Spatial analysis of the amenity value of green open space

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a v a i l a b l e a t w w w. s c i e n c e d i r e c t . c o m

w w w. e l s e v i e r. c o m / l o c a t e / e c o l e c o n

ANALYSIS

Spatial analysis of the amenity value of green open space☆ Seong-Hoon Cho a,⁎, Neelam C. Poudyal b , Roland K. Roberts a a

Department of Agricultural Economics, The University of Tennessee, 2621 Morgan Circle, Knoxville, TN 37996-4518, United States Department of Forestry, Wildlife and Fisheries, 274 Ellington Plant Science Bldg., Knoxville, TN 37996-4518, United States

b

AR TIC LE I N FO

ABS TR ACT

Article history:

The objective of this research is to determine the spatial variation in amenity values for both

Received 24 April 2007

quantity and quality of green open space in the housing market. Variables related to size,

Received in revised form

proximity, spatial configuration, and species composition of open space are endogenized in

27 August 2007

the global and local models in a hedonic price framework. Empirical evidence shows that

Accepted 2 October 2007

amenities of different features of open space vary according to the degree of urbanization. In

Available online 7 November 2007

summary, evergreen trees, a diverse landscape with fragmented forest patches, and more complex and natural forest edges are more highly valued in Rural–Urban interfaces. In

Keywords:

contrast, deciduous and mixed forests, larger forest blocks, and smoothly trimmed and

Hedonic pricing

man-made forest patch boundaries are more highly valued in urban core areas. As spatial

Locally weighted regression

variation in amenity values differs across a metropolitan area, the need for site-specific land

Open space

use management to fit the local characteristics is recognized.

Spatial configuration

1.

Introduction

Since urban sprawl has widespread ramifications for plant and animal habitats and human society, open space conservation becomes a major concern of the American community. Between 1998 and 2004, 935 out of 1215 conservation ballot measures were passed in the United States, raising close to $25 billion in funding for land conservation in 44 states (The Trust for Public and Land Trust Alliance, 2005). Voters have thus shown consistent support for open space protection. A key question, however, is the extent to which public open space is capitalized into nearby residential property values, and thus would increase property tax collection. Estimates of the effect of open space on the value of nearby property would be of use in estimating the cost of such initiatives and prioritizing the land parcels to be conserved as open space. McConnell and Walls (2005) reviewed more than 60 published articles that have attempted to estimate the value

© 2007 Elsevier B.V. All rights reserved.

of open spaces in the categories of general open space, parks, natural areas, greenbelts, forest preserves, wetlands, and agriculture. Hedonic methods with spatial analyses using geographical information systems (GIS) have gained popularity in recent years for measuring the value of open space. Despite the extensive use of the hedonic property method in valuing open space, few studies have valued the quality of open space. The quality of open space can be classified by composition and shape of open space. The valuation of openspace composition focuses on the comparison of amenity values among different types of open space. Anderson and Cordell (1988) found that a hardwood landscape is valued slightly more than a pinewood landscape. The valuation of open space with regard to its spatial configuration has become a matter of interest. Recent literature focused on the aesthetic value of land-use diversity and landscape quality in the surroundings (Geoghegan et al., 1997; Acharya and Bennett, 2001; Kestens et al., 2004). Using advances

☆

Senior authorship is shared by Seong-Hoon Cho and Neelam C. Poudyal. ⁎ Corresponding author. Tel.: +1 865 974 7411; fax: +1 865 974 9492. E-mail addresses: [email protected] (S.-H. Cho), [email protected] (N.C. Poudyal), [email protected] (R.K. Roberts).

0921-8009/$ – see front matter © 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.ecolecon.2007.10.012

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in GIS technology, the studies attempted to measure hedonic values of spatial configurations of open space. These studies employed various spatial indices commonly used in landscape ecology research. Palmer (2004) and Geoghegan et al. (1997) found that the composition and spatial pattern of land use in the surroundings are good predictors of scenic perception and housing value. Acharya and Bennett (2001) found that housing value is influenced by the landscape structure of a neighborhood. Morancho (2003) concluded that retaining numerous small green areas throughout a city is preferred to a smaller number of larger parks. Further, attempts have been made to value the quality of wetlands and agricultural open spaces. Mahan et al. (2000) evaluated the effects of wetland quality, including shape (e.g., linear or areal) and content (e.g., no vegetation, with emergent vegetation, with scrub-shrub) on property prices. Doss and Taff (1996) used measures of wetland content to estimate marginal values of wetland types. Reynolds and Regalado (1998) also examined the influences on property prices of different types of wetlands, such as forested and emergent palustrine, scrubshrub, and shallow pond wetlands. Similarly, attempts have been made to differentiate the quality of agriculture lands. Irwin (2002), Geoghegan (2002), and Geoghegan et al. (2003) looked at the effects of different types of agriculture land on housing values. They categorized agriculture land into potentially developable private, potentially undevelopable private, publicly owned and accessible, and conservation easement types. They found that vast differences could exist among the effects of land quality on property values as the quality of agriculture open space changes with the intensity of farming practices. There are two problematic implicit assumptions typically made in previous hedonic models that have evaluated open space. The first commonly used assumption that may cause biased estimation is endogeneity of the open space variables. Assuming exogeneity does not address the fundamental identification problems of housing values. Because the location of open space is largely determined by market forces, most open space variables, except public or preserved open space, will be endogenous to the housing price. Irwin and Bockstael (2001) addressed the problem of identifying land use spillovers, which arise in a hedonic residential price model when the open space is privately held and developable. They conducted a Hausman endogeneity test and concluded that their measures for private open space and privately owned conservation lands were endogenous, making the coefficients for these variables biased and inconsistent. Smith et al. (2002) considered open spaces that are “fixed”, in the sense that the land use is unlikely to change (e.g., public parks and golf courses), different from open spaces that are “adjustable”, such as agricultural or vacant properties. They suggested that because the location of adjustable open space is largely determined by market forces, it will be sensitive to diversity in buyer expectations, leading to endogeneity in the disposition of some land uses. Walsh (2007) evaluated open space policies using an empirical approach that incorporates the endogeneity of privately held open space in a locational equilibrium framework. The second problematic assumption typically adopted for evaluating open space using the hedonic model is that implicit prices are constant across a housing market. Geoghegan et al. (1997) applied a spatial expansion method that detects a

spatially varying relationship at the local level. Their study revealed that the marginal values of land-use diversity employing measures of percent of open space, diversity, and fragmentation of land uses vary by proximity to the central business district (CBD). They found that diversity in land use induces a positive externality on the value of housing in the immediate area and outer edge of the CBD, but it creates negative externalities in areas between them. Although Geoghegan et al. (1997) detected variation in marginal effects using a spatial expansion model, the model has some limitations. First, it is dependent on the complexity of the expansion equations. As a result, distributions of spatially varying parameter estimates might conceal important local variations within the broad trends represented by the expansion equations. Second, the form of the expansion equations is deterministic and demands a priori knowledge (Fotheringham et al., 2002). Unless the exact pattern of non-stationarity is known, these limitations likely bias the results from the spatial expansion model. Third, their expansion equations do not address the potential endogeneity of open space variables. In addressing some of these limitations, Cho and Roberts (2007) used locally weighted regression to estimate spatial variation in the values households’ place on open space as measured by neighborhood density. Unlike the spatial expansion method, no a priori assumption regarding a particular form of spatial non-stationarity is required in the locally weighted regression model (Cleveland and Devlin, 1988). Cho and Roberts (2007) found higher amenity values for lower housing density in sprawled areas relative to urban-core areas. Still, the housing density measure used for capturing the amenity value of open space in their study was lacking in three ways. First, they did not address the issue of open space endogeneity. Second, their measure of housing density was a rough proxy for open space because it did not exclude non-developable areas (e.g., airports and landfills). Third, their measure of housing density only reflected the quantity of open space without differentiating among qualities of open space, e.g., species composition and landscape of forested areas. The current research was directed toward identifying the spatial variation of amenity values for both quantity and quality of open space in the housing market. To achieve the objective, open space variables were endogenized in the ordinary least squares (OLS) and locally weighted regressions within the hedonic price framework. The quantity of open space was measured by its size and proximity while the quality of open space was measured by its spatial configuration and species composition. Marginal implicit prices for the open space variables were calculated and their local marginal effects were mapped to better understand the spatial variation in the effects of open space on housing prices. As spatial variation in amenity values differs across a metropolitan area, the need for site-specific land use management to fit the local characteristics is recognized.

2.

Methods

2.1.

Empirical model

The usual procedure was to first estimate the hedonic model with OLS. Endogeneity of the open space variables was then

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Table 1 – Definitions of variables used in the two-stage model Variable

Definition

Structural variables House price♦ Transaction price adjusted with house price index of Knoxville in year 2000 dollar value ($) Finished area House square footage (m2) Building age Age of the house in 2006 (years) Parcel size Size of parcel (m2) Stories Number of stories Garage Dummy variable for garage (1 if garage, 0 otherwise) Bedroom Number of bedrooms Brick Dummy variable for brick siding (1 if brick, 0 otherwise) Pool Dummy variable for swimming pool (1 if pool, 0 otherwise) Fireplace Number of fireplaces in house Condition Dummy variable for condition of structure (1 if excellent, very good and good, 0 otherwise) Quality Dummy variable for quality of construction (1 if excellent, very good and good, 0 otherwise) Neighborhood variables Population Number of persons per square km. in census density block group Income Median household income for census block group ($) Travel time to Average travel time to work for census block work group (min) Vacancy rate Housing vacancy rate in census block group Unemployment Unemployment rate for census block group rate Impairment Number of water impairments reported in the nearest water body Downtown Distance to the downtown (m) Water Distance to the nearest water body (m) Size of water Size of the nearest water body (m2) body Sidewalk Distance to the nearest sidewalk (m) Golf course Distance to the nearest golf course (m) Railroad Distance to the nearest railroad (m) High School dummy variables West 1 if West high school district, 0 otherwise Doyle 1 if Doyle high school district, 0 otherwise Powell 1 if Powell high school district, 0 otherwise Karns 1 if Karns high school district, 0 otherwise Halls 1 if Halls high school district, 0 otherwise Gibbs 1 if Gibbs high school district, 0 otherwise Fulton 1 if Fulton high school district, 0 otherwise Farragut 1 if Farragut high school district, 0 otherwise Central 1 if Central high school district, 0 otherwise Carter 1 if Carter high school district, 0 otherwise Bearden 1 if Bearden high school district, 0 otherwise Austin 1 if Austin high school district, 0 otherwise (reference) Other variables Season Prime rate

Dummy variable for season of sale (1 if April through September, 0 otherwise) Average prime interest rate less average inflation rate (continued on next page)

Table 1 (continued) Variable

Definition

Open space amenities Distance to Distance to nearest evergreen forest patch (m) nearest evergreen forest patch♦ Distance to Distance to nearest deciduous forest patch (m) nearest deciduous forest patch♦ Distance to Distance to nearest mixed species forest mixed patch (m) forest patch♦ Forest patch Number of forest patch per 100 ha in census density♦ block group Forest edge Edge of forest per hectare in census block density♦ group (perimeter to area ratio) Mean forest Average patch size of forest patch in the patch size♦ census black group (ha) ♦indicates the endogenous variable.

checked with the Smith-Blundell Test (Wooldridge, 2003, pp. 484). If endogeneity of the open space variables was detected, the instrumental variables (IV) approach was used to account for open-space endogeneity (Irwin and Bockstael, 2001), Ri ¼ aXi þ b Pˆi þei

ð1Þ

Pi ¼ dWi þ gi

ð2Þ

where Ri is the value of the house in parcel i; Xi is a vector of factors that determines the value for residential use of parcel i; Pi is a vector of open space measures around parcel i; ei is a random disturbance term; Pˆ i is the predicted value from Eq. (2); Wi is a vector of open-space instruments for parcel i; and ηi is a random disturbance term. Theoretically, six open space measures used in the model were thought to be endogenous because they are largely determined by market forces. For example, the national outdoor recreation survey dataset shows that 99% of the forest land in the study area (city of Knoxville and town of Farragut) is privately owned (Betz, 1997) and potentially subject to change in response to market forces. In the first stage, Eq. (2) was estimated using the instruments. The choice of the instrumental variable for the open space equation is difficult because uniqueness of functional form is rather arbitrary. Nonetheless, distance to downtown, distance to nearest water body, size of the nearest water body, distance to sidewalk, distance to golf course and distance to railroad were chosen as unique instrumental variables for each of the six open space equations of distance to nearest evergreen forest patch, distance to nearest deciduous forest patch, distance to nearest mixed forest patch, forest patch density, forest edge density and mean patch size of forest, respectively. In the second stage, Eq. (1) was estimated with either OLS or locallyweighted least squares regression after replacing Pi with their predicted values from Eq. (2)(Pˆ i).

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Fig. 1 – The study area showing the location of sample houses.

Henceforth, the locally weighted regression model is called the “local model” and the OLS model is called the “global model” because the later model assumes the relationship to be constant everywhere. Following Fotheringham et al. (2002), the second stage hedonic price equation for the local model is specified as:
 Ri ¼ b  Xˆ 1 þ e

ð3Þ

where Xˆ is a vector of variables including the predicted open space variables, β is a vector of parameters, and ε is a vector of random errors. ⊗ is a logical multiplication operator in which each element of β is multiplied by the corresponding element of Xˆ and 1 is a conformable vector of 1's. With n sets of local parameters, β takes the form: 0

b0 ðu1 ; m1 Þ B b0 ðu2 ; m2 Þ b¼B @ N N N b0 ðun ; mn Þ

b1 ðu1 ; m1 Þ b1 ðu2 ; m2 Þ N N N b1 ðun ; mn Þ

N N N N

N N N N

N N N N

1 bk ðu1 ; m1 Þ bk ðu2 ; m2 Þ C C N N N A bk ðun ; mn Þ

ð4Þ

where (ui,νi) denotes the coordinates (longitude, latitude) of house i.

Observations for houses in closer proximity to house i have more influence in the estimation of the local parameters than houses located farther away. That is,  1 bˆðui ; vi Þ ¼ XT wðui ; vi ÞX XT wðui ; vi ÞY

ð5Þ

where βˆ (ui,νi) represents an estimate of β(ui,νi) and w(ui,νi) is an n × n spatial weighting matrix. An adaptive bi-weight function is used to geographically weighted observations. The function is “adaptive” in the sense that the trace of w expands or contracts as the location changes. The advantage of this particular weighting function is that it has the desirable properties of being continuous while giving more weight to the nearest neighbors. Nearest neighbors are hypothesized to influence each other based on a continuous decay function. But observations outside the range of the nearest neighbors are assumed to have no influence on house i. The bi-weight function is h  2 i 2 if dij bdmax ðqÞ; otherwise wij ¼ 0; wij ¼ 1  dij =dmax ðqÞ

ð6Þ

where j represents a data point in space and i represents any point in space where local parameters are estimated, dij is the

407

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Table 2 – Descriptive statistics for variables used in the two-stage model Variables Structural variables House price ($) Finished area (m2) Building age (years) Parcel size (m2) Stories Garage Bedroom Brick Pool Fireplace Condition Quality Neighborhood variables Population density (people/acre) Income ($) Travel time to work (min) Vacancy rate Unemployment rate Impairment Downtown (m) Water (m) Size of water (m2) Sidewalk (m) Golf course (m) Railroad (m)

Mean

Std. Dev.

Minimum

Maximum

117,786.70 168.60 39.36 1791.39 1.26 0.53 3.00 0.25 0.05 0.67 0.59 0.39

94,609.26 89.11 24.38 1873.79 0.43 0.49 0.71 0.43 0.21 0.60 0.49 0.48

36,600 40.87 2 164.18 1 0 0 0 0 0 0 0

1,803,683 1220.14 107 49,450.72 3 1 8 1 1 9 1 1

1.28 24,092.91 21.59 0.06 0.04 0.47 10,876.18 2078.65 2164.88 394.10 2863.84 1622.72

0.81 11,192.19 3.10 0.03 0.03 0.99 7601.97 1144.83 4247.33 325.14 1375.17 1200.43

0.14 4482.00 0.00 0.00 0.00 0 791.83 13.46 2.44 7.08 126.52 7.60

30.05 76,797.00 32.53 0.27 0.51 3 30,168.61 6047.41 11,987.40 2849.85 7071.83 6085.66

High School dummy variables West Doyle Powell Karns Halls Gibbs Fulton Farragut Central Carter Bearden

0.23 0.08 0.002 0.04 0.0003 0.005 0.13 0.18 0.17 0.02 0.07

0.42 0.28 0.04 0.21 0.01 0.07 0.33 0.38 0.37 0.14 0.26

0 0 0 0 0 0 0 0 0 0 0

1 1 1 1 1 1 1 1 1 1 1

Other variables Season Prime rate (%)

0.56 7.24

0.49 1.63

0 4.67

1 9.23

467.98 325.51 481.40 5.17 34.55 3.75

409.14 283.07 440.94 3.52 32.39 7.28

0.30 0.30 0.30 0.00 0.00 0.00

2704.23 1558.07 3337.98 15.32 230.26 87.72

Open space amenities Distance to nearest evergreen forest patch (m) Distance to nearest deciduous forest patch (m) Distance to nearest mixed forest patch (m) Forest patch density (patches/100 ha) Forest edge density (m/ha) Mean forest patch size (ha) Number of observations: 9571.

Euclidean distance between points i and j, and dmax is the maximum distance between observation i and its q nearest neighbors (Fotheringham et al., 2002). The weight attributed to regression point i is one. Weights attributed to the j observations in the neighborhood of i are less than one and become zero when the distance between i and j is greater than dmax. Therefore, as dij increases, the influence of observation j on local regression point i decreases.

2.2.

Cross validation

A cross-validation approach selects the optimal number of neighbors (Cleveland and Devlin, 1988). The cross-validation function is, Cross validation ¼ min q

n  X 2 yi  yˆpi ðqÞ i¼1

ð7Þ

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Table 3 – Parameter estimates from the hedonic model Variables

Global model Coefficient

Structural variables Intercept ln (finished area) Building age ln (parcel size) Stories Garage Bedroom Brick Pool Fireplace Condition Quality Neighborhood variables Population density ln (income) Travel time to work Vacancy rate Unemployment rate School district dummy variables West Doyle Powell Karns Halls Bearden Gibbs Fulton Farragut Central Carter Other variables Season Prime rate Open space amenities ln (distance to nearest evergreen forest patch) ln (distance to nearest deciduous forest patch) ln (distance to mixed forest patch) Forest patch density Forest edge density Mean forest patch size Adj. R-square Residual sums of square Bandwidth (m) Number of Observation

Min

Local quartile

Median

Upper quartile

Max

Test for spatial variability (p-value)

−10.601 0.423 −0.004 −1.617 0.088 0.034 −0.011 0.022 0.025 0.012 0.013 0.093

−1.768 0.446 −0.003 −0.976 0.131 0.060 0.002 0.043 0.065 0.039 0.072 0.142

7.937 0.478 −0.002 0.106 0.145 0.066 0.008 0.054 0.075 0.044 0.080 0.156

14.498 0.502 −0.002 0.674 0.168 0.078 0.017 0.065 0.102 0.049 0.090 0.169

25.189 0.528 −0.000 1.474 0.199 0.111 0.033 0.086 0.140 0.072 0.226 0.216

0.000⁎⁎⁎ 0.090⁎ 0.000⁎⁎⁎ 0.000⁎⁎⁎ 0.050⁎ 0.090⁎

0.011 0.038⁎⁎⁎ 0.086⁎⁎⁎ 0.053⁎⁎⁎ 0.073⁎⁎⁎ 0.123⁎⁎⁎

0.444 0.017 0.000 0.028 0.009 0.010 0.007 0.012 0.020 0.009 0.011 0.015

− 0.026⁎⁎⁎ 0.349⁎⁎⁎ 0.001⁎ 0.229 − 0.094

0.007 0.028 0.003 0.149 0.195

−0.199 −2.771 −0.263 −7.572 −0.940

−0.083 −1.214 −0.155 −3.006 0.009

0.001 0.112 0.004 −0.444 0.166

0.156 2.401 0.092 3.309 0.313

0.253 3.840 0.236 5.547 12.907

0.000⁎⁎⁎ 0.000⁎⁎⁎ 0.000⁎⁎⁎ 0.000⁎⁎⁎ 0.000⁎⁎⁎

0.070 0.563⁎⁎⁎ 0.436⁎⁎⁎ − 0.023 0.937⁎⁎⁎ 0.046 − 0.081 0.075⁎ 0.040 − 0.139⁎⁎ 0.288⁎⁎⁎

0.053 0.100 0.140 0.074 0.288 0.060 0.080 0.044 0.046 0.058 0.071

−0.763 −0.320 −1.485 −1.192 −0.327 −1.090 −1.300 −0.933 −0.797 −1.431 −0.936

−0.035 0.031 −0.223 −0.117 0.467 −0.096 −0.177 −0.013 0.012 −0.169 −0.022

0.089 0.057 −0.038 0.013 0.493 0.058 −0.154 0.050 0.140 −0.008 0.059

0.131 0.118 0.114 0.061 0.530 0.222 −0.125 0.069 0.193 0.103 0.109

0.663 0.649 0.578 0.383 1.191 0.764 0.225 0.368 0.453 0.492 0.507

0.000⁎⁎⁎ 0.000⁎⁎⁎ 0.000⁎⁎⁎ 0.000⁎⁎⁎ 0.870 0.000⁎⁎⁎ 0.000⁎⁎⁎ 0.000⁎⁎⁎ 0.000⁎⁎⁎ 0.000⁎⁎⁎ 0.000⁎⁎⁎

0.024⁎⁎⁎ 0.002

0.008 0.002

−0.015 −0.001

0.009 0.000

0.014 0.003

0.024 0.004

0.056 0.009

0.070⁎ 0.350

0.055

0.053

−2.855

−1.175

0.054

2.104

3.597

0.000⁎⁎⁎

0.165⁎⁎⁎

0.050

−4.173

−2.536

0.165

1.624

3.580

0.000⁎⁎⁎

−3.061 −1.007 −0.006 −0.020 0.82 540.91 4084.75 9571

−1.875 −0.619 −0.002 −0.006

−0.086 0.002 0.000 −0.005

0.895 0.332 0.001 0.012

2.598 0.899 0.003 0.024

0.000⁎⁎⁎ 0.000⁎⁎⁎ 0.000⁎⁎⁎ 0.020⁎⁎

10.526⁎⁎⁎ 0.479⁎⁎⁎ − 0.004⁎⁎⁎ 0.133⁎⁎⁎ 0.152⁎⁎⁎ 0.065⁎⁎⁎

− 0.123⁎⁎ − 0.053⁎⁎⁎ 0.0003⁎⁎⁎ − 0.010⁎⁎ 0.78 677.90 9571

Standard error

Local model

0.059 0.012 0.00001 0.0005

0.280 0.060⁎ 0.170 0.170 0.000⁎⁎⁎ 0.010⁎⁎

⁎ P b 0.05, ⁎⁎ P b 0.01 and ⁎⁎⁎ P b 0.001.

where yˆ ≠ i(q) is the fitted value of yi with location i omitted during the fitting process. The optimal number of neighbors minimizes the cross-validation function. Thus, in the local model, only houses up to the nearest q neighbors are assigned non-zero weights with respect to house i. The influence of observations decreases as their distance increases from the regression point (ui,νi).

Standard errors for the i sets of regression parameters are based on the covariance matrix (cov) (Fotheringham et al., 2002), h T i1
 ˆ wðui ; vi Þ X ˆ ; cov bˆk ðui ; vi Þ ¼ r2i X

ð8Þ

with σi2 = e˜iVe˜ i / (q −k) being the variance associated with the ith regression point. The matrix w(ui,νi) is a diagonal n by n matrix

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with diagonal elements identifying the location of other houses relative to house i. The w matrix addresses spatial heterogeneity (Fotheringham et al., 2002). The statistical significance of the local estimates at the ith regression point is evaluated with ttests derived from the standard errors of the location-specific covariance matrices.

2.3.

Variables used

The explanatory variables used to explain the sales price of a home included variables representing structural, neighborhood, school district and forest amenity characteristics linked to each property in the data set (see Table 1). The key structural variables were the finished living area, building age, parcel size, number of bedrooms, fireplace and number of stories. Dummy variables were used to capture the presence of a swimming pool, garage, and brick exterior. Dummy variables for quality of construction and condition of the structure were derived from the county tax assessor's six-point ranking scale (1 if excellent, very good, and good; 0 otherwise). A seasonal dummy was included to capture the expected difference in housing prices between spring/summer and fall/winter. Previous studies found that the mortgage interest rate is a significant driver of housing price dynamics (e.g., Tsatsaronis and Zhu, 2004). Yearly prime interest rates (from the website

409

of the Board of Governors of the Federal Reserve System (2006)), which represent mortgage interest rates for the year of the sale transaction, were converted to real interest rates by subtracting the annual change in the consumer price index (CPI, 2006). Variables representing neighborhood features included population density, average travel time to work, housing vacancy rate, median household income and unemployment rate at the level of census block group. Population density represents the relative congestion of human population and also captures housing demand at the neighborhood level. Income and employment were expected to capture the economic condition and prosperity of the neighborhood. Average travel time to work was included as a spatial measure of the distance to the employment hub. Goodman and Thibodeau (1998) argued that the quality of public education strongly determines segmentation of housing markets. Hence, we included high school district dummies to control for the quality of education in the neighborhood. The quantity of open space was represented by the characteristics of size and proximity whereas the quality was represented by spatial configuration and species composition. The study area has little farmland and the major open space category is forest land. The amount of farmland was too small to be counted as open space in our study area. We classified

Fig. 2 – Coefficients of distance to nearest evergreen forest patch that are statistically significant at the 5% level.

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the nearest open space into three categories by species composition, including evergreen, deciduous, and mixed woodlots, and used proximities of each residence to these types of forest patches in the model. As obtained from National Land Cover Database (NLCD, 2001), a forest patch was categorized as an evergreen woodlot if 75% of the patch was dominated by trees whose canopy was never without green foliage. Similarly, deciduous patches included vegetation dominated by 75% of tree species that shed foliage in response to seasonal change. The mixed woodlots were those patches in which neither evergreen nor deciduous vegetation predominated. In addition to proximity of the nearest forest space of these three kinds, we also included the size and the spatial configuration of each open space type in the hedonic model. Mean patch size, patch density, and edge density of green open space at the census-block group level were used to analyze the effects of the size and spatial configuration of open space on house prices. Mean patch size measures the general size of forest patches in the neighborhood. Patch density measures the degree of spatial heterogeneity in the forest open space landscape. As a standard measure of landscape characteristics, patch density is computed as the number of patches per hundred hectares (MacGarigal and Marks, 1995). It measures the degree of fragmentation within a particular land use class (Nelson et al., 2004). The higher the patch density of open

space, the greater the diversity in land uses. Patch density can capture the visual and scenic diversity caused by fragmented patterns of open space within a neighborhood. Diversity and fragmentation are more highly valued as they allow easier access to convenient amenities such as shopping areas and public infrastructure (Geoghegan et al., 1997). A positive value of high patch density indicates a positive amenity value for landscape with a mix of open space and developed areas. Edge density measures the perimeter-to-area ratio and captures the value of scenic diversity and the complexity of open space boundaries (Nelson et al., 2004; Palmer, 2004). A positive value for high edge density implies greater value for rough edges and natural patches whereas a negative value of high edge density suggests greater value for smoother and synthetic open space boundaries. Previous studies found that a log transformation of the distance, dollar value, and area variables generally performed better than a linear functional form because the log transformation captures the declining effect of these distance variables (Iwata et al., 2000; Mahan et al., 2000; Bin and Polasky, 2004). The log transformation also corrects for heteroscedasticity in the dataset (Wooldridge, 2003). Thus, a natural log transformation for the distance, dollar, and area-related variables was used. If the correlation coefficient between two regressors is greater than 0.8, multicollinearity may be a serious problem

Fig. 3 – Coefficients of distance to nearest deciduous forest patch that are statistically significant at the 5% level.

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(Gujarati, 1995). Multicollinearity can be detected by variance inflation factors (VIF) (Maddala, 1992). The VIF is a scaled version of the multiple correlation coefficients between variable k and the rest of the independent variables. Specifically, vifk = 1 / (1 − R2k), where Rk is the multiple correlation coefficient. A rule of thumb is that multicollinearity may be a problem if the VIF is greater than 10 (Gujarati, 1995). We found five variables with VIFs greater than 10, namely proximities to park, greenway and downtown, and Doyle and Carter high school dummies. Because parks and greenways are classified as green open space, variables for proximities to green open space include proximities to parks and greenways for some houses, thus specific variables for proximities to parks and greenways were not included in the model. The other three variables with high VIFs were not excluded (Doyle and Carter high school dummies and proximity to downtown) for lack of sufficient justification.

3.

Study area and data description

The model is applied to the City of Knoxville and its contiguous Town of Farragut in Knox County, Tennessee (see Fig. -1). The Knoxville area was chosen as a case study because 1) it is one of the top ten most sprawling metropolitan regions in the United

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States (Ewing et al., 2003), and 2) it consists of low-density sprawling area in Rural–Urban interfaces and a compact highdensity urban-core area. The sprawling and compact highdensity developments in the Knoxville area conform with the purpose of this study because significant variation in relative values households place on different characteristics of open space is expected between these extremes. This research used five primary 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., sale price, lot size, and structural information, were obtained from Knoxville, Knox County, Knoxville Utilities Board Geographic Information System (KGIS 2006), and the Knox County Tax Assessor's Office (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 to identify different forest types in the study area. Multiple processing stages were required to create variables from the land cover dataset to represent various open space amenity characteristics. The raster pixels belonging to evergreen, deciduous and mixed vegetation were aggregated to yield vector patches of each of these vegetation types. The forest amenity variables, i.e., measures of distance, size, number of patches, and edge, were created using the GIS

Fig. 4 – Coefficients of distance to nearest mixed forest patch that are statistically significant at the 5% level.

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shape files of individual vegetation types and tools in ArcGIS 9.1 (ESRI, 2006). The boundary data, i.e., high school districts and jurisdiction boundaries, were obtained from the Knoxville-Knox County Metropolitan Planning Commission (KGIS, 2006). Environmental feature data such as shape files of water bodies and golf courses were found in 2004 Environmental Systems Research Institute Data and Maps (ESRI, 2006). Other environmental feature data such as GIS shape files for railroads were acquired from KGIS (2006). The individual parcel data are for single-family houses sold between 1998 and 2002 in the City of Knoxville and the Town of Farragut, Tennessee. A total of 9571 sales transactions were undertaken during this period (see Fig. 1 for the spatial distributions of all houses in the study area). Housing sale prices were adjusted to 2000 dollars to account for real estate market fluctuations in the Knoxville metro region. This adjustment was made using the local annual housing price index obtained from the Office of Federal Housing Enterprise Oversight (OFHEO, 2006) for the Knoxville metro statistical area. The study area consists of 159 census-block groups. Information from these census-block groups was assigned to houses located within the boundaries of the block groups. The timing cycle of the census and sales records did not match except in 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 spatial configurations and locations of forest patches were not expected to change appreciably during the study period. Detailed statistics for individual variables are reported in Table 2.

4.

Empirical results

The endogeneity test rejects the hypothesis that the six open space variables are exogenous at the 1% significance level (F-statistic of 14.63 and critical value of 2.80) justifying the instrumental variables approach for estimating Eq. (1). Results for the global and local models for the second stage hedonic model are presented in Table 3. The adjusted R2 for the local model (0.82) is higher than for the global model (0.78). Similarly, the residual sum of squares for the local model (541) is lower than for the global model (678). The higher adjusted R2 and lower residual sum of squares suggest that the local model fits the data better than the global model. A test for significant differences between the local and global models confirms that the local model outperforms the global model

Fig. 5 – Coefficients of forest patch densities that are statistically significant at the 5% level.

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with an F-value of 6.92, compared with a critical value of 1.51 at the 1% significance level. The dmax in Eq. (7) is approximately 4.1 km. Sensitivity analysis suggests that the median value of the local coefficients using a dmax of 6.15 km (50% greater than 4.1) and 2.05 km (50% less than 4.1) is fairly close to the median value when dmax is 4.1. However, with a dmax of 6.15 km, almost no variation in the local coefficients exists across the study area. As the dmax widens to 6.15 km, the spatial heterogeneity captured by the local model using the cross-validation approach is not captured and the local estimates are close to those estimated by the global model. This sensitivity analysis emphasizes the trade-off between a smaller dmax that retains the spatial heterogeneity inherent in the variables and the need to produce estimates that vary smoothly over the spatial regions of the study area (larger dmax). The coefficients for five of six open space variables are statistically significant at the 5% level. Stationarity for each of the six open space variables is rejected at the 5% significance level. This result indicates that the open space measures are spatially heterogeneous. The global model indicates that proximities to mixed forest are valued significantly more than proximities to homogeneous forest patches. This result suggests that forest species diversity is valued higher than mono-species. An alternative explanation is that the green

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space amenity value of mixed forest might be captured better than other types of forest in the study area because the Knoxville area is located in a transition zone of hardwood and conifer species where mixed forest patches are fairly abundant. Proximity to deciduous patches is negatively valued. This finding may be explained by the fact that deciduous trees defoliate during winter and do not provide year around greenery but add clean-up cost of litter fall. Variables capturing the landscape configuration of forests in a neighborhood, forest patch density, forest edge density and the mean size of a forest patch, are statistically significant at the 5% level in the global model. The negative effect of forest patch density indicates that residents of a neighborhood value a continuous forest tract more than one where the same amount of forest area is in fragmented and isolated patches. This result is consistent with previous findings that the spatial heterogeneity in a fragmented landscape decreases the coherence and scenic value of a neighborhood, and homogeneous landscapes have greater amenity values (Geoghegan et al., 1997; Acharya and Bennett, 2001; Nelson et al., 2004; Palmer, 2004). The positive result for edge density indicates that larger perimeters or edges for a given woodlot are valued higher. This is consistent with Kaplan and Kaplan (1989) and Palmer (2004) who found that a higher edge density that captures complex landscape shapes significantly adds to the

Fig. 6 – Coefficients of forest edge density that are statistically significant at the 5% level.

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scenic value in a neighborhood. The mean size of forest patches negatively affects the housing price in the global model, implying that neighborhoods packed with larger forest blocks are valued less. This finding is consistent with earlier conclusions that residents prefer neighborhoods containing relatively smaller patches (Morancho, 2003; Nelson et al., 2004). Evaluated at the mean house price of $117,787 and an initial distance of 1 km, moving 100 m closer to an evergreen woodlot increases the average house price by $692. Similarly, moving 100 m closer to a deciduous forest patch decreases the average house price by $589. An additional patch per hectare of forest in a neighborhood decreases the price of a house by $62. Likewise, an additional meter of edge per hectare of forest increases the housing price by $35. The marginal implicit price for the mean patch size reveals that an additional hectare in average forest patch size in the neighborhood decreases the housing price by $1178. The local marginal effects of the open space variables that are significant at the 5% level are mapped in Figs. 2–7. Interestingly enough, Figs. 2–5 consistently identify three unique areas in the northwest of Farragut, the west and south of the city center, and the northeast of the city center. Proximities to the three types of forest patches and forest patch density are consistently significant in the three cluster areas. The northwest of Farragut and northeast of the city

center are ‘Rural–Urban Interfaces’ that are characterized by relatively lower housing density. The west and south of the city center is the ‘Urban Core’ area that is characterized by relatively higher housing density. Proximities to evergreen forest are valued positively in the Rural–Urban Interfaces. In contrast, the proximities to deciduous forest and mixed forest are valued positively in the Urban Core area. These findings imply that deciduous (mostly hardwood species) and mixed forests are valued positively in the area where green open space is relatively scarce while evergreen trees (mostly conifer species) are valued positively in the area where green open space is relatively abundant. This suggests that the amenity values of forest types vary with the degree of urbanization. The positive effects of patch density are found in the Rural– Urban Interfaces while negative effects are found in the Urban Core area. One possible explanation for this opposite effect is that larger forest blocks are more valued in the Urban Core area where land is dominated by impervious surfaces and buildings with little vegetation. In contrast, the positive effect of forest patch density indicates that smaller and more numerous forest patches are valued more in the Rural–Urban Interfaces. This implies that fragmentation and a diverse pattern of landscape may be more highly valued when they result in the combined amenities of convenience and privacy,

Fig. 7 – Coefficients of mean forest patch sizes that are statistically significant at the 5% level.

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as is the case of the Rural–Urban Interfaces. This is consistent with findings by Geoghegan et al. (1997) in which fragmentation is valued more highly in rural areas where conveniences and facilities are scarcer. Fig. 6 shows the positive effects of edge density in the northeast of the city center that is characterized by Rural– Urban Interfaces and negative effects in the Urban Core area. This implies higher values for woodlots with rougher and more natural-looking boundaries in the Rural–Urban Interfaces where green space is relatively abundant and higher values of smoothly trimmed and man-made forest patch boundaries in the Urban Core area where green space is relatively scarce. Thus, city planners and urban-core dwellers can add aesthetic value by investing in landscaping to fine tune the boundaries of scarce and limited green spaces. As shown in the Fig. 7, positive effects of mean forest patch size are found within the perimeter of the city center while negative effects are found in the northwest of the city boundary. A gradual decrease in the positive value of larger forest blocks exists as one moves away from the city center. This result is not surprising because residents of the CBD may have stronger preferences to live near larger forest patches because of the scarce and limited green space. The unexpected negative effects in the northwest of the city boundary need further study.

5.

Conclusions

In this paper, we report spatial variation in amenity values of open space. Variables related to size, proximity, spatial configuration, and species composition of open space are endogenized in the global and local models of a hedonic price framework to evaluate amenity values for both quantity and quality of open space. Empirical evidence shows that the amenity values of different open space features vary according to the degree of urbanization. In summary, evergreen trees (e.g., conifer species) in a diverse landscape with fragmented forest patches and more complex and natural-looking forest edges are more highly valued in Rural–Urban Interfaces. In contrast, deciduous trees (e.g., hardwood species) and mixed forests species in larger blocks, and smoothly trimmed and man-made boundaries are more highly valued in the Urban Core area. As spatial variation in amenity values differs across a metropolitan area, the need for site-specific land use management to fit the local characteristics is revealed. Still, most land use policies are spatially homogeneous because providing one neighborhood with more amenities than another may not be viewed as equitable, even though it may be economically efficient. On the other hand, voluntary efforts such as conservation easements can be modified and adopted according to the results from this research without equity issues. Typically, conservation easements protect a big patch of land that has preservation value. Based on the value of diverse landscape with fragmented forest patches found in the Rural– Urban Interfaces, easements can target the protection of a zone of fragmented forest patches that are uniformly distributed over the residential landscape. Another implication of this study is that hedonic models cannot be complete without

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consideration of the spatial configuration of green open spaces within a neighborhood. More importantly, the locally varying relationships of the green space parameters, as discovered in this study, would improve the site-specific forecasts of housing values associated with the capitalization of local amenities. Similarly, real estate developers and city planners can preserve or enhance housing value by considering the size, spatial configuration, and species composition of open space in residential neighborhoods. For example, a site-specific conservation subdivision ordinance can be developed based on spatial variation in amenity values. Each conservation subdivision is required to set aside a minimum percentage of its adjusted tract acreage as open space. Typically, the minimum amount of the adjusted tract acreage and species compositions are defined rather arbitrarily without systematic consideration of household preferences about open space. Using the results of this study, a conservation subdivision ordinance with smaller adjusted tract acreage of evergreen trees might be better received in the Rural–Urban Interfaces while larger blocks of deciduous and mixed forests with smoothly trimmed edges might be better received in the Urban-Core area.

Acknowledgments The authors thank Tim Kuhn and Gretchen Beal of KnoxvilleKnox County Metropolitan Planning Commission and Keith G. Stump of Knoxville-Knox County-Knoxville Utilities Board Geographic Information System for providing school district and house price data.

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