Measuring the Benefits of Neighbourhood Park Amenities: Application and Comparison of Spatial Hedonic Approaches

  Environ Resource Econ (2010) 45:429–444 DOI 10.1007/s10640-009-9321-5 Measuring the Benefits of Neighbourhood Park Amenities: Application and Comparison of Spatial Hedonic Approaches Tadao Hoshino · Koichi Kuriyama Accepted: 3 September 2009 / Published online: 23 September 2009 © Springer Science+Business Media B.V. 2009 Abstract

  The hedonic price method was used to estimate the influence of parks on the rental prices of single-room dwellings in Setagaya Ward, Tokyo, Japan. A simple least squares method is not optimal when the data set contains spatial autocorrelation. To improve the accuracy of estimates, we employed spatial autoregression and kriging models, resulting in a higher validity of the spatial models compared to the least squares model. Kriging models were superior to others particularly in terms of prediction accuracy, indicating that these models should be employed if the objective is superior prediction rather than estimation. The results showed that the effect of parks on property values varied with the buffer distance and park size.

  Keywords

  Hedonic approach · Kriging · Spatial autocorrelation · Spatial regression models

  · Urban parks

1 Introduction

  Urban parks have various purposes, including improving urban environments and provid- ing communication opportunities. The importance of urban park improvements is widely recognised by local municipalities as an important attraction to consumer decisions about where to reside. Improved computer technology and the rapid popularisation of Geographic

  T. Hoshino Department of Social Engineering, Tokyo Institute of Technology, 2-12-1 Ookayama, Meguro-ku, Tokyo 152-8550, Japan e-mail: hoshino.t.ai@m.titech.ac.jp K. Kuriyama ( )

  B Division of Natural Resource Economics, Graduate School of Agriculture, Kyoto University, Oiwake-cho, Kitashirakawa, Sakyo-ku, Kyoto 606-8502, Japan e-mail: kkuri@kais.kyoto-u.ac.jp URL: http://homepage1.nifty.com/kkuri/index-e.html

  430 T. Hoshino, K. Kuriyama

  Information Systems (GIS) have made detailed data about land use widely available. The availability of such geographical data has rapidly advanced hedonic approach studies that estimate the effect of open spaces (e.g., Acharya and Bennett 2001 ; Cheshire and Sheppard

  

1995 ; Cho et al. 2006 ; Geoghegan 2002 ; Geoghegan et al. 1997 ; Irwin 2002 ; Irwin and

Bockstael 2001 ; Lutzenhiser and Netusil 2001 ; Shultz and King 2001 ; Smith et al. 2002 ;

Tyrvainen and Miettinen 2000 ). A common finding is that, on average, open spaces have

  positive effects on property prices, but that effects vary with the type of open space. For example, the global regression model of Cho et al. ( 2006 ) showed that moving 1,000 feet (

  ∼300 m) closer to the nearest park increases mean house prices by 172 USD, whereas the local model revealed that the effects of proximity to parks on housing prices vary with the individual park, ranging from 662 USD to 840 USD. Geoghegan et al. ( 1997 ) found that within a 0.1- km radius, the proportion of open space positively influences land prices, but negatively impacts them within a 1- km radius, and suggested that individuals prefer more diverse land uses at a large scale.

  In statistical analyses using spatial data, the importance of spatial correlations among observations of the efficiency and consistency of hedonic model estimates has been empha- sised. Spatial autocorrelation occurs when population members are related through their geo- graphic locations ( Dubin 1988 ). Spatial correlation is far from surprising in hedonic housing models, as omitted variables are generally spatially correlated. Specifying all of the many spatial characteristics affecting a property would result in a function that is too complicated to compute. Thus, studies tend to visualise spatial aspects of the data in an empirically man- ageable form. We focused on spatial autoregression models, which are commonly used in spatial econometrics ( Anselin 1988 ), and kriging models, which are commonly used in spa- tial statistics ( Cressie 1993 ) and geostatistics ( Wackernagel 2003 ). A hedonic approach using these explicit spatial regression techniques is called a spatial hedonic approach. Examples of empirical studies using the spatial hedonic approach to estimate the effect of environmental quality include Acharya and Bennett ( 2001 ) on open spaces, Cho et al. ( 2006 ) on water and green spaces, Kim et al. ( 2003 ) on air quality, Kim and Goldsimth ( 2009 ) on swine pro- duction, Leggett and Bockstael (2000) on water quality, and Paterson and Boyle ( 2002 ) on visibility. All of these studies employed spatial econometric models, e.g., spatial lag models or spatial error models. To the best of our knowledge, our study was the first to use kriging models to estimate the effects of environmental quality.

  1 Our primary objective was to measure the value of neighbourhood parks using a spatial

  hedonic approach in conjunction with a simple least squares hedonic approach and compare their validity. In Sect.

  2 , we describe the econometric models used. Section 3 contains an overview of the study area and an explanation of the data used for the analysis. In Sect. 4 , we discuss the estimation results, and in Sect. 5 we present our conclusions.

  2 Econometric Models

  Hedonic models were developed to deal with markets for differentiated products. The dif- ferentiated product varies depending on the specific characteristics or attributes of the model ( Palmquist 1999 ). The theoretical framework of the market for heterogeneous goods was

  1 In our definition, neighbourhood parks are parks in a residential neighbourhood that are available to all resi-

dents who can access them. Many of the amenities of neighbourhood parks are localised to the neighbourhood

and provide locally beneficial external economies. As Palmquist ( 1992 ) noted, local externality effects can be

calculated by simply estimating the hedonic price function, without the need to conduct a complex two-step

estimation procedure.

  

Measuring the Benefits of Neighbourhood Park Amenities 431

  originally developed by Rosen ( 1974 ), who explained the price of any unit of a differenti- ated good as a function of a bundle of characteristics. Housing prices are the most common example of this application. To specify housing structure characteristics, the characteristics are grouped into structural characteristics, such as area or number of rooms, as well as loca- tional characteristics, such as transportation accessibility or environmental amenities and disamenities.

  The simplest functional form used in hedonic studies is a linear regression model. If P is a vector of observed property values at N points on the plane, then the linear hedonic function is

  P

  (1) = Xβ + ε, where P is the N

  ×1 vector of property prices; X is the N × K matrix of regressors including

  s s l

  the intercept term, structural variables X with K characteristics, and locational variables X

  l s l

  with K characteristics such that 1

• K + K = K ; β is the K ×1 vector of the coefficients; and ε is the N × 1 vector of errors. The coefficients are simply estimated by OLS. However,

  OLS optimality inevitably fails in the presence of spatial autocorrelation. Below, we present the spatial econometric regression and the kriging models as typical solutions to the issue of spatial autocorrelation.

  2.1 Spatial Autoregression Models Two models are frequently used to represent the spatial autoregressive process: spatial error models and spatial lag models. In the former, spatial autocorrelation is considered to be caused by omitted variables, whereas in the latter, it is caused by spatial interactions (endogeneity).

2.1.1 Spatial Error Models

  Although spatial autocorrelation caused by omitted spatially correlated variables does not bias OLS estimates, the estimates will be inefficient, and, most troubling, standard errors will be biased, leading to inaccurate hypothesis testing ( Anselin 1988 ; Leggett and Bockstael

  ′

  )

  2000 ). This occurs because spatial autocorrelation in the error term, E(εε

  = , results in the formation of an error variance–covariance matrix with nonzero off-diagonal elements. In this situation, β should be estimated using a generalised least-squares (GLS) estimator

  ′ −1 −1 ′ −1

  β X )

  X P

  ˆ G L S for efficiency. The empirical issue is then to estimate the = (X elements of .

  One way to obtain the structure of directly is by modelling covariance as a function of the Euclidean distance between two locations. One of the most commonly used spatial process specifications is the autoregression form used in disturbances. In a general case, _{ } w

  11

  1N

  · · · w

  P

  = Xβ + ε; ε = λW ε + u   , .. . . .. , with W (2)

  .

  2 =  . .  ∼ u N ( I )

  0, σ w

  N N N 1 · · · w

  where λ is the spatial autoregression parameter, W is the N × N spatial weight matrix, and u is the N

  × 1 vector of the i.i.d. normal error term. The structure of the variance–covariance matrix becomes a nonzero off-diagonal matrix. In many previous empirical studies, each element of W has been defined simply as the inverse of the Euclidean distance. Alternatively, we can assume the existence of a boundary that is the greatest distance over which a value at one point is related to a value at another point. In this framework, the spatial interdependence

  432 T. Hoshino, K. Kuriyama

  relationship between pairs of points that are farther apart than this distance equals zero. This concept is the same as the range in the kriging model explained below. In either case, the important point is that both definitions consider only the distance between two points and

  2

  not direction, a condition called isotropy. Accordingly, the covariance of any two points that have the same distance between them will be the same, depending solely on distance, and the covariance converges to zero as the distance between them increases. This assumption

  3

  is called covariance stationarity. From these assumptions, we defined two practical and empirically manageable weight matrices, one with a simpler, more traditional form and the other with more flexibility:

  Flexible Simple

  2

  1 d _{i j 2} i

  = j

  h, i , (3) d

  1 if d i j < _{i j} − h = j w w

  i j i j

  = =

  i

  = j otherwise where d i j is the distance between points i and j , and h is the boundary distance to be esti- mated. The weight falls to zero when the distance between i and j equals h or more. These spatial weight matrices are row-normalized so that all row sums are set at 1. All unknown coefficients and parameters can be estimated using the maximum-likelihood method. The log-likelihood function is thus:

  N N

  1

  2 ′ ′ L P

  I I

  ln(2π ) ln σ ( ( ( = − − − − Xβ) − λW ) − λW )

  

2

  2 2 2σ (4)

  ×(P − Xβ) + ln |I − λW |

  

2

  , λ Equation (

  4 ) is maximised with respect to β, σ , and h simultaneously (or just λ and h by

  2

  4

  ) concentrating on β and σ to obtain maximum-likelihood estimates.

2.1.2 Spatial Lag Models

  Unlike spatial error autocorrelation, spatial autocorrelation caused by spatial interactions (endogeneity) biases the OLS estimates. To represent this type of spatial process, the spatial lag model is given as: _{ } w

  11

  1N

  · · · w

  P

  = ρW P + Xβ + u   , .. . . .. , with W (5)

  2 =  .  ∼ . . u N ( I )

  0, σ w

  N N N

  1

  · · · w assuming homoskedasticity in disturbances, where ρ is the spatial lag parameter. Similarly, all unknown coefficients and parameters can be estimated using the maximum-likelihood method. The log-likelihood function can be written as:

  N N

  1

  2 ′ L ( P ( P

  ln(2π ) ln σ = − − − − ρW P − Xβ) − ρW P − Xβ) + ln |I − ρW | .

  2

  2 2 2σ (6)

  2 The method to define and measure a distance must also be considered. Economic and social distance, as

well as geographical distance, may be applicable. The difference in significance between distance measures

should be a future research topic.

  3 However, using these assumptions could be too simplistic, as roads and other components of transport infrastructure are not radially symmetric ( Cheshire and Sheppard 1995 ).

  4 When many observations are involved, use of the generalized method of moments is beneficial because

evaluation of the determinant of the N Kelejian and Prucha

× N matrix is computationally problematic ( 1999 ).

  

Measuring the Benefits of Neighbourhood Park Amenities 433

2.1.3 Specification Tests

  To detect misspecification due to the spatial autocorrelation processes and to distinguish the nature of spatial autocorrelation in the error term (spatial error) and the dependent variable (spatial lag), we conducted modified Lagrange multiplier (LM) tests, which were developed by Anselin et al. ( 1996 ) and are computationally simple and robust. These tests are simple in that they are based on OLS residuals. For a detailed description of the calculation of the test statistics, refer to Anselin et al. ( 1996 ) or Florax and Nijkamp ( 2003 ).

  5

  2.2 Kriging Models Kriging is a minimum mean square error statistical procedure for spatial prediction that assigns a differential weight to observations that are closer to the location of the dependent variable ( Dubin et al. 1999 ). The prediction procedure corresponds to a spatial version of Goldberger’s best linear unbiased prediction (BLUP) method. There are several types of kriging models. To estimate hedonic price functions, a universal kriging model is employed, which is a combination of the standard multiple-linear regression and spatially correlated stochastic term to be estimated by ordinary kriging. Hence, the model assumes the presence of spatially correlated omitted variables, which correspond to the spatial error models.

  Spatial weights are computed from the estimated semivariogram or covariogram, and the covariogram corresponds to the variance–covariance function used to estimate . Estimating the covariogram requires several steps.

  We consider ε to be a spatially stochastic variable specifically tied to a particular location. Because modelling the joint distribution function of ε for every location, point by point, is nearly impossible, some simplifying assumptions are needed to allow the application of the stationary assumption. Let x represent the location of property i . Thus, S(x ) denotes the

  i i

  stochastic error of the hedonic price equation for a property located at x i . If a stochastic process is second-order stationary, then

  

E ) ), S(x ) ),

i i j i j (7)

  [S(x ] = µ, Cov[S(x ] = C(x − x where C is a covariogram. Equation (

  7 ) establishes that the first and second moments of

  distribution can be the same at all locations, and spatial interdependence is described solely as a function of the Euclidean distance between two points. This is a case of isotropy. The var- iance, C(0), is constant at any location. Alternatively, we can also assume that the difference

  ) between two values of S(x i is a stationary distribution, as follows:

  E i ) j ) i ) j ) i j ), (8)

  [S(x − S(x ] = 0, Var[S(x − S(x ] = 2γ (x − x where γ is called a semivariogram. This type of stationary phase is called intrinsic station-

  ary . If the process S is second-order stationary, an intrinsic stationary appears to be implied.

  Under the second-order stationary process, the relationship between the semivariogram and the covariogram can be written as:

  1 γ (

  d)

  Var = [S(x + d) − S(x)]

  2

  1

  1 Var Var = [S(x + d)] + [S(x)] − Cov[S(x + d), S(x)]

  2

  2 (9)

  = C(0) − C(d),

5 See, for example, Basu and Thibodeau ( 1998 ), Cressie ( 1993 ), and Wackernagel ( 2003 ) for a more detailed discussion of this issue.

  434 T. Hoshino, K. Kuriyama

  where d is the Euclidean distance between two points. Accordingly, a covariogram can be derived from the corresponding semivariogram. We used exponential and spherical semivari- ogram models, as shown below:

  Exponential if d = 0

  γ ( d

  Exp d

  ; θ) = θ 1 if 0 < d

  1

• θ − exp − θ
₂ ,

  (10) Spherical _{  = 0  } if d

  3 d d

  3

  1

  γ ( d θ if 0 < d

  Sph

  1

  2

  ; θ) = + θ θ − θ ≤ θ _{  }

  2 ²

  2 ²

  θ if d

  1

  2

• θ ≥ θ where θ indicates parameters to be estimated, with θ called the nugget; θ , the sill;
• θ

  1

  and θ , the range. The spherical semivariogram model actually reaches the specified sill,

  2

  θ , which is a straightforward “cut-off” for the boundary

• θ, at the specified range, θ

  2

  distance, h, in Eq. (

  3 ), whereas the exponential approaches the sill asymptotically. Notably,

  when d , the exponential semivariance reaches 95% of the sill value; this distance

  2

  = 3 × θ is called the practical range. The estimated parameters for the semivariogram are then used to compute the associated covariogram.

  The first step of the experimental procedure was to estimate the semivariogram parameters using OLS residuals. In the second step, we computed the corresponding covariogram, which

  ′ −1 −1 ′ −1

  ˆ X )

  X ˆ P

  then led to . β was estimated using the GLS estimator (X . Using the estimated GLS coefficients, the residuals can be recomputed and then used to re-estimate the new GLS estimator. This procedure was iterated until convergence.

3 Data

  3.1 Urban Parks in Setagaya Ward Situated on the southwestern edge of Tokyo’s 23 wards, Setagaya Ward has a population of approximately 810,000 and is the largest of the wards, with the 14th-highest population density (Population Census 2006). Because Setagaya is very convenient for transportation that accesses the business and commercial districts of Tokyo, it has become one of the most desirable residential zones, and its population is growing. The Setagaya Ward master plan emphasises the role of urban parks and green spaces in the residential environment. Some studies have assessed the effects of parks by focusing on whether the parks are developable or preserved, or whether they are privately or publicly owned ( Cheshire and Sheppard 1995 ;

  

Geoghegan 2002 ; Irwin and Bockstael 2001 ). Parks can also be classified by size, which

  is more useful than legal classification for our research about the effect of urban parks on property prices, as very few parks are privately owned in Setagaya Ward. In fact, all the parks in this analysis are somewhat publicly preserved parks. Accordingly, we assumed that park amenities did not differ greatly among similarly-sized parks. Thus, we did not control for park heterogeneity except by size and did not explicitly consider the endogenous problem for developable open spaces, as discussed by Irwin ( 2002 ) and Irwin and Bockstael ( 2001 ). Ideally, field surveys should be conducted to obtain detailed information about the character- istics of each urban park’s amenities to check the legitimacy of our assumption, although this

  

Measuring the Benefits of Neighbourhood Park Amenities 435

Table 1 Size classification of parks in Setagaya

  2

  2 Size (m ) Number of parks Average size (m ) 500–2,000 189 998.43 2,000–10,000

  48 3, 938.39 >10,000 21 83, 465.79 a

  Total 258 8257.86 Source : City of Tokyo, Summary of Setagaya Ward administration, ch 7 a

  2 : River terraces, greenbelts, and parks with an area of 0–500 m were excluded

  Fig. 1 Maps of the 23 Tokyo wards and Setagaya Ward

  process is quite costly. If our assumptions are not correct, our estimates may be somewhat biased. Table

  1 summarises the size classification of parks. The number of small parks is

  much larger than that of large parks. Figure

  1 shows a map of the 23 Tokyo wards, with the location of the parks used in this analysis marked in Setagaya Ward.

  3.2 Data Used for Analysis Data for 2,370 samples of single-room dwellings were collected from the entire area of Setagaya Ward. We limited our samples to single-room dwellings for both practical and social reasons. Practically, by limiting samples to a particular type of housing, we could min- imise the structural differences between samples. Thus, because we did not need to collect detailed information on common characteristics of diverse dwellings, we could use a parsi- monious set of regressors to explain a certain amount of variance in rent prices. Generally, multi-room dwellers (usually families) are likely to have a greater interest in park amenities. However, socially, we believe that clarifying the extent to which single-room dwellers (who

  436 T. Hoshino, K. Kuriyama

  are often young, single, and/or low income) prefer neighbourhood park amenities is also important for urban housing planning.

  The independent variable was the monthly rental price of a single-room dwelling, in 100-yen units (RENT). The prices and characteristics of dwellings, including AGE (age of dwelling), the log of WALK (time to walk from the nearest train station to the dwelling, in minutes), AREA (room area), and DENENd (a dummy variable, which is

  6

  1 when the nearest train station is a Denen-toshi line station, and 0 otherwise), were extracted in May–June 2007 from the website of Forrent, a private real-estate firm ( http://www.forrent.jp ). Our sample data included all single-room dwellings listed on the web page with monthly rents between 40,000 (380 USD) and 100,000 yen (950 USD). This range was set to eliminate unusually (in)expensive dwellings. The log of TAX (average tax payment of a ward inhabitant per payer population of the block), BUS- PL (number of businesses within the block area per hectare), and DAYTIMEPOP (ratio of daytime to nighttime population of the block) were created from Population Census 2006 and Setagaya Ward Statistics 2006 data. Because the inhabitant tax is pro- gressive, the TAX variable corresponds to the income level of each block. As both TAX and BUSPL increase, the rental price was also expected to increase, and as DAYTIME- POP increases, the price should decrease. Using block-level address geographical infor- mation, the Euclidean distances to Shibuya station (SHIBUYA) were calculated. Shibuya is one of the best-known districts in Japan because of its cultural and business vital- ity. Moreover, Shibuya station is an important transportation hub for anyone living in Tokyo. Thus, we inferred that as the distance to Shibuya station increases, the rental price decreases.

  The Setagaya Ward Administration summary (2006) contains information on the size and location of every park in Setagaya Ward. Because the effects of park amenities on property values is not observable if the distance to the parks is too great (except for versatile large parks), we needed to define the boundary of accessible distance. A more precise estimate would require that visitors be surveyed as to their origin, means of transportation to the park, and purpose of visit. The variables for park amenities were defined as the log of PARK450 (sum of park area within a 450-m radius of the residence block midpoint), log of PARK1000 (sum of park area within a 1,000-m radius of the residence block midpoint), and LARGEPd

  2

  (dummy variable, which is 1 when at least one park larger than 10,000 m exists within a 450-m radius of the residence block midpoint). These threshold distances were determined after extensive trials using different distances and the goodness-of-fit criterion. For the sev- eral neighbourhoods that had no parks within a 450-m radius, the value of ln PARK450 was set to 0.

  3.3 Data Aggregation Although structural characteristics were collected for all 2,370 samples, only a block-level address could be obtained for each property. To establish a one-to-one correspondence between block-level locational variables and specific dwellings, we had to aggregate each structural dwelling datum point into a block. Thus, if dwellings were highly heterogeneous even within the limited group of single-room dwellings, estimates could not be precise because some information was lost during aggregation. For the park variables, the distance

6 The word denen-toshi translates to “garden city” in English, implying a desirable living environment. The

  

Denen-toshi line is a major commuter train service connecting the southwestern suburbs of Tokyo to Shibuya

station, a major railway junction in western downtown Tokyo.

  

Measuring the Benefits of Neighbourhood Park Amenities 437

  7

  to parks was measured not from the property location, but from the block midpoint. Using the actual distance to the nearest park as a regressor would have yielded a clearer description of the relationship between the effects of park amenities and distance to the park, but the aggregated data did not allow us to use this specification. Thus, a good hedonic approach should include datasets that are as disaggregated as possible. In-depth analysis of how data aggregation affects estimates in the context of a spatial hedonic approach will be an important topic for future research.

  Additionally, heteroskedasticity often occurs when data are cross-sectionally aggregated. A traditional solution to this issue is to use the weighted least squares (WLS) method, with weights given by the number of samples in each block. Our preliminary analysis of a simple OLS model revealed that the p-value of the Breuch-Pagan test for heteroskedas- ticity was 0.092, so we decided to use the WLS method throughout our models defined in the previous section. Hence, the vector of rents P in the last section corresponds to

  √ √

  ′ N P , . . . , N P i i N N , where N i indicates the number of samples belonging to block i . _{ √ √ }

  ′ N , . . . , N

i N

  √ s √ s _{ i , . . . , N  ,} N

  X N

  X Similarly, regressor X corresponds to without the intercept i N

  √ l √ l

  N X , . . . , N

  X i N i N

  term. So, if the assumption of homoskedasticity for the vector of innovations u in Eq. (

  2 )

  and Eq. (

  5 ) holds at the individual level, the heteroskedasticity problems induced by spatial

  autocorrelation and by data aggregation can be solved by applying a combination of the spatial hedonic approach and the WLS method.

  Table

  2 lists the variables used and their definitions. Table 3 shows the descriptive statistics for all variables.

4 Results

  Table

  4 reports the results of the three specification tests. The spatial weight matrix used in

  the tests was the simple form of Eq. (

  3 ). The test of the statistic L M λ.ρ revealed the presence

  of a misspecification, with the standard WLS at 99% significance. The null hypotheses for both L M λ and L M ρ were rejected based on the results of two one-directional tests, indi- cating the presence of both spatial error and lag process. However, when we compared the magnitude of the statistics, L M ρ was much weaker than L M λ was. Thus, the main cause of the misspecification would be the spatial autocorrelation in disturbances caused by some omitted variables. This was a positive reason to apply GLS-type estimations to the data set, including the spatial error and kriging models.

  All coefficient and parameter estimation results from the five models (standard WLS, simple spatial lag, flexible spatial lag, simple spatial error, and flexible spatial error) and the two kriging models (exponential kriging, and spherical kriging) are reported in Table

  5 and 6 , respectively.

  7

2 In Setagaya Ward, the largest block is 0.496 km (1, Tamadutsumi Town), and the average block area is

  2

0.207 km . Thus, a 450-m radius is large enough to cover the size of each block. Hence, to approximate the

block level of park provision, our specification of park variables should be sufficient. In fact, all of the parks

relevant to our analyses were covered. Aggregation also affects the form of the spatial weight matrices, as this

study employs distance-based definitions. The distance used is not the distance between properties but that

between the midpoint of each block. Thus, the spatial correlation to be estimated is the correlation between

blocks. Although these aggregation effects are not necessarily detrimental to estimation, a detailed property

level spatial process should not be inferred.

  438 T. Hoshino, K. Kuriyama

  Table 2 Variables and their definitions Variable Definition √

  N Square root of the number of samples belonging to the block i i

  RENT Monthly rental price of a single-room dwelling (100yen) Structural variables AGE Age of dwelling (years)

lnWALK Log of minutes required to walk from the nearest train station to the dwelling

2 AREA Dwelling area (m )

  DENEN d Dummy variable: 1 when the nearest train station to the dwelling is a Denen-toshi line station; 0 otherwise Locational variables lnTAX Log of average ward inhabitant tax per payer population in the block BUSPL Number of businesses within the block area per hectare SHIBUYA Distance from the block to Shibuya station ( km) DAYTIMEPOP Ratio of block daytime population to nighttime population (%) Park variables lnPARK450 Log of the sum of park area within a 450-m radius of the block midpoint

lnPARK1000 Log of the sum of park area within a 1,000-m radius of the block midpoint

  2 LARGEP d Dummy variable: 1 when at least one park larger than 10,000 m exists within a 450-m radius of the block mid point; 0 otherwise

  Table 3 Descriptive statistics N = 244 Variable Mean Standard deviation Min Max

  √ N 2.857 1.247 1 7.348 i

  RENT 712.475 59.832 530 870 √

  

N 2, 054.368 948.045 570.000 5, 420.176

i ×RENT

  

AGE 14.986 5.033 1.857 36.200

lnWALK 2.098 0.552 0.693 3.807

AREA 20.726 2.496 13.590 30.968

DENEN d 0.274 0.426

  1

lnTAX 12.391 0.432 11.513 14.618

BUSPL 5.097 5.246 0.386 56.270

DAYTIMEPOP 96.501 80.900

  43.6 741.3

SHIBUYA 8.047 3.004 2.506 13.893

  Park variables

lnPARK450 7.821 2.605 12.967

lnPARK1000 10.643 1.159 6.608 13.340

LARGEP d 0.135 0.354

  1 Table 4 Specification tests L M L M L M

  λ.ρ λ ρ LM statistic 26.137*** 20.282*** 6.637*** Null hypothesis H H H : ρ = 0, λ = 0 : λ = 0 : ρ = 0

• Significance at the 0.01 level

  Measuring the Benefits o f N eighbourhood P ark Amenities 439

  Table 5 Estimation results Variables Standard WLS Spatial lag model Spatial error model Simple Flexible Simple Flexible √

  N i

  403.033*** (6.212) 403.085***(6.451) 403.569***(6.468) 474.550***(7.153) 483.868***(7.180) AGE

  −5.010*** (−11.877) −4.731*** (−11.215) −4.727*** (−11.327) −4.949*** (−12.077) −5.123***(−12.458) lnWALK −17.588*** (−3.916) −15.284*** (-3.454) −15.637*** (−3.588) −20.641*** (−4.452) −21.424*** (−4.544)

  

AREA 11.235*** (12.073) 11.181*** (12.469) 11.153*** (12.472) 11.476*** (13.358) 11.343*** (13.116)

DENEN d 19.322*** (4.100) 17.920*** (3.916) 17.404*** (3.802) 19.017*** (3.300) 21.142*** (3.636)

lnTAX 23.198*** (4.789) 23.503*** (5.036) 23.504*** (5.053) 18.256*** (3.642) 18.104*** (3.570)

BUSPL 1.468*** (3.658) 1.422*** (3.676) 1.449*** (3.759) 0.848** (2.206) 0.894** (2.286) SHIBUYA

  −9.136*** (−14.300) −9.361*** (−15.044) −9.427*** (−15.140) −9.392*** (−8.730) −9.124*** (−10.539) DAYTIMEPOP

  −0.070*** (−2.706) −0.063** (−2.525) −0.063** (−2.540) −0.062** (−2.592) −0.063*** (−2.619) lnPARK450 1.495** (1.962) 1.493** (2.034) 1.560** (2.132) 1.451* (1.914) 1.357* (1.780) lnPARK1000 −3.715** (−2.238) −3.593** (−2.246) −3.465** (−2.172) −3.696** (−2.033) −4.260** (−2.368) LARGEP d

  −3.135 (−0.522) −2.921 (−0.504) −3.590 (−0.622) −3.351 (−0.561) −2.802 (−0.468) Model parameters ρ 0.017** (2.455) ρ 0.018*** (2.781) λ 0.744*** (5.564) λ 0.415** (4.126) h 0.870 ( km)*** (22.938) h 0.929 ( km)*** (33.495) Log likelihood −1,404.253 −1,401.151 −1,400.297 −1,396.099 −1,395.939 Prediction error 64.713 63.998 64.086 63.846 63.285 Note : Dependent variable is

  √ N i × R E N T ; structural, locational, and park variables are weighted by

  √ N i ; N = 244; t-value in parentheses

• , **, * Significance at the 0.01, 0.05, and 0.1 levels, respectively

  123

  440 T. Hoshino, K. Kuriyama

  We focus first on the overall estimation results. For structural variables, we expected RENT to be positively related to AREA and DENENd and negatively related to lnWALK and AGE. The results showed that the estimated coefficients of these variables had the expected sign at a statistically significant level. For locational variables, we expected RENT to be posi- tively related to lnTAX and BUSPL and negatively related to SHIBUYA and DAYTIME- POP. In terms of the locational variables of park amenities, we expected the basic trend to be an improvement in the residential environment as the area of parks within a buffer increased. Thus, RENT was considered to be positively related to park variables. The esti- mated coefficients of the locational variables, except for park variables, were within our predictions. The park variable results showed that lnPARK450 was significantly positive, whereas lnPARK1000 was significantly negative, and LARGEPd was insignificantly nega- tive. Interestingly, Geoghegan et al. ( 1997 ) also observed that the effects of parks vary with long and short buffers, possibly suggesting that people prefer diverse land uses at a large scale. The significance of the two log variables indicates the presence of diminishing returns for parkland. The negative effect of LARGEPd contradicts the findings of some previous studies, including that of Hidano and Takebayashi ( 1990 ), who examined the value of access to large parks in Tokyo and found that the effect of proximity to large parks on land price is positive. This discrepancy between our results might derive from the different datasets used. Since residents of single-room dwellings often do not use parks, they derive the indirect benefit of a better living environment from parks, whereas multi-room dwellers or families benefit both directly from their use of parks, as well as indirectly. We assumed that large parks often present external diseconomies, including congestion and noise, for local residents, owing to diverse applications and facilities that attract many visitors globally. Thus, especially for

  8 single-room dwellers, negative effects of large parks can cancel out their positive effects.

  Next, we compared the individual results of the seven regression models. The first area of focus was the spatial autoregression model parameters. As predicted, the results indicated that both ρ and λ were significant in both the simple and flexible models; the magnitude of ρ was almost zero, whereas that of λ maintained a certain value. Then, the likelihood ratios between the spatial error models and the standard WLS and the spatial lag model demonstrated the validity of using spatial error models.

  We did not find a significant difference between the spatial error models and kriging models in terms of estimated coefficient values. We could not compute the log-likelihood values of kriging models without an additional distributional assumption. Figure

  2 a and b

  presents the estimated exponential and spherical semivariograms, respectively, which show a spatial interdependent relationship. Estimated h values for the flexible spatial lag model and the flexible spatial error model, and the practical range for the exponential model and range for the spherical model, were 0.870, 0.929, 0.688, and 0.630 km, respectively. The kriging models detected a shorter spatial autocorrelation than did the other two models, with the

  9 boundary of spatial correlation at a 0.630–0.929- km radius, on average, from the source.

  8 However, the value of large parks is not totally capitalised into local housing markets. The travel cost

method or contingent valuation method is most appropriate to evaluate such large parks. Thus, we should not

underestimate the social benefits of large parks from the estimation results.

  9 From the estimated boundary distance of spatial correlation (0.630–0.929 km), we may infer the spatial

correlation. We interpret the distance as the distance people can easily walk. We assumed that most single-

room dwellers do not have their own cars and that they walk to the nearest commuter station to catch a train.

  

According to the dataset, the average walking time to the station from each block midpoint is about 9.5 min.

If an average man walks 5 km/h, then the average distance to the nearest station is 0.792 km, which is just

between the estimated boundary distances. Therefore, we assume that the source of spatial correlation exists

within an area whose centre is each railway station.

  

Measuring the Benefits of Neighbourhood Park Amenities 441

Fig. 2 Estimated semivariograms

  442 T. Hoshino, K. Kuriyama

  Table 6 Estimation results of the Kriging models a

  Variables Kriging model Exponential Spherical √

  

N 465.701*** (7.240) 446.100*** (7.107)

i

  AGE −5.002*** (−12.573) −4.970*** (−12.630) lnWALK −20.216*** (−4.488) −19.017*** (−4.315)

  

AREA 11.273*** (13.163) 11.277*** (13.123)

DENEN d 19.929*** (3.772) 19.261*** (3.952) lnTAX 19.209*** (3.974) 20.370*** (4.327) BUSPL 0.970** (2.530) 1.125*** (2.946) SHIBUYA

  −9.401*** (−12.560) −9.390*** (−13.798) DAYTIMEPOP

  −0.065*** (−2.728) −0.067*** (−2.783) lnPARK450 1.439* (1.906) 1.456* (1.938) lnPARK1000 −4.068** (−2.351) −3.990** (−2.381) LARGEP d

  −2.274 (−0.383) −2.189 (−0.370) Model parameters 5,691.105 5,592.672

  θ θ

• θ

  1 + θ

  1 θ 787.970 θ 1,873.693 3 0.688 ( km) θ 0.630 ( km)

  × θ

  2

  2 Prediction error 61.203 61.363

• , **, * Significance at the 0.01, 0.05, and 0.1 levels, respectively

  a To calculate t-values of the kriging models, we used the estimated covariogram model

  In all models, magnitudes of coefficients for park variables were small. When the aver- age amount of park area within a 450-m radius was evaluated, we found that an addition

  2

  of a 5,000 m park within the radius increased monthly rents of single-room dwellings only

  2

  about 50 yen (0.45 USD; 1 USD = 105 JPY on 26/09/08). The addition of a 20,000-m park within the radius increased the monthly rental price about 140 yen (1.33 USD). However, at the same time, perhaps due to the external diseconomies specific to such a large park, the overall effect was about minus 150 yen (1.43 USD) for single-room dwellings. Meanwhile

  2

  at 0 parks within a 450-m radius, the addition of a 5,000-m park within the radius increased

  2

  monthly rents about 1,430 yen (13.59 USD). The addition of a 20,000-m park within the radius increased the monthly rental price about 1,230 yen (11.69 USD). Thus, even in an area with no parks, the addition of a medium-sized park would be more beneficial than the addition of a huge park. Note that these figures should be considered a lower bound, because the data set was restricted to single-room dwellings.

  4.1 Prediction Accuracy To compare the predictive power of the models, we created a measure of prediction error. We first randomly split the samples into two subsets, with one used to estimate parameters. By using the estimated parameters, we predicted the rental price of the other subset. We then computed the absolute differences between the predicted and true values and averaged

  N P

1 P (θ )

  them: j j N E

  j |P − ˆ |, where NP is the total number of samples in the prediction N P =1