Natural amenities in urban space – A geographically weighted regression approach

Landscape and Urban Planning 121 (2014) 45–54

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Research paper

Natural amenities in urban space – A geographically weighted regression approach Pia Nilsson ∗ Jönköping International Business School, Jönköping University, Department for Economics Finance and Statistics, P.O. Box 1026, SE-551 11 Jönköping, Sweden

h i g h l i g h t s • • • •

Adds to the literature by focusing on spatial patterns in marginal valuations. Employs a geocoded database and a geographically weighted regression approach. Results reveal significant intraregional heterogeneity in amenity assessments. Finds a greater competition for attributes high in demand, yet locally scarce.

a r t i c l e

i n f o

Article history: Received 22 February 2013 Received in revised form 14 August 2013 Accepted 31 August 2013 Available online 11 October 2013 Keywords: Open space amenities Local heterogeneity Geographically weighted regression model

a b s t r a c t Natural amenities play an important role in explaining intra-regional economic growth, because they increase the competition between places and the relative demand for housing. This paper shows that these relationships are strongly location-specific, such that the magnitude and the direction, of value assessments vary across the urban surface. The analysis in this study addresses spatial heterogeneity in the valuations of preserved open space amenities using Swedish house price data. The results show that marginal valuations of open space amenities are high in locations that are characterised by high population and housing densities and low or insignificant in areas where undeveloped lands are abundant, thus, supporting the hypothesis that a greater competition for those, locational attributes that are in high demand, yet locally scarce, results in higher marginal prices. © 2013 Published by Elsevier B.V.

1. Introduction Increasing urbanisation and altered lifestyle choices in cities around the globe have created a larger focus on preservation of natural amenities in urban areas (Brueckner, 2000; Carruthers & Ulfarsson, 2002; Wu & Plantinga, 2003). The increased focus on preservation efforts and their benefits stems from a growing awareness of the large number of aesthetic and environmental benefits generated by open space amenities (Hasund, Kataria, & Lagerkvist, 2011; Irwin & Bockstael, 2004). Cities are highly dependent on ecosystem services within and beyond their city limits (Bolund & Hunhammar, 1999). Likewise, natural amenities increase regional attractiveness by inducing migration and increasing housing prices (Rappaport, 2009). Adding to this, structural changes in the agricultural sector and a decline in the number of active farmers have contributed to a loss in permanent grasslands and open farmlands, assembling the preservation

∗ Tel.: +46 36 10 17 59; fax: +46 36 12 18 32. E-mail address: [email protected] 0169-2046/$ – see front matter © 2013 Published by Elsevier B.V. http://dx.doi.org/10.1016/j.landurbplan.2013.08.017

of open landscape amenities as a matter of growing importance. Sweden, as many other countries, has witnessed decay in the variety of open space amenities including many important ecosystem services, such as urban forests, cultivated lands and wetlands (Finck, Riecken, & Schröder, 2002; Ihse, 1995; Meeus, 1993). The purpose of this paper is to employ the hedonic pricing approach and analyse if open space amenities are capitalised into Swedish housing prices, thereby, addressing the economic values that are created by these non-market amenities. In particular, if economic values can be demonstrated through a premium on housing prices, this may alter the position of existing open space amenities in the formation of local land-use policy. The focus of the current research is on open space, but other types of amenities have also been examined in this literature, such as proximity to urban space, lakes and other waterscapes. There has emerged a growing literature on natural amenities and their influence on regional development and housing prices. A common finding in the migration literature is that natural amenities are significant factors influencing location decisions of individuals and firms (Bjerke, 2012; Knapp & Graves, 2006;

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P. Nilsson / Landscape and Urban Planning 121 (2014) 45–54

Partridge, Rickman, Ali, & Olfert, 2007). Similarly, many studies empirically address housing prices and their relation to various landscape amenities in the vicinity. Prior literature has identified positive values for proximity to open space amenities and the natural land cover surrounding household locations (Acharya & Bennett, 2001; Cho, Poudyal, & Roberts, 2008; Geoghegan, Wainger, & Bockstael, 1997; Kong, Yin, & Nakagoshi, 2007; Morancho, 2003; Poudyal, Hodges, Tonn, & Cho, 2009). Recent literature suggests that these relationships are local and that there is significant heterogeneity in the marginal valuation of natural amenities across space (Anderson & West, 2006; Chi & Marcouiller, 2011; Cho et al., 2008; Geoghegan et al., 1997; Partridge, Rickman, Ali, & Olfert, 2008; Wu, 2012). This literature finds that marginal effects are dependent on agglomeration and local development patterns and that average estimates substantially may over- or underestimate values. It is shown that open space proximity is valued highly but decays very quickly with distance (Geoghegan et al., 1997). It is also shown that positive economic flows are related to high levels of development and negative flows to low levels of development (Irwin & Bockstael, 2001; Walsh, 2003). Altogether, this research highlights that statistically significant local variables that exhibit strong intraurban variation are more informative for local land-use policy. In order to capture the local nature of these amenity types, this paper applies a geographically weighted regression model to study spatial variability in the benefits of living close to preserved open spaces. The spatial analysis employs a geographical database containing single-family homes sales in one growing regional housing market in Sweden, for the time 2000–2011. The results of this analysis confirm significant intraregional heterogeneity in how urban residents value open landscape amenities. Marginal effects are high in central areas where undeveloped land is relatively scarce and where population and home densities are high, whereas marginal effects are either low or insignificant in rural and peripheral areas. With the results, this paper is able to add evidence to this field of research by highlighting the local nature of housing markets and the importance of including spatial heterogeneity and the local approach in which natural amenities influence housing prices. Previous literature on open landscape amenities and house prices predominantly focus on estimating average marginal effects at the regional level. Compared to this, there is less information on how value assessments differ within regions and how this influence the relative demand for housing. The findings in this paper highlight the role of spatial heterogeneity in the analysis of housing markets concerning open space amenities by focusing on intraurban variability and spatial patterns in marginal valuations.

2. Previous studies and theoretical framework Amenities define as location-specific goods and services that make locations more attractive for housing and firms. They are often broadly categorised into those that relate to urban qualities and those that are pure natural assets. Urban amenities can be associated with positive externalities from agglomeration and intra-industry spillovers (Rivera-Batiz, 1988). In a very broad sense, a definition of urban amenities includes the positive externalities generated from agglomerations of people, firms, private and public goods and services, transportation facilities and physical infrastructure (Andersson & Andersson, 2006; Quigley, 1998). Natural amenities, on the other hand, are not tied to current economic conditions but comprise natural qualities, such as climate, topography, water resources and cultivated landscapes.

The spatial distribution of amenities is an important determinant of urban development patterns and plays a major role in shaping the urban spatial structure. Since the work of Schuler (1974), Yang and Fujita (1983) and Brueckner, Thisse, and Zenou (1999), there has emerged a growing literature on amenities and their relation to urban growth and local development patterns. Yang and Fujita (1983) extended the urban land-use model by Alonso (1964), Muth (1969) and Mills (1972) to include environmental externalities. They consider the influence of urban open space amenities on location decisions of different income groups. Adding to this, there are also many papers that focus on amenities and their relation to regional growth and development. Early studies with this focus have examined the influences of amenities on wages and house prices (Hoehn, Berger, & Blomquist, 2006; Roback, 1982; Rosen, 1979) and regional development (Ullman, 1954). Studies have also shown that amenities facilitate rural population growth (McGranahan, 2008; Partridge, Rickman, Ali, & Olfert, 2010; Partridge et al., 2008), job growth (Deller, Tsung-Hsiu, Marcouiller, & English, 2001) and generate compensating differentials in labour and housing markets (Landis, Elmer, & Zook, 2002; Partridge, Ali, & Olfert, 2010; Rosen, 1979; Schmidt & Courant, 2006). Building on this work, recent studies find that the spatial distribution of amenities and the interactions between natural amenities and agglomeration forces are significant in explaining urban development patterns and intra-urban location (Wang & Wu, 2011; Wu & Gopinath, 2008; Wu & Plantinga, 2003). Among other things, this literature finds that households are willing to endure a longer commuting to work if they can live in amenity-rich neighbourhoods. It is shown that when open spaces are located near to central locations they provide a more favourable trade-off between access to such amenities and commuting costs (Irwin et al., 2009; Wu, 2006). Further, these amenities are shown to have a positive influence on regional economic performance depending on factors, such as the size of the open space parcel, the relationship between size and amenity levels and transportation costs (Irwin & Bockstael, 2004; Wu & Plantinga, 2003). Among other things, it is shown that households in urbanised areas regard high density as a nuisance and are willing to trade accessibility to the centre against access to open space, larger homes and lower densities. Much of the research in this field have focused on the type of land-use patterns found in highly urbanised cities in the U.S., where more affluent households live on cheap land in the urban fringe and less affluent households live near the centre on expensive land (Glaeser, Kahn, & Rappaport, 2000; Margo, 1992; Mieszkowski & Mills, 1993). As noted by many, the type of land use patterns found in most European cities are reversed and high income households predominantly occupy centrally located expensive land (Hohenberg, Lees, & Hohenberg, 1995; Ingram, 1998). Brueckner et al. (1999) present an amenity based framework to explain intra-urban location by income, focusing on these diverging patterns. They suggest that, besides pure natural amenities, the historical and architectural amenities found in many European central cities explain part of the difference in location patterns. They show that households are attracted to central locations, not only because of lower commuting distance to work and natural amenities, but also because central cities inherently have a high quality of urban space. More recently, Andersson and Andersson (2006) show that physical infrastructures, such as cultural institutions, architecture and other historical amenities are key factors explaining the difference in attractiveness among European capital cities. Thus, premiums are paid for a variety of locational advantages, all of which have a significant impact on the development of new housing patterns and the evolving structure of urban areas (Smith, 1978). There is a large empirical literature that focuses on the relations between amenity supply, intraurban location and regional

P. Nilsson / Landscape and Urban Planning 121 (2014) 45–54

growth. Studies have shown that natural amenities facilitate rural population growth (McGranahan, 2008; Rappaport, 2004), job growth (Deller et al., 2001) and generate compensating differentials in labour and housing markets (Ferguson, Ali, Olfert, & Partridge, 2007). There are also an extensive number of hedonic studies that persistently show an inverse relationship between housing prices and distance to open space amenities. Tyrväinen and Miettinen (2000), Acharya and Bennett (2001), Irwin (2002), Morancho (2003), and Anderson and West (2006) to mention some. Tyrväinen (2001) and Cho et al. (2008) show that forests, water areas and wooded recreation areas are appreciated environmental characteristics in the urban environment and translate into higher housing prices. A recent study, focusing on apartment prices in Stockholm, finds that there are six urban qualities that are highly valued by urban residents. Among the highest ranked is access to high quality urban space; access to public transportation facilities and access to open space amenities (Spacescape, 2011). Similar urban quality models have been applied to cities such as Oslo and Copenhagen with comparable findings. For the purpose of exploring spatial variability and local nature of amenity valuations, the locally weighted regression approach (Cleveland & Devlin, 1988) and the geographically weighted regression approach (Brunsdon, Fotheringham, & Charlton, 1996; Fotheringham, Brunsdon, Charlton, & Fotheringham, 2002) have been increasingly used in the literature. These approaches are appealing in the study of housing prices since they provide a method to model the spatial structure of housing markets, incorporating local heterogeneity. Studies based on these approaches show that the marginal effects of most types of housing attributes have varying magnitudes and signs within urban house markets (Bitter, Mulligan, & Dall’erba, 2007; Cho, Lambert, Roberts, & Kim, 2010; Cho et al., 2008; Farber & Yeates, 2006; Lu, Charlton, & Fotheringhama, 2011). Recent contributions strongly suggest that greater competition for those housing attributes that are in high demand, yet locally scarce should result in higher marginal prices. There are also studies that address altered preferences for natural amenities resulting from temporal influences. Cho, Clark, Park, and Kim (2009) find that marginal valuations increase significantly over time, comparing sales conducted during 1989–1991 and 1999–2001, respectively. In a more recent study, they find significantly lower valuations of open space amenities during the recession year 2008 compared to the period 2000–2006 (Cho et al., 2010). Temporal patterns are thought to be a result of altered preferences and expenditure during times of recession.

3. Data and study area The analysis in this paper is geographically delimited to the study of the housing market in the Jönköping region, located in the south central part of Sweden. The region is the 10th largest out of Sweden’s 290 regions in terms of population size and 64th in terms of population density. The region is characterised by growth in population and growth in jobs. During the 20th century the population has grown with 10,000 inhabitants and the number of newly established firms has increased progressively, with 871 new firms registered in 2011. The region hosts a growing university and several large public authorities, which are the main employers. These growth figures have also translated into an attractive urban housing market in terms of both new constructions and sales from the existing stock. The regional housing market belongs to some of the fastest growing housing markets in Sweden in terms of its Tobin’s q value. Although the region has a relatively small central district in comparison with some of the largest cities in

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Fig. 1. Getis-Ord clusters w.r.t. sales price. This figure shows returned GiZ scores from cluster analysis w.r.t. sales price, classified using standard deviations (Getis & Ord, 1996). Points in red denote sales with prices significantly above the regional average (>2.58 Std.Dev.) and points in blue denote sales with prices significantly below the regional average (<−2.58 Std.Dev). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of the article.)

Sweden, it displays similar patterns of growth at the urban fringe with plans to expand the centre. Areas surrounding the urban centre are most urbanised with population densities around 6800 people per km2 , whereas peripheral areas have densities as low as 3 people per km2 . Both older and larger housing is generally found in the most urbanised areas north-west and north-east of the urban centre and along the lakeside, whereas newer housing is found scattered around rural and peripheral locations. The region is situated at the south end of Lake Vättern, which is the second largest lake in Sweden. The lake is an attractive natural characteristic that provides both aesthetic, recreational and ecosystem services. The housing data analysed in this study are obtained from the regions’ housing and development office. The data report transactions on all sales of owner occupied single-family homes during the time period 2000–2011. These transactions data and their prices are reported in Fig. 1. In order to explore the pattern of prices in more detail, cluster analysis was employed in an attempt to identify locations where houses sell for prices above the regional average. Fig. 1 illustrates that the urban house price gradient falls from high value homes near the centre to low value homes in the rural and peripheral parts of the region. Single-family homes that sell for prices significantly above the regional average are found in the north-west and north-east parts of the urban centre, along the lakeside. Although the figure shows sales that cover the whole period 2000–2011, the same price gradient appears when examining shorter time periods and when comparing prices prior to and after the crisis year 2008. The total number of single family homessales conducted during the studied time period equals 8300. From these transactions data only those sales that are representative in terms of the purchase price coefficient are included in the analysis, resulting in 6670 sales (these are presented in Fig. 1). The region is divided into 74 census tracts (three-digit level) as shown in the figure; these are used to define housing submarkets in the analysis that follows.

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4. Model formulation and explanatory variables The paper applies a geographically weighted regression model (GWR) (Brunsdon et al., 1996; Fotheringham et al., 2002) to examine spatial heterogeneity in the values placed on natural amenities by urban residents. In this model, housing prices are modelled according to their spatial nature and home sales are geographically weighted with their proximity to other sales in the sample. 4.1. The GWR estimator In contrast to a global model that estimates average coefficient values, GWR allows estimated coefficients to vary from location to location. A general version of the model can be expressed as: yi = ˇ0 (ui , vi ) +

n 

ˇz (ui , vi )xiz + εi

(1)

z=1

where yi denotes the dependent variable, in this case the price of house i at location i, ˇ0 (ui , vi ) denote the intercept coefficient at location i, xiz is the value of the zth explanatory variable at location i and ˇz (ui , vi ) is the local regression coefficient for the zth explanatory variable. Furthermore, (ui , vi ) denotes Cartesian x and y point coordinates and εi denotes the random location specific error term. Stated in matrix notation, the parameters are estimated using the following expression: ˆ i , vi ) = (X  W (ui , vi )X)−1 X  W (ui , vi )y ˇ(u

(2)

ˆ i , vi ) is the estimate of the location-specific parameter, where ˇ(u W (ui , vi ) is an n by n spatial weight matrix whose off-diagonal elements are zero and the diagonal elements denote the geographical weights of observed data at location i. The geographic weight structure (ui , vi ) is based on a Gaussian kernel function such that the influence of data points in the proximity of i is given larger weights in the estimation (Fotheringham et al., 2002). This paper uses an adaptive bi-square function to generate the geographic weights. An adaptive function fits the housing transactions data analysed in this paper since sales are highly clustered within the market area. This approach allows the bandwidth to increase its size when sample points are sparser and decrease its size when they are denser (Charlton, Fotheringham, & Brunsdon, 2009). Thus, home sales are hypothesised to influence each other within a certain range (based on a continuous decay function), but beyond this range they are assumed to have no influence on each other. The bi-square function can be expressed in the following way:





wij = 1 −

2

dij dmax (q)2

if dij ≤ dmax (q),

(3)

otherwise wij = 0

where j denotes the home sales point and i represent any sales point for which the parameters are estimated. Moreover, dij denotes Euclidean distance between the sales point i and j, the maximum distance between any point i and its q neighbours is denoted by dmax . As shown by Fotheringham et al. (2002), regression results are sensitive to the choice of neighbours and the chosen bandwidth may have a significant influence on coefficient estimates. Cleveland and Devlin (1988) suggest that the optimal number of nearest neighbours should be determined using a cross-validation score that minimises the residual sums of squares in the following way: N∗ = min q

n  i=1

[yi − yˆ (i) (N)]

2

(4)

Fig. 2. Spatial distribution of open spaces.

where yˆ (i) denotes the predicted value of observation i i.e. the predicted house price and N* is the optimum number of neighbours N* that minimises the residual sums of square. This implies that houses up to the nearest q neighbours get a positive weight and houses beyond get a zero weight. The empirical approach in this paper is to estimate Eq. (1) to examine spatially varying relationships across the urban market area. 4.2. Independent variables Geocoded transactions data holding prices and structural characteristics are provided by the regions’ housing and development office. Total sales price is used as dependent variable and independent variables are obtained from two geocoded databases: (i) the spatial distribution of open space amenities that are included in the region’s natural preservation programme (NVP), obtained from the housing and development office and (ii) the spatial distribution of waterscapes (lakes and rivers) obtained from the Swedish Meteorological and Hydrological Institute. 4.2.1. Open space amenities The amenity variables, of interest, consist of distance to the nearest open space area and its parcel size. Preserved open spaces enclose natural areas that are part of the regions natural preservation programme (NVP). The NVP programme contains 1654 natural areas including farmlands (mown meadows, natural pastures), preserved forests (deciduous forests, pine forests), wetlands, parks and green spaces. The spatial distribution of these natural areas is illustrated in Fig. 2. In this study, these preservation areas are treated as one category and no separation is made between natural types. Among the other open space variables are distance to Lake Vättern and distance to other lakes. Following Cho et al. (2008) and Poudyal et al. (2009) among others, Euclidean distance is used as a proxy for adjacency and distance variables are created using spatial joins (ArcView 10.1), defined as the distance from housing centroids to centroids of nearest amenities (nearest point or polyline). The

P. Nilsson / Landscape and Urban Planning 121 (2014) 45–54

theory suggests that open space amenities will be valued higher in dense areas and that larger parcels generate higher external benefits. Thus, the prediction is a negative elasticity for distance variables reflecting that benefits falls as distances are increased and a positive relation between prices and the size of the nearest parcel. To measure lake view, altitude is included as a proxy variable. This is constructed from a raster map obtained from The Swedish Cadastral and Land Registration Authority and measures height above the ground surface based on altitude lines. Altitude is an important variable for this particular housing market; many of the most attractive locations are located on the hillsides with view over Lake Vättern. Studies have found that open spaces tend to be endogenous variables in house price estimations (Cho et al., 2008; Irwin & Bockstael, 2001). These problems occur when land development is determined by market forces and when land is privately owned or have a high likelihood of being converted into private residential land in the future. These problems are mitigated in this study by including open spaces that are publicly available and preserved by the local government. Another difficulty of hedonic estimations including open space amenities is the potential problem with unobserved local heterogeneity (Anderson & West, 2006; Bates & Santerre, 2001; Irwin & Bockstael, 2004). Using a GWR approach is expected to mitigate these problems since the model captures spatial heterogeneity at the parcel level (Wu, 2012). One obvious limitation with this approach, using distance to the nearest amenity, is that it may fail to account for more distant but potentially important ones. Although this can be partly eluded by including the share of neighbourhood land consisting of open space (Cheshire & Sheppard, 1995; Geoghegan et al., 1997), others have shown that nearest is an accurate measure, controlling for size of the nearest parcel (Anderson & West, 2006).

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neighbourhood variables can be attained. This study may be limited in this regard since there is a possibility that these tracts are not perfect classifications of local markets. Three variables are included to indicate neighbourhood quality, median income is defined as per capita median income and crime is defined as number of reported serious crimes per 1000 people in the census tract. Further, local density is included to capture local agglomeration and is defined as population per square kilometre in the neighbourhood. A major disadvantage with the neighbourhood and open space variables is that they are not consistently measured over the studied time span. When examining neighbourhood characteristics for the available years (2000 and 2010) these are shown to be stable over the studied time period. Thus, the inability to update neighbourhood variables should not be considered an overly serious problem. As noted by Andersson and Andersson (2006) and Jackson and Mare (2009), among others, processes of neighbourhood change occur very slowly over time. 4.2.3. Residential characteristics and temporal factors Among the residential variables are residential quality, residential size and lot size. Residential quality scores are self-reported and collected by the Swedish tax authority. These scores reflect both interior and exterior quality and design such as number of rooms, number of bathrooms, access to central heating, car port etc. Variables to control for variation in prices that can be attributes to real estate market fluctuations are yearly fixed effects and mortgage interest rate. Mortgage interest rate is defined as the prevailing quarterly average mortgage rate at date of sale, converted to real interest by subtracting annual change in the consumer price index (Cho et al., 2008; Wu, 2012). Summary statistics of explanatory variables are reported in Table 1. 5. Estimations and results

4.2.2. Urban space and neighbourhood quality Premiums are paid for a variety of locational advantages, including access to urban spaces and their concentration of private and public goods and services. The development of the service sector of most cities, together with the decentralisation of retail and manufacturing activities have implied that distance to the one urban core area has become less relevant (Fujita & Ogawa, 1982; Mills, 1972). Studies find that assessing accessibility requires the measurement of distance to a larger set of urban spaces (Dubin & Sung, 1987; Theriault, Des Rosiers, Villeneuve, & Kestens, 2003). Variables included to capture the effects of proximity to urban spaces are distance to the nearest town and incremental distance to the urban centre. The first measures influences related to household access to local consumer services and the second is calculated as the distance from the housing centroid to the urban centre minus the distance to the nearest town of any size. Incremental distance to the urban centre is expected to capture the negative effect of having to travel farther to reach high quality urban space (Ali, Partridge, & Olfert, 2007). This method is useful here, owing to the high correlation between distance to lake Vättern and the city centre and the predictions are negative elasticities reflecting that benefits falls as the distances are increased. Spatial variability in the demand for housing is also highly influenced by social and economic quality of the neighbourhood. Income inequalities and the social profiles of neighbourhoods are highly mirrored in the urban house price surface (Hårsman, 2006; Theriault et al., 2003). While factors such as high median income level and educational attainment capture high social and economic neighbourhood status, crime rates and unemployment rates captures low status (Ceccato & Wilhelmsson, 2011; Dubin & Sung, 1990; Lynch & Rasmussen, 2001). In this paper, neighbourhood variables are measured at the three-digit level census tract level (Fig. 1), which represents the finest level of which

The empirical approach in this paper is to estimate a hedonic function, including amenity variables along with structural and locational control variables (Table 1). Local GWR estimates are compared to global estimates provided by ordinary least square. Consistent with the general GWR specification in Eq. (1), a hedonic function of the following form is estimated: ln pi = ˇi0 + ˇi1 ln i + ˇi2 ln i + ˇi3 ln i + ˇi4 i + εi

i = 1, 2, 3, . . ., 6670

(5)

where pi denotes sales price of house i sold at location i, ˇi0 denotes the intercept at location i,  i is a vector of house specific variables; i is a vector of neighbourhood characteristics;  i is a vector of distance gradients to urban centres and natural amenities (including parcel size). Moreover,  i is a vector of variables that capture time-specific factors, including yearly fixed effects and mortgage interest rate. Moreover, ˇi1 to ˇi4 represent vectors of associated parameters. The functional form of the estimated hedonic equation is logarithmic to capture diminishing effects in structural characteristics and distance variables (Andersson, 1997; Mahan, Polasky, & Adams, 2000). The logarithmic form is also shown to correct for heteroskedasticity. 5.1. Test for spatial variability Regression results are reported in Table 2, Model A reports the average marginal effects estimated using an ordinary least square method and GWR estimates are reported in Model B and Model C. Before turning to the interpretation of the results, a test for spatial variability is applied to test the relevance of using a GWR approach for these transactions data. While there are many possible methods, this study applies the approach in using an F distribution as a

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Table 1 Descriptive statistics. Variablea

Unit

Min.

Max.

Mean

Std.Dev.

Structural characteristics House priceb Living area Lot size Quality Age d.nearest town d.urban centre d.lake Vättern d.nearest lake d.nearest open space Size nearest open space Altitude Mortgage interest rate

SEK Square metre Square metre Number Number Metres Metres Metres Metres Metres Hectare Lines Per cent

100 30 80 6 1 83.60 16.75 0.47 6.38 1 0.1308 0 0.42

8200 651 50,208 99 312 39437.55 40352.31 34258.78 11036.21 4349.71 109.63 5 6.12

1467.248 137.24 1171.75 31.03 42.61 13,048 9899.82 4526.03 3533.01 1266.61 8.271 3 2.405

910.931 43.40 1681.56 5.01 28.77 6681.47 6682.26 4779.91 1865.05 834.82 11.633 2.5 1.285

Neighbourhood characteristics Median income Local density Crime

SEK Number inh./km2 Number/1000

159.900 3 0.025

301.231 6871 39.200

239.560 1165 5.64

a b

100.523 902 4.278

House-specific variables are measured at date of sale and neighbourhood variables in year 2000. In thousand Swedish kronor (SEK). Summary statistics in are average values for the period 2000–2011.

Table 2 OLS and GWR regression results, dependent variable ln price. Parameters

Model A (OLS)

Model B (GWR)a

Model C (GWR)

Test for spatial variability

Coeff. (Std.Err.)

Low

Median

High

Low

Median

High

p-Value

ln livingarea ln quality ln lot size Age Age square ln d.nearest town ln inc.d.urban centre ln localdensity ln crime ln median income ln d.Vättern ln d.lake ln d.pres.open space Size pres.open space Altitude Mortgage interest rate Yearly fixed effects Intercept

0.427 (0.021) 0.446 (0.033) 0.056 (0.012) 0.131 (0.033) −0.015 (0.009) −0.057 (0.009) −0.167 (0.011) 0.019 (0.005) −0.011 (0.001) 0.063 (0.006) −0.201 (0.006) −0.076 (0.009) −0.019 (0.007) 0.023 (0.005) 0.141 (0.032) −0.045 (0.004) Yes 12.641

0.132 0.008 0.004 0.003 0.032

0.446 0.379 0.106 0.086 −0.011

0.667 0.449 0.368 0.111 −0.043

−0.021 Yes 6.453

−0.031

−0.049

0.090 0.006 0.001 0.001 0.012 −0.016 −0.046 0.003 0.000 0.006 −0.023 0.0054 −0.003 0.0001 0.023 −0.029 Yes 3.476

0.401 0.370 0.086 0.072 −0.023 −0.066 −0.083 0.023 0.000 0.004 −0.176 −0.055 −0.039 0.021 0.131 −0.037

0.623 0.443 0.343 0.095 −0.362 −0.134 −0.176 0.078 0.000 0.008 −0.398 −0.176 −0.075 0.056 0.326 −0.040

0.0000a 0.0000a 0.0000a 0.0000a 0.0000a 0.0000a 0.0000a 0.0000a 0.1087 0.0295 0.0000a 0.0000a 0.0000a 0.0000a 0.0000a 0.5631

Global adj. R2 Local R2 AIC Condition number

0.468 0.321

0.601

0.659

0.816

10,168

0.261 9035 18

0.456 6846 25

a Low is the estimate at the 25th quintile, median the 50th quintile and high the 90th quintile. The estimations have also been performed for different time periods (2000–2003, 2004–2007 and 2008–2011 and excluding 2008–2009 transactions) in order to test if the crisis has any effect on coefficient values, the results are robust.

decision rule. The last column in Table 2 contains the results from this examination, where a low p-value (large F-statistic) implies that the parameters display significant spatial heterogeneity. Most of the parameters have p-values that are statistically significant at the 1% level. The exceptions are crime and median income shown to be either weakly significant or insignificant. This is likely reflecting that the market area is quite homogenous with respect to income levels and crime rates across census tracts. However, this can also reflect that the census tracts used to define homogenous neighbourhoods are unsuitable for this purpose. However, their coefficient estimates are significant and in line with expectations in Model A, in that high median income is positively related, and high crime rate shows a negative relation with price. Overall, the results obtained by the Leung et al. (2000) test for spatial variability validates the use of a GWR model for the analysis of these transactions data. The results in Table 2 show that the adjusted R2 of the model increase from 47% to 66% (median local value) and

the AIC criterion declines from 10,168 to 6846 when the model is estimated using the GWR approach in Model C, compared to the ordinary least square estimation in Model A. The median of the local R2 is 66%, with a maximum of 82% and a minimum of 45%. These results show the benefits of moving from a global model ordinary least square model to a local regression model. Local collinearity in GWR models is examined using condition numbers, which equals the square root of the largest eigenvalue divided by the smallest eigenvalue. Wheeler and Tiefelsdorf (2005) show that condition numbers that are greater than 30 indicates local multicollinearity and unstable results in GWR models. Also, variance inflation factors are used to test for multicollinearity among the explanatory variables in Model A. As shown in Table 2, condition numbers are low, suggesting that multicollinearity should not prevent the interpretation of results. The matrix in Eq. (2) results in 6670 coefficients for each parameter. For brevity, GWR estimates are reported by their quantile range.

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5.2. Spatial patterns in preserved open spaces The coefficient of distance to open space is significant and has the anticipated negative sign in both models, implying that increasing the distance to open spaces has a negative influence on prices. In Model A, the regional average marginal effect is significant at the 1% level and equals −0.019, indicating that the value of an average house increases with proximity to preserved open spaces with an elasticity of 1.9%. The results of Model C, shows that marginal effects varies significantly within the region. The coefficient value of the 10th percentile equals −0.003 and the value at the 90th percentile is equal to −0.075. From these results it is possible to calculate a price premium that gives a rough approximation of the increase in expenditures that an average household is willing to pay to live at a closer distance to open space amenities. Evaluated base on the regional average (-0.019) at mean price (1467,000 SEK) and an initial mean distance of 1266 implies that moving 100 m closer to open space amenities would increase the average house price by 2202 SEK. Based on the same assumptions using the median GWR coefficient (−0.039) implies a local premium of the size 4517 SEK. Further, using the coefficient value at the 90th percentile implies a local premium of the size 8692 SEK. These results confirm the findings of prior studies, that proximity to open space amenities raise housing prices (Anderson & West, 2006), they also confirm the approximate magnitude of the premium that are generated (Cho et al., 2008, 2009). However, most importantly the results validate significant spatial variability in the values placed on open space amenities (Cho et al., 2008; Wu, 2012). The positive and significant coefficient for the size of the nearest open space parcel has the anticipated positive sign, implying that larger parcels add more value to nearby housing than do smaller (Poudyal et al., 2009). The regional average estimate of the size coefficient is 0.023 and the local estimates vary between 0.0001 and 0.056. Turning to the other open space variables, the significant and negative coefficients of distance to Lake Vättern and other lakes are consistent with expectations (Benson, Hansen, Schwartz, & Smersh, 1998; Luttik, 2000). The coefficient value indicates that distance to lake Vättern has a relatively large influence on prices (−0.176), but less so when controlling for altitude and incremental distance to the city centre. It should be noted that the coefficient value of distance to Lake Vättern is 0.421 when incremental distance to the centre and altitude are excluded. As discussed, altitude is an important factor explaining house prices in the region since it can be regarded as a proxy variable for lake view. The coefficient value of altitude is significant and has the anticipated positive sign in both models and the regional average marginal effect (0.141) is consistent with the median GWR estimate (0.131). Distance to other lakes indicate an equivalent relation with prices, but is shown to be less influential based on its Median GWR coefficient value (−0.055). In order to provide information about local patterns in coefficient estimates a visual representation of coefficient values that are significant at the 1% level, for distance to nearest open space, are presented in Fig. 3. Fig. 3 maps the coefficient values obtained from Model C according to their quantile range. As can be seen in Fig. 3, there are some clusters with high marginal effects in the north-west and northeast parts near the urban centre. These areas are characterised by high population and housing densities and the supply of undeveloped lands are relatively scares in these areas. The highest marginal price estimates for both distance to and the size of nearest open space are found in areas west and north-west of the urban centre along the lakeside. Houses are generally expensive in these locations and neighbourhood median income levels are generally above the average. The types of preserved open spaces that can be found in the central parts of the region mainly consist of deciduous forests, pine forests, parks and green spaces. In particular, the high coefficient values found in the North West and more affluent parts of the

Fig. 3. Coefficients of distance to nearest preserved open space significant at the 1% level.

centre are likely to reflect high values placed on proximity to the central park. The central park is an attractive natural characteristic that provides aesthetic and recreational opportunities for nearby residents and many of the most expensive houses in the region are located close by the park. The type of natural areas that are found in the western parts of the urban centre mainly consist of deciduous forests, pine forests and green areas, natural types that are consistently shown to add value to housing prices. For example, Cho et al. (2008) find that proximity to such forest amenities is reflected in house prices most profoundly for homes located in urban core areas and in areas where green open spaces are scarce. Two clusters of relatively high marginal effects can also be found at the north-east upper side of the lake and some high coefficient estimates at some rural and peripheral locations. Interpreting these results calls for some care since relatively few sales are conducted in these areas. This could imply that estimations at these regression points are less sensitive to local heterogeneity since the bandwidth is increased. Although, the estimated coefficients for the opens space amenities in this study are in line with expected values and though it may be conclusive, the current study has some limitations that deserve future research. In particular, the separation of open space amenities into different natural type categories would be a useful extension. 5.3. Urban decay and residential characteristics In line with expectations, distance to nearest town and incremental distance to the urban centre are associated with negative and significant coefficient estimates, such that increased distances to both the nearest town and the increment from that town to the urban centre are negatively related with price. Evaluated based on median GWR estimates, coefficient values equals −0.066 and −0.083, respectively. These results indicate that the negative effect of having to travel farther to access local consumer services is smaller than the negative effect of larger distance to the urban core

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6. Conclusions

Fig. 4. Coefficient raster surface (a) ln residential and (b) ln residential quality size.

area, suggesting that some polycentrism is emerging (Farber & Yeates, 2006). Turning to structural characteristics, these are stable across the estimations when comparing their average marginal effects in Model A and the Median estimate in Models B and C. Additional living area and residential quality are positively related to sales price and the magnitudes of the coefficient estimates indicate that these are influential factors. Although consistent when measured at the median, coefficient estimates are shown to vary significantly across the study area. Additional living area varies between 0.090 and 0.623 and additional quality between 0.006 and 0.443. Lot size is also shown to be positively related to prices with a median coefficient value of 0.086 (Model C). The estimated coefficients show a smooth spatial pattern, such that higher coefficient estimates are found in locations near the centre, consistently falling as the distance to the centre is increased. Similarly, structural coefficients tend to be high in the more valuable western parts where demand for single-family homes is high and lower towards the rural and peripheral parts of the market area. Thus, the influence of location shows a clear pattern in the marginal price of structural attributes concerning location across the urban surface. These results are in line with previous findings (Bitter et al., 2007; Fik, Ling, & Mulligan, 2003), showing that there is significant spatial heterogeneity in key structural attributes within urban house markets. A raster coefficient surface of the spatial distribution of residential size and quality coefficients are presented in Fig. 4a and b.

The purpose of this paper is to examine spatial heterogeneity in preserved open space amenities and its effect on house prices. Recent data from one Swedish urban house market is used to estimate a geographically weighted hedonic function. A particular focus of the paper is to examine spatial heterogeneity in the benefits of proximity to open space amenities. Undeveloped land parcels that are part of the region’s preservation programme are included in this category. Preservation of these landscape amenities has become a matter of growing importance as the urban area is becoming more urbanised and continues to expand towards the fringe areas. The results in this paper reinforce prior findings showing that open landscape amenities are important determinants of urban house prices and thereby also of urban quality of life. Key findings suggest that there is a significant intraregional heterogeneity in how open space amenities influence housing prices. Coefficient estimates are shown to exhibit significant variation with clusters of high parameter values at some locations. In line with recent findings (Cho et al., 2008; Wu, 2012) this study finds that these amenities are valued higher in areas where undeveloped land is relatively scarce and where population and home densities are relatively high. These results imply that there is a need for locationspecific land use management in order to create economically efficient policies (sometimes called smart growth policies). In particular, local ecosystem services have shown to have a significant influence on the quality-of-life in urban areas and should play an important role in local land-use planning (Bolund & Hunhammar, 1999; Murphy, 1988). As argued in the literature, decisions on land-use should not only be motivated by economic arguments, but they should also include environmental motivations. Brueckner (2000) describes these types of market failures as an incapability of local governments to account for the economic values that are generated by such amenities and the values forgone when units of land are converted to urban use. Thus, an effective local planning is important for deriving the optimal use of these amenities and for acquiring their future status. Although this paper is focused on one specific region, with results pertaining to this particular housing market, the analysis can be expanded to include other urban housing markets since equivalent natural preservation programmes are found in regions all over Sweden and in many other parts of Europe. Because the objective of this study is to determine the spatial variation in the benefits of preserved open spaces the marginal valuations of the age effect, lot size valuations or other control variables are not considered explicitly, although this would be a useful extension. References

5.4. Sensitivity analysis To examine whether the conclusions from the estimations are robust the patterns in ordinary least square and GWR model residuals were examined to see to see if they are randomly distributed across the market area (Farber & Yeates, 2006). Employing the spatial autocorrelation (Moran’s I) tool on residuals of Model A shows that there are statistically significant clusters (1% level) of high and low residuals (model under- and over predictions). This is most likely due to the exclusion of locational variables to capture local heterogeneity (Wheeler & Tiefelsdorf, 2005). Examination of the GWR residuals shows that residuals are randomly distributed over the market and there are no visual patterns that indicate model over- or under predictions, the Moran’s I pvalue is significant at the 10% level. From this it appears that the GWR model accounts best for the spatial variation in house prices.

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