Hedonic Valuation of Land Protection Methods

Hedonic Valuation of Land Protection Methods: Implications for Cluster Development Robert W. Kling Colorado State University

T. Scott Findleyy Utah State University

Emin Gahramanov Deakin University

David M. Theobald Colorado State University

January 8, 2014 (First Draft: September 13, 2007)

Abstract This study estimates a generalized spatial hedonic pricing model to assess how residential property values are impacted by inclusion within cluster developments and by proximity to various types of protected land. The estimated model simultaneously controls for the spatial dependence of residential housing prices and for the presence of spatial autocorrelation. The sample includes 4,008 single-family housing sales transactions within the non-urban portions of Larimer County in northern Colorado. The empirical framework accounts for topographical diversity across the study region, as well as distinguishing between several distinct types of publicly and privately protected land. The key …ndings of the study are: (i) proximity to national or state park land and to city or county open space has a signi…cant positive impact on property values, while proximity to national forest land or to privately conserved land exhibits no signi…cant e¤ects; and, (ii) inclusion of a property within a cluster development decreases its value by 17 to 26 percent. These …ndings are robust to di¤erent estimation techniques and model speci…cations, which suggests important considerations for policymakers who design development rules and alternative land protection measures aimed at preserving open space in non-urban areas. JEL Classi…cation: Q51, R14, R31, R38 Key Words: hedonic valuation, cluster development, open space, spatial dependence, spatial autocorrelation This research was supported by USDA-CSREES contract 2003-35401-13801. The authors are indebted to George Wallace, Tawnya Ernst, and Sean Alley for their valuable assistance, and to Melissa Shelburne for assistance with the GIS programming/analysis. The authors also thank Robert Berrens, German Muchnik-Izon, and Ben Blau for helpful suggestions. The authors would like to acknowledge and thank Jim Payne and an anonymous referee for recommendations and constructive feedback during the peer-review process. Lastly, it should be noted that an earlier version of this manuscript was circulated under the title, “Hedonic Valuation of Land Protection Methods at the Rural–Urban Fringe: Implications for Cluster Development”. y Corresponding author: +001-435-797-2371; tscott.…[email protected]

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1

Introduction

In response to both urban and rural sprawl concerns, hundreds of local ballot initiatives have been approved across the United States, which legally support, …nance, and/or mandate open space conservation (Kline 2006). While tax-…nanced public acquisition of open space is one strategy, such e¤orts often face political and economic constraints on the acceptable tax burden. An alternative strategy operates through the local development planning process, called “cluster development”. Cluster development is characterized as having an approved number of residential housing units that are grouped together on land parcels or lots that are smaller in size and in closer proximity to each other than what residential zoning laws usually require. The remaining undeveloped land within the development is typically designated as open space for ecological, recreational, aesthetic, or agricultural purposes. An important unanswered question is how residential real-estate values are a¤ected by inclusion within cluster housing developments that are designed to provide open space that might be valuable to both the development residents and to the broader community. Several studies report that proximity to protected open space generates higher property values to homeowners (e.g., Kitchen and Hendon 1967; Weicher and Zerbst 1973; Correll et al 1978; Nelson 1988; Lee and Linneman 1998; Bolitzer and Netusil 2000; Lutzenhiser and Netusil 2001; Acharya and Bennett 2001; Smith et al 2002). Other studies have compared the impacts on property values resulting from open space that is simply undeveloped and open space that is protected from development for the long run (Geoghegan 2002; Irwin and Bockstael 2001; Irwin 2002; Geoghegan et al 2003). It is conceivable that a premium for protected open space is intrinsic to the values of properties within cluster developments. If they do provide su¢ cient internalized bene…ts to developers and eventual owners in the form of aesthetic and recreational opportunities in the protected space, then the market values of these developments would provide private motivation for developers to undertake cluster development. Yet in many areas, the cluster development approach to land management must be legally mandated and/or incentivized by policymakers, suggesting that private motives are small or non-existent. In such cases, mandated cluster development might impose signi…cant private costs without commensurate internalized bene…ts, as is often the case with imposed regulations (Cheshire and Sheppard 1989). Indeed, land management authorities frequently make appeals to perceived external bene…ts that will accrue to present and future citizens at-large, as rationale for such land-development policies. The present study examines whether open space conserved in cluster developments generates value for proximate homeowners. We consider the case of cluster development policy in Larimer County, Colorado where rural sprawl has received high attention by local land management authorities. Larimer County is a high-growth, high-amenity region of north-central Colorado, roughly 50 to 100 miles north of Denver. The county is bordered on the north by Wyoming and on the west by the Continental Divide. The county includes urban and rural areas, mountains and plains, and it is home to approximately 300,000 residents. The Land Use Code of Larimer County was modi…ed in the late 1990’s to require that all new residential housing subdivisions in non-urban areas be designed as cluster developments. Two types of cluster developments have been designated in the Code. One is known as a Rural Conservation Development (RCD), while the other is known as a Rural Land Use Plan/Process (RLUP). While both require that open space be preserved by private protective covenants or conservation easements, the two alternatives really di¤er only in what type of non-urban land is considered for subdivision and cluster development (Ernst and Wallace 2008; Wallace et al 2008). We employ a generalized spatial hedonic pricing model to estimate and examine the impact of cluster development practices in non-urban areas. More speci…cally, we measure the e¤ect of proximate protected lands of various types, in addition to and separate from the basic clustering

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e¤ect that has resulted from the creation of county-approved cluster developments. We use a sample of 4,008 non-urban single-family housing sales transactions from 2001 to 2004, and we employ a variety of model speci…cations. Our spatial hedonic model is “generalized” from the perspective that we are able to simultaneously control for the spatial dependence of observations and for spatial autocorrelation. We …nd that proximity to national or state park land and to city or county open space has a positive impact on property values, while proximity to national forest or to privately conserved land exhibits no signi…cant e¤ects. Although private conservation e¤orts do not have any measurable impact on property values in general, we do …nd that county-mandated cluster development lowers the value of an included property by 17 to 26 percent, depending on the model speci…cation. These …ndings suggest important considerations for developers, subsequent homeowners, and for policymakers who oversee policies that a¤ect land development and a property tax base.1 Yet, we acknowledge an important caveat with respect to our empirical …ndings and statistical inference: our estimated sample is comprised entirely of non-urban observations. As such, the possibility exists that cluster development might increase the values of included properties in urban areas where population densities are notably higher.2

2

Data

Larimer County, Colorado is topographically diverse from the perspective that the western portions of the county are very mountainous and are primarily comprised of Roosevelt National Forest and Rocky Mountain National Park. Indeed, the Continental Divide constitutes much of the western boundary of the county. However, ranch and farmland comprise much of the eastern portions of the county at much lower elevations. Over 50 percent of Larimer County is publicly owned, providing a wide spectrum of recreational opportunities for residents and tourists. The cities of Fort Collins and Loveland are the largest in the county and lie at the edge of the mountain-plain interface. The town of Estes Park and the smaller community of Red Feather are located high in the mountains to the west of Fort Collins and Loveland, while several other smaller surrounding towns, such as Wellington, Timnath, and Berthoud, are located on the plains in the more eastern portions of the county. Larimer County has experienced rapid commercial and housing development into unprotected open space (such as private agricultural and ranch land), but the county also contains signi…cant amounts of federal-, state-, county-, and city-protected open space. Our data are drawn from three distinct sources focusing on single-family residential properties only. Housing characteristics, as well as the most recent nominal sales price for each respective property, were obtained from Larimer County Assessor’s data. Demographic characteristics for each single-family residential property within our data set were obtained from Census 2000 of the U.S. Census Bureau. Lastly, the spatial attributes of interest were drawn from a GIS-based open space analysis package, known as the Colorado Ownership, Management, and Protection (COMaP) project of the Natural Resource Ecology Laboratory at Colorado State University. We categorized each property as urban, rural, or GMA. A property is de…ned as urban if it is located within an incorporated city limit, as GMA if the property is located within the county’s “Growth Management 1

Although some studies report that protected open space might increase a local property tax base (e.g., Geoghegan et al 2003), the evidence is inconclusive as to whether protected open space is capitalized into land values (e.g., Blakely 1991; Nickerson and Lynch 2001; Irwin and Bockstael 2001; Geoghegan 2002). 2 Geoghegan et al (1997) report that increased landscape fragmentation may have a negative or positive e¤ect on property values, depending on whether a property is located in an urban or rural area. Anderson and West (2006) …nd that properties with high population densities implicitly value proximity to parks by a factor of three.

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Area”, or as rural if the property is located outside of both incorporated cities and the GMA.3 For computational purposes and to focus on the main objectives of this study, we narrowed down our data from approximately 36,000 properties with sales transactions to exactly 4,008 observations to include only those that have a rural or a GMA designation. We thereby focus our statistical analysis on those parts of the county which can, overall, be considered the urban-rural interface. This also concentrates our econometric analysis on those parcels with a sales transaction within the years 2001 to 2004 in order to control for possible macroeconomic e¤ects in housing markets that might be expected over larger periods of time. Furthermore, we used the local Denver-BoulderGreeley, CO Consumer Price Index of the U.S. Bureau of Labor Statistics to convert all nominal sales prices into July–December 2004 housing prices in order to control for the e¤ects of in‡ation.4 In the case of repeated sales transactions for a particular property during the sample period, we included the most recent transaction only. Moreover, we include yearly dummy variables to control for varying market conditions over the four-year period of the sample (2001, 2002, 2003, where 2004 is the default). Our …nal list of housing characteristics acquired from Larimer County Assessor’s data include parcel square feet (ParcelFT2 ), building square feet (BldgFT2 ), …nished basement square feet (BsmntFinFT2 ), garage square feet (GarageFT2 ), number of bedrooms (Bedrooms), age of the home (Age), and a dummy variable for central air conditioning (DummyAC).5 We also include, as neighborhood characteristic variables, the following demographic data from Census 2000 at the block group level for each observation: median household income (MedHHInc), percent of the census block group that is white (% White), median age of the population (MedAge), housing density (HousDens, units/km2 ), and percent of the properties that are renter-occupied (% RentOcc). COMaP is the most comprehensive, detailed, and up-to-date spatial database about various types of open space protection by federal, state, county, and city governments as well as nongovernmental and privately protected lands in Colorado. Using GIS software we computed Euclidean distances, measured in meters, from each single-family residential property in the sample to the closest location of each respective type of open space documented within COMaP. A partial, non-exhaustive list of the speci…c types of publicly protected open space includes city parks, city dog parks, city open space, city natural areas, city or county golf courses, county open space, county natural areas, state parks, state wildlife areas, state …sheries, state habitat areas, national forest land, and national park land.6 Distance to various types of city or county open space are summarized with the City/CountyED variable, distance to national forest land is summarized with the NForED variable, and Euclidean distance to national park, state parks, or state wildlife lands are summarized with NPark/SPark/SWldED. In addition to publicly protected lands, we also computed Euclidean distance from each observation in our data set to privately protected land held by non-governmental organizations, private land trusts, or to open space that is associated with cluster developments. This distance measure is summarized as the NGO/Trust/PrProtED variable. As an alternative to Euclidean distance, we employ several dummy variables that indicate the proximity of a single-family residential property to di¤erent types of protected open space. For example, we use a proximity dummy variable that measures whether city or county open space 3 The Growth Management Area (GMA) is the creation of an intergovernmental planning cooperation e¤ort and is essentially an agreed band of county land that closely surrounds the cities and is likely headed for development and/or annexation. 4 The Denver-Boulder-Greeley, CO CPI is listed in semi-annual increments by the U.S. Bureau of Labor Statistics. 5 We narrowed down our list of parcel characteristics using a correlation coe¢ cient, whereby we eliminated potential regressors with a correlation coe¢ cient greater than 0.6 to reduce the risk of collinearity in the estimation. 6 Euclidean distance is but one type of distance measure with which one might attempt to capture the e¤ects of open space protection on housing prices. An alternative measure might be that of driving distance that could potentially capture access bene…ts to open space.

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exists within a half-kilometer radius extending in any direction from each property (DCity/County 0.5km; see also DNGO/Trust/PrProt 0.5km for proximity to privately protected lands, DNFor 0.5km for proximity to national forest, and DNPark/SPark/SWld 2km for proximity to national or state park lands).7 Additional proximity dummy variables measure whether di¤erent types of open space exist within a concentric band of half a kilometer to two kilometers (DCity/County 0.5km-2km and DNFor 0.5km-2km) and within a concentric band of two kilometers to …ve kilometers (DNPark/SPark/SWld 2km-5km). Lastly, but of particular importance, we include a dummy variable that indicates whether a particular single-family residential property is part of a cluster development (DummyRCD/RLUP for Rural Conservation Development or Rural Land Use Plan/Process).8 In order to control for possible intra-county di¤erences in the local real estate market (di¤erences in prices that are due purely to di¤erences in locations within the county), we classify observations in our sample with two additional dummy variables (EstesDummy and SouthDummy). The EstesDummy includes those observations that are in the mountain areas near Rocky Mountain National Park and the town of Estes Park, whereas the SouthDummy includes those properties that are located in the southern areas of the county near Loveland and Berthoud, with shorter commute time to Denver. The default location is the northern plains along with some northern mountain areas, including those areas that are in the vicinity of the city of Fort Collins.

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Spatial Hedonic Pricing Models

Following Rosen (1974) on hedonic pricing theory, let the price of a house be a function of its various attributes when the housing market is in equilibrium. Formally, P is a n 1 vector of the natural logarithm of housing prices, where n denotes the number of observations. S is a n k matrix of structural characteristics. N is a n l matrix of neighborhood characteristics. L is a n m matrix of locational or spatial characteristics. The objective is to estimate a hedonic price function, P = f (S; N; L; ; ; ), (1) where , , are the respective vectors of parameters. Some complications may arise in the estimation of equation (1). First, observations might possess spatial dependence in which the values of observations in one location might depend on the values of observations at other locations. Ordinary least squares estimates are biased and inconsistent if observations are spatially dependent. As such, statistical inference is likely to be incorrect. Second, it is possible that spatial dependence or correlation might exist in some of the causal factors that are omitted from the hedonic price function. Least squares estimates are unbiased, yet ine¢ cient if the error structure possesses spatial dependence.9 Consider the case of spatial dependence across observations in the sample. Following LeSage and Pace (2009) and others, this can be controlled for and represented by a spatial lag or spatial autoregressive model (SAR), P = W1 P + S + N + L + , 7

(2)

Conceptually, such measures might capture access bene…ts to open space. We attempt to capture the internalized e¤ect on housing price from inclusion in a cluster development by using this dummy variable (DummyRCD/RLUP). Mentioned previously, the Euclidean distance measure (NGO/Trust/PrProtED) and the proximity dummy variable (DNGO/Trust/PrProt 0.5km) are separately intended to control for the external e¤ects of cluster development on housing prices. 9 See Anselin (1988), Kim et al (2003), Taylor (2003), LeSage and Pace (2009), and Neumayer and Plümper (2010). 8

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where is the spatial autoregressive coe¢ cient, where W1 is a n n row-standardized spatialweight matrix which captures a de…nition of the “neighborhood” (e.g., by distance, contiguity, shared jurisdiction, etc.), and where is the n 1 vector of independent and identically distributed (iid) error terms. We assume that the intercept term does exist, yet we suppress it here for notational convenience.10 Now consider the case in which the error structure exhibits spatial correlation. This is due to the fact that a housing price observation at any location is a function of both the local explanatory variables and the omitted variables at neighboring housing observations. Such features across space can be accounted (controlled) for by employing the spatial error model (SEM), P=

S+ N+ L+ , = W1 + ,

(3)

where is the coe¢ cient on the spatially correlated error structure, and where is a n 1 vector of iid errors. Two common tests for spatial autocorrelation are the Moran’s I test and a Lagrange Multiplier test (Anselin 1988). It is possible that spatial dependence in observations and in the error structure is simultaneously present across a sample that is to be estimated. In such cases, the econometric model can be represented by a generalized spatial model (SAC), which controls for both spatial dependence across observations and spatial correlation in the error structure. More speci…cally, P = W1 P + S + N + L + , = W2 + ,

(4)

where W2 is an arbitrarily chosen n n row-standardized spatial-weight matrix that is de…ned di¤erently across space from W1 .11 It is especially important to employ (4) if there is evidence that the residuals of the spatial lag/autoregressive model (SAR) exhibit autocorrelation across space (LeSage and Pace 2009). Lastly, maximum-likelihood estimation is convenient for estimating the generalized spatial model (SAC), or alternatively, the spatial lag/autoregressive model (SAR) or spatial error model (SEM) which are special cases of the generalized model when = 0 and = 0, respectively.

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Estimation

4.1

Spatial-Weight Matrices

Employing either the spatial lag/autoregressive model (SAR) or the spatial error model (SEM) requires the use of a spatial-weight matrix. Moreover, the generalized spatial model (SAC) requires the use of two di¤erent spatial-weight matrices that are de…ned in alternative ways. Given that a spatial-weight matrix is used to control for the impact of any one observation on neighboring observations across space, the speci…cation of a spatial-weight matrix captures some type of relationship about what it means to be in a “neighborhood”. In the case of the present data set, Larimer County is partly mountainous. As such, the term “neighborhood”is sometimes viewed as long, narrow stretches of a canyon or county road. Indeed, it is often more reasonable to consider two properties as neighbors if they reside two miles apart within a shared canyon, as opposed to the case where two properties are contiguous yet reside on 10 11

It could be assumed that the n 1 vector of ones is included in one of the matrices of explanatory regressors. See Taylor (2003) and LeSage and Pace (2009) for more on the speci…cation of the spatial-weight matrices.

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opposite sides of a mountain ridge. We therefore utilize two alternative location identi…ers that …t the concept of neighborhood within the context of our data set: census block groups and zip codes. In the creation of one of the spatial-weight matrices, any two observations are identi…ed as neighboring if the two observations exist within the same census block group. And in the creation of the other spatial-weight matrix, any two observations are deemed to be neighbors if they reside within the same zip code. Both spatial-weight matrices are row-standardized, meaning that the elements within each row sum to unity.

4.2

Estimated Models with Spatial Regressors and Spatial Controls

We estimate versions of the econometric models which include spatial regressors that are measured as the natural logarithm (LN) of Euclidean distance from each observation to various types of open space (City/CountyED, NGO/Trust/PrProtED, NForED, NPark/SPark/SWldED). And as an alternative to Euclidean distance measures, we also estimate versions of the models with spatial regressors in the form of proximity dummy variables (DCity/County 0.5km, DCity/County 0.5km2km, DNGO/Trust/PrProt 0.5km, DNFor 0.5km, DNFor 0.5km-2km, DNPark/SPark/SWld 2km, DNPark/SPark/SWld 2km-5km). More speci…cally, these proximity dummy variables measure whether speci…c types of open space reside within a de…ned radius or band extending in any direction from each observation. To capture and control for spatial e¤ects, we estimate a version of the spatial lag/autoregressive model (SAR) with the Euclidean distance spatial regressors and an alternative version with the proximity dummy variables. In using both categories of regressors in the SAR model, we also examine what happens when the two di¤erent versions of spatial controls (spatial-weight matrices by census block groups and by zip codes) are alternatively employed. We also test for the presence of spatial autocorrelation in the least-squares residuals. To accomplish this, we compute the Moran’s I-statistic and a Lagrange multiplier test statistic. With Euclidean distance spatial regressors, the Moran’s I-statistic is 13.4 when the spatial-weight matrix is de…ned by census block group and the Moran’s I-statistic is 9.1 when the spatial-weight matrix is de…ned by zip code. Both of these computed values are much greater than the critical value of 1.96, such that the null hypothesis of no spatial correlation can be soundly rejected. The corresponding Lagrange multiplier statistics are calculated as 128.6 and 45.7 when the spatial-weight matrix is de…ned by census block group and by zip code, respectively. These computed values are also much greater than the critical value of 6.635, which also indicates that the null hypothesis of no spatial correlation can be rejected. These test statistics are reported in Table 1 and they indicate the presence of spatial correlation in the residuals of the least-squares estimator. As such, it is appropriate to estimate the spatial error model (SEM) when the Euclidean distance spatial regressors are in use. With proximity dummy variables for spatial regressors, the Moran’s I-statistic is 14.7 and 9.6 when the spatial-weight matrix is de…ned by census block group and by zip code, respectively. These computed values are again greater than 1.96, the critical value for this hypothesis test. The corresponding Lagrange multiplier statistics are 156.7 and 50.9 when the spatial-weight matrix is de…ned by census block group and by zip code, respectively. These test statistics are reported in Table 2 and they indicate the presence of spatial dependence in the least-squares residuals when the proximity dummy variables are used as spatial regressors. Again, the spatial error model (SEM) is appropriate to control for such spatial autocorrelation when the proximity dummy variables are used as an alternative to the Euclidean distance measures. To check for robustness, we estimate versions of the models without any spatial regressors (except the dummy variable that demarcates whether or not an observation is part of a cluster development). It should be noted for the sake

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of completeness that spatial correlation exists in the least-squares residuals. This is re‡ected by the fact that the Moran’s I-statistic is 14.2 and 8.9 when the spatial-weight matrix is de…ned by census block group and by zip code, respectively. Likewise, the corresponding Lagrange multiplier statistics are 157.1 and 48.9 (see Table 3). Therefore, the spatial error model (SEM) is appropriate to control for spatial dependence in the error structure when all spatial regressors are deliberately omitted from the estimation. Lastly, an important issue still remains concerning the use of the spatial lag/autoregressive model (SAR). Namely, the residuals of an estimated SAR model may still exhibit spatial autocorrelation despite the fact that its use is controlling for the presence of spatial dependence across observations. Therefore, it is important to test whether both types of spatial e¤ects are simultaneously present. If spatial autocorrelation does happen to exist in the residuals of the SAR model, then use of the generalized spatial model (SAC) is needed to concurrently control for both spatial dependence across observations and spatial correlation in the residuals. The presence of spatial correlation in the residuals of the SAR model is indeed con…rmed via a Lagrange multiplier test: the test statistic is 68.7 and 117.9 with the use of Euclidean distance spatial regressors when the spatial-weight matrices are de…ned by census block group and by zip code, and vice versa respectively; the test statistic is 73.0 and 139.6 with the use of proximity dummies for spatial regressors when the spatial-weight matrices are de…ned by census block group and by zip code, and vice versa respectively; and lastly, the test statistic is 71.3 and 133.7 when all spatial regressors are deliberately excluded from the estimation and when the spatial-weight matrices are de…ned by census block group and by zip code, and vice versa respectively. All of these computed statistics are greater than the critical value. Therefore, the use of the generalized spatial model (SAC) is warranted.

5 5.1

Results Organization

We report our empirical …ndings in Tables 1–3 for variants of the spatial lag/autoregressive model (SAR), the spatial error model (SEM), and the generalized spatial model (SAC), in addition to the least-squares estimator (OLS) which is used to check robustness. Observations in the vector P are measured as the natural logarithm of housing price. Many of the regressors are also measured in the natural logarithm (LN). Table 1 summarizes our …ndings when Euclidean distances to various forms of open space are used as spatial regressors. Table 2 summarizes our …ndings when the proximity dummies are alternatively incorporated as spatial regressors. And lastly, Table 3 provides a robustness check on our empirical …ndings from the perspective that the estimated models do not have any spatial regressors, just controls for spatial dependence in both the observations and in omitted variables. Concerning the spatial econometric estimators, the symbol “N” in Tables 1–3 denotes the fact that the census block groups de…nition of neighborhood was used as the row-standardized spatialweight matrix, W1 , and the zip codes de…nition was employed as the secondary row-standardized spatial-weight matrix, W2 . More speci…cally, the spatial-weight matrix de…ned by census block groups was used to represent W1 in the estimation of the spatial lag/autoregressive model (SAR), the spatial error model (SEM), and the generalized spatial model (SAC), de…ned above by equations (2), (3), and (4). In contrast, the spatial-weight matrix de…ned by zip codes was only used for W2 in the estimation of the generalized spatial model (SAC). Conversely, the symbol “ ”in Tables 1–3 denotes the case where the spatial-weight matrix de…ned by zip codes was used to represent W1 in the estimation of the SAR, SEM, and SAC spatial models, whereas the spatial-weight matrix by census block groups was used only for W2 in the generalized spatial model (SAC).

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5.2 5.2.1

Detailed Findings and Discussion Cluster Development

Concerning the primary focus of this study, our estimated results (DummyRCD/RLUP in Tables 1–3) suggest that housing prices are unequivocally lower if a property resides within a cluster development, all else equal. This …nding is robust to whether or not the estimator controls for spatial dependence and/or spatial autocorrelation since the OLS estimator also captures this negative e¤ect. Moreover, the …nding is robust even if spatial regressors are excluded from the estimation (see DummyRCD/RLUP in Table 3). Following the procedure outlined in the Appendix, we calculate that the construction of a residential housing unit in a cluster development decreases its value or price by approximately 18 percent in the spatial lag/autoregressive model (SAR) speci…cation. The marginal price impact estimate is a 17 percent decrease in the generalized spatial model (SAC) speci…cation. The estimated coe¢ cient parameters of the spatial error model (SEM) and of the least-squares estimator (OLS) can be interpreted directly in determining the marginal impacts: cluster development decreases the price of a house by approximately 26 percent. Given the implied damage estimates that come from the SAR and SAC speci…cations, it is interesting to note that controlling for spatial dependence across housing price observations leads to damage estimates that are 8 to 9 percentage points lower than when such dependence is not accounted for, as in all SEM and OLS speci…cations. Thus, it appears that controlling for the spatial dependence of observations a¤ects the damage estimates from inclusion in a cluster development to a much larger extent than by only controlling for spatial autocorrelation (spatial dependence in omitted variables from the hedonic price function). This is due to the fact that the damage estimate of 17 percent in the SAC speci…cation (which controls for both spatial dependence and spatial autocorrelation) is very close to the estimate of 18 percent in the SAR speci…cation (which controls for spatial dependence only) relative to the damage estimate of approximately 26 percent in the SEM speci…cation (which controls for spatial autocorrelation only). It is possible that the negative impact on the value of a house from being in a cluster development is the result of a supply-side e¤ect in which real-estate developers incur lower costs in providing clustered infrastructure needs for developments (Theobald and Hobbs 2002; Burchell et al 2005). However, most observations in our sample consist of secondary sales to subsequent (not original) homeowners. As such, housing prices are more likely to re‡ect demand-side willingness-to-pay for such types of houses, where sales transaction prices will re‡ect other considerations aside from initial construction costs. It is more likely that the negative impact on housing values by inclusion in a cluster development is the result of a regulatory decrement to real-estate values when developers are not free to respond to pure market incentives. Indeed, the Rural Land Use Plan/Process (RLUP) in Larimer County allows developers to realize a “density bonus” of up to 100 percent in terms of the number of additional approved parcels or lots that local regulators normally allow within a development (Ernst and Wallace 2008). A RLUP involves less oversight by regulators in exchange for a higher required amount of protected open space in the cluster development. In contrast, the “density bonus” usually ranges from 5 percent to 10 percent when cluster developments are designated as Rural Conservation Developments (RCD). This is because the required proportion of protected open space is much lower than in the RLUP case. From the perspective of policy prescription, a density bonus that is proportional to the per-house value discount from mandated clustering might serve to compensate developers such that cluster development is undertaken on an otherwise voluntary basis. Such an approach is likely to be revenue-neutral in terms of its e¤ect on the county property tax base. Actual practices by county regulators appear to straddle the bonus magnitude implied by such a prescription.

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5.2.2

Proximity to Other Types of Protected Open Space

We …nd that city and county open space has a positive impact on housing prices, in general. Indeed, the spatial regressor of Euclidean distance to open space maintained by Larimer County and by cities in the county indicates a positive impact on housing values, meaning that housing prices decrease as distance to public open spaces increases (see City/CountyED in Table 1). If city or county open space exists within a radius of 0.5km to 2km from an observation, then the spatial lag/autoregressive model (SAR) and the generalized spatial model (SAC) with proximity dummy spatial regressors (and where W1 is de…ned by census block groups) also capture a positive impact on housing prices at the 1 percent and 5 percent levels of signi…cance respectively (see DCity/County 0.5km-2km in Table 2). National parks and state protected lands, such as state parks, a¤ect housing prices positively in our non-urban sample. More speci…cally, housing prices increase as Euclidean distance to national parks, state parks, or state protected wildlife lands decreases (NPark/SPark/SWldED in Table 1). However, the proximity dummy spatial regressors indicate that the positive e¤ect is predominantly con…ned to a 2km radius from the boundary of such publicly protected lands, given that the proximity dummy of a 2km to 5km radius exhibits a statistically signi…cant e¤ect on housing prices only at the 5 percent level of signi…cance in a version of the SEM model and at the 10 percent level in a version of the SAC model (see respectively, DNPark/SPark/SWld 2km and DNPark/SPark/SWld 2km-5km in Table 2). It is important to note that national parks, state parks, and state protected lands do not generally exhibit a statistically signi…cant impact on housing prices under the leastsquares estimator, which is likely due to the fact that OLS does not control for spatial dependence in observations nor in the error structure. The positive e¤ect on housing values from proximity to public lands, such as national or state parks and protected county or city lands, is likely due to the fact that these types of lands tend to be highly visible and accessible for recreational purposes, which likely secures their status as publicly protected lands. Yet, we …nd that proximity to national forest land has no meaningful impact on housing prices (NForED in Table 1 and DNFor 0.5km and DNFor 0.5km-2km in Table 2). Indeed, only one version of the estimated models captures any e¤ect on housing price, which is at the 10 percent level of signi…cance (see Table 2 for DNFor 0.5km corresponding to SAR model where W1 is de…ned by census block groups). The lack of any statistical impact on housing values from proximity to national forest land is possibly due to its relative abundance in many of the rural areas of Larimer County, Colorado. Our econometric estimates also indicate a lack of any statistically signi…cant e¤ect on prices that might result from proximity to privately protected lands, such as land that is owned or maintained by non-governmental organizations, private land trusts, and/or proximity to (but not inclusion in) cluster developments. From NGO/TrustPrProtED in Table 1 and from DNGO/Trust/PrProt 0.5km in Table 2, one can see that this …nding is robust across all estimated speci…cations of the spatial hedonic model and to the least-squares estimator. Intrinsic to these speci…c results is the fact that there does not exist any external bene…t or cost from residing in close proximity to a cluster development. The lack of proximity value to privately protected lands might be due to the fact that many of these lands are not visibly identi…able to the public at large or because there might be a perceived uncertainty about the permanence of such private measures to preserve open space.

10

5.2.3

Other Determinants and Spatial E¤ects

It is important to control for the major (and obvious) determinants of housing prices across all speci…cations of the hedonic price function, noting that the e¤ects of several core property attributes on housing prices are robust across all estimated models, as reported in Tables 1–3. The size of a land parcel (ParcelFT2 ), the total square feet of a house (BldgFT2 ), neighborhood median income (MedHHInc), and the median age of homeowners (MedAge) all generate statistically signi…cant positive e¤ects on the price of a house. Moreover, housing density (HousDens, units/km2 ) appears to have a positive impact on property values in the rural sample. Finished basement square feet (BsmntFinFT2 ) and garage size (GarageFT2 ) generate statistically signi…cant estimates without any practical economic impact on housing prices. The age of a house (Age), air conditioning (DummyAC), the number of bedrooms (Bedrooms), neighborhood racial composition (% White), and the percentage of renter-occupied structures (% RentOcc) do not appear to have any signi…cant e¤ects on housing prices in our non-urban sample. Lastly, the presence of spatial dependence across housing prices and also in the error structure (spatial autocorrelation) is highly signi…cant. Indeed, the estimated values of con…rm the presence of spatial dependence in the sample since it is always signi…cant at the 1 percent level when the census block group de…nition of neighborhood is used as the row-standardized spatial-weight matrix, W1 , and since the estimated values of are usually signi…cant at the 1 percent level when the zip code de…nition is alternatively used as W1 . In addition, the estimated values of are always signi…cant at the 1 percent level regardless of whether the census block group de…nition or the zip code de…nition is used to represent W1 and W2 . These estimates con…rm the presence of spatial autocorrelation in the least-squares residuals and in the residuals of the spatial lag/autoregressive model (SAR). This was anticipated given that the Moran’s I-statistics and the Lagrange multiplier statistics are statistically signi…cant. The statistical signi…cance of the estimated values of and verify (ex post) the importance of having estimated the generalized spatial model (SAC).

6

Summary and Concluding Remarks

This study estimates several alternative speci…cations of a spatial hedonic pricing model to assess how residential property values are impacted by inclusion within cluster developments and by proximity to various types of protected land. Speci…cations of the econometric model control for the spatial dependence of housing prices within a de…nition of a “neighborhood” and for the presence of spatial autocorrelation. The statistical sample is comprised of 4,008 single-family residential sales transactions in the non-urban portions of Larimer County, Colorado from 2001 to 2004. The alternative speci…cations of the estimated hedonic model appear to capture many of the major in‡uences on the values of single-family homes at the urban-rural interface. Indeed, we …nd that proximity to national or state park land and to city or county open space has a signi…cant positive impact on property values, while proximity to national forest land or to privately conserved land exhibits no signi…cant e¤ects. Of particular importance, we …nd that inclusion of a property within a cluster development decreases its value by 17 to 26 percent, depending on the model speci…cation. It is important to remember that our estimated sample is comprised entirely of nonurban observations. Therefore, the possibility remains that inclusion of a property within a cluster development might increase its value in urban areas where population densities are signi…cantly higher. Our …ndings suggest important considerations for policymakers who design development rules and alternative land protection measures aimed at preserving open space in non-urban areas. Indeed, our …ndings give support to the idea that cluster development implemented by county man-

11

date at the urban-rural interface cannot be expected to otherwise arise from private market incentives. Properly planned incentives might make the implementation of cluster developments not only value-neutral for developers, but also revenue-neutral for property tax districts. The rationale for requiring cluster development in land-use policy is often based on an assumption that protected open space provides bene…cial social externalities. If positive externalities really have come into existence as a result of the creation of cluster developments in the non-urban areas of Larimer County, then it is likely that such bene…ts are being realized by the citizenry in a way that is not captured by our spatial econometric methodology. Further investigation might include statistical analysis on a much more detailed sample that would need to measure the potential existence of social externalities that result from the mandating of cluster development. In the absence of such creative statistical measures, the robustness of our spatial econometric results suggests that the central conclusions of this study would likely be una¤ected with sensitivity to the speci…cation of the spatial-weight matrices, proximity measures, housing characteristics, among other potential regressors.

Appendix: Marginal Price Impact Calculations A complication arises in measuring the marginal impact of an open space variable in the spatial lag/autoregressive model (SAR) and in the generalized spatial model (SAC), given that the price vector is not speci…ed explicitly in terms of the explanatory regressors in (2) and (4). As such, it is necessary to …rst present the models in explicit form. Following Kim et al (2003), a series of algebraic rearrangements yields the marginal bene…t (implicit price) of an arbitrary spatial variable, @P1 =@l1m @P1 =@l2m @P @P2 =@l1m @P2 =@l2m 0 = ::: ::: @ll @Pn =@l1m @Pn =@l2m

::: @P1 =@lnm ::: @P2 =@lnm = ::: ::: ::: @Pn =@lnm

l

[I

Wr ]

1

,

(A1)

0

where l is a 1 n row vector of one spatial characteristic, I is n n identity matrix, and r = 1; 2 in our setup. The Jacobian matrix in (A1) implies that a price at one point in space is a¤ected by a marginal change in one unique locational characteristic at that particular point and by the marginal changes of locational characteristics at all other points. To obtain the overall impact, we sum across the space such that @P0 i = l [I Wr ] 1 i reduces to l 1 1 i, where i is a given @ll

column of the I matrix and where 1=(1

) is a spatial multiplier (Kim et al 2003).

References Acharya, G. & Bennett, L.L. (2001). Valuing open space and land-use patterns in urban watersheds. Journal of Real Estate Finance and Economics, 22(2-3), 221-237. Anderson, S.T. & West, S.E. (2006). Open space, residential property values, and spatial context. Regional Science and Urban Economics, 36(6), 773-789. Anselin, L. (1988). Spatial econometrics: Methods and models. Dordrecht: Kluwer. Blakely, M. (1991). An economic analysis of the e¤ects of development rights purchases on land values in King County, Washington. M.S. thesis, Washington State University. Bolitzer, B. & Netusil, N.R. (2000). The impact of open spaces on property values in Portland, Oregon. Journal of Environmental Management, 59(3), 185-193.

12

Burchell, R.W., Downs, A., McCann, B., & Mukherji, S. (2005). Sprawl Costs: Economic Impacts of Unchecked Development. Washington, DC: Island Press. Cheshire, P. & Sheppard, S. (1989). British planning policy and access to housing: some empirical estimates. Urban Studies, 26(5), 469-485. Correll, M.R., Lillydahl, J.H. & Singell, L.D. (1978). The e¤ects of greenbelts on residential property values: some …ndings on the political economy of open space. Land Economics, 54(2), 207-217. Ernst, T. & Wallace, G.N. (2008). Characteristics, motivations, and management actions of landowners engaged in private land conservation in Larimer County Colorado. Natural Areas Journal, 28(2), 109-120. Geoghegan, J. (2002). The value of open spaces in residential land use. Land Use Policy, 19(1), 91-98. Geoghegan, J., Wainger, L.A. & Bockstael, N.E. (1997). Spatial landscape indices in a hedonic framework: an ecological economics analysis using GIS. Ecological Economics, 23(3), 251-264. Geoghegan, J., Lynch, L. & Bucholtz, S. (2003). Capitalization of open spaces into housing values and the residential property tax revenue impacts of agricultural easement programs. Agricultural and Resource Economics Review, 32(1), 33-45. Irwin, E.G. (2002). The e¤ects of open space on residential property values. Land Economics, 78(4), 465-480. Irwin, E.G. & Bockstael, N.E. (2001). The problem of identifying land use spillovers: measuring the e¤ects of open space on residential property values. American Journal of Agricultural Economics, 83(3), 698-704. Kim, C.W., Phipps, T.T. & Anselin, L. (2003). Measuring the bene…ts of air quality improvement: a spatial hedonic approach. Journal of Environmental Economics and Management, 45(1), 24-39. Kitchen, J.W. & Hendon, W.S. (1967). Land values adjacent to an urban neighborhood park. Land Economics, 43(3), 357-360. Kline, J.D. (2006). Public demand for preserving local open space. Society and Natural Resources, 19(7), 645-659. Lee, C-M. & Linneman, P. (1998). Dynamics of the greenbelt amenity e¤ect on the land market— the case of the Seoul’s greenbelt. Real Estate Economics, 26(1), 107-129. LeSage, J. & Pace, R.K. (2009). Introduction to spatial econometrics. Boca Raton: Chapman & Hall/CRC Press. Lutzenhiser, M. & Netusil, N.R. (2001). The e¤ect of open spaces on a home’s sales price. Contemporary Economic Policy, 19(3), 291-298. Nelson, A.C. (1988). An empirical note on how regional urban containment policy in‡uences an interaction between greenbelt and exurban land markets. Journal of the American Planning Association, 54(2), 178-184. Neumayer, E. & Plümper, T. (2010). Making spatial analysis operational: Commands for generating spatial-e¤ect variables in monadic and dyadic data. The Stata Journal, 10(4), 585-605. Nickerson, C.G. & Lynch, L. (2001). The e¤ect of farmland preservation programs on farmland prices. American Journal of Agricultural Economics, 83(2), 341-351. Rosen, S. (1974). Hedonic prices and implicit markets: product di¤erentiation in pure competition. Journal of Political Economy, 82(1), 34-55.

13

Smith, V.K., Poulos, C. & Kim, H. (2002). Treating open space as an urban amenity. Resource and Energy Economics, 24(1-2), 107-129. Taylor, L.O. (2003). The hedonic method. In A primer on non-market valuation, edited by P.A. Champ et al., Dordrecht: Kluwer, 331-393. Theobald, D.M. & Hobbs, N.T. (2002). A framework for evaluating land use planning alternatives: protecting biodiversity on private land. Conservation Ecology, 6(1), 5. Wallace, G.N., Theobald, D.M., Ernst, T., & King, K. (2008). Assessing the Ecological and Social Bene…ts of Private Land Conservation in Colorado. Conservation Biology, 22(2), 284-296. Weicher, J.C. & Zerbst, R.H. (1973). The externalities of neighborhood parks: an empirical investigation. Land Economics, 49(1), 99-105.

14

Table 1. Estimation Results with Euclidean Distance Spatial Regressors Variable OLS SAC N SEM N SAR N SAC

SEM

SAR

2.044

4.108***

1.419***

(1.601)

(12.840)

(3.390)

-0.067***

-0.066***

-0.067***

-0.067***

(-4.261)

(-4.388)

(-4.333)

(-4.387)

(-4.367)

-0.121***

-0.115***

-0.120***

-0.116***

-0.121***

-0.121***

(-7.505)

(-7.676)

(-7.332)

(-7.625)

(-7.643)

(-7.641)

-0.129***

-0.131***

-0.129***

-0.129***

-0.133***

-0.131***

(-7.832)

(-8.042)

(-7.869)

(-7.943)

(-7.941)

(-8.078)

(-7.990)

0.015

-0.004

-0.011

0.001

-0.011

-0.005

-0.002

(0.978)

(-0.192)

(-0.480)

(0.049)

(-0.514)

(-0.205)

(-0.145)

0.152***

0.075**

0.106***

0.098***

0.086**

0.077**

0.100***

(5.615)

(2.324)

(2.692)

(3.554)

(2.080)

(2.061)

(3.617)

LN(ParcelFT2 )

0.082***

0.081***

0.089***

0.080***

0.086***

0.084***

0.080***

(16.229)

(15.764)

(16.377)

(16.012)

(15.507)

(16.036)

(15.892)

LN(BldgFT2 )

0.521***

0.491***

0.497***

0.499***

0.494***

0.504***

0.511***

(25.085)

(24.210)

(23.829)

(23.340)

(23.909)

(24.218)

(25.400)

BsmntFinFT2

0.000***

0.000***

0.000***

0.000***

0.000***

0.000***

0.000***

(13.096)

(12.496)

(12.548)

(13.320)

(12.409)

(12.203)

(12.968)

GarageFT2

0.000***

0.000***

0.000***

0.000***

0.000***

0.000***

0.000***

(4.999)

(4.713)

(4.703)

(4.690)

(4.676)

(4.947)

(4.899)

0.025

0.016

0.013

0.018

0.013

0.021

0.023

(1.569)

(1.019)

(0.794)

(1.172)

(0.820)

(1.346)

(1.503)

Constant 2003 2002 2001 SouthDummy EstesDummy

DummyAC LN(Bedrooms) Age LN(MedHHInc) % White LN(MedAge) LN(HousDens, units/km2 ) % RentOcc DummyRCD/RLUP LN(City/CountyED) LN(NGO/Trust/PrProtED) LN(NForED) LN(NPark/SPark/SWldED)

R2 , pseudo-R2 Lik

3.777***

2.928***

3.494***

2.802***

(8.992)

(8.236)

(4.929)

(5.607)

-0.064***

-0.068***

-0.065***

(-4.164)

(-4.482)

-0.120***

(-7.412) ***

-0.130

0.010

0.010

0.012

0.007

0.011

0.014

0.009

(0.424)

(0.453)

(0.526)

(0.297)

(0.489)

(0.592)

(0.392)

0.000

0.000

0.000

0.000

0.000

0.000

0.000

(1.290)

(0.337)

(0.616)

(0.616)

(0.586)

(0.669)

(1.160)

0.313***

0.113***

0.357***

0.106***

0.314***

0.284***

0.267***

(8.877)

(3.814)

(6.601)

(3.947)

(10.013)

(7.239)

(8.912)

-0.402**

-0.167

-0.398

-0.192

-0.287

-0.256

-0.210

(-2.215)

(-0.894)

(-1.406)

(-1.056)

(-1.148)

(-1.394)

(-1.239)

0.331***

0.233***

0.323***

0.221***

0.338***

0.327***

0.346***

(5.150)

(3.543)

(3.030)

(3.661)

(3.158)

(4.947)

(5.430)

0.021***

0.025***

0.029***

0.025***

0.026***

0.019***

0.020***

(3.808)

(4.387)

(3.385)

(4.463)

(2.985)

(3.471)

(3.728)

-0.025

-0.025

-0.002

-0.051

0.039

0.012

0.045

(-0.280)

(-0.295)

(-0.015)

(-0.590)

(0.259)

(0.133)

(0.514)

-0.254***

-0.260***

-0.244***

-0.262***

-0.246***

-0.261***

-0.258***

(-5.550)

(-5.689)

(-5.320)

(-5.812)

(-5.365)

(-5.665)

(-5.677)

-0.032***

-0.029***

-0.022**

-0.032***

-0.021**

-0.026***

-0.028***

(-4.219)

(-3.784)

(-2.331)

(-4.232)

(-2.167)

(-3.191)

(-3.791)

-0.010

0.000

-0.008

0.000

-0.005

-0.008

-0.001

(-1.381)

(-0.027)

(-0.935)

(0.054)

(-0.548)

(-1.105)

(-0.140)

0.001

-0.006

-0.003

-0.009

-0.004

0.003

-0.005

(0.138)

(-0.899)

(-0.365)

(-1.437)

(-0.469)

(0.430)

(-0.817)

-0.011*

-0.019***

-0.025***

-0.014**

-0.024***

-0.022***

-0.014**

(-1.654)

(-2.852)

(-3.302)

(-2.288)

(-3.163)

(-3.298)

(-2.250)

—

0.280***

—

0.299***

0.143*

0.219***

(9.514)

(1.668)

—

—

0.358***

0.474***

0.428***

0.542***

(48.044)

(78.829)

—

(62.859)

(122.147)

—

(12.588)

(6.289)

0.52

0.53 0.53 0.52 0.53 0.52 0.52 2107.4 -188.0 -191.4 2110.3 -209.7 -209.6 Moran I-statistic: 13.4 > 1.96 Moran I-statistic: 9.1 > 1.96 LM-statistic (OLS): 128.6 > 6.635 LM-statistic (OLS): 45.7 > 6.635 LM-statistic (SAR): 68.7 > 6.635 LM-statistic (SAR): 117.9 > 6.635 *** n = 4008; Asymptotic t-statistics in parentheses; Levels of signi…cance: 1% level, ** 5% level, * 10% level.

—

SAR: P = W1 P + S + N + L + ; SEM: P = S + N + L + where = W1 + . SAC: P = W1 P + S + N + L + where = W2 + . N: W1 de…ned by Census Block Groups, W2 by Zip Codes; : W1 de…ned by Zip Codes, W2 by Census Block Groups.

15

Table 2. Estimation Results with Proximity Dummy Spatial Regressors Variable OLS SAC N SEM N SAR N SAC

SEM

SAR

3.068***

2.097***

2.469***

2.016***

0.929*

3.392***

0.654***

(7.632)

(4.483)

(4.085)

(4.877)

(1.670)

(8.028)

(2.619)

-0.062***

-0.066***

-0.063***

-0.065***

-0.064***

-0.066***

-0.065***

(-4.015)

(-4.356)

(-4.145)

(-4.243)

(-4.231)

(-4.292)

(-4.242)

-0.119***

-0.121***

-0.114***

-0.120***

-0.116***

-0.121***

-0.121***

(-7.468)

(-7.666)

(-7.289)

(-7.602)

(-7.640)

(-7.605)

-0.134***

-0.135***

-0.133***

-0.132***

-0.139***

-0.135***

(-8.115)

(-8.295)

(-8.118)

(-8.093)

(-8.177)

(-8.493)

(-8.254)

0.008

-0.003

-0.012

0.002

-0.012

-0.017

-0.008

(0.546)

(-0.152)

(-0.502)

(0.144)

(-0.523)

(-0.623)

(-0.515)

0.164***

0.068**

0.099**

0.102***

0.077*

0.048

0.102***

(6.059)

(1.963)

(2.381)

(3.730)

(1.891)

(1.163)

(3.698)

LN(ParcelFT2 )

0.078***

0.079***

0.089***

0.078***

0.086***

0.082***

0.077***

(15.059)

(15.060)

(16.161)

(15.421)

(15.631)

(15.804)

(14.809)

LN(BldgFT2 )

0.527***

0.495***

0.502***

0.502***

0.498***

0.508***

0.515***

(25.408)

(22.833)

(24.164)

(24.587)

(24.045)

(25.050)

(24.965)

BsmntFinFT2

0.000***

0.000***

0.000***

0.000***

0.000***

0.000***

0.000***

(13.240)

(12.484)

(12.657)

(13.411)

(12.506)

(12.323)

(13.041)

GarageFT2

0.000***

0.000***

0.000***

0.000***

0.000***

0.000***

0.000***

(5.070)

(4.710)

(4.653)

(4.704)

(4.638)

(4.901)

(4.929)

0.026

0.015

0.011

0.018

0.011

0.020

0.023

(1.636)

(0.930)

(0.664)

(1.140)

(0.694)

(1.233)

(1.505)


DummyAC LN(Bedrooms) Age LN(MedHHInc) % White LN(MedAge) LN(HousDens, units/km2 ) % RentOcc DummyRCD/RLUP DCity/County 0.5km DCity/County 0.5km-2km DNGO/Trust/PrProt 0.5km DNFor 0.5km DNFor 0.5km-2km DNPark/SPark/SWld 2km DNPark/SPark/SWld 2km-5km

R2 , pseudo-R2 Lik

(-7.378) ***

-0.133

0.015

0.014

0.017

0.011

0.015

0.018

0.012

(0.663)

(0.623)

(0.739)

(0.476)

(0.675)

(0.806)

(0.538)

0.000

0.000

0.000

0.000

0.000

0.000

0.001

(1.369)

(0.579)

(0.965)

(0.830)

(0.898)

(0.911)

(1.303)

0.353***

0.135***

0.407***

0.116***

0.349***

0.309***

0.289***

(10.220)

(3.892)

(15.717)

(3.889)

(15.313)

(8.041)

(8.307)

-0.361**

-0.127

-0.361

-0.125

-0.244

-0.213

-0.157

(-2.022)

(-0.682)

(-1.217)

(-0.708)

(-0.870)

(-1.215)

(-0.866)

0.274***

0.199***

0.285**

0.169***

0.306***

0.307***

0.301***

(4.284)

(2.942)

(2.343)

(2.820)

(2.764)

(4.963)

(4.786)

0.028***

0.028***

0.035***

0.030***

0.031***

0.022***

0.025***

(5.144)

(4.875)

(3.919)

(5.570)

(3.565)

(3.980)

(4.656)

0.049

0.044

0.076

0.007

0.109

0.094

0.107

(0.546)

(0.462)

(0.477)

(0.081)

(0.779)

(0.947)

(1.272)

-0.267***

-0.274***

-0.259***

-0.278***

-0.260***

-0.274***

-0.272***

(-5.805)

(-5.966)

(-5.591)

(-6.141)

(-5.637)

(-5.901)

(-5.962)

-0.013

-0.005

-0.028

0.012

-0.027

-0.041

-0.009

(-0.358)

(-0.123) **

(-0.713)

(0.329) ***

(-0.711)

(-1.089)

0.020

0.010

(-0.236) *

(1.449)

(2.212)

(0.929)

(2.876)

(1.022)

(0.605)

0.032

0.017

0.025

0.020

0.022

0.019

0.022

(1.042)

(0.567)

(0.787)

(0.635)

(0.714)

(0.627)

(0.716)

0.024

0.037

0.019

0.047

0.027

(1.655)

0.006

0.047

0.039

0.056*

0.043

0.009

0.032

(0.213)

(1.425)

(1.081)

(1.947)

(1.212)

(0.272)

(1.151)

-0.022

0.015

0.012

0.015

0.016

-0.012

-0.002

(-0.819)

(0.507)

(0.357)

(0.558)

(0.482)

(-0.392)

(-0.069)

0.021

0.062***

0.082***

0.044**

0.080***

0.068***

0.036*

(1.070)

(3.032)

(3.314)

(2.290)

(3.311)

(3.229)

(1.847)

-0.004

0.028

0.043**

0.016

0.039*

0.026

0.002

(-0.200)

(1.539)

(2.022)

(0.904)

(1.867)

(1.427)

(0.137)

—

0.293***

—

0.323***

0.165*** (3.566)

—

0.236***

(21.200)

—

0.408***

0.505***

0.456***

0.626***

(57.054)

(88.468)

—

(71.328)

(146.336)

—

(13.869)

0.52

0.53 0.53 0.52 2104.6 -189.5 -194.9 Moran I-statistic: 14.7 > 1.96 LM-statistic (OLS): 156.7 > 6.635 LM-statistic (SAR): 73.0 > 6.635 n = 4008; Asymptotic t-statistics in parentheses; Levels of signi…cance: *** 1% level,

—

(6.470)

0.53 0.52 0.52 2109.9 -214.2 -214.0 Moran I-statistic: 9.6 > 1.96 LM-statistic (OLS): 50.9 > 6.635 LM-statistic (SAR): 139.6 > 6.635 ** 5% level, * 10% level.


16

Table 3. Estimation Results without Spatial Regressors Variable OLS SAC N SEM N SAR N

SEM

SAR

1.236

3.353***

0.750***

(1.089)

(8.300)

(2.949)

-0.066***

-0.066***

-0.067***

-0.066***

(-4.230)

(-4.305)

(-4.305)

(-4.330)

(-4.295)

-0.121***

-0.115***

-0.120***

-0.116***

-0.121***

-0.121***

(-7.515)

(-7.768)

(-7.312)

(-7.615)

(-7.668)

(-7.640)

-0.136***

-0.140***

-0.135***

-0.138***

-0.140***

-0.139***

(-8.325)

(-8.670)

(-8.352)

(-8.549)

(-8.416)

(-8.598)

(-8.520)

0.005

-0.011

-0.013

-0.008

-0.014

-0.009

-0.011

(0.376)

(-0.554)

(-0.570)

(-0.585)

(-0.634)

(-0.368)

(-0.781)

0.158***

0.083***

0.115***

0.113***

0.093**

0.074**

0.106***

(6.794)

(2.771)

(3.518)

(4.666)

(2.323)

(2.126)

(4.322)

LN(ParcelFT2 )

0.077***

0.075***

0.085***

0.074***

0.082***

0.078***

0.074***

(15.736)

(15.368)

(15.987)

(15.487)

(14.968)

(15.710)

(15.223)

LN(BldgFT2 )

0.531***

0.502***

0.508***

0.509***

0.505***

0.515***

0.520***

(25.717)

(25.028)

(24.640)

(23.933)

(24.430)

(25.466)

(25.848)

BsmntFinFT2

0.000***

0.000***

0.000***

0.000***

0.000***

0.000***

0.000***

(13.436)

(12.798)

(12.845)

(13.731)

(12.654)

(12.454)

(13.302)

GarageFT2

0.000***

0.000***

0.000***

0.000***

0.000***

0.000***

0.000***

(5.073)

(4.731)

(4.708)

(4.700)

(4.682)

(4.980)

(4.932)

DummyAC

0.027*

0.017

0.015

0.019

0.015

0.025

0.025

(1.731)

(1.118)

(0.943)

(1.201)

(0.989)

(1.585)

(1.614)


LN(Bedrooms) Age LN(MedHHInc) % White LN(MedAge) LN(HousDens, units/km2 ) % RentOcc DummyRCD/RLUP

R2 , pseudo-R2 Lik

2.970***

2.283***

2.670***

2.235***

(7.841)

(5.566)

(4.341)

(5.493)

-0.063***

-0.067***

-0.064***

(-4.067)

(-4.413)

-0.120***

SAC

(-7.394) ***

-0.136

0.015

0.010

0.013

0.005

0.011

0.016

0.008

(0.634)

(0.436)

(0.565)

(0.212)

(0.494)

(0.741)

(0.389)

0.000*

0.000

0.000

0.000

0.000

0.000

0.000

(1.656)

(0.847)

(1.133)

(1.063)

(1.071)

(1.256)

(1.574)

0.365***

0.142***

0.390***

0.133***

0.335***

0.323***

0.292***

(11.657)

(4.532)

(12.582)

(4.918)

(10.948)

(9.363)

(9.898)

-0.340*

-0.074

-0.276

-0.069

-0.156

-0.180

-0.103

(-1.950)

(-0.407)

(-0.996)

(-0.396)

(-0.580)

(-1.041)

(-0.601)

0.255***

0.185***

0.274**

0.159***

0.296***

0.270***

0.285***

(4.107)

(2.931)

(2.410)

(2.760)

(2.772)

(4.525)

(4.736)

0.029***

0.028***

0.035***

0.029***

0.031***

0.023***

0.025***

(5.771)

(5.213)

(4.667)

(5.784)

(3.712)

(4.696)

(5.130)

0.071

0.062

0.117

0.027

0.149

0.112

0.127

(0.824)

(0.686)

(0.770)

(0.322)

(1.059)

(1.154)

(1.545)

-0.263***

-0.266***

-0.240***

-0.280***

-0.243***

-0.259***

-0.271***

(-5.794)

(-5.856)

(-5.254)

(-6.247)

(-5.340)

(-5.620)

(-6.015)

—

0.276***

—

0.292***

0.153

0.227***

(13.614)

(1.505)

—

—

0.372***

0.480***

0.439***

0.559***

(51.755)

(80.480)

—

(66.447)

(412.721)

—

(12.966)

(7.024)

0.52

0.53 0.53 0.52 0.53 0.52 0.52 2097.2 -196.5 -202.4 2103.0 -220.7 -218.7 Moran I-statistic: 14.2 > 1.96 Moran I-statistic: 8.9 > 1.96 LM-statistic (OLS): 157.1 > 6.635 LM-statistic (OLS): 48.9 > 6.635 LM-statistic (SAR): 71.3 > 6.635 LM-statistic (SAR): 133.7 > 6.635 *** n = 4008; Asymptotic t-statistics in parentheses; Levels of signi…cance: 1% level, ** 5% level, * 10% level.

—


17