Public purchases and private preferences: Challenges for analyzing public open space acquisitions

Urban Forestry & Urban Greening 11 (2012) 179–186

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Public purchases and private preferences: Challenges for analyzing public open space acquisitions Erik E. Nordman a,∗ , John Wagner b,1 a

Natural Resources Management, Biology Department, Grand Valley State University, Allendale, MI, USA Forest Resource Economics, Department of Forest and Natural Resources Management, State University of New York College of Environmental Science and Forestry, Syracuse, NY, USA b

a r t i c l e

i n f o

Keywords: Hedonic model Implicit price Long Island Nonmarket valuation Open space Policy

a b s t r a c t The traditional hedonic model uses market purchases to estimate implicit prices. Hedonic models composed of only public land purchases violate key assumptions of hedonic model theory. The resulting implicit prices cannot be interpreted as the purchasing agency’s maximum willingness to pay. The problems are illustrated using a hedonic model of public land purchases in the Town of Brookhaven, on Long Island, New York, USA. The model reveals negative elasticities for attributes for which the agency has stated positive preferences. For example, the presence of unique glacial landforms (a positive attribute) was associated with a 97% increase in property cost. However, if purchasing the open space property prevented development that is incompatible with existing land uses (also a positive attribute), the property cost decreased by 69%. The results confirm that elasticities and implicit prices derived from open space “public hedonic models” should be interpreted in the context of the broader market for land, not as the agency’s willingness to pay. The work has implications for open space preservation policies in urbanizing regions. © 2012 Elsevier GmbH. All rights reserved.

Introduction Urban forests provide ecosystem services than can enhance the well-being of nearby residents and increase surrounding property values (Anthon et al., 2005; Præstholm et al., 2002), but forested open space properties are becoming increasingly scarce in rapidly developing metropolitan areas (Alig et al., 2004). Fee simple land purchases and the purchase of development rights have become attractive, though not the only, policy tools for protecting forested open space in urbanizing regions (Harper and Crow, 2006). Public agencies must decide which properties and what locations will best meet the public’s need for urban forests and open space. Information on the value of the public benefits of urban forests and open space as well as the acquisition costs can lead to more effective conservation decisions (Nordman and Wagner, 2010; Ferraro, 2006; Ando et al., 1998; Babcock et al., 1997). Economists and policy scholars have a variety of analytical tools for estimating non-market benefits, such as travel cost models, contingent valuation method, and hedonic models. Several studies have been published in which the hedonic technique was used to analyze public land and easement purchases and afforestation

∗ Corresponding author. Tel.: +1 616 331 8705; fax: +1 616 331 3446. E-mail address: [email protected] (E.E. Nordman). 1 Tel: +1 315 470 6971; fax: +1 315 470 6535. 1618-8667/$ – see front matter © 2012 Elsevier GmbH. All rights reserved. doi:10.1016/j.ufug.2011.12.004

projects (Lynch and Lovell, 2002; Anthon et al., 2005; Larkin et al., 2005; Mashour et al., 2005; Loomis et al., 2004, 2006). We expect that more applications of hedonic models in public land purchases will appear as more communities adopt open space preservation policies. Therefore it is critical to understand how such models can be applied and how their results should be interpreted. In this paper we provide guidance to urban planners, policy researchers, and other practitioners on how to apply and interpret hedonic models of public purchases in order to avoid costly policy mistakes. We analyze the techniques used to estimate property values of preserved forested open space in an urbanizing landscape and illustrate some of the challenges associated with “public hedonic models” using a case study in the Town of Brookhaven, on Long Island, New York, USA. The paper provides an example on how hedonic modeling can be applied in urban land preservation, discusses some limitations of the technique, synthesizes work from related fields in environmental economics, and provides some suggestions for moving forward in light of these limitations. In the following section we present the conventional theory of hedonic modeling, as developed by Rosen (1974), given perfect competition and then discuss the implications of hedonic modeling given imperfect competition which may describe more accurately the markets of public urban forest open space purchases. Following that we review the small but growing body of literature regarding economic models of public open space preservation. We use these studies to illustrate a number of challenges with respect to the

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theory of hedonic pricing. In the final section we propose a refined interpretation of how environmental attributes explain variation in open space acquisition costs through a case study in the Town of Brookhaven, NY (“Brookhaven”). Methods Theory: Rosen’s hedonic model Rosen (1974) formalized the theory supporting the hedonic model and laid the foundation upon which current hedonic models are built. Rosen’s hedonic theory states that the market price of a differentiated consumer good is a function of its utility-bearing characteristics. A hedonic model is essentially a regression model that links a good’s price, the dependent variable, with its various attributes, the independent variables. To describe it more formally, let C be vector of characteristics of good X, such that X can be described by its characteristics xi = xi (ci1 , ..., cij , ..., cin ) where cij is the jth quality of model i of good X. The hedonic price function then is px = px (ci1 , . . . , cij , . . . , cin ).

(1)

The partial derivative of the hedonic regression equation with respect to any characteristic in the model reveals that characteristic’s implicit price (Freeman, 2003). That is, the resulting regression model coefficients describe how a small change in one of the attributes affects the good’s price, all else being equal. The hedonic price function is identical to the market price. As the title of Rosen’s article suggests, pure competition is a key assumption. For only under the condition of pure competition will the model produce the desired results: the buyer’s willingness to pay for the good’s characteristics (Rosen, 1974). Pure competition leads to the following conditions. First, buyers are price takers, that is, they add zero weight to the market. Second, buyers and sellers make decisions that maximize their utility and their perfect matching leads to equilibrium prices. Third, the distributions of buyer preferences and seller costs determine the market clearing price (Rosen, 1974). In addition to these conditions, buyers are assumed to purchase only one unit of the consumer good. However, this assumption may be relaxed if the multiple units are purchased to satisfy different needs (for example, a primary residence and vacation home) (Palmquist, 2005). Rosen (1974) described the market as a series of bids and offers from buyers and sellers, respectively. Under the pure competition assumption, the buyer’s bid curve ( i ), or marginal willingness to pay, is tangent to the market price curve p(Ci ). Likewise, the seller’s offer curve (i ), or marginal willingness to accept, is also tangent to the market price curve p(Ci ). Under equilibrium conditions, the maximum bid and minimum offer curves have equal slopes and “kiss” at quantity Ci * (Fig. 1). The resulting locus is the implicit price for Ci *. Under equilibrium conditions, the marginal willingness to pay is equal to the maximum willingness to pay. In thick markets with many buyers and sellers, any consumer or producer surplus is eliminated (Harding et al., 2003). The standard hedonic model assumes that the market adjusts instantaneously to changes in demand or supply, including new entrants to the market (Freeman, 2003).

Fig. 1. Hedonic prices without excess surplus (Harding et al., 2003).

Freeman (2003) noted that markets may not actually react instantaneously to the entry of new buyers. If the market does not adjust instantly, the bid and offer curves will not kiss the hedonic function. The implicit price resulting from the hedonic model will not accurately reflect the buyer’s willingness to pay. Cotteleer et al. (2008) and Harding et al. (2003) described how market imperfections can distort the hedonic function. Cotteleer et al. (2008) demonstrated that farmers tend to buy parcels that are close to their existing farms. There are relatively few parcels for sale within the local area at any one time. The thin market for local farmland lacks perfect competition and the land prices deviate from the competitive market price. The lack of competition prevents the bid and offer curves from coming together at the hedonic price function. Hedonic models of all kinds of real estate transactions can be compromised by thin markets and other distortions. Knight (2008) summarized many of these challenges, yet noted that most hedonic models for housing ignore them. As Harding et al. (2003) note, the bid curve floats above the hedonic price function and the offer curves hang below (Fig. 2). The difference between the two curves at the point at which their slopes are equal is the excess surplus. This excess surplus is divided between the buyer and seller (Harding et al., 2003). In such cases the implicit price defined by the market will not be equal to the buyer’s maximum bid or maximum willingness to pay. The buyer’s maximum willingness to pay would be greater than the observed implicit price, which is the minimum price for the attribute the buyer must pay based on the market. Under these conditions, the model’s coefficients could not be properly interpreted as the maximum willingness to pay. It is reasonable to expect that hedonic models of public land purchases may encounter the same challenges. Like the farmers

Imperfect competition and market disequilibrium A number of factors can lead to imperfect competition and market disequilibrium, such as non-instantaneous changes to new entrants (Freeman, 2003), thin markets and differences in bargaining power (Harding et al., 2003; Cotteleer et al., 2008). Imperfect competition can lead to problems interpreting an implicit price as a maximum willingness to pay.

Fig. 2. Hedonic prices with excess surplus (Harding et al., 2003).

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in Cotteleer et al. (2008), public agencies (and local land trusts) are usually looking to buy parcels close to existing open space properties, parcels with peculiar features, such as a rare geologic formation or a threatened species, or parcels that have a desirable attribute, such as a wetland. The market for such properties is likely to lack perfect competition and the hedonic model may not accurately reflect the agency’s willingness to pay. This idea is explored in greater detail in the “Estimation Results” section. Finally, it is well recognized that public goods like those derived from public lands as well as public open space itself are undersupplied by markets; however, a discussion of this literature is beyond the scope of this article and modeling this undersupply was not the primary purpose of the hedonic model presented below. Public land purchases As urban forested open space in metropolitan areas becomes scarcer, public agencies have sought ways to preserve these remaining properties and the ecosystem services they provide. A number of economists have used hedonic models to estimate implicit prices for land attributes based on public purchases of land or development rights or public afforestation projects (Lynch and Lovell, 2002; Anthon et al., 2005; Larkin et al., 2005; Mashour et al., 2005; Loomis et al., 2004, 2006). The effect of public open space purchases or afforestation projects on residential housing values is a relatively straightforward hedonic application (for example Anthon et al., 2005; see also McConnell and Walls, 2005 for a review). However the use of public purchases themselves as the object of hedonic modeling presents some challenges. A public agency is just one of many buyers of vacant land within a market, most of whom are interested in development. That the agency purchases multiple properties does not pose problems with the hedonic theory because each property is assumed to meet a different need and be in a different location, for example, improving water quality or providing unique recreation opportunities. However, the focus on public land likely violates the perfect competition and market equilibrium assumptions. The market may not be in equilibrium because of new entrants and thin local markets for open space properties. Public agencies have always acquired land for a variety of reasons, but the land markets may not have adjusted to the recent surge in conservation purchases. The public agency may also be targeting those properties with attributes such as wetlands that few private buyers are interested in purchasing. The relatively small group of potential buyers may not adequately reflect the diversity of conservation values, as espoused by the public agency. The public buyer’s eclectic preferences for conservation may enable them to gain a potential surplus in such a thin market. In addition, if the sellers are not able to segment the market so as to differentiate among buyers, then the implicit prices would not represent the maximum willingness to pay for a buyer with eclectic preferences. Again, the implicit prices would reflect the current market. Buyers with eclectic preferences would capture the additional surplus. Cotteleer et al. (2008) describe a thin-market situation in local farmland markets. These authors show that the bid and offer curves are not tangent to one another in thin markets. Another problem, not related to market equilibrium, is one of sampling and statistical inference. Hedonic models use market prices to estimate the maximum willingness to pay for a characteristic of buyers across that market. The market price is determined by both private and public buyers. A hedonic model that includes only public purchases amounts to a non-random sample of all purchases in the market. Hedonic models in general can show sample selection bias because they are based on properties that have sold, not on all properties in the market area (Jud and Seaks, 1994). For this and the market equilibrium problems, implicit prices

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derived from hedonic models of public purchases cannot be interpreted as the agency’s equilibrium willingness to pay for a land attribute. These challenges do not mean that a hedonic approach cannot be applied to public land purchases. Rather, it demands that the expected coefficient signs and resulting implicit prices be carefully considered and interpreted. Under some conditions, a systematically biased marginal willingness to pay can be used to determine an upper or lower bound of the characteristic’s implicit price (Freeman, 2003). A property value model, as opposed to a true hedonic model, can be used to explain variation in acquisition cost based on land attributes without estimating willingness to pay (Wichelns and Kline, 1993). However the expected coefficient using the public agency’s preferences may not be the same as the expected coefficient using the broader market’s preferences. This can lead to unexpected results, but which are consistent with the theoretical treatment above. The problems are most obvious when the coefficients have signs that are opposite of what was expected based on the public agency’s stated preferences. The following paragraphs elaborate on this issue. A number of researchers have estimated implicit prices for land attributes for public land or easement purchases (Lynch and Lovell, 2002; Larkin et al., 2005; Mashour et al., 2005; Loomis et al., 2004, 2006). From the purchasing agency’s perspective, any variable that brings conservation benefit would be expected to have a positive sign. In other words, the agency would have a positive willingness to pay for ensuring that wetlands, endangered species, or unique geological features are preserved. However, these same attributes may be valued differently by private buyers who dominate the vacant land market. The presence of wetlands or endangered species restricts building which would reduce the market price for such parcels and in turn, this would be reflected in the implicit prices for these attributes. Loomis et al. (2004, 2006) analyzed public open space purchases in Colorado and coined the term “public hedonic model” for such analyses. In their description of the public hedonic model, Loomis et al. (2004) concluded that “. . .the resulting prices of attributes reflect the public’s marginal willingness to pay for these attributes” (p. 84). The authors acknowledged that public and private buyers have difference motivations for their purchases. Loomis et al. used supply-side and opportunity cost variables in their public hedonic model to account for that difference. In their original public hedonic model (2004), Loomis et al. found that all of their environmental variables had the expected positive regression coefficients. In a subsequent analysis (Loomis et al., 2006) wetland and other variables were included in the similar public hedonic model. The authors had ambiguous expectations on the sign of the wetlands variable and noted the tension between public and private buyers. The presence of wetlands had a negative model coefficient which they interpreted as a negative implicit price, or willingness to pay. Loomis et al. (2006) concluded that “the low opportunity cost to landowners appears to offset the increased value to open-space buyers” (p. 197). In this case, the negative coefficient clearly does not reflect the public agency’s maximum willingness to pay for wetlands. Rather the negative coefficient, as Loomis et al. correctly conclude, is the result of the opportunity cost to landowners. Mashour et al. (2005) studied conservation easements in Florida. Their hedonic model incorporated nine explanatory variables, including percent of land in wetlands. The State of Florida, the purchasing entity, has a clear preference for protecting wetlands and presumably would be willing to pay a premium for wetland properties. The authors however, used private market preferences for their expected signs, namely a negative sign for wetlands. The resulting coefficient did have a negative sign.

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Fig. 3. Study area showing open space property acquisition cost (2005$).

These authors pointed out the benefit of this information for bargaining with the state over easement prices. Mashour et al. (2005, pp. 779–780) stated Also, a value for wetlands may be initiated by incentives from agencies. If agencies are interested in having landowners preserve their wetlands, a value must be placed on them. Until there is a stated incentive for asking landowners to protect their wetlands, much less a disincentive as illustrated in this study, wetlands will continue to be lost. They misinterpret the market-based implicit price for the agency’s willingness to pay for wetlands. This is an example of the confusion generated by using public purchases to estimate market implicit prices. The implicit prices do not accurately reflect the agency’s willingness to pay. Larkin et al. (2005) analyzed public purchases within Florida’s Conservation and Recreation Lands (CARL) program. The hedonic model included a number of land attributes, such as the number of elements designated as Florida Natural Areas Inventory (FNAI) features within a project area and priority criteria for inclusion in the CARL program. The agency has a clear and documented preference for purchasing properties that have FNAI elements and meet the CARL criteria. Yet the hedonic model of CARL purchases showed that variables for FNAI elements and two of the priority criteria actually had negative coefficients. The results are inconsistent with the interpretation of implicit price as a maximum willingness to pay. Like Mashour et al. (2005), Larkin et al. (2005) interpreted the results from the perspective of a typical hedonic model, but this leads to confusion between agency and private market preferences. They noted correctly that “. . .the resulting implicit prices should be considered lower-bound estimates of the total public or social value of these lands” (Larkin et al., 2005, p. 128). However, they state Moreover, the estimated implicit prices of natural land attributes and pressures to convert the open-space lands will reflect the shadow value of preservation as opposed to the value inferred from nearby residential or agricultural uses (Larkin et al., 2005, p. 116). As demonstrated above, the estimated implicit prices do not reflect the shadow value of preservation. Larkin et al. (2005) also implied that the state places a higher priority on natural elements than on historical elements because of their respective implicit prices. The implicit prices based solely on public purchases are

unreliable indicators of the agency’s relative priorities and using them as such could lead to inefficient conservation policies. Lynch and Lovell (2002) used only easement purchases for their hedonic model of agricultural land preservation programs in Maryland. Conservation easements are typically purchased by public agencies, land trusts notwithstanding, so the public purchases are in effect the entire easement market. As such, the results of Lynch and Lovell’s (2002) model may be a more accurate reflection on an agency’s willingness to pay for environmental characteristics. A Long Island case study In this section, we present an illustrative hedonic analysis of public land purchases in the Town of Brookhaven, on New York State’s Long Island. The objective is to illustrate the challenges of interpreting the hedonic model coefficients in light of the theoretical limitations described above. We estimated a hedonic model of public urban forested open space purchases and compared the results with Brookhaven’s own documented preferences. Brookhaven evaluated each candidate property using a checklist called a Parcel Ranking Sheet (PRS). A candidate property received points on the PRS based on the presences of key environmental and social attributes, such as the presence of wetlands (see Section 4.4 for details). If we assume that the market equilibrium conditions are met and that the public hedonic model’s results can be interpreted as estimates of the agency’s willingness to pay, then the coefficients should have the same sign, if not magnitude, as the documented preferences in the PRSs. Negative implicit prices for attributes that contribute positively to the PRS score would indicate that excess surpluses exist that can be captured by the agency (Fig. 2), and that the implicit prices should not be interpreted as the agency’s willingness to pay. While other hedonic models of public open space purchases have used land evaluation criteria as model variables, our work is unique in the explicit comparison between the regression model coefficients and the PRS stated preferences. Study area The Town of Brookhaven in Suffolk County, New York, lies roughly 60 miles east of Manhattan on eastern Long Island (Fig. 3). Brookhaven’s population grew to more than 450,000 in 2000 from less than 50,000 in 1950. This tremendous growth has changed Brookhaven’s character from a largely agricultural region to one

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Fig. 4. Study area showing open space property Parcel Ranking Sheet (PRS) scores.

of sprawling residential and commercial development. Full buildout of all available open space is expected by 2025 (Regional Plan Association, 2004). Town officials feared that the growing population would strain the area’s environmental resources, in particular the drinking water aquifer below the town. Town officials, with voter approval, implemented a land acquisition program to preserve what open space remains (Town of Brookhaven, 2004) (Figs. 3 and 4). The Carmans River corridor, one of Brookhaven’s treasured environmental resources, connects the South Shore Estuary Reserve with the Central Pine Barrens, a unique complex of ecosystems occupying the eastern half of Brookhaven and two other townships in eastern Suffolk County. The pine-oak forests, forested wetlands, and tidal marshes of the Carmans watershed support a native brook trout population, more than 40 other fish species, and such threatened species as osprey (Pandion haliaetus) and eastern mud turtle (Kinosternon subrubrum) (New York State Department of State Division of Coastal Resources, 2007). New York State has designated several sections of the river as Scenic and Recreational Rivers (US Fish and Wildlife Service, 1997). The Central Pine Barrens region is divided into two development zones: a Core Preservation Area of undeveloped pine barrens, and a Compatible Growth Area in which appropriate patterns of development are allowed (Central Pine Barrens Joint Planning and Policy Commission, 2007). The western portion of Brookhaven, outside the Central Pine Barrens, is heavily suburbanized. As of 2000, 63% of Brookhaven’s land area was classified as residential, commercial, or industrial, and another 34% was either protected or unsuitable for development. The remaining 3% (5336 acres) is available for development. Half of this developable acreage was projected to be developed by 2010, and further reduced to just over 1000 acres by 2020 if the trends of the last 40 years continue (Regional Plan Association, 2004).

Property cost (cost) The purchase cost for each project was the hedonic model’s dependent variable. A project refers to one or more parcels that were purchased together. Most projects consisted of only a single parcel; others contained multiple parcels, as in a subdivision. It was not possible to assign purchase costs to individual parcels in a project. Parcels within a project were usually contiguous, though in rare cases they were not. Cost data were supplied by Brookhaven.

Thirty-five project purchases were recorded from 2001 through 2005 for which complete PRS and cost information was available. Acquisition costs were adjusted to 2005 dollars using the Consumer Price Index for housing (all U.S. city average, Series ID: CUUR0000SAH). The real estate market on Long Island was especially strong during this time and raised concerns about the validity of using multiple years’ sales in a single data set. A Chow test was performed in SPSS to test whether the regression parameters (expressed as 2005 dollars) were equal across years. The Chow test failed to reject the null hypothesis that regression parameters were equal across years (F = 0.474, p = 0.75, N = 35), so the data could be treated as one set. The data set is relatively small, but other hedonic models of public purchases have used data sets of similar size. For example, Wichelns and Kline (1993) used 34 observations in their model of easement purchases. Larkin et al. (2005) used 65 public open space purchases across the entire state of Florida and their model included 23 different variables. The number of observations in our dataset is appropriate for the focused geographic area and the limited number of model variables. The mean cost for an open space project in the data set was $1,112,483, ranging from about $10,000 to $9,000,000. The mean cost per acre of $89,034 was consistent with a recent analysis of residential development in Brookhaven which assumed a vacant land cost of $150,000 per acre (Long Island Builders Institute Inc, 2004). The mean purchased property size was 12.0 ha (29.6 ac).

Explanatory variables (documented preference set) Brookhaven’s Division of Land Management evaluated each nominated project using a documented checklist called the PRS. Each PRS comprised 55 variables in six categories: Physical, Size, Location, Community Values, Aesthetic Values, and Farmland. Physical attributes included the presence of a unique geological landform (e.g. a kettle hole) or a rare ecological community (e.g. a red maple swamp). Size is simply the property size in acres. Location variables described the property’s adjacency to public land, location within a flood zone, and other spatial attributes. A property’s public benefit, such as recreation opportunity and preventing an incompatible land use, was described in the Community Values category. Aesthetic values described a site’s views from major roads, water views, and other scenic vistas. Farmland variables included adjacency to active farms and highly productive agricultural soils. A property received points for having a key feature, such

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Table 1 Sample checklist from a Parcel Ranking Sheet (PRS). Each PRS contains six categories (Physical, Size, Location, Community Values, Aesthetic Values, and Farmland) and a total of 55 variables. Parcel Ranking Sheet

Part II (detailed) Point value

I. Physical characteristics A. Does the property contain a unique geological landform such as a 5 (1) A kettlehole 5 (2) A dune 5 (3) A bluff Points B. Does the site contain wetlands identified as 50 (1) Intertidal marsh 50 (2) Freshwater wetlands 35 (3) High marsh 25 (4) Adjacent area, within 150 ft of a wetland Points

as a freshwater wetland (Table 1). A higher PRS score indicates higher desirability for preservation. This is a standard, though not necessarily the best, method for evaluating properties for conservation purposes (Nordman and Wagner, 2010). A single project, the unit of PRS evaluation and purchase, could include multiple parcels. The number of parcels within a project ranged from 1 to 47, with a mean of 5.2 parcels per project. As with Cost, it was impossible to tease apart the environmental characteristics for each individual parcel within a project. All the information in the PRSs and used in the hedonic model were completed by the same individual at the Brookhaven Division of Land Management (D. Cole, personal communication). This ensured consistency across site visits. The data on environmental attributes were collected directly from Brookhaven’s PRSs. No interpretation or aggregation was performed at this stage. The 55 PRS variables were clearly too many to include in the regression model given the relatively small number of observations. Factor analysis (SPSS Inc., 2005) was used to select variables for inclusion in the regression analysis. The factor analysis data set included all variables from the PRS coded with their point values. Points ranged from zero if the attribute was absent to 50 for intertidal marshes and freshwater wetlands. Properties received one point for each acre in size. Factor analysis with varimax rotation resulted in eight components. The variable most associated with each component was then chosen for inclusion in the hedonic model. The eight variables selected by factor analysis represent four

of the six PRS categories: physical, community values, aesthetic values, and farmland. Property size was not among the variables most associated with the components, nor was a location variable. However property size is a theoretically important variable and was chosen for inclusion in the hedonic model. The hedonic model data set included the variables identified in the factor analysis, but the data were coded as dummy (binary) variables. Most of the environmental attributes occur discretely, for example, a property either has water views or it does not. In the PRS, a property cannot receive more points for better water views. It therefore is logical to transform the data to a binary form for hedonic analysis. The property size variable (Size) was the area (ha) of the property that was actually purchased. The PRS sheets included information on the size of candidate properties, but the PRS size sometimes differed from what was actually purchased. Size was entered into the model as a log-transformed continuous variable. Table 2 defines the variables and lists the summary statistics and expected signs. All of the model coefficients are expected to have positive signs because these attributes contribute positively toward the PRS score. Because of the positive PRS score, we can assume that Brookhaven has a preference for these attributes and would be willing to pay a premium to secure them. As part of the exploratory data analysis, total property acquisition cost (Cost) and cost per acres (CostAcre) were tested for correlation with PRS total score (Score). Hedonic model specification Hedonic model theory does not set restrictions on the choice of hedonic price functional form as long as the model’s first derivative with respect to an environmental amenity (disamenity) is positive (negative) (Freeman, 2003). The preceding section showed that one environmental characteristic can be viewed as an amenity by some (e.g. public buyers) and a disamenity by others (e.g. private buyers). For this analysis, we follow the hedonic model specification methods used by the previous hedonic analyses of open space. The hedonic price functional form was specified using linear, log-linear, and log–log forms, but only the log–log form is presented here (Eq. (2)): ln C = E␤E + ln S␤S + ␧

(2)

where C is the (n × 1) vector of acquisition costs (Cost) and n is the number of observations (35); E is an [n × (k + 1)] matrix of

Table 2 Explanatory variables for the hedonic model of Brookhaven’s open space purchases. Category

Physical

Variable

Description

Mean (S.D.)

Hypothesized sign

Cost

Acquisition cost (2005 $) (dependent variable)

$1,112,483 (1,681,942)

n/a

Kettle Hole

The property contains a kettle hole depression, a unique glacial landform; 1 if present, 0 otherwise The property contains some other type of unique glacial landform; 1 if present, 0 otherwise The property contains a freshwater wetland; 1 if present, 0 otherwise The area of the purchased property (hectares)

Other Landform Freshwater Wetland Size

Size

Community values

Passive Recreation

Incompatible Use Aesthetic values

Road View Water View

Farmland

Farm Road

The property provides an opportunity for the establishment of a passive recreational area (nature preserve, greenbelt) Acquisition will prevent development that is incompatible with existing land uses; 1 if present, 0 otherwise The site contains important views located along major road corridors; 1 if present; 0 otherwise The site has potential for water view, or public access to a water view; 1 if present, 0 otherwise The site is farmland and has long frontage along a major roadway; 1 if present, 0 otherwise

0.11 (0.32)

Positive

0.17 (0.38)

Positive

0.57 (0.50)

Positive

11.98 (25.51)

Positive

0.80 (0.41)

Positive

0.11 (0.32)

Positive

0.20 (0.41)

Positive

0.40 (0.50)

Positive

0.14 (0.36)

Positive

E.E. Nordman, J. Wagner / Urban Forestry & Urban Greening 11 (2012) 179–186 Table 3 Hedonic model parameter estimates, log-linear form with ln Cost as the dependent variable. Category

Variable

ˇ

SE

p-Value

Constant

11.40

0.41

0.00*

Physical

Kettle hole Other Landform Freshwater Wetland

−0.05 0.68 0.08

0.37 0.30 0.20

0.90 0.03* 0.69

Size

ln Size

0.59

0.09

0.00*

Community values

Passive Recreation Incompatible Use

0.67 −1.17

0.33 0.37

0.05* 0.01*

Aesthetic values

Road View Water View

0.24 −0.29

0.29 0.24

0.43 0.22

Farmland

Farm Road

0.14

0.38

0.72

2

R = 0.90, *

2 Radj

= 0.86, SE = 0.58, F = 23.58, p < 0.01, N = 35.

Significant at ˛ = 0.05.

observations on k on-site environmental attribute dummy variables derived from the Parcel Ranking Sheets; ␤E is the [(k + 1) × 1] vector of parameter estimates for the on-site environmental attributes (E); S is the (n × 1) vector of a continuous property size variable (Size); ␤S is the (n × 1) vector of parameter estimates for the continuous size variable; and ␧ is an (n × 1) vector of error terms which are assumed to be independent and identically 2 distributed. The Radj was calculated for the specified model to determine how the attributes contribute to variation in acquisition cost. The dependent variable in hedonic models often exhibits spatial autocorrelation, which can result in unbiased but inefficient OLS estimators and biased variance estimates. If left uncorrected spatial autocorrelation in the dependent variable can affect both the precision of the parameter estimates and the reliability of hypothesis tests (Dubin, 1998). We tested for spatial autocorrelation in Cost using the Moran’s I index in ArcGIS 9.1 (ESRI, 2005). No spatial autocorrelation was detected. Estimation results Parcel Ranking Sheet total score (Score) was not significantly correlated with either acquisition cost (Cost) (r2 = 0.10, p = 0.55, N = 35) or cost per acre (CostAcre) (r2 = −0.11, p = 0.52, N = 35). The hedonic model estimation results are presented in Table 3. The log–log regression model explained more than 85% of the variation 2 = 0.86), which is consistent the performance of sevin cost (Radj eral previous hedonic models of open space (Wichelns and Kline, 1993; Lynch and Lovell, 2002; Loomis et al., 2004; Mashour et al., 2005). Four of the nine explanatory variables were statistically significant (p ≤ 0.50). Three variables had unexpected negative signs, though only one of them (Incompatible Use) was statistically significant. Following Wichelns and Kline (1993) and Loomis et al. (2004), we illustrated each statistically significant independent variable’s elasticity, that is, the percentage change in the dependent variable associated with a one-unit increase in an independent variable, all else being equal. The dependent variable was log-transformed, so each dummy variable coefficient (␤E ) was transformed using the exponential function ((eˇ E) − 1) to yield the elasticity for that variable. The presence of a unique glacial landform other than a kettle hole (Other Landform) was associated with a 97% increase in the property cost ((e0.68 ) − 1 = 0.97). The presence of passive recreation opportunities was associated with a 95% increase in cost. The Incompatible Use variable was associated with a 69% decrease in property cost.

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Discussion and conclusion Correlation and regression estimates PRS score (Score) and acquisition cost (Cost) were not correlated. This suggests that the characteristics Brookhaven looks for in a candidate property are not necessarily those that are valued by the broader vacant land market. This is a valuable lesson for Brookhaven: the town is avoiding the “crown jewels” problem of open space preservation. In situations where conservation benefits are closely tied to purchase price, using a benefit score as the sole criterion for ranking candidate properties can lead to less costeffective choices (Babcock et al., 1997). Our data show that this is not the case in Brookhaven. The regression model is statistically significant, indicating that the variables explain a reasonable amount of variation in acquisition cost. For land managers looking to understand what factors influence acquisition costs, regression analysis with property characteristics is an effective tool. Implications for Brookhaven and public hedonic models The regression coefficients do explain variation in acquisition cost, but managers should use caution in interpreting their significance as implicit prices, that is, estimates of the agency’s willingness to pay. If the hedonic model of public purchases did reflect an agency’s willingness to pay, we would expect all environmental characteristics to have positive coefficients. Our case study of Brookhaven, like other models using public purchases, has shown an inconsistency here. All of the variables contribute positively to PRS scores. Therefore we expected all variables to show positive regression coefficients. The unexpectedly negative regression coefficient for Incompatible Use contradicts Brookhaven’s preferences as stated in the PRS. The resulting implicit price estimates cannot be interpreted as a reliable measure of Brookhaven’s willingness to pay for the land attributes. The Incompatible Use variable highlights the problem. If acquisition of the site would prevent development that is incompatible with existing land uses, then the property earns 10 points on the PRS. Brookhaven has a clearly documented preference for such properties, yet the Incompatible Use coefficient is not positive. The positive regression coefficients resulted when Brookhaven’s preferences for open space properties aligned with those of private buyers. Properties that have recreation opportunities are generally dry and without steep slopes and would be desirable to the broader vacant land market. Similarly, farm properties with long frontages along major roadways would be attractive for commercial development or subdivisions. Attributes with negative coefficients are those that are not desirable to most private buyers, especially residential developers. The hedonic model estimates how the market, not a small subset of buyers, values a good’s characteristics. In spite of these challenges, hedonic models of public urban forested open space or easement purchases can provide valuable information to the purchasing agency, especially when combined with ranking criteria like PRS scores. Many agencies, including Brookhaven, collect land attribute data before making a purchase offer. The agency can use a hedonic model with land attribute and price data from previous sales to estimate the purchase cost of newly evaluated candidate properties. Estimated costs could be used to screen out properties that are obviously too expensive, or could be combined with real estate appraisals to improve purchase negotiations, and, if purchased, could be used to update the model coefficients. Perhaps most importantly, the differences between the estimated implicit prices and PRS or similar scores may help identify the most cost effective properties (Wichelns and Kline, 1993;

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Larkin et al., 2005; Mashour et al., 2005). For example, our model shows that Incompatible Use had negative effect on purchase cost, while Passive Recreation and Other Landform had positive effects on cost. Both sets of attributes provide similar benefit scores, yet Brookhaven could achieve those benefits at less cost by preferentially focusing on properties that would prevent development that is incompatible with existing land uses. High scoring attributes with negative implicit prices would be most desirable from this perspective (see Nordman and Wagner, 2010). Potential solutions to the problem The case study of the Town of Brookhaven on Long Island demonstrated the discrepancy between the implicit price estimates and the agency’s own stated preferences for open space attributes. An implicit price estimate from a hedonic model that includes only public land purchases cannot be reliably interpreted as the purchasing agency’s willingness to pay. It can, however, be narrowly interpreted as that attribute’s effect on the purchase cost. If a land manager desires to know the implicit price of environmental characteristics, the hedonic model must include all vacant land purchases in the area, both public and private. This technique will provide the maximum willingness to pay based on all participants in the market. The conservation agency’s effect on prices could be incorporated into such a model by including a “public purchase” variable. This variable could also interact with other environmental characteristics (for example, public × wetland). For example, Cotteleer et al. (2008) used variables to account for market power and characteristics of buyers and sellers for farmland in the Netherlands. This is an area that requires further investigation. Conclusion The case study of the Town of Brookhaven on Long Island demonstrated the discrepancy between the implicit price estimates and the agency’s own stated preferences for open space attributes. Care must be taken when developing hedonic models for open space. An implicit price estimate from a hedonic model that includes only public land purchases cannot be reliably interpreted as the purchasing agency’s willingness to pay. It can, however, be narrowly interpreted as that attribute’s effect on the purchase cost. If interpreted properly, the hedonic model can be used to estimate a purchase price of a candidate urban open space property and improve the cost effectiveness of open space preservation programs. The availability of the agency’s stated preferences, in the form of the PRS scores, offered a unique opportunity to compare these preferences to the regression model coefficients. Our findings have significance beyond open space preservation. Economists engaged in biodiversity conservation often use hedonic models, and these models could encounter challenges similar to the one we have presented here. Economists, such as those reviewed in Naidoo et al. (2006), have long advocated for cost effective approaches to biodiversity conservation. However disciplinary barriers still thwart the adoption of such approaches. Future work should focus on not only refining methods for identifying cost effective environmental conservation, but also overcoming the disciplinary or institutional barriers to such methods. Acknowledgements The authors thank Mr. Dennis Cole and the Town of Brookhaven Division of Land Management for the data on the open space program.

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