!Measuring the impact of large-scale transportation projects on land price using

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doi:10.1111/j.1435-5957.2008.00192.x
Measuring the impact of large-scale transportation projects
on land price using spatial statistical models*
Morito Tsutsumi1, Hajime Seya2
1
2
University of Tsukuba, Graduate School of Systems and Information Engineering, Tsukuba 305-8573, Japan
(e-mail: [email protected])
PASCO Corporation, 1-1-2 Higashiyama, Meguro-ku, Tokyo 153-0043, Japan (e-mail: [email protected])
Received: 14 September 2007 / Accepted: 8 May 2008
Abstract. Large-scale transportation projects such as the construction of a commuter railway
accessible to metropolises have a significant regional impact. This study attempts to measure
this impact using spatial statistical models and land price data. First, dynamic changes in the
land price are analysed and the so-called announcement effect is presented using the spatial
interpolation techniques. Second, various types of land price models are constructed by employing the existing methods of spatial econometrics and geostatistics; their estimates and project
benefits are compared and discussed, particularly from the viewpoint of policy implications.
JEL classification: C21, L92
Key words: Land price, spatial error model, spatial process model, spatial hedonic approach,
benefit evaluation
I Introduction
Large-scale transportation projects such as the construction of a commuter railway accessible
to metropolises have a significant regional impact. Since property values are strongly affected
by the accessibility of a location, the relationship between the two has long been of interest.
Furthermore, the property values increase even before the change in accessibility, that is, before
the commencement of the construction of a project; this is known as the announcement effect.
There has been progress in empirical researches on property markets that consider the spatial
dependence. Roughly summarized, there are two research fields concerning spatial dependence
– spatial econometrics and geostatistics. However, to the best of our knowledge, hardly any
research has been conducted to analyse the dynamical change in land price that is affected by a
real transportation project and identify when the announcement effect appears.
* The authors are grateful to the anonymous reviewers for their valuable comments. This work was partially
supported by the Japanese Ministry of Education, Science, Sports and Culture, Grant-in-Aid for Scientific Research (C),
20560485, 2008.
© 2008 the author(s). Journal compilation © 2008 RSAI. Published by Blackwell Publishing, 9600 Garsington Road,
Oxford OX4 2DQ, UK and 350 Main Street, Malden MA 02148, USA.
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M. Tsutsumi, H. Seya
The first objective of this study is to demonstrate an analysis of property values for
understanding their dynamical change using a case study of the Tsukuba Express (TX) line – the
last commuter railway that drastically improved the accessibility of Central Tokyo, Japan – by
a geostatistical approach. This paper focuses on the land price as the property value, and uses the
officially assessed land prices provided by the Ministry of Land, Infrastructure and Transport,
Japan. This data set has the advantage of being collected annually from almost fixed sites.
One of the conventional approaches used to evaluate the benefits of infrastructure projects is
the application of the hedonic approach developed by Rosen (1974) to property values. When a
hedonic approach is applied using a regression model, the importance of considering the spatial
dependence among data should be reconsidered.
Many empirical studies have analysed the benefits of environmental changes on property
values based on a hedonic approach by considering the spatial dependence (e.g., Kim et al.
2003; Anselin and Le Gallo 2006; Anselin and Lozano-Gracia 2007). However, with regard
to the evaluation of the benefits of transportation projects based on this approach, only a few
studies have considered the spatial dependence. For example, Yiu and Wong (2005) analysed
the effects of the expected improvements in transportation on the housing prices without
considering the spatial effects.
Among several studies on spatial hedonic modelling, Can (1992), Tsutsumi et al. (1999), and
Anselin and Le Gallo (2006) employed the spatial econometrics approach, while Dubin (1992)
and Valente et al. (2005) employed a geostatistical approach. Although many researchers have
suggested the importance of considering the spatial dependence, no significant studies except
for those conducted by Militino et al. (2004), Neill et al. (2007), and Páez et al. (2008) have
compared the results of both approaches. Some literatures suggest that when social economic
data is used, the former approach is preferable because the assumptions of the latter – secondorder stationarity and continuity in space – are overly strong and unrealistic (e.g., Anselin and
Bera 1998; Ismail 2006). On the other hand, Militino et al. (2004) do not agree that the former,
that is, the spatial weight matrix approach, is more appropriate for modelling hypothetical
spatial relationships because it requires a priori specification of a spatial weight matrix, which
may affect the final results.
Hence, the second objective of this study is to compare the estimates of both approaches and
discuss them from the viewpoint of the evaluation of project benefits.
The remainder of this paper is organized as follows. Section 2 introduces the outline of the
TX line and the study area. It then describes the details of the land price data. In Section 3, land
prices are interpolated by a geostatistical approach and the dynamical changes in the land prices
are discussed. In Section 4, land price models are constructed by employing the existing
methods of spatial econometrics and geostatistics for evaluating the amount of the benefits of the
TX line project. Section 5 presents the conclusions.
2 Outline of the TX line and the data
2.1 Outline of TX line and study area
The TX line connects Akihabara city, Tokyo Prefecture and Tsukuba city, Ibaraki Prefecture, and
has a length of 58.3 km; it commenced operations on 24 August, 2005. The total project cost was
approximately 830 billion yen (approximately 7 billion dollars). The TX line has reduced the
travel time from Akihabara to Tsukuba from 85 min (using the existing Joban line or a highway
bus) to 45 min. The impact of the TX line is expected to be significant because there had been
no rail connectivity prior to it in most of the areas along the line. Furthermore, many urban
improvements or development projects are expected, particularly near the new stations. The
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Impact of large-scale transportation projects on land price
387
Joban line
Joso line
Tsukuba Sta.
TX line
Moriya Sta.
Minami-Nagareyama Sta.
Akihabara Sta.
Other lines
TX line
Fig. 1. Study area and main stations along the TX line
Table 1. History of the Tsukuba Express project
Year
History
1991
1999
Establishment of Metropolitan Intercity Railway Company
Formulation of project by Ministry of Land, Infrastructure and
Transport, Japan
Commencement of construction
Commencement of operation
2001
2005
study area, comprising 18 municipal districts, is shown in Figure 1. Furthermore, a brief
overview of the project history of the TX line is shown in Table 1.
2.2 Description of the land price data
In this paper, we use the officially assessed land price data provided by the Ministry of Land,
Infrastructure and Transport, Japan. The assumption regarding the hedonic price function is that
it is based on the market price. On the other hand, the officially assessed price is not the market
price but the appraised price. Japan’s valuation standard recommends that appraisers refer to the
market price when appraising a property. In other words, a market-value-based valuation is
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M. Tsutsumi, H. Seya
generally applied. The most common methodologies used for estimating the market value
include the sales comparison method, capitalized earnings or discounted cash flow method, and
cost method – the same as those described in the International Valuation Standards.
However, the disadvantage of market price data is that they may suffer from market
imperfections; namely, they incorporate forced prices resulting from buying or selling sprees.
Thus, the market price data themselves are not always appropriate for hedonic price modelling;
instead, the officially assessed land price data are more appropriate in this context. Moreover, the
latter have the advantage of being collected annually from almost fixed sites, including mediumsized cities. Hence, the latter is useful for both analysing the dynamic trend for identifying when
the announcement effect appears and constructing statistically reliable models.
We use the data collected annually from 1995 to 2006 (inclusive); the number of sites from
which data were collected is 630 for each year.
3 Understanding the dynamical changes in land price in the study area
3.1 Preliminary analysis of land prices
Figure 2 shows the change in the average land price in each prefecture in the study area, scaled
to the price in 1995. Note that the land price in the study area fell almost continuously from 1995
to 2006 after Japan’s ‘bubble economy’ collapsed in the early 1990s. Thus, under such conditions, it is difficult to intuitively comprehend the impact of the TX line. In order to eliminate
such trends from the data, we use the average price of land outside the study area (surrounding
area). The summary of the data is shown in Table 2.
The procedure used to remove the undesired trends in the land price data of the study area
using the land price data of the surrounding area is discussed below. In brief, the land price in
the study area in the year t is weighted by the prefecture-specific ratio of the average price of
land in the surrounding area in the same year and that in the surrounding area at the beginning
of the time period (1995). The calculation procedure is as follows.
First, let the study area and surrounding area be denoted as DA and DB ∈ D ⊂ ℜ2, respectively, and each area comprises of four domains divided by prefecture, where D is the entire area
of interest (including both the study and surrounding areas), and k (k = 1, 2, 3, 4) is an index
denoting Ibaraki, Chiba, Saitama and Tokyo prefectures, respectively (Figure 3).
4
4
k =1
k =1
DA = ∪ DAk , DB = ∪ DBk , D = DA ∪ DB .
Index
1
Ibaraki
0.9
0.8
Saitama
0.7
0.6
Chiba
0.5
Tokyo
0.4
0.0
95 96 97 98 99 00 01 02 03 04 05 06 Year
Fig. 2. Changes in land price for each prefecture in the study area
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Impact of large-scale transportation projects on land price
389
Table 2. Changes in parameters of covariance function in Ibaraki Prefecture
Year
Nugget
Partial-sill
Range
95
96
97
98
99
00
01
02
03
04
05
06
0.245
0.223
0.184
0.132
0.110
0.110
0.0961
0.0784
0.0601
0.0480
0.0400
0.0394
0.362
0.345
0.324
0.327
0.297
0.265
0.247
0.238
0.230
0.225
0.223
0.234
12.0
11.8
11.2
9.43
9.44
10.7
11.0
10.8
10.2
9.94
9.71
9.51
DA1
DB3
DB1
DA3
DA4
DA2
DB2
DB4
Fig. 3. Definition of the domains
Then, let the prices at the observed sites in the study and surrounding areas be denoted
as psi ∈DAk (t ) = { p ( si ; t ) si ∈ DAk , t ∈ T } and psi ∈DBk (t ) = { p ( si ; t ) si ∈ DBk , t ∈ T } , respectively,
where si ∈ D ⊂ ℜ2 {i = 1, . . . , 1369 (= 630 + 759)} represents the observed sites, and
t ∈ T ⊂ ℜ (t = 1995, . . . , 2006) denotes the observed years.
Next, let the average land price in study area DAk and surrounding area DBk in the year t be
denoted as
1
qDAk (t ) =
(2)
∑ ps ( t ) ,
DAk si ∈DAk i
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M. Tsutsumi, H. Seya
qDBk (t ) =
1
DBk
∑p
si ∈DBk
si
(t ) ,
(3)
where |DAk| and |DBk| denote the number of observed sites in DAk and DBk, respectively (e.g.,
|DB1| = 107). Using qDBk (t ) , the land price in DAk is weighted as
p∗si ∈DAk (t ) = psi ∈DAk (t )
qDBk (t )
qDBk (1995)
,
(4)
and the average land price in DAk can be calculated as
q*DAk (t ) =
1
DAk
∑ p∗ (t ).
si ∈DAk
si
(5)
3.2 Kriging
In order to understand the dynamical changes in land price, we prepare interpolated land price
maps for the period of interest. As a geostatistical technique, (ordinary) kriging is used for
spatial interpolation. Using kriging, the land price of the new site s0 ∈ DAk is interpolated by the
weighted sum of the observations as
{
} ∑ λ ln {p∗ (t )},
ln p∗s0 ∈DAk (t ) =
i,t
si ∈DAk
si
(6)
where li,t is the weight assigned to the observation at the site si ∈ DAK (i = 1, . . . , n) in the year
t. In this paper, the logarithm of the land price is considered. The weight vector is given by
−1
lt = Sˆ t−1 cˆt + Sˆ t−1 1 ( 1′ Sˆ t−1 1) (1 − 1′ Sˆ t−1 cˆt ) ,
(7)
where lt and 1 are n ¥ 1 vectors whose elements are denoted by li,t and 1, respectively. S t and
ct are the variance-covariance matrix and the covariance vector respectively, whose elements are
given by a covariance function C(dij), where dij is the Euclidean distance between i and j.
There are three parameters that characterize the form of the covariance function – nugget,
partial-sill and range. For more details, see Cressie (1993). In this analysis, the so-called
spherical covariance function is chosen,
(dij ≥ φt )
⎧0
⎪
3
⎪ ⎡ 3 ⎛ dij ⎞ 1 ⎛ dij ⎞ ⎤
C ( dij ) = ⎨σ t2 ⎢1 − ⎜ ⎟ + ⎜ ⎟ ⎥ (0 < dij ≤ φt )
⎪ ⎣ 2 ⎝ φt ⎠ 2 ⎝ φt ⎠ ⎦
⎪τ 2 + σ 2
otherwise,
⎩ t
t
(8)
where τ t2, σ t2, and ft represent the nugget, partial-sill, and range in the year t, respectively.
These parameters are estimated by using the weighted least-squares (WLS) method (Cressie
1985); the parameters are estimated for each prefecture.
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Impact of large-scale transportation projects on land price
391
3.3 Designing the interpolated land price maps using kriging
Table 2 and Figure 4 show the estimates of the covariance function and their changes in Ibaraki
prefecture, which is the farthest from Tokyo and is considered to have experienced the most
drastic changes in land price in the period of interest.
The nugget variance, which represents the microscale component and a measurement-error
component, and the sill variance (nugget + partial-sill), which represents the variance of the
spatial process, decrease from 1995 to 2005. This suggests that the diversity in land prices
decreased. However, in 2006, the sill variance is greater than that in the previous year, implying
an increase in the variance of the observed land prices. Of course, there are some sites where the
land price increased. The range parameter, which represents the extent of the existing spatial
correlation, exhibits a gradual decrease from 2001. It is also notable that the range and partialsill drastically change from 1997 to 1998, suggesting a significant change in the land price in this
period.
We prepared the land price maps using the above mentioned kriging technique. The interpolation was performed by considering the logarithm of the land price; however, a map based on
the actual scale appears to be more useful for the immediate determination of the dynamic
impact, and hence, the interpolated results are back-transformed for mapping as
⎡
⎤
exp ⎢ ∑ λi, t ln p∗si (t ) ⎥ .
⎣ si ∈DAk
⎦
{
}
(9)
Such back-transformation leads to the median estimator (Tolosana-Delgado and PawlowskyGlahn 2007). Figure 5 shows the increments in the land prices from the previous year at each site
as calculated by
⎡
⎤
⎡
⎤
exp ⎢ ∑ λi ,t ln p∗si (t ) ⎥ − exp ⎢ ∑ λi ,t −1 ln p∗si (t − 1) ⎥ (t = 1996, . . . , 2006 ) .
⎣ si ∈DAk
⎦
⎣ si ∈DAk
⎦
{
}
{
}
(10)
The spatial distribution of the land price drastically changes from 1997 to 1998 and from
1999 to 2000. Moreover, the land price near Tsukuba Station, which is located around one of the
most densely populated areas in Ibaraki Prefecture, begins to increase from 2001. The relative
increase (cessation of the decreasing trend) in land price is considered to be the result of the
announcement effect; the results show that the impact is the greatest around Tsukuba Station.
Nugget, Partial-sill
Range (km)
14
0.40
0.35
12
range
0.30
10
0.25
8
pa rtia l-sill
0.20
6
0.15
4
nugget
0.10
2
0.05
0
0.00
95 96 97 98 99 00 01 02 03 04 05 06 Year
Fig. 4. Changes in the parameters of the covariance function in Ibaraki Prefecture
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M. Tsutsumi, H. Seya
Tsukuba Sta.
Moriya Sta.
95–96
99–00
96–97
97–98
00–01
01–02
98–99
02–03
1,000 yen/m2
~ 45
~ 35
~ 25
~ 15
~0
~ - 15
~ - 25
~ - 35
03–04
04–05
05–06
0
15 km
~ - 45
Fig. 5. Interpolated land price map (increments) showing the Voronoi area of the TX stations in Ibaraki prefecture
prepared by using the other stations shown in Fig. 2
Since the macroeconomic trend of the data is removed, the relative increase in land price
from 2001 is considered to be caused by the announcement effect. However, when we observe
the map carefully, a drastic change can be observed from 1997 to 1998 and from 1999 to 2000.
Initially, it was planned that the TX line would commence operations in 2000; hence, it is
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Impact of large-scale transportation projects on land price
393
possible that these changes are also the result of the announcement effect. These findings
suggest that using the data after 1997 may lead to an underestimation of the benefit. Therefore,
we use the data of the year 1995 for constructing hedonic land price models.
4 Constructing various land price models
In this section, various land price models are constructed using the existing methods of spatial
econometrics and geostatistics for evaluating the amount of benefits of the TX line project. As
mentioned above, we use the data of the year 1995 for constructing land price models.
4.1 Spatial dependence in regression analysis
Let the standard multiple linear regression model, which we call the basic model (BM), be
denoted as
y = X b + e,
(11)
where y is an n ¥ 1 vector of the dependent variables; X, an n ¥ k matrix of the explanatory
variables; b, a k ¥ 1 vector of the trend parameters; and e, an n ¥ 1 vector of the i.i.d. errors. The
standard assumptions are
E (e ) = 0,
(12)
Var (e ) = σ ε2 I,
(13)
where 0 is a null n ¥ 1 vector; I, an n ¥ n identity matrix; and σ ε2 , the variance of the errors.
Eqaution (13) is rarely satisfied because of the existence of the spatial dependence. When the
spatial dependence exists, the ordinary least-squares estimator is no longer statistically reliable
(e.g., Cliff and Ord 1981; Anselin 1988). Although the standard assumption is violated if the
structure of W is known, the parameters can be estimated by the generalized least-squares (GLS)
method based on
Var (e ) = S = σ ε2 W .
(14)
However, there is hardly any case wherein the structure of W (or S ) would be known; hence,
some assumptions are necessary to structuralize S. Roughly speaking, there are two types of
methods for this – the spatial econometric approach and the geostatistical approach.
As spatial econometric approaches, the spatial lag model (SLM) and spatial error model
(SEM) are often used to consider the spatial dependence. These models consider the spatial
dependence by structuralizing the dependence among dependent variables or errors; accordingly,
the variance-covariance matrix is structuralized indirectly. On the other hand, as geostatistical
approaches, the spatial process model (SPM) is used to consider the spatial dependence. The SPM
is a technique in which the variance-covariance matrix is structuralized directly. These differences
in the manner of structuralizing the variance-covariance matrix cause differences in the trend
parameters, which lead to differences in the amount of evaluated benefits.
The marginal benefit derived from the SLM is affected by the types of underlying externalities, that is, technological externality or pecuniary externality (Small and Steimetz 2006; Anselin
and Lozano-Gracia 2007). In practice, however, it is difficult to identify the type of externalities
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M. Tsutsumi, H. Seya
that really cause the spatial dependence among observations; hence, the SLM is not always useful
for the evaluation of the benefits of a transportation project. On the other hand, SEM eases such
explicit modelling. Hence, as the spatial econometric model, we adopt the SEM and not the SLM.
4.1.1 SEMs
SEM is expressed as
y = Xb + e,
e = λW e + u, u ∼ i.i.d . (0, σ u2 ) ,
(15)
where l is an autoregressive parameter; W, an n ¥ n spatial weight matrix; and u, an n ¥ 1 vector
of the i.i.d. errors u whose variance is given by σ u2 . Several methods have been proposed to
obtain the elements of W (see Anselin 1988), for example, the distance-based weight is given by
(i = j )
,
(i ≠ j )
⎧0
wij = ⎨ 2
⎩1 dij
(16)
where dij is the Euclidean distance between i and j. Here, W is in the row-standardized form. The
model described by Equation (14) leads to the variance-covariance matrix
−1
S = σ u2 ⎡( I − λW )′ ( I − λW )⎤ .
⎣
⎦
(17)
The parameters are estimated by the maximum likelihood method (Ord 1975; Anselin 1988) or
other methods such as a generalized method of moments (Kelejian and Robinson 1993) and a
two-stage least squares (Kelejian and Prucha 1998)]. For more details, see LeSage and Pace
(2004, 2008) and Anselin (2006).
Although Equation (15) considers only the spatial autocorrelation, a model considering the
spatial heteroscedasticity has also been developed by LeSage (1997, 1999). It has been recognized that SEM results in a homogeneous variance of errors and inhibits robust estimation in the
cases where outliers exist. Geweke (1993) proposed a method employing a simple regression
model exhibiting a nonconstant variance by assuming different values for every observation, and
LeSage (1997, 1999) extended it to spatial econometric models. The Bayesian spatial error
model (BSEM) is given by
e = λW e + u, u ~ N (0, σ u2 V ) , V = diag ( v1 , , vn ) ,
(18)
where diag(•) denotes the diagonal matrix, and vi represents the relative variance assigned to the
site si. The parameters are estimated by the Bayesian method. For more details, see LeSage
(1997, 1999) and Kakamu et al. (2008).
4.1.2 SPM
When SPM is used, the error term is typically assumed to be second-order stationary that is
{
}
E ε *si ∈DA = 0,
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Impact of large-scale transportation projects on land price
{
395
}
Cov ε *si ∈DA , ε *sj ∈DA = C ( dij ) ,
(20)
where ε *si ∈DA and ε *sj ∈DA represent the errors for the observed sites si ∈ DA and sj ∈ DA,
respectively. Such an assumption underlies the following equation
S = σ 2 H (φ ) + τ 2 I,
(21)
where H is an n ¥ n matrix whose elements Hij are given by covariance functions, and I is an
n ¥ n identity matrix. Note that SPM is a technique in which the variance-covariance matrix is
structuralized by a function depending only on the Euclidean distance (if isotropy is assumed).
There are some methods to estimate the parameters, including the Bayesian approach. For more
details, see Cressie (1993), Banerjee et al. (2004), Schabenberger and Gotway (2005), and
Diggle and Ribeiro (2006).
4.2 Constructing spatial hedonic models
In this subsection, various land price models are constructed by employing the preliminary
approaches, and the amounts of the benefits are evaluated based on each model.
The details of the study area and the land price data have already been explained in section
2. We use the data for 1995 to construct the hedonic models, as explained in section 3. In section
3, the parameters of the model were estimated for each prefecture because the mean land price
differs in each prefecture. However, with respect to the regression analysis, the difference of the
mean in the data are explicitly considered; hence, the data from all the prefectures are used for
the estimation in this section.
Different markets would have different hedonic price functions; hence, separate models are
constructed for each market, that is, residential areas (447 sites), commercial areas (124), and
industrial areas (64). This paper presents the results for the case of residential areas.
The dependent variables are obtained as their logarithms, as explained in section 3. The
explanatory variables are shown in Table 3. Regarding the explanatory variables, the expected
signs of the estimates of the variables named ‘capacity’ and ‘fire’ are positive, while those for
‘station’ and ‘time dist.’ are negative.
In this paper, we compare the BM, SEM, BSEM, and SPM. As the spatial weights for the
SEM and BSEM, the distance-based weight is used (Eq. (16)), and the Gaussian function used
as the covariance function for the SPM is given by
(dij ≥ φ )
⎧0
⎪
2
⎛ dij ⎞ ⎤
⎪ ⎡
C ( dij ) = ⎨σ 2 ⎢exp ⎜ − 2 ⎟ ⎥ (0 < dij ≤ φ )
⎝ φ ⎠⎦
⎪ ⎣
⎪⎩τ 2 + σ 2
otherwise.
(22)
Table 3. Explanatory variables
Abbreviates
Capacity
Station
Time dist.
Fire
Explanatory variables
Floor-area ratio based on legislation (%).
Distance to the nearest station (m).
Time distance to Tokyo Station from the nearest station (min).
Fire-prevention district dummy (Yes: 1, No: 0).
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M. Tsutsumi, H. Seya
In order to estimate the parameters of the SPM, a method using WLS and GLS is used
(e.g., Schabenberger and Gotway 2005), and those for SEM are estimated by the maximum
likelihood method (e.g., Anselin 1988). The parameters of the BSEM are estimated by the
Bayesian estimation method via the Markov Chain Monte Carlo (MCMC) method by
following the prior distributions, that is, the multivariate normal distribution for b, inversegamma distribution for σ u2 , and uniform distribution for l. r/vi is assumed to independently obey the c2(r) distribution, where r is the degree of freedom. These conditions are
given by
b ~ N ( c, T ), σ u2 ∼ IG ( a, b ) , λ ∼ U ( −1, 1) , r vi ∼ i.i.d . χ 2 (r ) r .
(23)
The number of iterations are 6,100, and the first 100 samples are discarded (i.e., burn-in). The
convergence of the MCMC method is confirmed by Geweke’s method (see LeSage 1999).
Diffuse priors are assumed for b and σ u2 , that is, c = 0, T = I ¥ 1012, and a = b = 0 are the initial
values. It is also assumed that r = 4, which is associated with the heteroscedasticity (LeSage
1999).
4.3 Results of parameter estimation and benefit evaluation
Table 4 shows the results of parameter estimation (by OLS) of the BM. The trend parameters are
all statistically significant, and the signs of the estimates are intuitionally acceptable. However,
Figure 6 clearly shows the existence of spatial autocorrelation of the residuals. Positive residuals
exist around the newly built stations, especially near the Tsukuba Station, while negative
residuals exist along the existing local railways.
The spatial autocorrelation and heteroscedasticity of the residuals are detected. The standardized Moran’s I statistic is 12.9 and the adjusted Breusch–Pagan statistic (Anselin 1988, pp.
122–123) is 119. Both suggest the existence of spatial autocorrelation and heteroscedasticity.
The null hypotheses of no existence of spatial autocorrelation and heteroscedasticity were
rejected at a significance level of 1%.
Table 5 shows the results of parameter estimation of the SEM and BSEM, and Table 6 shows
that of SPM. The fitness to the observations is improved when SEM and BSEM are used as
compared to BM.
Conventionally, the benefits of transportation projects are evaluated by multiplying the
(expected) time saved by the project by the marginal benefit of the associated variables and
market area. For this case study, ‘station’ and ‘time dist.’ are such variables.
Table 4. Parameter estimates of the BM
Estimate
Std. error
p
Intercept
Capacity
Station
Time dist.
Fire
12.29
0.2338
-0.04198
-1.454
0.9924
0.0765
0.0120
0.00768
0.0413
0.0823
0.00
0.00
0.00
0.00
0.00
Sigma2
Adjusted R2
AIC
0.0613
0.888
27.7
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Impact of large-scale transportation projects on land price
397
Fig. 6. Spatial distribution of residuals (BM)
Table 5. Parameter estimates of the SEMs
SEM
Estimate
Intercept
Capacity
Station
Time dist.
Fire
Lambda
Sigma2
Adusted R2
AIC
11.76
0.2372
-0.06303
-0.9432
0.1762
0.9450
0.0347
0.936
-148
BSEM
Std. error
p
Estimate
Std. error
p
Geweke
0.205
0.00957
0.0107
0.108
0.103
0.00
0.00
0.00
0.00
0.09
12.27
0.2259
-0.06466
-1.316
0.3984
0.129
0.0161
0.0183
0.105
0.172
0.00
0.00
0.00
0.00
0.00
0.07
0.15
0.27
0.62
0.76
0.0218
0.00
0.7910
0.0317
0.928
0.0564
0.00
0.42
0.96
–
–
–
In case the dependent variables are log-transformed, the marginal benefits are given by
∂y
= β m y.
∂xm′
(24)
Then, in our case, the amount of benefit is evaluated by the following equation;
Papers in Regional Science, Volume 87 Number 3 August 2008.
398
M. Tsutsumi, H. Seya
Table 6. Parameter estimates of the SPM
Estimate
Std. error
p
Intercept
Capacity
Station
Time dist.
Fire
12.16
0.2258
-0.07386
-1.191
0.5329
0.113
0.00902
0.0107
0.0888
0.0824
0.00
0.00
0.00
0.00
0.00
Nugget
Partial-sill
Range
0.0225
0.0305
12.9
n
∑ (β
i =1
station
⋅ yi ⋅ Δxi , station ⋅ Si + β timedist . ⋅ yi ⋅ Δxi , timedist . ⋅ Si ),
(25)
where bstation · yi and btimedist. · yi are the marginal benefits associated with ‘station’ and ‘timedist.’
of the observed site i, respectively; Si is the market area of i; and Dxi,timedist. and Dxi,station are the
changes in ‘station’ and ‘timedist.’ at i between before and after the project.
The sites considered for evaluating the benefits need not necessarily be the same as the
observed sites. In fact, many literatures about project benefits evaluation using the hedonic
approach use different sites such as the central points of municipalities. It is notable, however,
that when spatial econometric models are used as the hedonic price function, the formations of
the sites are required to be the same because the structure of W depends on the formation.
The estimates for these variables are both negative, as expected, but rather different among
the models. For example, the estimates for ‘station’ of BM are relatively low as compared to
that of the other spatial models, but high for ‘timedist.’ Furthermore, the estimates for ‘time
dist’ differ significantly between the SEM and BSEM. This difference is caused by that in the
estimates of the autoregressive parameter. In case the study area is relatively large and spatial
heteroscedasticity exists, the use of the BSEM is recommended because the SEM based on the
maximum likelihood method is not robust to the outliers. Basically, the amount of benefits is
proportional to the estimates; hence, this difference is very serious, as explained in detail in the
next section.
4.4 Evaluated benefits of the TX line project
The study area may not be sufficiently small to apply the hedonic approach for benefit evaluation. Therefore, the amounts of benefit may be over-evaluated. However, our concern is not the
total amount of benefit itself, but the difference among the benefits evaluated by each model. We
discuss this problem below.
The evaluated amounts of benefits are 9,470 (BM), 6,900 (SEM), 9,140 (BSEM), and 8,590
(SPM) billion yen, respectively. (Since the total project cost was approximately 830 billion yen,
the evaluated amounts could be overestimated.) In case the model does not consider both the
spatial autocorrelation and the heteroscedasticity (BM), the derived benefit is relatively high,
while that of the models that consider only the spatial autocorrelation (SEM, SPM) is relatively
low. The model that considers both the spatial autocorrelation and the heteroscedasticity
(BSEM) evaluate intermediate benefits.
Figures 7 and 8 show the estimated benefit per square metre to the residential area based on
BM and SEM, respectively. BM overestimates the benefits because the parameters are overestimated. The pattern of overestimation exhibits characteristics similar to those shown in Figure 6
where residuals are plotted.
Papers in Regional Science, Volume 87 Number 3 August 2008.
Impact of large-scale transportation projects on land price
399
Fig. 7. Evaluated benefit incidence per square metre (BM)
The benefit estimated by BM is more than 1.3 times that estimated by SEM. From the
viewpoint of project evaluation, these differences are quite important because the difference
directly affects the cost benefit ratio.
Although both SEM and SPM consider the spatial autocorrelation of the error terms, the
estimated amount of benefits by the latter is 1.2 times that estimated by the former. On the other
hand, BSEM and SPM estimate similar amounts of benefits. However, it is not easy to conclude
the reasons that lead to these magnitude relations. For example, the Voronoi areas are larger
around Tsukuba and smaller around Akihabara, which may affect the differences between SEM
and SPM.
5 Concluding remarks
This study measured the impact of large-scale transportation projects on the land price through
a case study of the TX line by using spatial statistical models. The main findings are as follows:
First, this study shows a very simple procedure to specify the appearance time of the
announcement effect: (1) removing the undesired trends from the data in the study area by using
the data from outside the study area and (2) designing interpolated land price maps using the
kriging technique. As mentioned above, there has been no significant research about a method
Papers in Regional Science, Volume 87 Number 3 August 2008.
400
M. Tsutsumi, H. Seya
Fig. 8. Evaluated benefit incidence per square metre (SEM)
to specify when the announcement effect appears. We believe that this paper contributes and
provides a tool to identify such announcement effects by employing spatial statistical modellings.
Second, various land price models were constructed by employing the existing methods
of spatial econometrics and geostatistics, and their estimates were compared. No significant
research has evaluated the benefit using both approaches and presented a comparison of the
results. The empirical analysis verified that a lack of sufficient consideration of both the spatial
dependence and spatial heteroscedasticity can lead to serious mistakes in project evaluation
based on the hedonic approach.
Although both SEM and SPM consider the spatial autocorrelation of the error terms, their
estimated amount of benefits are quite different. On the other hand, BSEM and SPM estimate
similar amounts of benefits. Thus far, it has not been easy to conclude whether these magnitude
relations occur accidentally or consequently.
References
Anselin L (1988) Spatial econometrics: Methods and models. Kluwer Academic Publishers, Dordrecht
Anselin L (2006) Spatial econometrics. In: Mills T, Patterson K (eds) Palgrave handbook of econometrics: Volume 1,
econometric theory. Palgrave Macmillan, Basingstoke
Papers in Regional Science, Volume 87 Number 3 August 2008.
Impact of large-scale transportation projects on land price
401
Anselin L, Bera A (1998) Spatial dependence in linear regression models with an introduction to spatial econometrics.
In: Ullah A, Giles DE (eds) Handbook of applied economic statistics. Marcel Dekker, New York
Anselin L, Le Gallo J (2006) Interpolation of air quality measures in hedonic house price models, spatial aspects. Spatial
Economic Analysis 1: 31–52
Anselin L, Lozano-Gracia N (2007) Errors in variables and spatial effects in hedonic house price models of ambient air
quality. Empirical Economics 34: 5–34
Banerjee S, Carli B, Gelfand A (2004) Hierarchical modelling and analysis for spatial data. Chapman & Hall/CRC,
London/Boca Raton
Can A (1992) Specific and estimation of hedonic housing price models. Regional Science and Urban Economics 22:
453–474
Cliff AD, Ord JK (1981) Spatial processes: Models and applications. Pion, London
Cressie N (1985) Fitting variogram models by weighted least squares. Mathematical Geology 17: 563–586
Cressie N (1993) Statistics for spatial data: Revised edition. John Wiley & Sons, London
Diggle PJ, Ribeiro Jr PJ (2006) Model-based geostatistics. Springer, New York
Dubin RA (1992) Spatial autocorrelation and neighborhood quality. Regional Science and Urban Economics 22:
432–452
Geweke J (1993) Bayesian treatment of the independent student-t linear model. Journal of Applied Econometrics 8:
19–40
Ismail S (2006) Spatial autocorrelation and real estate studies: A literature review. Regional Science and Urban
Economics 35: 57–82
Kakamu K, Polasek W, Wago H (2008) Spatial interaction of crime incidents in Japan. Mathematics and Computers in
Simulation 78: 276–282
Kelejian HH, Prucha IR (1998) A generalized spatial two-stage least squares procedure for estimating a spatial
autoregressive model with autoregressive disturbances. The Journal of Real Estate Finance and Economics 17:
99–121
Kelejian HH, Robinson DP (1993) A suggested method of estimation for spatial interdependent models with autocorrelated errors, and an application to a county expenditure model. Papers in Regional Science 72: 297–312
Kim CW, Phipps TT, Anselin L (2003) Measuring the benefits of air quality improvement: A spatial hedonic approach.
Journal of Environmental Economics and Management 45: 24–39
LeSage JP (1997) Bayesian estimation of spatial autoregressive models. International Regional Science Review 20:
113–131
LeSage JP (1999) The theory and practice of spatial econometrics. URL: http://www.spatial-econometrics.com
LeSage JP, Pace RK (2004) Advances in econometrics: Spatial and spatiotemporal econometrics. Elsevier Science,
Oxford
LeSage JP, Pace RK (2008) Introduction to spatial econometrics. Chapman & Hall/CRC, London/Boca Raton
Militino AF, Ugarte MD, Garcîa-Reinaldos L (2004) Alternative models for describing spatial dependence among
dwelling selling prices. Journal of Real Estate Finance and Economics 29: 193–209
Neill HR, Hassenzahl DM, Assane DD (2007) Estimating the effect of the air quality: Spatial versus traditional hedonic
price models. Southern Economic Journal 73: 1088–1111
Ord JK (1975) Estimation methods for models of spacial interaction. Journal of American Statistical Association
79(349): 120–126
Páez A, Long F, Farber S (2008) Moving window approaches for hedonic price estimation: An empirical comparison
of modelling techniques. Urban Studies 45: 1565–1581
Rosen S (1974) Hedonic prices and implicit market, product differentiation in pure competition. Journal of Political
Economy 82: 34–55
Schabenberger O, Gotway CA (2005) Statistical methods for spatial data analysis. Chapman & Hall/CRC, London/
Boca Raton
Small KA, Steimetz S (2006) Spatial hedonics and the willingness to pay for residential amenities. Economics Working
Paper, no.05-06-31, University of California, Irvine
Tolosana-Delgado R, Pawlowsky-Glahn V (2007) Kriging regionalized positive variables revisited: Sample space and
scale considerations. Mathematical Geology 39: 529–558
Tsutsumi M, Shimizu E, Ide H, Fukumoto J (1999) On regularization methods for regression analysis in the presence
of spatially correlated errors: Application to hedonic regression of land price. Journal of Eastern Asia Society for
Transportation Studies 3: 87–95
Valente J, Wu SS, Gelfand A, Sirmans CF (2005) Apartment rent prediction using spatial modelling. Journal of Real
Estate Research 27: 105–136
Yiu CY, Wong SK (2005) The effect of expected transport improvements on housing prices. Urban Studies 42: 113–125
Papers in Regional Science, Volume 87 Number 3 August 2008.
doi:10.1111/j.1435-5957.2008.00192.x
Medición del impacto de proyectos de transporte de gran
escala en el precio del suelo utilizando modelos estadísticos
espaciales
Morito Tsutsumi and Hajime Seya
Resumen. Los proyectos de transporte de gran escala tales como la construcción de un tren
suburbano de acceso a una metrópolis tienen un impacto regional significativo. Este estudio
intenta medir este impacto utilizando modelos estadísticos espaciales y datos del precio del
suelo. Primero, se analizan cambios dinámicos en el precio del suelo y se presenta el llamado
efecto de anuncio utilizando técnicas de interpolación espacial. Segundo, se construyen varios
tipos de modelos de precio del suelo mediante el empleo de métodos existentes de econometría
espacial y geoestadística; se comparan y discuten sus estimaciones y los beneficios del proyecto,
en particular desde el punto de vista de sus implicaciones políticas.
JEL classification: C21, L92
Palabras clave: suelo, precio del suelo, modelo de error espacial, modelo de proceso espacial,
enfoque hedónico espacial, evaluación de beneficios
© 2008 the author(s). Journal compilation © 2008 RSAI. Published by Blackwell Publishing, 9600 Garsington Road,
Oxford OX4 2DQ, UK and 350 Main Street, Malden MA 02148, USA.
Papers in Regional Science, Volume 87 Number 3 August 2008.
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