Neighborhood green and services diversity effects on land prices: Evidence from a multilevel hedonic analysis in Luxembourg

Landscape and Urban Planning 143 (2015) 100–111

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Neighborhood green and services diversity effects on land prices: Evidence from a multilevel hedonic analysis in Luxembourg Marie-Line Glaesener a,b,1 , Geoffrey Caruso a,∗ a b

Institute of Geography and Spatial Planning, Belval, Luxembourg Luxembourg Institute of Socio-Economic Research, Belval, Luxembourg

h i g h l i g h t s • • • • •

First multilevel hedonic model with landscape amenities and neighbourhood services. Opposite effects of landscape diversity at different distances. Spatial heterogeneity effects in the valuation of local land-use diversity. No impact of services diversity at sub-municipal scale. Multilevel model captures context effects and spatial autocorrelation.

a r t i c l e

i n f o

Article history: Received 13 December 2014 Received in revised form 30 May 2015 Accepted 5 June 2015 Available online 18 July 2015 Keywords: Hedonic pricing Multilevel approach Cross-regressive model Land-use diversity Neighborhood amenities

a b s t r a c t The article aims at revealing the role of green space diversity and the mix of neighborhood services on the price of residential land in Luxembourg. We use a multilevel approach to estimate a hedonic model in order to benefit from the hierarchical structure of the data and to reveal spatial heterogeneity in the valuation of these neighborhood qualities. In addition to standard accessibility and socio-economic variables, we include geographical variables in the form of neighborhood mix indices and a Shannon diversity index of land-uses. Via a spatial cross-regressive specification we also test whether our nested levels are able to capture most of the spatial dependence. Our results show that the presence of a mix of services and green space does not directly impact prices, but that the diversity of land-uses (Shannon index) matters, and has negative effects when considered within immediate proximity and positive effects within a walking distance. Land use effects however vary spatially and emphasize the contrast between regions that are particularly attractive and picturesque, and the former industrial conurbation. In our case we also show the ability of the multilevel approach to capture spatial auto-correlation effects. © 2015 Elsevier B.V. All rights reserved.

1. Introduction The spatial distribution of residential land values around cities mainly arises from trading-off accessibility to jobs against housing consumption (Alonso, 1964; Fujita, 1989). However neighborhood qualities and landscape features add up to this trade-off and add further complexity to the spatial structure of land values. Cheshire and Sheppard (1995) emphasized the need to consider a broad

∗ Corresponding author. Tel.: +352 46 66 44 6625. E-mail addresses: [email protected] (M.-L. Glaesener), [email protected] (G. Caruso). 1 The work presented in this paper is part of the outcome of the Ph.D thesis undertaken at the University of Luxembourg in the Institute of Geography and Spatial Planning between 2009 and 2014. http://dx.doi.org/10.1016/j.landurbplan.2015.06.008 0169-2046/© 2015 Elsevier B.V. All rights reserved.

range of location-specific attributes, and over the last 20 years numerous studies have attempted to include local amenities in the analysis of land prices to better understand how much these local features are decisive in residential choice. Since urban growth patterns challenge sustainability and social goals, and many urban and land-use planning actions seek to address them at the local scale (municipality or smaller), it is particularly important for the success of urban policies that the benefits of local amenities are well understood to design effective and acceptable neighborhood plans. Of particular attention here is the presence, spatial distribution and diversity of both land-uses and green space, and neighborhood retail and services around residential places. Recent theoretical advances have shown that the local arrangement of green space impact on urban form and its scattered or leapfrogging nature (Caruso, Peeters, Cavailhès, & Rounsevell, 2007; Caruso et al., 2011). Brueckner, Thisse, and Zenou (1999)

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also showed the impact of urban versus exurban amenities on the income sorting of households and it is well-known since Tiebout (1956) that the provision of local public goods is an important aspect of residential competition. On the empirical side, results are less clearly conducive (see below) but there is a trend to use more micro-scale data and GIS to better measure these elements. Many hedonic studies now embed local amenities and proximity to services or shops. However very few consider the diversity of both services and land-uses and very few look at the spatial heterogeneity of their valuation. We can hypothesize that those local effects vary considerably with the wider landscape or socio-economic context, even after controlling for the most important socio-economic drivers that would proxy a Tiebout effect and the center-periphery contrast. We contribute such an analysis here using developable land transactions in the Grand Duchy of Luxembourg as a case study. We use a multilevel approach, which is still uncommon in spatial hedonic analysis. Our expectation is to capture additional contextual effects after controlling for neighborhood scale attributes and standard center-periphery trade-off. Moreover the structure of the data available in Luxembourg lends itself to the multi-scale approach. The remainder of the paper is organized as follows: in Section 2 we conduct a short review of the empirical literature that is most directly linked to our thematic scope and methods. Then we present the study area and the different data-sets (Section 3). The implementation of the approach is then described as applied to our case study (Section 4). Results are discussed in Section 5 before concluding.

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2. Literature review

of open-space, mainly at micro-scale, have been identified and analyzed in Brander and Koetse’s (2011) meta-analysis. These studies include either distance measures to different green amenities (Cho, Poudyal, & Roberts, 2008; Des Rosiers, Thériault, Kestens, & Villeneuve, 2002; Kestens, Thériault, & Des Rosiers, 2004; Shultz & King, 2001) and/or consider landscape amenities in varying buffer zones (Cavailhès et al., 2007; Kadish & Netusil, 2012; Melchiar & Kaprovà, 2013; Sander, Polasky, & Haight, 2010; Youssoufi, 2011). Using the same data-set as herein, Glaesener (2014) has tested for these spatial proximity effects at aggregated scale but showed that the lack of spatial precision for this particular data-set does not allow to capture close proximity effects with sufficient robustness. Besides proximity to different green amenities, the purchase decision of land consumers is also influenced by the configuration of the neighboring land-uses. Geoghegan, Wainger, and Bockstael (1997) show that increasing land-use diversity affects property values in two ways: negatively as they introduce higher chances of negative visual and noise externalities, but in the meantime positively as diversity may implicitly signify the proximity of important local urban amenities. Based on their findings, increased land-use diversity is expected to be valued negatively in immediate proximity, while within walking distance a positive impact is expected. Furthermore, spatial variation in the marginal effects of land-use diversity can be expected. Geoghegan et al. (1997) show that diversity is valued differently by consumers with distance to CBD and that it is generally not a desirable feature in the suburban area. In this study, we follow this literature steam on pricing the presence and proximity of land-uses. We also consider the spatial heterogeneity (as Geoghegan et al., 1997 or Cho et al., 2008), but we do so via a multi-scale setting that fits our data and, we expect, can identify non-stationary marginal effects across space.

2.1. The value of neighborhood services and green

2.2. Spatial effects and the multilevel approach

We review here some empirical literature on the value of proximity and diversity of both neighborhood services and land-uses. This review is not meant to be exhaustive but to pick up the rationale for our empirical experiment and the closest related work. The impact of local public goods and externalities within the city has been largely discussed since Tiebout (1956). Residential land consumers benefit from the presence of different local urban amenities (e.g.: public services, education and sports facilities, health care, retail). Fujita and Thisse (2013) claim that, as for commuting to work, consumers rather prefer short trips to retail and services. Moreover, the spatial pattern of exogenous amenities in a city (e.g.: natural and historical amenities) impacts on the location of different income groups within the urban area (Brueckner et al., 1999). Several hedonic pricing studies have investigated the impact on property values of distance to different local urban amenities (Des Rosiers & Thériault, 2006; Öner, 2013; Thériault, Des Rosiers, & Vandersmissen, 1999; Youssoufi, 2011). Urban amenities generally accounted for are, among others, measures of school quality (Clapp, Nanda, & Ross, 2008; Kiel & Zabel, 2008; Thériault et al., 1999; Uyar & Brown, 2007), distance to public open-space (Espey & Owusu-Edusei, 2001; Mahmoudi, Hatton MacDonald, Crossman, Summers, & van der Hoek, 2013; Wu & Dong, 2014) or the proximity of retail and services (Thériault, Des Rosiers, & Joerin, 2005; Youssoufi, 2011; Öner, 2013). Besides proximity to different local urban amenities, a rich diversity of the offer has been shown to have a positive marginal effect on individuals’ utility (Brueckner et al., 1999; Youssoufi, 2011). Considering explicitly the diversity of urban amenities is however not so frequent in the hedonic pricing context and we do not know of studies that would have analyzed its spatial variation in a multi-scalar context. The role of local green and diversity has been addressed in many hedonic pricing studies. Over 52 studies addressing the valuation

The hedonic pricing method (Rosen, 1974) is applied to estimate the implicit value of the non-market attributes composing land prices, from which consumers obtain utility, under the assumption of a unitary market in equilibrium. This assumption however prescribes that the implicit prices of the attributes are invariant. However, market segmentation might arise when consumers’ demand for a particular structural or location-specific characteristic is highly inelastic and that the preference for this characteristic is shared by many other consumers (Goodman & Thibodeau, 1998). Such market segmentation usually causes the emergence of submarkets, in which “persistent and significant disparities in attribute prices are present across housing bundles and urban space” (Orford, 2000, p.1645). Spatial heterogeneity is likely to arise if the priceattribute relationship varies spatially by such sub-markets, so if the marginal price of a plots characteristics’ varies substantially with its location in space (Le Gallo, 2004). Consequently OLS estimates, imposing spatial homogeneity, will be miss-specified and affect the validity of diagnostic tests (Anselin & Lozano-Gracia, 2009). Different methods to account for this spatial heterogeneity have been considered in the hedonic context (i.e.: geographically weighted regression; Cho et al., 2008, spatial expansion method; Geoghegan et al., 1997). Besides spatial heterogeneity, spatial dependence might also bias estimation results, and different auto-regressive estimation methods have been developed to account for this (among others Anselin, 1988; Elhorst, 2010; Ward & Gleditsch, 2008). These models should allow to identify and correct for the potential bias induced by spatial dependence and have been largely applied in hedonic literature, that will not be further reviewed here. According to Orford (2000) the auto-regressive functions developed in spatial econometrics literature can be seen as “technical fixes” to the problems of modeling spatial data, especially as they

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do not account for the issues related to spatial heterogeneity. As an alternative, Orford (2000) proposes the multilevel approach. This approach has been widely applied among others in the field of education studies (Hill & Rowe, 1996) and health research (Chaix, Merlo, & Chauvin, 2005; Duncan, Jones, & Moon, 1998; Lebel, Kestens, Clary, Bisset, & Subramanian, 2014; Park & Kim, 2014) and with increasing interest as well from other economic fields (Fontes, Simões, De Oliveira, & Hermeto, 2009; Meijer & Rouwendal, 2006), for instance to evaluate business performance and strategies at different levels (Favero & Lopes, 2011) or the relation between infrastructure and income convergence (Almeida & Guimarães, 2014). To date there have been few implementations of this approach in the hedonic pricing context. Moreover, to the best of our knowledge, existing applications have not considered residential land but focused on housing markets. The multilevel modeling approach accounts for the hierarchical data structure by modeling price variability at each of the spatial levels. In addition, it allows individual observations belonging to a particular spatial unit to be more similar than a random sample (Jones, 1991). The multilevel approach models the structure of the variation not accounted for by the explanatory variables and it does not assume a constant variance captured by a single error term (Orford, 2000). The assumption of a unitary housing market is relaxed and estimation biases related to spatial effects should be captured by this approach. With the independence assumption relaxed and the intra-group correlation explicitly modeled, more efficient estimates are obtained and thus inference becomes more reliable (Chasco & Le Gallo, 2013). Goodman and Thibodeau (1998) introduced the concept of multilevel modeling in the hedonic pricing context as a method to delineate housing sub-markets. Orford (2000) relies on this approach to investigate means to contextualize the hedonic specification to capture additional spatial dynamics of local housing markets and to model explicitly the processes leading to spatial auto-correlation in house prices. Chasco and Le Gallo (2013) implement a three-level multilevel hedonic model to measure the marginal impact on house prices of objective and subjective measures of air and noise pollution in down-town Madrid. Besides dwelling size, they consider the noise and pollution variables as random effects at different scales. They find that air pollution is only varying randomly at the highest neighborhood level, while noise pollution is perceived mainly at the census tract. Chasco and Le Gallo’s (2013) results confirm the local nature of noise in compared to air pollution. Djurdjevic, Eugster, and Haase (2008) aim mainly at accounting for aggregated data at two levels and they allow the marginal effect of dwelling size to vary across municipalities. Brunauer (2013) apply a four level structured additive regression model, incorporating spatial effects and complex interactions at the different levels, to decompose the distribution of the spatial heterogeneity effect over Austria. They highlight the importance of the inclusion of neighborhood attributes to explain spatial heterogeneity. Doubts have been raised on the multilevel model’s ability to capture all spatial effects. With regard to spatial error dependence in multilevel models, Elhorst and Zeilstra (2007) made first advances to combine the multilevel framework to the more standard spatial econometric error model. Multilevel models with spatial fixed and spatial random effects have been discussed by Corrado and Fingleton (2011), however raising several issues related to the estimation of such spatial multilevel models. More recently, Park and Kim (2014) applied a spatially filtered multilevel model using eigenvectors function as additional explanatory variables. Almeida and Guimarães (2014) tested several spatial multilevel models and found that the spatial effects, operating in the relationship between infrastructure and income convergence, were captured only by the multilevel spatial autoregressive (SAR) model. In the context of

neural tube defects, Ren, Wang, Liao, and Zheng (2013) relied on a multilevel model with spatial autocorrelated errors structure and show how these account for remaining spatial error dependence. In the hedonic pricing context, Chasco and Le Gallo (2012) illustrate that the multilevel approach only accounts for some part of spatial dependence by adding spatial multipliers. Following Chasco and Le Gallo (2012), the robustness of our results, with regard to spatial dependence, will be tested via a cross-regressive multilevel model. Overall the originality of our paper is to test the ability of the multilevel model to identify spatial heterogeneity in estimating the marginal effects of local amenities on land prices; in particular neighborhood services and land-use diversity. 3. Study area and data 3.1. Context In a context of sustained economic and demographic growth the part of built-up surface has almost doubled in the last 20 years (Chilla & Schulz, 2011). The distribution of population and its growth is not homogeneous in space, population densities and land prices are declining from the capital-city, namely Luxembourg (Fig. A1 Map A). Besides the agglomeration of Luxembourg, strongest population growth is mainly observed in the more rural and remote regions of the country. The evolution of these fundamental parameters and their spatial distribution illustrate the ongoing outward urban growth in Luxembourg, leading to a mixed periurban belt under strong under urban influence (high commuting rates) with a rural character (low population densities and residential areas scattered within agricultural land) (Caruso, 2005; Cavailhès, Frankhauser, Peeters, & Thomas, 2004a; Cavailhès, Peeters, Sekeris, & Thisse, 2004b; Irwin & Bockstael, 2007). Local authorities in Luxembourg are aware of these periurbanisation trends and a more careful management of open-space has been an important issue in recent planning policies. The “Programme Directeur de l’Aménagement du Territoire” (PDAT) (MIAT, 2003) suggests to strengthen secondary urban centers and encourages households to settle in more compact and denser urban areas in predefined regional centers (“decentralized concentration”; MIAT, 2004). More specifically the PDAT aims at directly influencing residential preferences to reach these goals. A recent evaluation of the planning measures (CEPS/INSTEAD, 2008) revealed however that these measures were of limited success, mainly because the fundamentals of urban growth were underestimated in first place. Moreover, we can argue about the acceptability of measures that specifically target preference choices with regard to the qualityof-life and neighborhoods. In this perspective there is a need in Luxembourg for more detailed insights on the land consumers’ preferences for the characteristics of the local geographical context. 3.2. Data Quantitative research, on real estate market in Luxembourg, is to date mainly exploratory and aggregated at municipal scale (e.g.: Decoville, Feltgen, & Durand, 2013). Due to data privacy concerns, the location of the residential land transactions was only available at sub-municipal (section) level. Further, socio-economic variables based on census data are only available at municipal scale the second important administrative and planning level in Luxembourg (Chilla & Schulz, 2011). With regard to the parcels’ structural information at transaction scale, we were thus confronted to three hierarchically nested levels: transactions, sections and municipalities.

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We describe variables at each level below and descriptive statistics are given in Appendix Table A1. Four groups of variables were considered in order to account for the structural characteristics, accessibility to Luxembourg-city, the neighborhood variables and eventually the socio-economic controls. We show here our final model specification for these effects. Further details can be found in Glaesener (2014) and the summary statistics for the explanatory variables are illustrated in Appendix Table A1. 3.2.1. Level One: Transactions The developable land transactions, registered at the notaries between January 2007 and December 2011, were provided by the Administration of Deeds (AED). After different steps of data cleanup, the data-set contains 6367 observations, on average 19.83 are registered per section and 57.16 per municipality. Their spatial distribution is illustrated in Appendix, Fig. A1 Map A. The transaction price was deflated to the value of January 2007-euros based on the consumer price index generated on a monthly basis by the National Statistics Institute (STATEC). Limited information on the structural characteristics of the parcels was available. Property size is considered to estimate the marginal effect of an additional are to a mean-sized parcel. In multilevel hedonic literature, a random slope is generally allowed for the price-size relationship at the higher level(s). Allowing the marginal effect of size to vary at higher spatial level(s), hence a coefficient per spatial unit, is expected to account for size related heteroskedasticity (Djurdjevic et al., 2008; Jones & Bullen, 1994; Orford, 2000; Treg, 2010). The random intercept and slope models are further discussed in Sections 4.2 and 4.3. Further, a binary variable is included to identify plots sold with a building plan (dVFA), since they were found to register higher unit prices and to be of smaller size. dVFA transactions are assumed to be generally sold by professional real estate developers to individual end-users, mostly in the framework of larger development projects. This variable is thus expected to capture for the marginal impact of the implication of professional developers in a land transaction. 3.2.2. Level Two: Sections 3.2.2.1. Accessibility to CBD. Following urban economic literature, access to the main employment center is considered as the major determinant of property prices (Alonso, 1964; Fujita, 1989). Therefore, time-distance to Luxembourg-city was included in two ways. First, travel-time by road network (tLUXci ) was computed based on an application generalizing the itinerary function of Google Maps® (Medard de Chardon & Caruso, 2010). Second, travel-time by public transport (tLUXpi ) was generated via Mobiliteit.lu®, an official online schedule engine for public transport in Luxembourg. These travel-time measures are expected to identify the negative marginal effects of distance to Luxembourg-city and furthermore provide insights into differences in the valuation of individual and public transport. 3.2.2.2. Local urban amenities. The urban amenity data-set was generated based on different official and on-line sources and represents the main retail and public service opportunities. To identify the marginal impact of service diversity and to avoid multicollinearity issues, a diversity index (DI) was generated following Youssoufi (2011). The diversity index is formalized in Eq. (1), where nc designates the quantity of observations for the cth category and n the total amount of retail and service opportunities per section. DI =

 nc 2 c

n

(1)

The different local urban amenities have been weighted according to the frequency of their use. Further information on the

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variables considered and the weighting can be found in Glaesener (2014). Since consumers are assumed to value proximity to a diverse offer of local urban amenities a higher DI is expected to be valued positively by land consumers and should capture an urban concentration effect. 3.2.2.3. Green and land-use diversity measures. The different landuse diversity measures are based on the land-use data provided by the Land Registry (Administration du Cadastre et de la Topographie, 2008a, 2008b). As discussed earlier, green land-use diversity is expected to be considered by land consumers in their purchase decision. In this perspective, based on the index displayed in Eq. (1), a diversity index for green land-use (DIGreen) was generated with based on the area (n) occupied by different green land-uses (forest, brushwood, watershed, rivers, vineyards, gardens, pastures and crop-land (c)) was generated. The index varies between 0 and 1; with 1 being maximum diversity and 0 standing for the presence of a single land-use (Appendix Fig. A1 Map B). DIGreen should identify the marginal effect of green land-use diversity on land price. Further, to account for differences in the valuation of diversity with regard to proximity to the available land, the Shannon land-use diversity index was generated. This diversity index considers on the one hand the richness of land-uses and on the other hand their proportional area distribution, the evenness (Jenness, Brost, & Beier, 2013). The Shannon diversity indices were computed using the open-source add-in provided by Jenness et al. (2013). Two extents were considered (100 m and 1000 m) around all plots registered as available (AP), similar to what was done at micro-scale in previous studies (Baranzini, Ramirez, Schaerer, & Philippe, 2008; Geoghegan et al., 1997; Luke, 2004; MIAT, 2003; Mieszkowski & Mills, 1993; Peeters et al. 2015; Treg, 2010; Turner, 2005; Wu & Dong, 2014; Youssoufi & Foltête, 2013). Following Geoghegan et al. (1997), the 100 m radius should capture the effect of diversity in the immediate neighborhood and the 1000 m radius the effect of increased diversity in walking distance to AP (Appendix Fig. A1 Maps C and D). In general, a positive marginal effect of increased land-use diversity price is expected within walking distance (mAPsh1000), while in the close proximity (mAPsh100) the effect is expected to be negative. These marginal effects are expected to be non-stationary through space and will hence be considered in the fully random model, see later. Finally, the ratio of available plots (rAP) relative to the existing built-up area was considered. This ratio is based on the area of all available plots that is divided by the sum of all developable land available and the parcels occupied by residential land-use. This variable should on the one hand allow to account for the supply of land and on the other hand provide insights into its marginal impact on price that could be either positive (Nilsson, 2014; Ooi & Le, 2013) or negative (Kiel & Zabel, 2008; Liu & Hite, 2013). 3.2.3. Level three: Municipalities Individuals value the social and economic composition of their neighborhood and have preferences for more homogeneous neighborhoods (Mieszkowski and Mills, 1993); this neighborhood context should be controlled for to approximate spatial heterogeneity and allow to capture some additional contextual effects at the municipal scale. Socio-economic neighborhood characteristics in hedonic pricing models considered in this study were provided by the National Statistic Agency (STATEC) at municipal scale (Table A1). In this context, unemployment rate or median income are frequently considered as a proxy for disposable income (Chasco & Le Gallo, 2013; Treg, 2010) while age or education level (Beron, Murdoch, & Thayer, 1999; Brunauer, 2013; Chasco & Le

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Gallo, 2013; Treg, 2010) are usually considered as a proxy for social composition or structural weakness of a neighborhood. The part of population above 65 years and unemployment rate are expected to characterize residents’ socio-economic weaknesses and to have a negative marginal impact on land prices. Furthermore population density and its variation rate may be seen as a measure for demand and relative scarcity of residential land (Treg, 2010; Brander & Koetse, 2011). Therefore, population variation between 2001 and 2007 and density should approximate, respectively, the marginal effect of a high demand for real estate and the scarcity of undeveloped space. Information on income or the level of education were not available to this research. 4. Methods The standard procedure in the multilevel modeling literature is to start with an Unconditional Model (UM) to determine whether there is price variability at the three levels identified in our data, namely the transactions (i), the sections (j) and the municipalities (k). In case the variances equal zero, no sub-market effects are present and a single-level model would be sufficient to the data. With the UM confirming price variability at the three levels, the Random Intercept Model (RIM) is estimated, accounting for the explanatory variables and eventually we present the Fully Random Model (FRM) where random slopes are added for selected explanatory variables for which we want to identify spatial segments.

the differential to the mean municipal, respectively, to the overall intercept. The level-one error term (Rijk ) is assumed to follow a normal distribution, with mean zero and constant variance; the higher level residuals (V00k and U0jk ) are assumed to be independent from the lower level residuals. The variance between transactions within sections within municipalities, var(Rijk ), is denoted by  2 . 02 is the variance of the mean section price between sections within municipalities var(U0jk ) compared to mean municipal price and ϕ02 is the variance of the mean price between municipalities, var(V00k ), compared to the overall mean transaction price. The RIM implies that the price-attribute relationship does not vary according to the different levels; however this relationship can differ between the spatial levels in more ways (Snijders & Bosker, 1999). The RIM is however a restrictive specification if the marginal effect of the explanatory variables varies in space. 4.3. Fully random model (FRM) In the FRM, the explanatory variables can vary according to a higher-level distribution, by specifying, in the three level context, one or two additional macro-models, which should control for residual heteroskedasticity at the individual level. By including additional macro-models for the slope for the two higher levels to Eq. (1), the FRM takes the following form: Yijk = 000 + 100 xijk + ˇjk xijk + (V10k xijk + V00k + U1jk xijk + U0jk + Rijk )

4.1. Unconditional model (UM) and intraclass correlation coefficients (ICC) Under UM we denote a multilevel model including no fixed explanatory variables except for the overall intercept (Jones & Bullen, 1993). Different intraclass correlation coefficients (ICC) can be computed to identify at degree of price variability of the different levels. First, the ‘level-two ICC’ expresses the similarity of mean section prices for sections within a same municipality. The interpretation would be that if one selects randomly two sections within one municipality and calculates the mean transaction price in one of the two sections, the average transaction price in the other section could be predicted reasonably accurately (Snijders & Bosker, 1999). Second, the ‘ICC for level-two (and three) relative to levelone expresses the likeness of transaction prices in a same section within a same municipality, measuring cluster homogeneity Jones and Bullen (1994).

(3)

The random part of the model is completed by two additional error terms (V10k xijk and U1jk xijk ), allowing conclusions on the marginal effect of the explanatory variable with regard to the intercepts of the higher units;  100 xijk describing the overall slope. Their





variances are denoted var U1 jk = 12 for the random section slope and var (V10 k ) = ϕ12 for the municipal slope. The covariance terms (cov(U0jk ; U1jk ) = 01 and cov(V00k ; V10k ) = ϕ01) allow the random intercepts and slopes “to co-vary according to a higher-level, joint distribution” (Jones & Bullen, 1994, p.257). A more exhaustive presentation of the multilevel approach and technique can be found in Luke (2004) or Snijders and Bosker (1999) and with focus on the hedonic model specification by Jones (1991), Jones and Bullen (1993, 1994), Orford (2000).

4.2. Random intercept model (RIM)

4.4. Cross-regressive multilevel model (CRMM)

In the RIM, the intercept catches random effects, considering all explanatory variables as fixed through the different spatial levels. The functional form of hedonic pricing models has been largely discussed in literature (Ahlfeldt, 2011; Dube, Des Rosiers, & Thériault, 2011). In the following models the semi-log functional form will be applied following the approach suggested by Verbeek (2008), often applied in multilevel modeling context (Chasco & Le Gallo, 2013; Giuliano, Gorden, Pan, & Park, 2010; Shin, Saginor, & Van Zandt, 2011; Treg, 2010). We will estimate a three level RIM that can be denoted as follows:

To test the multilevel model’s ability to account for spatial autocorrelation, Chasco and Le Gallo (2012) estimated a CRMM. They added a set of spatially lagged explanatory variables as control variables and concluded that they were not able to fully capture the spatial auto-correlation in their model. This approach relies on the ‘spatial multiplier’ model as presented in Anselin (2003), adding to the right-hand-side of the equation a set of spatially lagged explanatory variables. This model assumes spatial effects within the observed x variables only (Morenoff, 2003). As the spatial lags (Wxijk ) are at the right-hand-side of the equation, there will not be an endogeneity problem and thus the model can be estimated via multilevel approach.



Yijk = 000 + ˇjk xijk + V00k + U0jk + Rijk



(2)

The dependent variable Yijk refers to the natural log of the price of a transaction i in section j within municipality k, with a single explanatory variable ˇjk xijk and  000 , the overall intercept. The error part of the model contains three random terms (V00k , U0jk , Rijk ), one for each level describing the differential to the higher level intercept. With Rijk , the error term at level one, describing the differential to the average section price; U0jk and V00k being, respectively, the random term estimated at section or municipal scale, describing

Yijk = 000 + 100 xijk + Wxijk + (V10k xijk + V00k + U1jk xijk + U0jk + Rijk )

(4)

If the multilevel model accounts properly for spatial autocorrelation, the spatially lagged variables should not be significant (Chasco & Le Gallo, 2012).

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Table 1 OLS and fixed effects. Dependent variable: lnprice OLS (1) Level 1 Intercept lnSize dVFA Level 2 tLUXci tLUXpi DI rAP mAPsh100 mAPsh1000 DIGreen Level 3 VarPop0701 pAbove65y rUnemployment PopDens Spatial lags dVFA DI rAP DIGreen VarPop0701 pAbove65y rUnemployment AIC Log Likelihood Moran’s I

Transaction 12.420*** (0.007) 0.612*** (0.010) 0.188*** (0.017) Section −0.012*** (0.001) −0.003*** (0.001) −0.030 (0.026) 0.007*** (0.001) −0.297*** (0.070) 0.214*** (0.040) −0.142 (0.083) Municipality −0.001 (0.001) −0.006 (0.003) −0.018** (0.006) 0.000*** (0.000)

9674 −4822 0.025***

RIM (3)

FRM (4)

CRMM (5)

12.420*** (0.014) 0.613*** (0.011) 0.214*** (0.018)

12.420*** (0.016) 0.608*** (0.019) 0.230*** (0.017)

12.430*** (0.027) 0.608*** (0.019) 0.227*** (0.017)

−0.013*** (0.002) −0.002* (0.001) −0.014 (0.042) 0.005* (0.002) −0.324** (0.113) 0.178* (0.070) 0.005 (0.146)

−0.014*** (0.002) −0.003* (0.001) −0.029 (0.041) 0.005* (0.002) −0.375* (0.138) 0.187* (0.076) −0.096 (0.140)

−0.013*** (0.002) −0.003* (0.001) −0.038 (0.041) 0.005 (0.002) −0.387** (0.116) 0.239*** (0.066) 0.093 (0.168)

−0.001 (0.002) −0.007 (0.006) −0.009 (0.012) 0.000** (0.000)

−0.002 (0.002) −0.007 (0.006) −0.020 (0.012) 0.000** (0.000)

−0.002 (0.002) −0.003 (0.008) −0.008 (0.015) 0.000* (0.000)

9580 −4773 −0.009

−0.084 (0.119) −0.031 (0.081) −0.002 (0.004) −0.419 (0.276) −0.001 (0.004) −0.007 (0.012) −0.015 (0.018) 9346 −4642 −0.007

9323 −4638 −0.008

Signif. codes: p < 0.1; * p < 0.05; ** p < 0.01-, *** p < 0.000; (standard errors).

To identify and test for spatial relationships that might exist between residential land transactions and to generate the spatial lags for the selected explanatory variables, a contiguity based spatial weight matrix (SWM) was generated. As from the 521 sections, only 321 register more than three transactions, hence some isolated sections appear on the section map (Appendix: Fig. A1, maps B–D). In previous research, the continuity matrix at section scale was identified as translating the spatial relationship among observations best. By the contiguity matrix, non-zero weights are defined between all transactions within a same section as well as with the sections sharing a border (if available). We consider that observations are not neighbors to themselves and row-standardize the matrix. Overall 2.24% non-zero weights and on average 142.88 links per observation are counted.

(2008), the average predicted price is of 283,064 euros for a typical transaction of mean size and of type other than dVFA, with all variables grand-mean centered (except dVFA). Moran’s I (Table 1) and the Lagrange multiplier tests (Table 2) confirm significant spatial error auto-correlation while no significant spatial lag dependence is detected by the robust LM-test (Table 2). This spatial error dependence is expected to be accounted for by the three-level model presented in the next section. Multicollinearity was measured by variance inflation factors test (VIF) and test scores are all below 5. The null hypothesis of homoskedastic residuals was rejected by the Breusch–Pagan test, suggesting non-constant variance of the error terms.

5. Results

The multilevel models, accounting for the three-level nested hierarchical structure of the data, have been estimated by restricted maximum likelihood (REML), according to Snijders and Bosker (1999) the difference between the maximum likelihood (ML) and REML method is that the latter estimates the variance components while taking into account the loss of degrees of freedom resulting from the estimation on the regression parameters, while ML does not. We use the “lme4” package (Bates, Maechler, Bolker, & Walker, 2013) in R (R Core Team, 2013). The significance levels of the fixed terms have been computed using the “lmerTest” package by Kuznetsova, Brockho, and Christensen (2013),

We first discuss the results of the single level model (Section 5.1) and the related spatial tests (Table 2). In Section 5.2, we present the results of the multilevel models with a stepwise introduction of random intercepts and slopes, of corresponding spatial tests and of the cross-regressive multilevel model. Fixed and random effects can be found, respectively, in Tables 1 and 3. Municipal random effects are illustrated in Figs. 1 and 2. Finally, we discuss marginal effects in Table 4.

5.2. Multilevel models

5.1. Single level hedonic model In the single level model (OLS (1)), the structural and accessibility measures in general confirm the expectations based on the findings from urban economic theory. The global effect for retail and service diversity (DI) is found to be non-significant. While the general green diversity index (DIGreen) has a negative impact though of low significance, mean Shannon land-use diversity indices show the expected signs. Applying the method suggested by Verbeek

Table 2 LM-test results for OLS model. Lagrange multiplier test

Lagrange Multiplier test p-Value

LMerr

RLMerr

LMlag

RLMlag

174.64 0.000

96.04 0.000

78.62 0.000

0.01 0.915

106

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Fig. 1. Random Intercepts at municipal level.

obtaining p-values by implementing “Satterthwaite approximation” for denominators’ degrees of freedom. The unconditional model, identifies that 7.5% of the total variance in the transaction price is located between sections within municipalities, while 16% of the total price variance is between municipalities (model 2 (UM) in Table 3). Single- or two-level models are hence rejected. The level-two ICC being 68% suggests that mean section prices within a municipality are alike, while the ICC for level-two relative to level-one indicates that transaction prices are not varying homogeneously between sections of a same municipality. Map A in Fig. 1 illustrates the random intercepts of the UM at municipal scale, that is the variation of the mean municipal price to the overall intercept. As expected municipal mean prices above the overall intercept are observed for most of the municipalities in the southern part of the country, while in the north below average means are estimated in general.

5.2.1. RIM: Price variability partly explained The ability of the fixed explanatory variables, added in model 3, to account for a significant part of the price variability is confirmed by the LR-test. Only 9.1% of the price variance is now located at the two higher levels, according to ICC for level-two relative to levelone. A considerable part of between transaction variance remains unexplained; which is not surprising with regard to the poor information on the structural transaction characteristics available and the aggregated scale of the contextual variables. Only 1.7% of the total unexplained price variance is located between municipalities. The decrease of the level-two ICC, indicates that most of the variance at the higher levels is located between sections, suggesting that the explanatory variables were able to capture a large amount of the between municipal price variability. Map B in Fig. 1, illustrates the variation of the municipal intercept relative to the overall intercept after including explanatory

M.-L. Glaesener, G. Caruso / Landscape and Urban Planning 143 (2015) 100–111

107

Fig. 2. Random coefficients of Shannon diversity.

variables. Mainly transactions located in municipality of and around Luxembourg-city and some regional urban centers are observed to register higher variance from the overall mean. The high coefficient for Erpeldange, located between the municipalities of Ettelbruck and Diekirch, together forming as the Nordstad (Map C Fig. 1), is also most notable. All else constant, a typical transaction within Erpeldange is on average 7% more expensive than the overall national mean. Explanatory variables remain similar to OLS results (model (1) Table 1), those insignificant remain insignificant and DIGreen as well as most socio-economic variables turn insignificant (Table 1) in the multilevel model. To wrap up we find that: (i) tests confirm residual spatial dependence and heteroskedasticity; (ii) the utility of a three-level hierarchical model is confirmed; (iii) large proportion of price variability is located between transactions due to omitted structural variables; and (iv) the explanatory variables capture an important part of the variance. 5.2.2. FRM: Spatial heterogeneity for size and land-use diversity We are interested in the non-stationarity of neighborhood amenities, and analyzed random coefficients for them. Besides, Table 3 Random effects. UM (2)

0.079

0.005

mAPsh100 ϕ12 )

cov ϕ1 , ϕ2

0.006 0.501 0.044 0.077 0.020

 

Level 2: Sections in municipalities 02

   2 2

FRM (4)

Variance

 

Level 3: Municipality ϕ02

   2 2 cov ϕ0 , ϕ1   mAPsh1000 ϕ22  2 2 cov ϕ0 , ϕ2  2 2

RIM (3)

0.132 0.037

0.020

0.024

lnSize 12

0.062

cov 0 , 1

−0.029



Level 1: Transactions  2 Total variance Level-2 ICC ICC for level 2 relative to level 1

0.377 0.493 0.682 0.235

0.246 0.246 0.190 0.091

0.225 0.475 0.197 0.118

since the literature indicates the importance of spatial heterogeneity for plot size, we also analyzed this relationship. We report the FRM fixed effects in Table 1 and the FRM random coefficients for the significant variables, i.e. Shannon land-use diversity and plot size, are detailed in Table 3 and illustrated in Fig. 2. The LR-test indicates that including random variation of plot size between sections performs best, whereas no significant spatial variation was identified between municipalities. Allowing random variation of the size-price relationship within sections further explains between transaction variance ( 2 ). Random slopes for DIGreen and DI, did not lead to a significant improvement of the model (Results are available upon request). Our results related to Shannon land-use diversity measures (mAPsh100 and mAPsh1000) support the findings of Geoghegan et al. (1997). The slopes were allowed to vary between municipalities (model 4), which adds to the overall explanatory power. In map C (Fig. 1) we illustrated the variance to the overall intercept of the average estimated municipal intercept of the FRM. Including land-use diversity indices mitigates the positive variations of the capital-city Luxembourg, and mainly two submarkets emerge. First, the municipalities of the Nordstad positively stand out. Second, in the former industrial south, a relatively high negative variation from the overall intercept is observed. In these two segments, a typical transaction is valued differently by developable land consumers, which merits further investigation to be related with the polycentric policy goals set by at national level. The fixed effects of the land-use diversity variables indicate the expected marginal effects and barely change from the RIM (model 2). For plot size and Shannon indices the results of the global model are mostly confirmed. For the two Shannon indices, inversions of the sign of the marginal effect across municipalities are observed. On the one hand, land-use diversity in proximity to all available plots is valued positively in the Nordstad municipalities, in the north-west and in some municipalities in the south-east of Luxembourg, the Moselle valley region (Map A in Fig. 2). Further, increased land-use diversity in walking distance is valued negatively in some of the municipalities, in particular in the

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Table 4 Marginal effects. OLS (1) Level 1 lnSize (+10%) dVFA Level 2 tLUXci tLUXpi rAP mAPsh100 (0.1) mAPsh1000 (0.1) Price of a typical transaction

RIM (3)

Transaction/plot 6.12% 6.13% 20.71% 23.83% Section −1.15% −1.30% −0.31% −0.24% 0.68% 0.46% −2.97% −3.24% 2.14% 1.78% 283,064 D 280,184 D

FRM (4) 6.08% 25.81% −1.35% −0.29% 0.46% −3.75% 1.87% 277,217 D

former industrial south but also in some of the periurban municipalities north of Luxembourg-city (Map B Fig. 2). The covariance term (ϕ12) describes a positive relationship between the random coefficients of the Shannon diversity indices; the more a 0.1 increase in diversity in mAPsh1000 is valued positively, the weaker is the negative effect of mAPsh100. Not allowing random coefficients would have led to wrong conclusions, as there are local variations in how diversity in different extents is valued. The fixed effects remain almost unchanged (Table 1), and we now discuss the marginal willingness to pay for the significant variables of interest provided in Table 4. According to the fully random model (model 4) residential land consumers in Luxembourg are estimated to be willing to pay almost 6.08% more for a 10% size increase to an average-sized parcel. Existing development plans are highly significant through all models; consumers are willing-to-pay almost 26% more for a typical transaction with existing plans. An additional minute to Luxembourg by car lowers a typical transactions’ price by 1.35%, while by public transport’s negative impact is of 0.29% per additional minute. These findings confirm the relative importance of individual transport over public transport in consumers’ preferences; nevertheless public transport has a significant impact on developable land prices in Luxembourg. The overall negative impact of increased mAPsh100 is slightly strengthened in model 4, as is the overall coefficient of mAPsh1000 after allowing random slopes for the landuse diversity indices between municipalities. An 0.1 above mean increase of the diversity indices has an overall marginal effect of −3.75% for close diversity and 1.87% for diversity in walking distance. To summarize, we find that (i) the marginal effect of size varies between sections within municipalities; (ii) neither service nor green diversity have a significant impact; (iii) spatial market segments around the Nordstad and the former industrial south; and (iv) we confirm spatial variation in the marginal effects of land-use diversity. 5.2.3. CRMM: MLM captures spatial effects The non-significant Moran’s I test for the conditional residuals of the multilevel models (Table 2) suggests that no spatial error dependence remains after accounting for the different levels. This is confirmed by the cross-regressive multilevel model (CRMM) suggested by Chasco and Le Gallo (2012). The results of the CRMM estimation (Model 5 in Table 2) show that the fully random model (FRM—3), as specified in this case study, captures all spatial processes. Based on the findings of Morenoff (2003), Chasco and Le Gallo (2012) did not include the spatial lag of all explanatory variables (not considering accessibility and pollution variables) because of issues related to multicollinearity. Similar observations were made here, we could neither consider the spatial lags of the random slope variables, nor those of population density and the accessibility measures.

The LR-test confirms that the model is not significantly improved by including the spatial multipliers conversely to what Chasco and Le Gallo (2012) found in their case study. In our case, none of the spatial lags are significant, meaning that the observed neighborhood sections’ values do not influence other transactions in the neighborhood.

6. Conclusion In this paper, we have attempted to measure the effect of neighborhood diversity of both services and land-uses on developable land prices as well as its variation across space. We applied the multilevel approach to capture contextual effects, beyond neighborhood and center-periphery effects. Our analysis confirmed the usefulness of the multilevel approach with three levels for our case study. The RIM confirmed that an important part of price variability is explained by the fixed explanatory variables and by considering these three levels. Allowing random slopes for plot size and land-use diversity indices showed spatial variation in their marginal effects on land price in Luxembourg. Parcel size is not valued homogeneously within municipalities, suggesting differentiated local planning policies within each municipality or at least structural differences within municipalities that complement the standard urban economic trade-off (plot size-commuting costs) even after controlling for municipal Tiebout effects through neighborhood services. The Shannon indices for land-use diversity have consistently demonstrated across models positive value for in walking distance and a negative value in immediate proximity, which is in line with literature. Moreover, we observe spatial variations of these valuations across Luxembourg. We observe that both indices are valued positively in regions that are particularly attractive and picturesque. Conversely, negative values were obtained for both indices in the former industrial conurbation, suggesting that the composition of the diversity matters within neighborhoods, especially in these regions where a negative perception of brown fields is likely. Both findings indicate that more importance should be given to landscape contextual effects when assessing the effects of land-use proximity. Although we were expecting significant effects from green diversity, the significance disappeared when the multiple levels were considered. This is probably a data aggregation effect which somehow confirms previous findings that green amenities should be considered at a more local scale with further geographic detail. Similarly, our inability to capture the positive effect of having a more diverse offer of urban amenities suggests that even the municipal scale is too small. This would require further investigation, but is not surprising in the Luxembourgish context where service supply is high and car ownership is among the highest in the World, thus attenuating the spatial distribution of service amenities. Beyond our thematic contribution, our application shows that the multilevel approach is useful to analyze spatial heterogeneity, and comforts the findings of Orford (2000) rather than Chaix et al. (2005) or Chasco and Le Gallo (2012), as discussed in Section 2.2, in the sense that it removes spatial auto-correlation effects. Our finding is based on a CRMM, but caution should be paid to this result because of the aggregated spatial unit where our transactions were recorded. Spatial multilevel models as suggested recently by Almeida and Guimarães (2014) or the multilevel model with autocorrelated error structure as discussed in Ren et al. (2013) could additional insights. Further research should also consider endogeneity effects, especially because we take interest in neighborhood amenities and the risk of reverse causation that might exist between households’

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location choice and the offer in local public amenities can be important. Treating endogeneity of residential decision with good instruments within a multilevel approach is an interesting additional challenge.

We would also like to thank two anonymous reviewers and the editor for their comments. This research received the financial support of the Fonds National de la Recherche Luxembourg (AFR grant number: PHD-09-095).

Acknowledgments Appendix A. We are grateful to Dominique Peeters, Luisito Bertinelli and Julie Le Gallo for insightful discussions on previous versions of the paper.

109

Fig. A1 and Table A1.

Fig. A1. Maps of main variables.

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Table A1 Summary statistics. Variable

Description (Unit)

Level 1 lnPrice lnSize dVFA Level 2 tLUXci tLUXpi DI rAP mAPsh100 mAPsh1000 DIGreen Level 3 VarPop0701 pAbove65y rUnemployment PopDens

Transaction ln of price deflated to 2007-euros ln of plot size (are) Development project (dummy) Section Time to Luxembourg-city by car (min) Time to Luxembourg-city by public transport (min) Shopping and service diversity (index) Vacancy rate (%) Shannon Index in radius of 100/1000 m around AP (index) Green diversity (index) Municipality Population variation between ‘01 and ‘07 (%) Part people above 65 years (%) Unemployment rate (%) Population density (hab/km2 )

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Mean

Min

Max

Expected

12.46 1.58 0.19

9.58 −0.46 0.00

14.87 3.92 1.00

DV + +

28.64 41.30 0.64 0.11 1.29 1.63 0.57

4.52 8.00 0.00 0.01 0.99 0.85 0.08

77.73 122.00 0.91 0.36 1.68 2.07 0.75

− − + + − + +

9.39 12.67 4.33 330.58

−2.96 6.84 2.07 22.39

36.30 20.04 9.92 2080.35

+ − − +

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