issues of functional form and model misspecification in hedonic
valuation method. Several functional forms ranging from linear to non-linear model exist in the
literature. A box cox transformation method was utilized in this study, as it was the best fitting
model. A small constant value was added to all non-dummy variables that had zero values before
20
logarithmic transformation of the variable. Adding a small constant before logarithmic
transformation is not uncommon (Frank and Antweiler , 2002; MaCurdy and Pencavel, 1986).
For a semi log model, the dependent variable was transformed logarithmically. In the double log
model, the dependent variable and all variables except the dummy independent variables were
transformed logarithmically.
In addition to functional form and the model specification, spatial dependencies, either
due to a structural relationship between the observations (e.g., geographic proximity accounts for
some of the value of the homes, as described above), the omission of spatially correlated
variables with the explanatory variables (e.g., proximity to unobserved characteristics, such as
employment opportunities), or spatially autocorrelated errors have been demonstrated as of high
importance in valuation (e.g., spatial lagged dependencies (Se Can and Megbolugbe, 1997; Bell
and Bockstael, 2000; Leggett and Bockstael, 2000; Gawande and Jenkins-Smith, 2001).
Anselin (1988) describes spatial regression models that attempt to incorporate these
effects. Using a spatial lag model, spatial dependence is defined as follows:
The effect of the spatial lag is assessed through the parameter
and a spatial weighting
matrix , which defines the spatial relationships among the property prices. Alternatively, the
spatial error model suggested by Anselin (1988) is defined as:
In this model, the spatially weighted error term is used to avoid bias and inefficiency in
parameters as compared with the OLS error term.
21
Results and Discussion
The results of the semi log and double log models of non-spatial and spatial hedonic
pricing methods are provided in Tables 7 and 9. All significant variables showed the expected
signs in both models. However, based on the results from the box-cox transformation procedure,
the double log model was considered to be a better fitting model to estimate both spatial and
non-spatial hedonic models. In addition, in the case of misspecifications in the data such as nonnormality and heteroscedasticity, the double log model provided more robust estimates than did
the linear or a semi- log model. Cropper et al. (1988) showed that the double log model
performed particularly well when compared with the other models such as semi log and linear in
case of misspecifications in hedonic model and found that the double log model performed the
best to estimate property prices. Some variables such as number of bedrooms and acreage on
waterfront showed high multicollinearity (variation inflation factor was more than 10). Thus,
they were dropped from the model.
Most of the variables are significant except for stories and Grove vs. other school district,
meaning that homes sold in Grove school district or homes with multiple levels did not differ
significantly in price from homes not in those categories. In both the semi log and the double log
models, all the significant variables had expected signs. Increases in lot size, the number of
bathrooms, house acreage, garage capacity, higher elevation, the availability of central air
conditioning, existence of a basement, dock, water frontage, and city water connection increased
the sale price. However, increases in the distance from lake, house age and having a septic sewer,
and need for possession of flood insurance decreased the house price. With 2015 serving as the
base year for sales, the sold year variable was negative, indicating for each year earlier than
2015, the house sale price was lower. The estimates of most of the significant dummy variables
were similar in both semi log and double log models. The presence of dock increased the house
price on average by approximately 26% (double log model) or 29% (semi log model) compared
to a house sold without a dock. Waterfront houses were on average 45% costlier than nonwaterfront houses. Being required to possess flood insurance decreased the house price by 9% in
the double log model.
22
Table 7. Parameter estimates of the variables for the semi-log and double log of non-spatial
hedonic model.
Semi-Log Model
Coefficient.
Std. Err.
Double Log Model
Coefficient
Lot size
0.013***
0.002
0.072***
Max elevation (meter)
0.003***
0.001
0.926***
Distance (1000 meter)
-0.042***
0.005
-0.062***
House age (years)
-0.009***
0.000
-0.042***
Air conditioning
0.236***
0.018
0.213***
Basement
0.013
0.024
-0.038
Days on market
0.0001*
0.000
-0.006
Dock
0.291***
0.023
0.258***
Waterfrontage
0.427***
0.020
0.427***
Garage capacity
0.123***
0.008
0.016***
Electric heating
0.063***
0.015
0.081***
Grove vs other school district
0.0001
0.016
0.060
Septic vs city sewer
-0.065*
0.018
-0.056**
Stories
0.005
0.019
-0.002
Total bathroom
0.102***
0.015
0.275***
House area (square foot)
0.0004***
0.0001
0.853***
City water
0.056
0.028
0.074*
Community water
-0.074***
0.028
-0.036
Flood insurance
-0.019
0.028
-0.095***
Sold year
-0.009***
0.002
-0.002
Constant
9.847***
0.183
0.284
Number of observation
3967
2
0.739
0.742
Adjusted – R
Note: Dependent Variable is Ln (House sold prices)
***, ** and * represents statistical significance at 1%, 5%, and 10%, respectively.
Std. Err.
0.007
0.183
0.006
0.003
0.019
0.024
0.004
0.023
0.021
0.001
0.015
0.015
0.018
0.031
0.027
0.028
0.028
0.028
0.028
0.002
1.033
A test of spatial dependence was conducted. Moran’s I was statistically significant, which
shows that there is significant spatial dependence in the data (Table 8). Thus, a spatial model that
incorporates spatial dependence is required. Based on the fit statistics and the likelihood of the
sale price of a house being dependent on the price of the neighboring houses, a spatial lag model
23
was considered as the best fitting model in this study. The spatial lag hedonic model was
estimated using maximum likelihood regression.
Table 8. Moran I estimation of the data
Variable
Statistic
Moran’s I
0.322 ***
*** denote statistical significance at 1% level.
The results of the selected spatial lag model are provided in Table 9ii. The autoregressive
parameter coefficient lambda was positive and statistically significant, indicating a strong spatial
autocorrelation in the dependent variable. For all other household characteristics, neighborhood
characteristics, and spatial characteristics, variable coefficients are also provided in Table 9.
Despite the issue of spatial dependence, the variable estimates for spatial and non-spatial models
were similar. The non-spatial model was used to compute the implicit prices or the willingness to
pay for each variable in the hedonic model.
24
Table 9. Parameter estimates of the variables for the semi-log and double log spatial hedonic models.
Semi-Log Model
Coefficient.
Lot size
Max elevation (meter)
Distance (1000 meter)
House age (years)
Air conditioning
Basement
Days on market
Dock
Water frontage
Garage capacity
Electric heating
Grove vs other school district
Septic vs city sewer
Stories
Total bathroom
House area (square foot)
City water
Community water
Flood insurance
Sold year
Constant
Std. Err.
0.014***
0.002
0.004***
0.001
-0.033***
0.005
-0.010***
0.000
0.230***
0.019
0.011**
0.024
0.0001*
0.000
0.297***
0.023
0.446***
0.020
0.121***
0.008
0.073***
0.015
-0.034
0.018
-0.036*
0.018
0.007
0.019
0.104***
0.015
0.000***
0.000
0.025
0.028
-0.078***
0.028
-0.013
0.028
-0.010***
0.002
9.592***
0.188
Note: Dependent Variable is Ln (House sale prices)
***, ** and * represents statistical significance at 1%, 5%, and 10%, respectively.
Double Log Model
Coefficient
0.082***
1.096***
-0.061***
-0.042***
0.211***
-0.041*
-0.006
0.262***
0.443***
0.015***
0.090***
0.027
-0.036**
-0.001
0.284***
0.838***
0.050*
-0.035
-0.091***
-0.002
-0.652
Std. Err.
0.008
0.185
0.006
0.003
0.019
0.024
0.004
0.023
0.022
0.001
0.015
0.017
0.018
0.031
0.027
0.028
0.028
0.028
0.028
0.002
1.033
25
Table 9. Continued.
Semi-Log Model
Log likelihood
-2225.74
Double Log Model
-2232.85
lambda
0.00002***
0.00002***
sigma2
0.179***
0.179***
As the double log model was a better fitting model to the data, the estimates from the
double log model were used to compute the marginal willingness to pay for each attribute or the
implicit prices for each variable. The marginal implicit prices of housing characteristics are not
constant due to the nonlinearity of the hedonic function. The implicit prices or willingness to pay
estimates are computed by differentiating the hedonic price function with respect to each
variable (Table 10). The willingness to pay was estimated over the sample average values. For
example the marginal implicit price of having dock is $43,646. In other words, on average, the
house sale price for a resident with a dock is $43,646 more at the time of the sale for our time
period than a similar house without a dock. Likewise, the marginal implicit price of a waterfront
house is $73,766 more than a non-waterfront property sold in the Grand Lake area.
26
Table 10. Implicit prices/Marginal willingness to pay for the significant variables in double-log,
non-spatial model.
Variables
$ per attribute on average
Lot size
$3,420
Max elevation (meter)
$750
Distance (1000 meter)
-$8,493
House age (years)
-$268
Air conditioning
$35,240
Dock
$43,646
Water frontage
$73,765
Garage capacity
$1,808
Electric heating
$14,982
Septic vs city sewer
-$6,080
Total bathroom
$23,523
House area (square foot)
$80
City water
Flood insurance
$8,386
-$15,156
Willingness to pay prices is evaluated at the sample means.
Based on the implicit prices for the amenity variables from the hedonic model, the annual
payment of property tax based on the county for distance to the lake, a dock, lake frontage, and
elevation is computed based on the millage rate (Table 11). The lake frontage characteristic of a
house added $643 (Ottawa) to $702 (Mayes) to annual property taxes. Every 1000 meter closer
to the lake a house adds $74 (Ottawa) to $81 (Mayes) to property tax collections, depending on
the county. The presence of dock or docks added $380 (Ottawa) to $415 (Mayes) to property tax
collections by county. Every meter increase in elevation of a residential parcel added $6.5
(Ottawa) to $7.1 (Mayes) to the annual property tax.
27
Table 11. Contribution of lake amenities to annual property tax.
Counties
Average
Millage Rate
Dock
Lake
Frontage
Elevation
(meters)
0.077
Distance to
Lake (1000
meters)
$74.921
Delaware
$385.016
$650.704
$6.613
Craig
0.080
$77.206
$396.758
$670.550
$6.814
Ottawa
0.076
$74.020
$380.388
$642.884
$6.533
Mayes
0.083
$80.769
$415.069
$701.496
$7.129
Average
0.079
$76.729
$394.308
$666.408
$6.772
Source: Lansford, 2016
28
Conclusions

Matched pair analysis of Grand Lake and Lake Eufaula residential home sales from
2013-2015 shows that being on or near Grand Lake, on average, adds $47,850 value
per home sale compared to a similar home sale at Lake Eufaula.

Analysis of Grand Lake residential sales from 2000-2015 shows that having water
frontage increases residential property values by 43% compared to properties that do
not have water frontage.

Analysis of Grand Lake residential sales from 2000-2015 shows that having dock
access increases the average house price by about 25%.

Using the average millage rates for annual property taxes in the four counties around
Grand Lake, water frontage, dock access, distance to lake, and elevation, contributed
$666, $394, $77 per 1,000 meters, $7 per meter, respectively to annual property tax in
the Grand Lake region.

The property values for water frontage, elevation, and docking access are a direct
result of the natural and managed features of Grand Lake.
In the future, if spatially explicit information on water quality and boating congestion
becomes available, additional lake amenity values to homeowners could be analyzed. The values
presented in this report are a subset of the total value the lake provides to users, property owners
and the tax revenue collected by the community. There are other values such as ecosystem
values, recreational values for visitors, hydropower, flood control, and municipal supply. The
information herein provides a reference for GRDA to support maintaining the quality and
aesthetics of the lake through its enforcement and environmental programs.
29
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32
Endnotes
ii
Let x be the vector of the covariates used for a specific house in each group, and the z
variable indicates whether the house is located in a specific region i (z = 1, if located in Grand
Lake, or z = 0, if located in Eufaula lake). The propensity score
is defined as a conditional
probability to be located in the region i, given the covariates, that is to say,
Matching on
Pr Z|x .
will balance the distributions of x between the regions i (Rosenbaum and
Rubin,1983). At this point, the matching estimator presents two issues. First, the functional form
for
∙ is unknown; therefore it must be estimated from the available data. Secondly,
is a
continuous metric, so it is impossible for two
to match exactly; it is therefore necessary to
choose an objective criterion to match similar
. The literature highlights different functional
forms for the probability distribution. In this study, we used a logit model to estimate
.
ii
A spatial weight matrix was created to run a spatial model. The spatial weight matrix
summarizes the spatial configuration of the data. The spatial weight matrix was originally
constructed by Moran (1948) and Geary (1954) based on the notion of contiguity that a spatial
unit is either joint to the other spatial unit by a point or they share a common boundary. This
approach to the classification of space is useful when analyzing geographical units such as
counties, states, or voting districts. However, where direct contiguity is not common and
individual observations are much smaller, such as real estate sales data where direct neighbors do
not frequently sell their houses in a similar time period, this type of spatial weight matrix fails to
adequately capture space. Thus, the spatial weight matrices in such studies are based on defining
the number of nearest neighbors or the neighbors within certain distance thresholds. In this study,
we considered a distance-based spatial weight matrix where every spatial unit is a neighbor of
other spatial units, but a higher weight is given to the nearest spatial unit and a lower weight is
given to the farthest spatial unit. This is commonly referred to as an inverse distance weighting
scheme.
33