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2 Step 2 – Open-Space Demand Estimation

2 Step 2 – Open-Space Demand Estimation

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Demand for Open Space and Urban Sprawl



179



Nevertheless, those three variables with high VIFs were not excluded for lack of

sufficient justification.



3 Study Area and Data

Knox County, Tennessee was chosen as a case study for this research because (1)

Knoxville is the eighth most sprawling U.S. metropolitan region (Ewing et al. 2002),

and (2) the area consists of both rapid and slow regions of housing growth. Knox

County is located in East Tennessee, one of the three “Grand Divisions” in the state.

The City of Knoxville is the county seat of Knox County. Knoxville comprises

101 miles2 of the 526 miles2 within Knox County. Total populations of Knoxville

and the Knoxville Metropolitan Area were 173,890 and 655,400 in 2000, respectively (US Census Bureau 2002). The University of Tennessee and the headquarters

of Tennessee Valley Authority (TVA) are near downtown Knoxville, and the US

Department of Energy’s Oak Ridge National Laboratory is 15 miles northwest of

Knoxville. These institutions are the major employers of the area. Maryville is

located approximately 14 miles southwest of Knoxville and it is home to ALCOA,

the largest producer of aluminum in the United States. Farragut, a bedroom community, is located along the edge of the western end of Knox County (see Fig. 1). The

Smoky Mountains, the most-visited National Park in the United States, and a large

quantity of lake acreage (17 miles2 of water bodies) developed by the TVA are on

Knoxville’s doorstep.

It is important to note that push/pull factors of the geography surrounding

the study area were not modeled because data were not available. However, to

our knowledge, no other hedonic studies have successfully addressed this issue.

Admittedly, these omitted factors may cause some estimates to be biased. But understanding this context beforehand aids in the interpretation of patterns generated by

mapped coefficients. It is also important to note that the results of this study may not

be representative of other urban areas. The data set does not represent most typical

urban areas, and because of the local amenities and job opportunities, Knox County

may be more of an outlier case compared to other rapidly growing metropolitan

areas. Nevertheless, the methods used in this case study can be applied to other

urban areas where similar data exist.

This research used five GIS data sets: individual parcel data, satellite imagery

data, census-block group data, boundary data, and environmental feature data. The

individual parcel data, i.e., sales price, lot size, and structural information, were

obtained from the Knoxville, Knox County, Knoxville Utilities Board Geographic

Information System (KGIS 2009), and the Knox County Tax Assessor’s Office. Data

were used for single-family home sales transactions between 1998 and 2002 in Knox

County, Tennessee. A total of 22,704 single-family home sales were recorded during this period. Of the 22,704 houses sold, 15,500 were randomly selected for this

analysis. County officials suggested that sales prices below $40,000 were probably

gifts, donations, or inheritances, and would therefore not reflect true market value.



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S.-H. Cho



Fig. 1 Study area



Officials also suggested that parcel records less than 1;000 ft2 might be misinformation. Therefore, parcels smaller than 1;000 ft2 were eliminated from the sample

data. There were 15,335 observations after eliminating these outliers. Selecting a

random sample of sales transactions saved time in running the GWR. Prices were

converted to 2000 (year) dollars to account for real estate market fluctuations in the

Knoxville metro region. This adjustment was made using the annual housing price

index for the Knoxville metro statistical area obtained from the Office of Federal

Housing Enterprise Oversight (OFHEO 2006).

Land cover information was derived from Landsat 7 imagery for 2001. The classified national land cover database from the multi resolution land characteristics

consortium (NLCD 2001) includes the GIS map used in the analysis to identify

open space in the study area. There are 21 land cover classifications in the NLCD

2001 database. Of the 21 classified land covers, 11 classifications were considered

as open space in our study.7 The open-space classification was loosely based on the

definition of “open area” or “open space” in Sect. 239-y of the General Municipal

Law (Open space inventory 1999).8



7

The 11 classifications include developed open space, barren land (rock/sand/clay), deciduous

forest, evergreen forest, mixed forest, shrub/scrub, grassland/herbaceous, pasture/hay, cultivated

crops, woody wetlands, and emergent herbaceous wetlands.

8

Section 239-y defines “open area” as any area characterized by natural beauty or, whose existing

openness, natural condition or present state of use, if preserved, would enhance the present or

potential value of abutting or surrounding development or would offer substantial conformance



Demand for Open Space and Urban Sprawl



181



1 mile



1 mile buffer

Transaction parcel in downtown area

Open space

0 0.125 0.25 0.5

Built area



0.75



1

Miles



1 mile buffer

Transaction parcel in rural area

Open space

0 0.1250.25

Built area



0.5



0.75



1

Miles



Fig. 2 Transaction parcel with surrounding open space and 1.0-mile buffer



To define the open-space demand for individual households, the space in the

11 open-space classifications was aggregated within a 1.0-mile radius (buffer) of

each housing sales transaction (see Fig. 2). Buffer sizes found in the literature were

not consistent, resulting in different estimates of open space value (McConnell

and Walls 2005). For example, Geoghegan et al. (2003) used two buffers, a 100m radius around the property and a 1,600-m radius. Acharya and Bennett (2001)

also used a 1,600-m buffer. Nelson et al. (2004) used 0.1-mile, 0.25-mile, and 1.0mile buffers and Irwin (2002) used a 400-m buffer. Lichtenberg et al. (2007) used

buffers of 0.5, 1, and 2 miles. Although buffer sizes are arbitrarily chosen without

using a systematic framework, a 1-mile buffer was chosen for this study because the

1-mile distance is what can be enjoyed within an easy walk assuming sidewalks or

uncongested roads.

The boundary data, i.e., high school districts and jurisdiction and growth boundaries, were obtained from the Knoxville-Knox County Metropolitan Planning Commission (KGIS 2009). Three classifications of land, i.e., rural areas, urban growth

area (UGA), and planned growth area (PGA), and jurisdiction boundaries are used

to capture the effects of regional core boundaries, as well as, inner and outer suburb

boundaries. The rural areas include land to be preserved for farming, recreation, and

other non-urban uses. The UGA is reasonably compact but adequate to accommodate the entire city’s expected growth for the next 20 years. The PGAs are large

enough to accommodate urban growth expected to occur in unincorporated areas



with the planning objectives of the municipality or would maintain or enhance the conservation of

natural or scenic resources.



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S.-H. Cho



over the next 20 years (MPC 2001). Most current residential development exists

within the boundaries of Knoxville and Farragut while the UGA and PGA serve as

designated areas for future development. Farragut and UGA also function as suburb

boundaries.

Environmental feature data such as water bodies and golf courses were found in

the Environmental Systems Research Institute Data and Maps 2004 (ESRI 2004).

Other environmental feature data such as railroads were acquired from KGIS (2009).

The study area consists of 234 census-block groups. Information from these censusblock groups was assigned to houses located within the boundaries of the block

groups. The timing of the census and sales records did not match except for 2000.

However, given the periodic nature of census taking, census data for 2000 were

considered proxies for real time data for 1998, 1999, 2001, and 2002. By the same

token, variables created from the 2001 national land cover database were used as

proxies for the other years because open space was not expected to change appreciably during the study period. Detailed statistics for individual variables are reported

in Table 1.



4 Empirical Results

The overall performance of the hedonic price and open-space demand equations

estimated with GWR, GWR-SEM, and OLS are compared in Table 2. The OLS

model is called the “global model” hereafter, in contrast to the GWR models (GWR

and GWR-SEM). The spatial error Lagrange Multiplier (LM) statistic for the GWR

model is 82% lower than the LM statistic for the global model, and the GWR-SEM

model reduces the spatial LM statistic by 96% compared with GWR. In the openspace demand equation, the spatial LM statistic for the GWR model is 39% lower

than for the global model, and the GWR-SEM model further reduces the spatial

LM statistic by 4% compared with GWR. Nevertheless, the null hypothesis of no

spatial error autocorrelation is still rejected in the hedonic and open-space demand

equations using the GWR-SEM estimation method. Spatial error autocorrelation

remains in both equations. Although the local models significantly mitigate spatial

autocorrelation in both equations, they do not completely eliminate it and, thus,

the statistical results must be interpreted with caution. As a result, the GWR-SEM

model can be viewed as a complement to the global model rather than an alternative

to it.

In the hedonic model, the Akaike Information Criterion (AIC) for the GWRSEM model is 3,045, lower than for the global model (4,655), and slightly lower

than for the GWR model (3,502). The error sum of squares for the GWR-SEM

model is 1,066, lower than for the global model (1,206) and slightly lower than for

the GWR model (1,085). The global F -test comparing the global and local models

confirms that the GWR and GWR-SEM models outperform the global model. Given

these diagnostics, estimates from the GWR-SEM specification are used to calculate



Demand for Open Space and Urban Sprawl



183



Table 2 Comparison of performance among OLS, GWR, and GWR-SEM

Statistic

Hedonic price (Dependent

Open-space demand (Dependent

variable D ln (Housing price))

variable D ln (open-space area

within 1-mile buffer)

OLS

GWR

GWR-SEM

OLS

GWR

GWR-SEM

Error sum of

1,206

1,085

1,066

490

220

77

squares

Global F test

11.05

21.59

187.48

21.59

2,786

497

18

189,902

115,905

111,263

Spatial error LM

testa

AIC

4,655

3,502

3,045

8;948

21;189

1,130

a

Critical value for LM test at 0.01% is 15.14 (1 degree of freedom)



marginal implicit prices of open space and create maps. The marginal implicit prices

are mapped to visually highlight their spatial variations.

In the open-space demand equation, the corrected AIC for the GWR model is

21;189, lower than for the global ( 8;948) and the GWR-SEM (1,130) models. The error sum of squares for the GWR-SEM model is 77, lower than for the

global (490) and the GWR (220) models. The global F-test comparing the global and

local models confirms that the GWR and GWR-SEM models outperform the global

model. The overall fit of the GWR-SEM model is better than the GWR model, and

the GWR-SEM model more effectively accounts for spatial error autocorrelation.

Given these diagnostics, the estimates of the demand for open space are discussed

based on the GWR-SEM estimates.

The results of the global hedonic price equation and the open-space demand

equation are presented in Table 3. The estimates from the local model (GWR-SEM)

are too numerous to show in Table 3. Instead, the coefficients for open space in the

hedonic model and the coefficients for the variables closely associated with urban

sprawl, i.e., income, house and lot size, housing density, and price of open space

that are significant at the level of 5% are mapped in the Figs. 3–8.

The positive coefficient for open space in the global hedonic model indicates

that households place significant value on more open space in the area surrounding

their houses. An additional 10; 000 ft2 of open space within a 1.0-mile buffer adds

$42 to the value of a house, other things constant. The estimated marginal implicit

prices for open space for individual households, that are significant at the 5% level

in the hedonic GWR-SEM model, are mapped in Fig. 3. The map indicates that

open space significantly influences housing prices in the entire study area and the

amenity values of open space increase from the east toward west Knox County.

The open space area within a 1-mile buffer varies inversely with price and directly

with income. According to the regression results of the global open-space demand

equation, the price elasticity of open-space demand is 0:07. The income elasticity

of open-space demand in the global model is 0.07. Both elasticities are significant at

the 1% level. The results imply that the demand curve for open space is downward

sloping on average and open space is a normal good in the Knoxville area; demand

for open space increases with household income.



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S.-H. Cho



Table 3 Parameter global estimates of global (OLS) models

Variable

Dependent Variable = ln

(house price)

Coefficient

Std. Error

Intercept



3:830



Dependent Variable = ln

(open space)

Coefficient

Std. Error



1:274



14:392



0:124



0:545

0:049



0:009

0:005



0:070

0:031

0:026

0:029



0:004

0:005

0:002

0:002



0:021



0:086

0:070



0:004



Variables closely associated with urban sprawl

Income

ln (Finished area)

ln (Lot size)

Housing density

ln (Open space)

ln (Price of open space)

Structural variables

Age

Brick

Pool

Garage

Bedroom

Stories

Fireplace

Quality of construction

Condition of structure



0:004

0:073

0:060

0:091

0:016

0:096

0:042

0:168

0:098



0:000

0:006

0:010

0:006

0:005

0:007

0:005

0:007

0:006



0:002



0:000



Census block-group variables

Vacancy rate

Unemployment rate

Travel time to work



0:079

0:059

0:000



0:094

0:147

0:001



0:006

1:116

0:008



0:059

0:061

0:001



Distance variables

ln (Dist. to CBD)

ln (Dist. to greenway)

ln (Dist. to railroad)

ln (Dist. to sidewalk)

ln (Dist. to park)

ln (Park size)

ln (Dist. to golf course)

ln (Dist. to water body)

ln (Size of water body)



0:044

0:027

0:002

0:019

0:002

0:017

0:004

0:036

0:005



0:032

0:004

0:003

0:004

0:005

0:004

0:007

0:003

0:001



0:283

0:026

0:020

0:027

0:039

0:021

0:056

0:007

0:004



0:009

0:002

0:002

0:002

0:002

0:002

0:003

0:002

0:001



High school district dummy variables

Doyle

0:248

Bearden

0:046

Carter

0:233

Central

0:100

Fulton

0:039

Gibbs

0:202

Halls

0:127

Karns

0:080



0:057

0:021

0:028

0:017

0:024

0:025

0:023

0:013



0:548

0:152

0:141

0:135

0:214

0:145

0:117

0:031



0:010

0:008

0:013

0:008

0:010

0:011

0:011

0:008

(continued)



Demand for Open Space and Urban Sprawl

Table 3 (continued)

Variable



Powell

Farragut

Austin

Other variables

Knoxville

Flood

Interface

Urban growth area

Planned growth area

Season

Prime CPI

Adjusted R2



185



Dependent Variable = ln

(house price)

Coefficient

Std. Error

0:110

0:020

0:079

0:030

0:027

0:230

0:056

0:017

0:001

0:021

0:006

0:024

0:003

0:732



0:013

0:024

0:009

0:014

0:011

0:005

0:001

0:730



Dependent Variable = ln

(open space)

Coefficient

Std. Error

0:082

0:010

0:251

0:011

0:016

0:016

0:049

0:009

0:002

0:077

0:067



0:009

0:015

0:006

0:008

0:006



0:000



0:001



, , and indicate statistical significance at the 1%, 5%, and 10% levels respectively. Sample

size is 15,335 and the optimal number of neighbors is 6,080



Fig. 3 Marginal implicit price of open space (10,000 square foot increase in open space)



Figure 4 shows that areas exist within Knox County where the demand for open

space is upward sloping. This may be explained by speculative investing in open

space in these regions. Generally, people invest in houses with rising values. These

kinds of investments can result in an upward sloping demand curve for houses

(Dusansky et al. 2004). Likewise, people may be inclined to invest in houses that are

surrounded by open space of greater value for the same speculative purpose. Those



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S.-H. Cho



Fig. 4 Price elasticity of open-space demand



–0.02 to 0.00

0.00 to 0.16

0.16 to 0.22



0



25



5



10



15



20

Miles



Fig. 5 Income elasticity of open-space demand



Demand for Open Space and Urban Sprawl



Fig. 6 Lot size elasticity of open-space demand



Fig. 7 Finished-area elasticity of open-space demand



187



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S.-H. Cho



–0.07 to 0.03

0.03 to 0.00

0.00 to 0.04



0



25



5



10



15



20

Miles



Fig. 8 Housing-density elasticity of open-space demand



areas are mostly inside Knoxville and Farragut, with some exceptions. Figure 5

shows that the demand for open space is more responsive to changes in income

in the western end of Knoxville than in the rest of the County. The highly responsive demand for open space to changes in income in this area is consistent with the

case of Connecticut communities (Bates and Santerre 2001).

The patterns in the southwest corner of Knox County and the town of Farragut

probably result from this area being a bedroom community with affluent neighborhoods where many individuals work in private high-tech occupations; for example,

scientists at the Oak Ridge National Laboratory or faculty at the University of Tennessee. This area has experienced rapid development of residential and commercial

properties because of its location with respect to commuting. Demand for houses in

this area is also driven by access to amenities such as shopping areas, parks, public

infrastructure, and privacy on the urban fringe.

Open space area within a 1-mile buffer is positively associated with finished

area and lot size at the 1% level. These results imply that properties with larger

houses and lot sizes are likely to have greater open space within a 1-mile buffer.

The finished-area (representing house size) elasticity of open-space demand is 0.03,

and the lot-size elasticity of open-space demand is 0.03. Contrary to the findings

of other studies where open space was a substitute for large residential lots (e.g.,

Thorsnes 2002), these results imply that house and lot sizes, and open space are

complementary goods (on average) within the study area.

Figures 6 and 7 show regions with negative lot-size elasticities of open-space

demand and negative finished-area elasticities of open-space demand mostly inside



Demand for Open Space and Urban Sprawl



189



of Knoxville boundary, indicating substitutability between house and lot size, and

open space. The results indicate that house and lot size, and open space can be

both complimentary and substitute goods depending on the local area, with complementarities being the dominant relationship on average and substitutability existing

inside the Knoxville boundary.

The open space area within a 1-mile buffer is negatively associated with housing density at the 1% level. The housing-density elasticity of open-space demand is

0:03. This result implies that houses located within areas of lower density housing are likely to have greater open space within a 1-mile buffer. Most areas, other

than some area near the western end of Knoxville, have negative housing-density

elasticities (Fig.8).



5 Conclusions

This case study examined the demand for open space in Knox County, Tennessee,

United States. A GWR was modified to simultaneously model spatial heterogeneity and spatial error autocorrelation issues. The approach allows local elasticities of

demand for open space to be measured and mapped. The empirical findings suggest that amenity values for open space are higher in west Knox County, and the

demand for open space is more responsive to changes in income in the western end

of Knoxville than the rest of the County. These patterns observed in the western

end of Knoxville and in southwest Knox County coincide with the characteristics

of preferences of persons employed by the Oak Ridge National Laboratory and the

University of Tennessee. We also find that house and lot size, and open space can be

complimentary or substitute goods, depending on the location, with complementarities being the dominant relationship on average while substitutability exists inside

of city boundary.

Given the results, local officials may consider adopting location-specific policies.

A smart growth policy encouraging higher-density housing with more surrounding

open space might be fruitful in some parts of Knox County because the county

has significant amenity values for open space as a whole. Local policymakers may

encourage greater amounts of locally owned private and public open space in west

Knox County, given the higher amenity values for open space. For example, some

households may be more willing to pay into a fund designed to preserve neighborhood open space by purchasing development rights. Under this scenario, promoting

compact development by stimulating demand for locally owned open space will

likely be more successful in areas where demand for open space is higher because

households would be more inclined to endorse and participate in programs or policies preserving open space, at least in the short term. However, with greater supply

flexibility and occupier mobility, alongside growing open space demand, households can move to locations with more open space in the medium-to-long term.

This mobility could give rise to sprawl over the longer term as households demand

greater amounts of open space farther from the city center. Thus, the purchase of



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