The impact of agricultural conservation easement on nearby house prices: Incorporating spatial autocorrelation and spatial heterogeneity

Journal of Forest Economics 25 (2016) 78–93

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The impact of agricultural conservation easement on nearby house prices: Incorporating spatial autocorrelation and spatial heterogeneity James Yoo ∗, Richard Ready California Baptist University, Online and Professional Studies, Suite 200 Tyler Plaza, Riverside, CA 92883, United States

a r t i c l e

i n f o

Article history: Received 25 April 2016 Accepted 7 September 2016 JEL classification: Q1 Q18 Keywords: Spatial econometric model Developed and undeveloped land use Agricultural conservation easement Forest land use Hedonic price method

a b s t r a c t The impact of farmland under agricultural conservation easement (ACE) contract on the values of nearby residential properties is investigated using housing sales data in two Pennsylvania counties. ACE-protected farmland had a positive impact on nearby property values in one study county but a negative impact in the other. The paper also looks at the impact of forest land use, and discovers that preserved forest land had a positive impact on the nearby property values in both counties. House prices showed strong spatial correlation in both counties, and a spatial error components (SEC) model fit the data better than the OLS model, a spatial-lag model (SLM), or a spatial autoregressive error model (SEM). Geographically weighted regression (GWR) showed that the impact of ACE-protected farmland on nearby property values varied within one of the two study counties, with positive impacts in some parts of the county and negative impacts in other parts. The impact of forest cover on property values also varied, with positive impacts within both counties. A new hybrid GWR-SEC model is introduced that incorporates both spatial correlation in prices and spatial heterogeneity in the model parameters. Statistical goodness of fit measures showed that the GWR-SEC model fit better than the GWR model or a hybrid GWRSEM model. © 2016 Department of Forest Economics, Swedish University of ˚ Published by Elsevier GmbH. All Agricultural Sciences, Umea. rights reserved.

∗ Corresponding author. Tel.: +1 951 343 3900. E-mail address: [email protected] (J. Yoo). http://dx.doi.org/10.1016/j.jfe.2016.09.001 ˚ Published by Elsevier GmbH. All rights reserved. 1104-6899/© 2016 Department of Forest Economics, Swedish University of Agricultural Sciences, Umea.

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Introduction Agricultural and public forest lands are known to play a critical role to play in supplying recreational services, food supply, and regulating services such as climate regulation through carbon sequestration and pollution buffering, to name a few (Millennium Ecosystem Assessment, 2005; Yoo et al., 2014). Between 1982 and 2007, however, 23 million acres of farmland were lost to commercial, industrial or residential development, representing an area the size of Indiana (AFT, 2010). Between 1982 and 1997, approximately 10.3 million acres of private forest land was converted to developed uses (USDA, 2005). As the population growth continues, it is expected that agricultural and forest lands will continue to be converted to developed uses. State and local governments have taken a variety of actions to prevent loss of farmland or forest lands to development including both regulatory approaches (e.g. zoning, transfer of development rights) and acquisition approaches (e.g. purchase of development rights and outright purchase of land) (Storm et al., 2009). A widely used mechanism is the purchase of development rights through Agricultural (or forest) Conservation Easements (ACE), where an easement is sold by the land owner to a government agency or land trust. The easement allows the owner to continue farming, but prohibits improving or developing the land for any purpose other than agricultural production (forest conservation). Because of its nonregulatory, voluntary nature, ACEs (or forest conservation easement) have been a popular conservation tool for preventing farmland loss. Without knowing the economic values of forest and agricultural lands, however, it is not possible to manage the purchase of development rights efficiently in a market. One of primary goals of this study is, therefore, to consider the implicit prices of forest and agricultural lands. Several reasons are commonly stated to motivate using public resources to preserve farmland or forest lands in near-urban areas. These include maintaining the viability of family farms, providing fresh food close to urban centers, and discouraging urban sprawl. Another common argument made for protecting farmland and forest lands is that it provides nearby residents with local amenities such as aesthetics, wildlife habitat, recreation, and improved water quality (relative to developed land uses). But living near farms could also be undesirable to nearby residents because of noise and odors created by animal and crop production. Whether, on balance, preserved farmland generates positive or negative local amenity impacts is an empirical question, the answer to which has implications for land use planning policy (Sander and Polasky, 2009). A common approach to assess the local amenity impacts of different land uses is to measure the capitalized value of those impacts on nearby residential property prices by estimating a hedonic price function. Several studies have shown that houses with more open space nearby tend to sell for higher prices than similar houses with less open space nearby, indicating that open space tends to generate positive local amenity impacts (McConnell and Walls, 2005). However, studies that look specifically at open space that has been protected through ACEs have generated conflicting results. A series of studies conducted in Maryland found that houses located near open space sold for higher prices than similar houses not located near open space, and that preserved open space was associated with a higher price premium than developable open space (Irwin and Bockstael, 2001; Irwin, 2002; Goeghegen, 2002). Another Maryland study (Goeghegen et al., 2003) reported mixed results, where permanent open space had positive significant impacts in two counties with high development pressure, but did not have significant price effects in a third county with lower development pressure. In contrast, Ready and Abdalla (2005), in a study conducted in southeastern Pennsylvania, find that houses located near agricultural land under ACE were worth less than similar houses not located near ACE-protected farmland. They argue that the observed price difference may be due to the fact that eased farms tend to be more intensely managed than farms not under easement and therefore might not be as desirable to live near. These studies used broadly similar approaches, leading to the conclusion that the impact of ACEprotected farmland on nearby property values differs in different places. The purpose of this study is to directly explore spatial variation in the amenity and disamenity impacts of ACE on nearby property values both between counties and within counties. Within-county heterogeneity is explored by estimating Geographically Weighted Regression (GWR) models that allow the parameters of the hedonic price function to vary spatially within a study region. Several studies have used GWR to explore spatial

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heterogeneity in the impact of open space on nearby house prices (Cho et al., 2008; Cho et al., 2009b; Pavlov, 2000; Fotheringham et al., 2002). These studies found that the capitalization of open space varies significantly over a region. A GWR approach has not yet been used to determine whether the impact of ACE-protected farmland varies spatially in important ways. A second issue that arises when estimating hedonic price functions is possible spatial correlation in house prices or in omitted variables (Anselin, 1988; Kim et al., 2003). Recent hedonic studies valuing open space have incorporated spatial lags in the dependent variable (Payton et al., 2008; Sander et al., 2010), spatial autocorrelation in the errors (Kuethe, 2012), or both (Conway et al., 2010) to avoid possible bias or inefficiency of estimated parameters. These studies consistently find that incorporating spatial structure into the estimated hedonic price function significantly improves data fit over a simple OLS method. Two recent hedonic pricing studies have combined the GWR approach to account for spatial heterogeneity with spatial autocorrelation in the errors. Cho et al. (2008), in a study of the effects of zoning, find that accounting for spatial correlation in the errors improved the fit of a GWR model, while Kim et al. (2010), in a study valuing air quality, find the opposite. In this study, we use a model that is similar to that used by Cho et al. (2008) and by Kim et al. (2010), but with one important advance. Cho et al. (2008) and Kim et al. (2010) estimate one global value of the spatial autocorrelation coefficient. We allow that parameter to vary spatially. Finally, we introduce a new model that combines the GWR approach with the spatial error components (SEC) model of Kelejian and Robinson (1993). Methodology Study Areas The area of study is 2 Pennsylvania counties, Chester County located immediately west of Philadelphia and York County located in south central Pennsylvania. Chester County has a higher population density (665 persons per square mile in 2010) than York County (481 persons per square mile; US Census of Bureau, 2010). Chester County has a higher median income ($81,380) than York County ($56,833). Both counties have higher density and higher median income than the state average. From 2000 to 2009, the population in both counties grew at a faster rate than for the state as a whole (15.1% in Chester, 12.4% in York, 2.6% in Pennsylvania). Agricultural land accounts for 34.7% of total county land in Chester County but 50.5% of the total county land in York County (Census of Agriculture, 2007). Both Chester and York counties have been aggressive in purchasing agricultural conservation easements. As of 2013, Chester County had purchased ACEs on 29,352 acres (18% of its total farmland) while York County had purchased easements on 38,123 acres (13% of its total farmland). Hedonic Models In this paper, the hedonic price method is used to explore whether farms with ACE’s have positive or negative local amenity impacts that are capitalized into the price of neighboring residential properties. The hedonic pricing model has its foundation on Rosen’s seminal work (1974) and is based on the assumption that market goods such as a home consist of different bundles of attributes or characteristics. A house is described by a vector of K characteristics, x = x1 ,. . .,xK , that includes (1) structural characteristics of the property such as lot size and square footage of living area, (2) locational characteristics such as proximity to employment centers, and (3) neighborhood characteristics including surrounding land uses. A hedonic price function, Y(x1 ,. . .,xK ), maps the equilibrium price of a house as a function of its characteristics, and is determined by the demand and supply of houses with different characteristics in the local market. Individual households choose the house that gives them the highest utility, subject to their budget constraints. A 1st order condition for the household’s utility maximization equates the marginal implicit price for each attribute, ∂Y/∂xk , with the household’s marginal rate of substitution between the attribute, xk , and money. The marginal implicit prices therefore represent the amounts that households would be willing to pay to obtain a marginal increase in the level

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of each attribute. A positive marginal implicit price indicates that the attribute is an amenity, while a negative marginal implicit price indicates the attribute is a disamenity. Accounting for spatial correlation in house prices The hedonic price model is conventionally estimated via simple OLS regression. However, OLS fails to address two issues, potential spatial correlation in house prices and spatial heterogeneity in the parameters of the hedonic price function. House prices can be spatially correlated for several different reasons, and the statistical implications of spatial correlation depend on the structure that generates it. First, house prices may be influenced directly by the prices of neighboring houses. For example, a home located in a high-priced neighborhood may tend to sell for more than an otherwise-identical home located in a lower-priced neighborhood. In such cases, the assumption of uncorrelated errors and independent observations is violated, and OLS parameter estimates will be biased (Anselin,1988; Kim et al., 2003). This issue is typically addressed by estimating a spatial lag model (SLM). Alternatively, the unobserved error terms for each house could be spatially correlated. This could occur if there exist omitted variables or measurement errors that are spatially correlated. In such cases, OLS parameter estimates will be unbiased, but inefficient (Kim et al., 2003). A common model to account for spatiallycorrelated errors is the spatial autoregressive error model (SEM) In both the SLM and SEM model, any error that affects the property value at one location is assumed to also influence the property values at neighboring locations. However, this is not a realistic assumption in the presence of idiosyncratic measurement error. Suppose that the size of a house at one location is recorded incorrectly in the dataset, with the recorded size less than the actual size. Further suppose that buyers and sellers know the true value. The error term for this observation will tend to be positive because the house will sell for more than predicted by the hedonic model. However, this error will not influence prices of neighboring houses. It is an idiosyncratic error that only affects one observation. The spatial error component (SEC) model (Kelejian and Robinson, 1993) separates spill-over errors (errors that affect neighbors similarly) from idiosyncratic (house-specific) measurement errors. The SEC model has two error terms, and is expressed as: Y = X␤ + u and u = W v + ␸

(1)

where v is the spillover (contagious) error term and ␸ is the idiosyncratic (house specific) error term. The two errors are assumed to be distributed as follows E(v) = E(␸) = 0

(2)

E(vv ) = ␴2v In

(3)

E(␸␸ ) = ␴2ϕ In

(4)

E(uu ) = ␴2v WW  + ␴2␸ In = u

(5)

A Generalized Method of Moments (GMM) approach is used to estimate the model parameters. First, the variances, ␴2v and ␴2␸ , are obtained by regressing squared residuals from an OLS regression on a vector of diagonal values of WW’ and an intercept. These estimated variances are then plugged ˆ u . In the absence of instrumental back into (5) to obtain an estimated variance-covariance matrix, ˝ variables, a consistent estimator for ␤ is given by ˆ = (X   ˆ −1 X) ␤ u

−1

ˆ −1 Y X u

ˆ = (X   ˆ −1 X) V (␤) u

−1

(6) (7)

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Although the SEC model captures the intuitive idea that some errors in house prices are purely idiosyncratic, very few applications exist in the hedonic pricing literature. Accounting for spatial heterogeneity in parameters The models presented thus far assume that the parameters of the hedonic price function are constant across the study region. Geographically weighted regression (GWR) (Cleveland and Devlin, 1988) allows parameters to vary within a study region. Around each observation, i, a local regression is estimated that uses only near neighbors to i and that gives higher weight to observations located closer to i. For each observation a local parameter vector, ␤i is estimated as follows: ␤i = (X  Si X)

−1

X  Si Y

(8)

where Si is a diagonal N × N regression weights matrix. The jth diagonal of Si , sij , denotes the weight of the jth observation in the regression around the target point i, and is generated by a kernel function that depends on the distance between j and i. Two modeling decisions must be made when constructing the matrix Si . First, a bandwidth must be chosen that defines how many neighbors are given positive weight in the local regression. The bandwidth can either be fixed (all observations within a fixed distance are given positive weight) or adaptive (the distance cutoff is adjusted so that a constant proportion of the observations in the dataset is given positive weight). When the density of observations varies, a fixed bandwidth can result in local regressions that include very few observations, resulting in high variance. Because the density of house sales varies widely throughout our study counties, and ACEs are primarily located in areas with lower housing density, we use an adaptive bandwidth. Choosing an adaptive bandwidth size (proportion) involves a trade-off between bias and variance (Fotheringham et al., 2002). As the bandwidth size increases, each local regression will include more observations, generating smaller variance, but higher bias if the bandwidth spans areas with different coefficient values. Conventionally, the optimal bandwidth size is determined by either a cross-validation (CV) technique (Cleveland and Devlin, 1988) or the Akaike Information Criterion (AIC) (Brunsdon et al., 1999; Fotheringham et al., 2002). The CV approach did not work well for this application. Most observations in the dataset have no land within 400 m with ACE protection. The CV technique generated an optimal bandwidth that was small, resulting in many local regressions with singular results for the ACE variable, or results with very high variance. We therefore rely on the AIC to choose the bandwidth. Second, a kernel function must be chosen that calculates the value of sij (i.e. the regression weight) for each observation within the bandwidth. Several different kernel functions are used in the literature for this purpose. We use the tri-cube kernel function given by

 sij =

 1−

sij = 0,

dij

3  3 if dij < dmax ,

dmax

(9)

otherwise

where dij is the distance between observation j and target observation i and dmax is the maximum distance set to attain the desired bandwidth size. Standard errors for each local regression are calculated based on the covariance matrix shown in Fotheringham et al. (2002), Cov(␤i ) = ␴2i (X  Si X) ei  ei

−1

(10)

where ␴2i = Q −K , Q is the number of neighbors and K is the number of variables Given the greater flexibility of GWR parameters, GWR always provides a better data fit than OLS. Three different approaches have been taken to test whether the improvement in model fit is statistically significant, indicating spatial heterogeneity of coefficients: Leung’s test (Leung et al., 2000), a Monte Carlo Significance test (Brunsdon et al., 1999), and local heterogeneity test (Paez et al., 2002). All procedures are computationally intense. In this study, Leung’s

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approximated F test is adapted to test the spatial variability of attribute coefficients over the region. Accounting for both spatial correlation and heterogeneity Cho et al. (2009a, 2009b, 2010) and Kim et al. (2010) estimate a GWR-SEM model that estimates a local weighted SEM model for each observation. We also estimate a GWR-SEM model, but with one difference from earlier studies. Cho et al. (2010) and Kim et al. (2010) estimate one spatial correlation parameter and use that global estimate in all local SEM regressions. We estimate a unique spatial correlation parameter for each local regression. Finally, we estimate a new model, the GWR-SEC model, that combines the spatial error components model with the GWR approach. The estimation procedure is straightforward. First, a basic GWR is run for each observation i, generating a vector of coefficients and a vector of residuals. The GMM approach 2 ˆ ␸␫ and described earlier is then used to estimate local values of the two error component variances, ␴ 2

␴ ˆ vi . The GMM approach does not constrain the estimated variances to be positive. If either of the estimated error component variances turns out to be negative in a local regression, that indicates that the SEC model does not fit that local data, and the ordinary GWR regression results are retained for that observation. Data Much of the data used in this analysis were assembled by Loiacono (2008). Digitized parcel maps and Computer Assisted Mass Appraisal (CAMA) files containing assessment data for each parcel were provided by Chester and York County Assessment Offices. The CAMA data includes a land use code for each parcel, from which land use maps were constructed. Lands protected from development through means other than ACE’s, including public lands and lands held by land trusts, were identified from maps generated by the National Gap Analysis Program (GAP). Information on residential parcels such as structural characteristics of the house, year built, last date of sale, and sale price were obtained from the CAMA files. Data were assembled for detached single-family residential homes sold between 2003 and 2007. Explanatory variables are classified into 4 categories: structural characteristics of the properties, locational characteristics, surrounding land use, and year of house sale. Computational constraints limited the number of variables that could be included in some of the spatial models investigated here. Four structural variables were chosen for inclusion that provided the most explanatory power: age of the house, above-ground living area, basement area, and lot size. Three sets of locational characteristics were included. For each property, distances were calculated to major centers of employment, which were Baltimore, Harrisburg, and York for York County and Philadelphia and Wilmington for Chester County. School district test scores were from Pennsylvania System of School Assessment (PSSA) standardized tests. Population density was measured in 2000 at the block group level. Surrounding land use was measured in 7 categories: recreational lands including golf courses, ball fields, and hunting clubs, commercial land such as office buildings, schools, apartment buildings and churches; industrial land including factories, junkyards, and landfills; single family detached residential land; other types of residential land including townhomes and duplexes; currently undeveloped land that is not protected from development; and undeveloped land protected from development by ACE contract. The 7 land use variables were measured as proportions within 400 m of each residential parcel and are mutually exclusive. To capture the impact of different types of open space, the proportion of undeveloped land for agricultural use and the proportion with forest cover including preserved public forest, woodland, etc, were measured within 800 m of each residential parcel. The omitted open space type was non-forested, non-agricultural lands. Finally, year-of-sale dummy variables were included to capture temporal variation in house prices. The total number of observations for the estimation is 22,586 for Chester County and 15,712 for York. Table 1 summarizes the datasets for both counties, and shows that houses in Chester County tend to be newer, larger, and more expensive than those in York County.

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Table 1 Descriptive statistics of variables. Variable

Mean value Chester

York

451,090

243,319

Deflated house sale price (2007 $)

0.731 2686 116.9 22.5

0.583 2052 100.6 31.8

Log of Size of property in acres Square footage of total residential space Square footage of basement Age of house at time of sale

14.79 0.779

3.982 3.371 2.005 20.638 0.7158

Natural log distance to Wilmington Natural log distance to Philadelphia Natural log distance to Baltimore Natural log distance to Harrisburg Natural log distance to York Population Density (1000 people per sq.mile). PSSA average score per school district/100

0.2778

0.376

Forest800

0.4295

0.2214

Other residential

0.026

0.056

Residential Commercial Industrial Recreation Developable ACE protected

0.436 0.1175 0.022 0.0149 0.304 0.0085

0.450 0.099 0.030 0.027 0.316 0.0071

Sale value Structural characteristics Log(lot size) Residential area Basement area Age Locational characteristics Wilmington Philadelphia Baltimore Harrisburg York Population density PSSA score Land use Ag800

3.222 3.481

Proportion of undeveloped land within 800M of the house in agricultural land cover Proportion of undeveloped land within 800M of the house in forest land cover Proportion of land within 400M of the house in other residential use Proportion. . .in single family residential use Proportion. . ..in commercial use Proportion. . ..in industrial use Proportion. . ..in recreation use Proportion. . ..undeveloped but developable Proportion. . ..that has ACE in place at time of sale

Results and discussion OLS results The first columns of Tables 2 and 3 show the OLS regression results for the hedonic price model for Chester and York Counties, respectively. The dependent variable in the regressions is the natural log of house price, measured in constant 2007 dollars. Estimates of the coefficients for structural and locational variables are quite consistent between the two counties. As expected, larger lot size and more residential space are associated with higher house prices, though the impact of lot size on house price is not quite significant in York County. Older houses and houses with more of their square footage below grade sell for lower prices. Houses with longer commuting distances sell for lower prices, with the exception of commuting distance to York City. Houses located in neighborhoods with higher population density sell for lower prices, while houses located in school districts with higher standardized test scores sell for higher prices. The impacts of land use differ between the two counties. The omitted land use variable in the models was single family residential land, so the land use coefficient estimates in Tables 2 and 3 represent the marginal impact of a change in the proportion of each type of land on house price, compared to having that land in single family residential use. Having a higher proportion of industrial or commercial land within 400 m decreases property values in both counties, This is consistent with results from Irwin (2002). Ready and Abdalla (2005) also find a negative effect for industrial land, but find an insignificant effect for commercial land. The coefficients for non-single family residential land and for recreational land are both positive in Chester County but negative in York County. It is not clear why these coefficients might differ between the two counties. Both land use categories include a diverse mix of uses. Loiacono (2008) speculated that, particularly for recreational lands, the mix of

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Table 2 Parameter Estimates from OLS, SLM, SEM, and SEC Models for Chester County. Variable

OLS coefficient(t-stat)

S-Lag coefficient(t-stat)

SEM coefficient(t-stat)

SEC coefficient(t-stat)

0.0805(52.15)*** 0.00024(192.22)*** −0.0002(−52)*** −0.0043(−79.48)***

0.0802(58.88)*** 0.00024(160.16)*** −0.0002(−45.19)*** −0.0042(−101.36)***

0.0828(51.29)*** 0.00024(180.19)*** −0.0002(−43.11)*** −0.0042(−76.87)***

−0.088(−13.71)*** −0.4844(−15.58)***

−0.0306(−1.71) −0.2385(−12.37)***

−0.1301(−20.01)*** −0.5452(−54.51)***

0.1432(5.99)*** −0.2898(−13.75)*** −0.0272(−2.94)** 0.1176(9.07)*** −0.0035(−4.66)** −0.0886(−3.92)*** 0.0465(5.43)*** 0.0543(13.82)***

0.1317(5.88)*** −0.2828(−14.02)*** −0.0193(−2.05)* 0.1692(9.09)*** −0.0203(2.73)** −0.1303(−5.92)*** 0.0959(9.08)*** 0.1205(9.27)***

0.1364(5.53)*** −0.3107(−14.35)*** −0.0224(−2.24)* 0.1354(6.55)*** −0.0189(−2.37* −0.0904(−3.7)*** 0.0925(8.53)*** 0.1025(8.08)***

0.041(12.47)*** 0.0636(17.98)*** 0.067(21.73)*** 0.0658(19.46)*** −0.0008(−12.34)*** 0.4132(3.83)*** 0.17(9.63)*** – – –

0.0421(8.92)*** 0.0628(13.32)*** 0.0667(14.18)*** 0.0652(13.66)*** −0.0008(−11.43)*** 0.4455(14.17)*** – 0.925(1211.04)*** – –

0.0408(8.64)*** 0.0629(13.35)*** 0.0677(14.41)*** 0.0679(14.18)*** −0.0008(−11.6)*** 0.6549(29.49)*** – – 0.0281(64.34)*** 0.0701(2.46)**

Structural variable 0.0811(51.51)*** Log(lot size) 0.00025(183.93)*** Residential area −0.0002(−42.15)*** Basement area −0.0042(−76.38)*** Age Locational variable −0.1324(−33.81)*** Wilmington Philadelphia −0.5533(−76.23)*** Land use 0.1261(5.17)*** Other residential Industrial −0.3205(−14.91)*** Commercial −0.0296(−2.99)** Recreation 0.1246(6.19)*** Developable −0.04(−5.16)*** −0.093(−3.93)*** ACE protected Forest800 0.1132(11.43)*** Ag800 0.1183(10.34)*** Year dummy (reference year:2007) 0.04(8.02)*** Y2006 Y2005 0.0632(12.72)*** 0.0648(13.09)*** Y2004 Y2003 0.0646(12.83)*** Population density −0.0009(−12.31)*** 0.6573(41.57)*** PSSA score ␳ – – ␭ – ␴2␸ ␴2v – * ** ***

Significant at the 5% level. Significant at the 1% level. Significant at the 0.1% level.

land uses within the category could differ between the two counties, generating different house price impacts. The coefficient on developable land within 400 m is negative for both counties. This category includes farmland not under ACE protection, but it also includes other types of currently undeveloped land such as forests and land covered by brush or other unmanaged vegetation. More insight can be obtained on the relative impact of different types of undeveloped land by looking at the land cover measures for undeveloped land within 800 m of the house. Here, the omitted category is undeveloped land that is neither farmland nor forested, and would include brushland and unmanaged nonforested lands. Houses located in areas where undeveloped lands have higher proportions of forested land or farmland sell for higher prices in Chester County. The results are consistent for York County for forested land, but not for farmland. In York County, houses located in areas where more of the undeveloped land is farmland sold for lower prices. The coefficient on land under ACE contract, the variable of primary interest here, is significant and negative in Chester County but is significant and positive in York County, providing evidence that the impact of ACE-protected farmland on nearby property values varies from county to county.

SLM, SEM and SEC model results The SLM, SEM and SEC models require the construction of a spatial weights matrix, W. Elements of W were calculated based on the distance between each pair of observations, according to the

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Table 3 Parameter Estimates from OLS, SLM, SEM, and SEC Models for York County. OLS coefficient(t-stat)

Variable

Structural variable 0.0035(1.88) Log(lot size) 0.00035(143.92)*** Residential area Basement area −0.0002(−33.08)*** Age −0.004(−63.78)*** Locational variable −0.4543(−25.57)*** Baltimore Harrisburg −0.0231(−3.1)** York 0.0513(20.8)*** Land use −0.2968(−11.47)*** Other residential Industrial −0.4602(−17.99)*** Commercial −0.2853(−16.64)*** Recreation −0.1589(−6.45)*** Developable -0.0333(-2.83)** ACE protected 0.0844(2.5)* 0.0391(2.85)** Forest800 Ag800 −0.1015(−7.78)*** Year dummy (reference year: 2007) 0.0255(4.04)*** Y2006 0.0229(3.61)*** Y2005 Y2004 −0.0023(−0.35) 0.0365(5.42)*** Y2003 Population density −0.0027(−31.22)*** PSSA score 0.608(32.36)*** – ␳ – ␭ – ␴2␸ ␴2v – * ** ***

S-Lag coefficient(t-stat)

SEM coefficient(t-stat)

SEC coefficient(t-stat)

0.0022(1.19) 0.00035(144.09)*** −0.0002(−32.89)*** −0.0039(−63.48)***

0.0004(0.19) 0.00034(109.91)*** −0.0002(−32.93)*** −0.004(−63.68)***

0.0017(0.91) 0.00034(137.12)*** −0.0002(−32.72)*** −0.0041(−63.79)***

−0.4105(1137.9)*** −0.0085(−2.3)* 0.0471(19.98)***

−0.3311(−29.98)*** 0.0272(2.4)* 0.0665(10.75)***

−0.4468(16.12)*** −0.0156(−1.34)** 0.0511(14.01)***

−0.3107(−12.11)*** −0.4285(−16.87)*** −0.2594(−15.37)*** −0.1482(−6.06)*** -0.023(-1.97)* 0.1013(3.02)** 0.0229(1.68) −0.1293(−9.95)***

−0.3116(−12.04)*** −0.443(−17.11)*** −0.2704(−15.72)*** −0.1433(−5.78)*** -0.023(-1.97)* 0.0724(1.94) 0.1228(6.94)*** −0.021(−1.28)

−0.3185(−11.76)*** −0.4256(−16.31)*** −0.2563(−14.49)*** −0.1223(−4.74)*** -0.0478(-3.85)*** 0.0688(1.79) 0.1006(6.07)*** −0.0445(−2.91)

0.0254(4.04)*** 0.0022(3.49)*** −0.0039(−0.59) 0.0356(5.32)*** −0.0027(−31.48)*** 0.5547(31.32)*** 0.07(46.56)*** – – –

0.0238(3.81)*** 0.0164(2.66)*** −0.01(−1.53) 0.0262(4.01)*** −0.0026(−31.3)*** 0.5643(26.5)*** – 0.744(371.6)*** – –

0.0227(3.71)*** 0.0184(2.99)** −0.0067(−1.05) 0.0297(4.55)*** −0.0025(28.43)*** 0.6304(30.44)*** – – 0.0394(49.96)*** 0.1098(4.17)***

Significant at the 5% level. Significant at the 1% level. Significant at the 0.1% level.

following formula Wij = 1 −

Lij Dmax

Wij = 0, P˜ij =

if Lij < Dmax

if Lij > Dmax

Wij N 

,

(11)

Wij

j=1

where Lij is the distance between observation i and j, Dmax is the maximum cut-off distance for neighbors, and P˜ij is the row-standardized weight for ith row and jth column. There is no clear-cut rule for selecting the cut-off distance for neighbors. LM statistics were calculated for the SEC model in both counties for various cut-off distances. The LM statistic peaked at 2500 m for York County, but increased continuously for Chester County. Results for SEM, SLM, and SEC models were robust in terms of coefficient sign and size for cutoff distances less than 2500 m. A weights matrix with a small cut-off distance can have many observations with zero neighbors, which prevents estimation of some of the models. Based on all of these considerations, 2500 m was selected as the cut-off distance for the spatial weights matrix for both counties for all three spatial models. The SLM, SEM and SEC models were estimated for each county. Coefficient estimates are presented in Tables 2 and 3. Coefficient estimates of all models are broadly consistent in sign and significance with the OLS results, though the magnitudes vary some across models. Lagrange Multiplier (LM) tests

J. Yoo, R. Ready / Journal of Forest Economics 25 (2016) 78–93

87

Table 4 LM Test Statistics for Spatial Dependence. County

Model

LM test statistics

Null: no spatial dependence

York

SLM SEM SEC SLM-Robust SEM-Robust

74 2,624 8,203 0.2540 2,550

Reject Reject Reject Fail to reject Reject

Chester

SLM SEM SEC SLM-Robust SEM-Robust

996 20,980 55,139 282 20,266

Reject Reject Reject Reject Reject

were conducted for the presence of spatial dependence in each of the three spatial models (Anselin, 1988; Anselin and Bera, 1998; Anselin, 2001 for the SLM and SEM; Anselin and Moreno, 2003 for the SEC). All of the LM test statistics are distributed as 2 (1). The LM tests are summarized in Table 4. The LM tests show that all three spatial models fit the data significantly better than the OLS model. LM statistics provide a test for choosing between OLS and SLM/SEM/SEC, but not for choosing among the SLM, SEM, and SEC models. Robust LM-tests (see Anselin, 1988, 2001 for this test in detail) are often used to choose between the SLM and the SEM. The standard approach is to calculate robust LM statistics for both the SLM and SEM. If only one of the robust LM tests is significant, then that is the preferred model. If both robust LM tests are significant, then the model with the larger test statistic is chosen. According to this rule, the SEM is favored over the SLM in both counties. A robust LM statistic for the SEC model is not available, so a similar approach cannot be used to choose between the SEM and SEC models. A pseudo-R2 has been proposed as a means of comparing model fit among different spatial models (Overmars et al., 2003; Anselin, 1992; Kim et al., 2010). A pseudo-R2 is calculated as one minus the ratio of prediction error variance over the variance of the dependent variable. The calculated value of the pseudo-R2 was higher for the SEC model than for the SEM in both counties (0.876 versus 0.828 in Chester County, 0.832 versus 0.828 in York County). This result, that the SEC model provides better data fit than the SEM, is consistent with the results from Wang and Ready (2005). Focusing, then, on the coefficient for ACE-protected farmland in the SEC models, we see that the impact of ACE-protected farmland on nearby house prices is negative and statistically significant in Chester County, consistent with the OLS results. For York County, the impact is positive, as it was in the OLS model, but only marginally significant in the SEC model. Comparing the two counties, the estimated coefficient for ACE-protected farmland for Chester County is significantly different from the estimated coefficient for York County (t = 3.49). The results from GWR Having established that county-level estimates of the impact of ACE-protected farmland on nearby property values differs between York and Chester Counties, and that the difference is statistically significant, we next turn to the question of whether the impact varies within either of these two counties. This was done through GWR estimation. Adaptive bandwidths were investigated including 5% to 10% of all observations. Bandwidth sizes of 5%, 5.5% and 6% produced coefficients with higher variance. Bandwidth sizes of 8%, 9%, and 10% yielded similar spatial patterns, but higher AIC values, indicating a loss of locality in the GWR. A bandwidth size of 7% of all observations was selected for both counties (1100 observations for York and 1581 observations for Chester). Using the tri-cube kernel and a 7% bandwidth, GWR models were estimated for both counties. Leung et al. (2000) approximate F test was conducted and indicated that the GWR model significantly improved model fit relative to the OLS model in both counties (F(9356,15690) = 7.5068 in York

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Fig. 1. The spatial distribution of ACE impacts in York and Chester counties under GWR model.

County, F(12356,22565) = 12.5491 in Chester County). This provides evidence that at least some of the parameters of the hedonic price model do vary spatially within each county. Of particular interest here is whether the coefficient on ACE-protected farmland varies spatially within each county. Fig. 1 shows the spatial distribution of positive and negative estimates of the coefficient on ACE-protected land in York and Chester Counties from the GWR models. Only statistically significant coefficient estimates are included in Fig. 1. The maps show that, in both counties, being near land under easement contract could have either amenity or disamenity impacts to nearby residents. In York County, the area with positive estimated easement impacts is bigger than the area with negative estimated easement impacts, while the opposite is the case in Chester County. This difference is consistent with the results from the OLS and SEC models, in that the estimated coefficients of the global models reflect the dominant impact for each county. Table 5 presents Leung’s approximate F-test for the land use variables. The F-tests showed that the marginal implicit price of ACE-protected land exhibits statistically significant spatial variation in Chester County but not in York County. In fact, the marginal implicit price for ACE-protected land in Table 5 Tests for Spatial Variability for Land Use Variables. York Variable

York F-statistics

DF1

DF2

Chester variable

F-statistics

DF1

DF2

Other Residential Industrial Commercial Recreation Developable ACE Forest800 Ag800

8.030*** 2.122*** 4.267*** 3.713*** 13.239*** 1.300 5.821*** 5.805***

1987.6 240.6 2069.8 854.54 1038.4 6.515 427.63 478.69

15,701 15,701 15,701 15,701 15,701 15,701 15,701 15,701

Other Residential Industrial Commercial Recreation Developable ACE Forest800 Ag800

5.249*** 7.562*** 5.185*** 2.040** 5.906*** 2.880*** 5.617*** 6.980***

1059.9 421.58 2555 421.58 5845.2 14.18 3594.1 4980.7

22,577 22,577 22,577 22,577 22,577 22,577 22,577 22,577

DF1: degrees of freedom for numerator. DF2: degrees of freedom for denominator. * Significant at the 5% level. ** Significant at the 1% level. *** Significant at the 0.1% level.

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89

Table 6 OLS and SEC Regression Results for Subsamples of York and Chester Counties. Variable OLS ACE SEC ACE ␴2␸ ␴2v Sample Size * ** ***

York County Subsample I

York County Subsample II

Chester County Subsample I

Chester County Subsample II

−0.1427 (−0.88)

0.1131 (3.22)**

−0.1234 (−4.78)***

0.1721 (2.50)*

−0.0119 (−0.06) 0.0256 (21.13)*** 0.2510 (5.52)*** 2241

0.0795 (2.02)* 0.0409 (46.19)*** 0.0818 (2.97)*** 13,471

−0.1271 (−4.83)*** 0.0299 (54.93)*** 0.0444 (1.52) 6869

0.1487 (2.02)* 0.0206 (24.91)*** 0.1142 (0.81) 15,717

Significant at the 5% level. Significant at the 1% level. Significant at the 0.1% level.

York County is the only land use variable that does not show statistically significant spatial variation in the estimated coefficient. To confirm whether the impact of ACE-protected land on nearby property values does actually vary within each county, each county was divided into two regions based on the maps in Fig. 1. Within each county, townships where most GWR regression results provided positive estimates of the ACE coefficient were included in Subsample II, while townships that had predominantly negative estimated ACE coefficients were included in Subsample I. For York County, 8 townships in the central part of the county are included in subsample I with the remaining 59 townships in subsample II. For Chester County, subsample II includes 10 townships in the central part of the county, with the surrounding 61 townships in subsample I. For each county for each sub-sample, OLS and SEC models were estimated. The estimated ACE and spatial parameters from these sub-sample models are summarized in Table 6. Both the OLS and SEC regressions for Chester County showed that the estimated marginal implicit price for ACE-protected land was indeed positive in subsample II and negative in subsample I, with both estimates significantly different from zero. Further, the estimated ACE coefficient for subsample II was significantly different from the estimated coefficient for subsample I (t = 4.02 for OLS; t = 3.53 for SEC). For York County, the ACE coefficient was also positive and significant in subsample II, but was not significantly different from zero in subsample I, and the estimates for the two subsamples were not significantly different from each other (t = 1.54 for OLS; t = 0.45 for SEC). Thus, the split sample analysis supports the GWR results that showed that there is spatial heterogeneity in the impact of ACE-protected farmland on nearby property values in Chester County, but not in York County. To get a sense of the economic values of ACE-protected farmland and forest land use, we computed implicit prices by increasing ACE-protected land and forest cover by 10% within a specified radius of buffer, using mean property values and estimated coefficients from the SEC model. Table 7 reports implicit prices of ACE-protected farmland and forest cover in two study counties. The results show the value of an average residential property with 10% more forest cover within a 800 m buffer is $417 higher in Chester County, and $245 higher in York County, which is consistent with previous literature.

Table 7 Implicit prices of ACE-protected farmland and forest cover in Chester and York Counties. County

Implicit price of increasing ACE-protected farmland by 10% ($)

Implicit price of increasing forest cover by 10% ($)

Chester York

−407.785 167.40

417.26 244.78

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Table 8 Goodness of Fit Statistics for GWR-OLS, GWR-SEM, and GWR-SEC. Model York County GWR-OLS GWR-SEM GWR-SEC Chester County GWR-OLS GWR-SEM GWR-SEC

SSE

RMSE

Pseudo-R2

Spatial error LM

486.32 487.34 279.27

0.031 0.031 0.018

0.872 0.872 0.926

19.51 14.49 1193.20

473.61 474.55 243.81

0.021 0.021 0.011

0.909 0.909 0.953

45.20 15.94 2035.10

A 10% increase in ACE-protected farmland within a 400 m buffer of a representative property decreases the property value by $408 in Chester County, while adding $167 in York County. Result from GWR-SEC and GWR-SEM Earlier we found that both the SEC model and the SEM were favored over OLS according to the LM statistics. If the global model for each county shows significant spatial dependence, then local regressions may also show spatial dependence. The GWR-SEM and GWR-SEC models were estimated with unique spatial correlation parameters estimated for each local regression. In each local regression, if the estimated spatial correlation parameter or the estimated spillover error variance was not statistically significant different from zero, then the GWR-OLS result was retained.1 Calculating an F-test for spatial variability for the GWR-SEM or the GWR-SEC would require inverting N different N × N matrices with N = 15,712 for York County and N = 22,586 for Chester County, which was computationally infeasible. We therefore do not conduct F-tests whether the GWR-SEM or GWR-SEC model fit the data significantly better than the SEM and SEC models, respectively. However, alternative measures can be used to compare the three GWR models. Table 8 shows the sum of squared errors (SSE), the root mean square error (RMSE), the pseudo-R2 , and the spatial error LM for the GWR-OLS, GWR-SEM and GWR-SEC models for both counties. All of these statistics were constructed based on the residuals obtained from each model (Kim et al., 2010; Cho et al., 2010; Paez et al., 2007). All four measures indicate that the GWR-SEC model fits the data better than either the GWR-OLS or the GWR-SEM in both counties. The four measures do not provide consistent ranking between the GWR-SEM and the GWR-OLS models. Fig. 2 shows the spatial distribution2 of statistically significant ACE coefficient estimates in York and Chester counties under the GWR-SEC model. The spatial pattern is similar to that obtained from the GWR-OLS. In Chester County, the GWR-SEC model generated fewer statistically significant local estimates of the ACE coefficient than did the GWR-OLS model (6107 for GWR-SEC; 6523 for GWR-OLS), but the opposite occurred in York County (3162 for GWR-SEC versus 2323 for GWR-OLS). The spatial pattern of estimated ACE coefficients from the GWR-SEM model was similar to that shown in Fig. 2 for the GWR-SEC model, but fewer local coefficient estimates were statistically significant (1889 in York County, 5286 in Chester County). While the spatial distribution of easement coefficients obtained from GWR-SEC and GWR-SEM do not give us qualitatively different results relative to GWR-OLS, the estimated parameter variances of the GWR-OLS may be biased if either the SEC or SEM model is the correct data generation process. An additional advantage of the spatial models is that they provide important information on the spatial error processes in housing prices in each county. From the GWR-SEC model, the relative importance

1

For clarity, the GWR model with OLS local regressions is hereafter referred to as the GWR-OLS model. We conducted two-sample mean comparison tests, to see if estimated coefficients on ACE-protected farmland and forest cover are statistically different across GWR, GWR-SEM, and GWR-SEC models. The results show the estimated coefficients on forest cover were not statistically different across all models in both counties. The estimated coefficients on ACE-protected farmland are not statistically different across all models in York County, while those are statistically different between GWR-SEM and GWR-SEC models in Chester County. The results are available upon request from the authors. 2

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Fig. 2. The spatial distribution of ACE impacts in York and Chester counties under GWR-SEC model.

of spillover error versus local errors can be assessed by calculating the ratio of the estimated spillover error variance divided by the estimated local error variance. The median spillover/local variance ratio was 13.6 in York County and 52.3 in Chester County, indicating that spatial correlation in the errors may be stronger in Chester County than in York County. Similarly, the average of the estimated local correlation coefficients from the GWR-SEM model, ␥, tend to be higher in Chester County (Mean = 0.142) than in York County (Mean = 0.076). Spatially correlated errors will not tend to bias parameter estimates, but can bias estimated standard errors. The higher degree of spatial correlation in Chester County, and the consequent higher potential for bias in the estimated standard errors, could account for the finding that the GWR-OLS model resulted in more statistically significant local estimates of the ACE coefficient than did the GWR-SEC or the GWR-SEM model in that county. Conclusion and policy implications The impact of agricultural conservation easements on nearby house prices is investigated using a variety of spatial hedonic models. The results show that there is evidence of both spatial correlation in house prices and spatial heterogeneity in the hedonic price function parameters. Among global models (models that do not incorporate spatial heterogeneity in parameters), the spatial error components model of Kelejian and Robinson (1993) fit the data better than OLS, and better than the either the SEM or SLM models. This result is consistent with our intuition that some errors in measurement will be spatially correlated, but that other measurement errors will be idiosyncratic. In both study counties, the hedonic price coefficient for ACE-protected farmland had larger estimated standard errors in the SEC model than in the OLS model, suggesting bias in the OLS standard error estimates due to spatial dependence. Very few hedonic price studies have employed the SEC model to date. We hope the results presented here encourage others to explore this model. GWR models and split sample analysis showed that there was significant heterogeneity in the estimated ACE parameter within one of the two study counties, but not in the other study county. Among models that incorporate spatial heterogeneity in the hedonic price model parameters, the GWR-SEC model introduced here fit the data better than the GWR-SEM of Cho et al. (2009a, 2009b, 2010) and Kim et al. (2010) or the more familiar GWR-OLS model. While the GWR-SEC model did

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not generate qualitatively different information on the spatial distribution of positive and negative impacts from ACE-protected farmland, it is important to account for spatial dependence in the data to assure that hypothesis tests are unbiased. The estimated coefficient from the SEC model for ACE-protected farmland was negative in Chester County and positive in York County, and the difference between the two estimates was statistically significant. This result is consistent with previous research, which has shown that the impact of ACEprotected farmland can vary from county to county. What is new with this study is that we found significant spatial heterogeneity in the impact of ACE-protected farmland at smaller spatial scales (within a county). Ready and Abdalla (2005) argue that the impact of ACE could be positive or negative depending on the magnitude of the amenity benefit from agricultural open space and the disamenity from the intensive animal production. 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