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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. Papers in Regional Science, Volume 87 Number 3 August 2008. 386 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 Papers in Regional Science, Volume 87 Number 3 August 2008. 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 Papers in Regional Science, Volume 87 Number 3 August 2008. 388 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 Papers in Regional Science, Volume 87 Number 3 August 2008. (1) 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 Papers in Regional Science, Volume 87 Number 3 August 2008. 390 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. Papers in Regional Science, Volume 87 Number 3 August 2008. 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 Papers in Regional Science, Volume 87 Number 3 August 2008. 392 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 Papers in Regional Science, Volume 87 Number 3 August 2008. 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 Papers in Regional Science, Volume 87 Number 3 August 2008. 394 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, Papers in Regional Science, Volume 87 Number 3 August 2008. (19) 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). Papers in Regional Science, Volume 87 Number 3 August 2008. 396 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 Papers in Regional Science, Volume 87 Number 3 August 2008. 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. 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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.