Measuring The Benefits of Urban Green Areas: A Spatial Hedonic Approach

Transcription

1 Measuring The Benefits of Urban Green Areas: A Spatial Hedonic Approach An-Ming Wang Ph.D. Student, The Graduate Institute of Urban Planning, National Taipei University, Taipei, Taiwan Tel: Fax: wam@iris.seed.net.tw Abstract The green areas perform important environmental and recreational functions. For example, they absorb atmospheric carbon, maintain a certain degree of humidity in the atmosphere, regulate rainfall, moderate the temperatures, restrain soil erosion and they also form the basis for the conservation of fauna and flora etc. In the cities, moreover, the green area s endowments improve urban amenities and create the advantaged condition for economical capital accumulation. For the above reasons, this paper analyzes the link between housing prices and urban green area endowments using the hedonic technique as the methodological approach. Hence, our empirical study uses the real estate trading data of Taipei city and attempts to measure the influence of green areas on property values. However, housing price data are inherently spatial, which means that the traditional (non-spatial) hedonic price model may not only be affected by the magnitudes of the estimates and their significance, but also result in serious errors in the interpretation of standard regression diagnostics. For the spatial effects, our research further adapts two popular spatial-econometric models: the spatial-lag model and the spatial error model. Results showed that (1) urban green areas had a significant impact on housing prices. (2) The generalized moments (GM) procedure of the spatial error model is more efficient than ordinary least squares (OLS) procedure of the traditional hedonic model. (3) Relative to the true estimates of the spatial-lag model, the OLS estimates of the traditional hedonic model tend to inflate the coefficients of the housing characteristics. (4) Relative to the traditional hedonic model, the estimated mean willingness-to-pay (WTP) for marginal improvement (mean marginal benefit) in different green variables for the spatial-lag model is higher. We tend to support a conclusion that the traditional (non-spatial) hedonic model results in an underestimation of the benefits of an improvement in the urban green area variable. Keywords: Urban green areas; Hedonic price method; Spatial effect; Spatial-lag model; Spatial error model; Marginal benefit 1

2 1. Introduction Markets respond to price singles. If a resource, whether it be a barrel of oil, a patch of swamp or old-growth forest, or a breath of fresh air, is priced to reflect its true and complete cost to society, goes the argument, market will ensure that those resources are used in an optimally efficient way. (Alper, 1993: 1884) The green areas perform important environmental and recreational functions. For example, they absorb atmospheric carbon, maintain a certain degree of humidity in the atmosphere, regulate rainfall, moderate the temperatures, restrain soil erosion and they also form the basis for the conservation of fauna and flora, etc. In the cities, moreover, they can provide acoustic isolation, since urban green areas work as an acoustic screen between traffic roads and residential areas. Plants have individual and collective aesthetic value, playing an important role in the conservation of a pleasant landscape, being sometimes the link between residential urban areas and industrial areas. City parks and gardens are also the setting for many recreational activities (children s play areas, walking, jogging, etc.). All these endowments of green areas create the advantaged condition for economical capital accumulation and explain the influence of environmental variables on the prices of dwellings (Morancho, 2003). However, the economic valuation of the urban green areas benefits is not immediate as, from an economic point of view, the urban green areas are non-market goods as other urban public goods and environmental resources without a market price, their true and complete social cost does not directly react to free economic markets. So that these urban green areas can be properly considered in the cost-benefit analyses of public urban planning policies, the evaluation of non-market goods becomes the useful instrument to carry out the planning and policies. At present, there are several developing evaluation methods for non-market goods in economic theory, such as hedonic price method (HPM), contingent valuation method (CVM), production function method (PFM), etc. The different non-market goods and situations are satisfied with different evaluation methods. For example, if we want to evaluate the natural environment benefit of urban areas, the hedonic price method could be more appropriate than other methods, because the application of the hedonic price technique to valuing the benefits of urban green areas can be directly estimated by the true housing market trading behavior. This true revealed market behavior is one of the advantages of the hedonic method relative to other environmental valuation methods such as contingent valuation. Therefore, the topic of this paper is limited to 2

3 an evaluation of urban green areas by the hedonic price method. In addition, one another important purpose is to emphasize further the spatial issue within the hedonic price method. It is very possible that sales prices of houses are influenced by location effects that vary systematically over space, since there is a great spatial similarity in housing prices. The hedonic price model has some serious econometric problems when spatial effect is present but ignored. Although this spatial issue of hedonic model estimation receives more and more attention (e.g., Sengupta, et al., 2003; Bastian, et al., 2002), very few empirical studies by spatial hedonic approach exist in current literature (other than Kim, et al., 2003). Therefore, the primary objective of this paper is an empirical study that focuses on estimating the benefits of urban green areas by means of the spatial hedonic framework of Kim, et al, It is to extend an explicit spatial econometric methodology, in conjunction with a basic hedonic housing price model, to measure the marginal value of increasing green areas in Taipei, Taiwan. To attain the primary objective, this study explicitly considers spatial effects in estimating the hedonic model. We estimate two alternative econometric models that incorporate spatial effects: a spatial-lag model and a spatial error mode. Besides, we compare the urban green areas marginal benefits both from the spatial hedonic model and a traditional (non-spatial) hedonic model. The remainder of the paper consists of the following: Section 2 illustrates the theoretical foundations of the hedonic price method. Section 3 discusses the spatial issues of estimating hedonic price models. Sections 4 & 5 provide several estimation results of empirical models for the traditional hedonic model, the spatial error model and the spatial-lag model. Section 6 discusses marginal benefit estimation, followed by the conclusions in Section Theoretical Foundations of Hedonic Price Method (HPM): The Conceptual Framework (Markandya, et al., 2002) The hedonic price method measures the welfare effects of changes in environmental assets and services by estimating the influence of environmental attributes on the value of some market goods, usually of houses. In attempting to isolate the effects of environmental attributes on the price of houses we have to explain the price of a house by means of its characteristics. If we take house price to be a function of all the features of the house, that is, structural characteristics (number of rooms, central heating, garage space and so on), neighborhood characteristics, and environmental 3

4 characteristics then the following relationship can be identified: P h h ( S, K, S ; N, K, N ; E, KE ) = f for all houses h, (1) h1 hj h1 hk h1 hm where, P h represents house price; h represents a unit of housing; f h represents the function that relates the house characteristics to price; S hi, K S denote different hj structural characteristics of the house; characteristics; and E h1 hm N,K, N denote different neighborhood hi hk, KE denote different environmental characteristics. The function above is called hedonic price function. Fixing the level of all the other characteristics of a house, we are able to focus on the relationship between the price of the house and the environmental attribute under investigation. Economic theory does not provide much information on the shape of the hedonic price function, whose only certain characteristic is that its first derivative with respect to an environmental characteristic is positive (negative) if the characteristic is a good (bad). Freeman (1993) suggests that there are a priori reasons to expect the hedonic function for an amenity to be concave from below. The concavity of the hedonic price functions suggests that those individuals with high marginal willingness to pay who currently experience high levels of the environmental attribute, would have a low willingness to pay at the margin for additions to the environmental attribute. A possible hedonic price function, all the other independent variables equal, is depicted in Figure 1. Figure 1: Hedonic price function of houses Source: Markandya, et al., 2002 For an improvement in the environmental attribute E, say from E 1 to E 2, the individual maximum WTP for the improvement would be correctly reflected by the change in the individual s bid function, say, the distance ab in Figure 2. 4

5 Unfortunately, the bid functions are not easy to estimate, because it would require data on the behavior of the same individuals for different levels of the environmental attributes. A more feasible way of estimating the willingness to pay would be to use the change in the hedonic price function to approximate the maximum WTP for the environmental change. The estimated hedonic equation would give the distance ac the measure of the benefit. Hence, the HPM, using the results of the econometric estimation described above, would result in an overestimation of the benefits of an improvement, or an underestimation of the costs of deterioration. Figure 2: Hedonic price function as a locus of individuals equilibria Source: Markandya, et al., 2002 Can the overestimation (underestimation) be corrected by adapting the method? Rosen (1974) proposed a two-stage procedure to estimate the marginal maximum WTP functions of individuals, that is, their implicit inverse demand functions, utilizing the results of the estimation of the hedonic price function described above. By partially differentiating the hedonic price function with respect to E, he obtains the implicit marginal price function of the environmental good: P P h impl. E = (2) E This partial derivative is interpreted as the price paid by the individuals for the last unit of the environmental attribute, purchased by choosing a given house instead of another one with one unit less of the environmental attribute, other things equal. Estimated implicit prices for different houses refer to different individuals. Every estimated implicit price is only one observation of the true individual demand curve and corresponds to the individual WTP for a marginal unit of environmental good only for that specific level of environmental good purchased. Therefore, the implicit 5

6 marginal price function cannot be viewed as an implicit (inverse) demand curve. Hence, it does not represent the maximum marginal WTP of the individual for one more unit of the environmental attribute, unless we assume that all the individuals have the same structure of preferences and the same income. If this assumption does not hold, the various individuals i will have different implicit (inverse) demand curves D i E in Figure 3. As the figure shows, there will be only one point of the type ( ) where the marginal WTP for one more unit of E equals the marginal implicit price of E. Nevertheless, in the second stage, the implicit price can be regressed on the observed quantities of the environmental attribute and some socioeconomic characteristics of individuals. This second-stage estimation, under some restrictions, could allow the identification of the implicit inverse individual demand function. Figure 3: Implicit marginal price function of the environmental attribute E Source: Markandya, et al., 2002 The area under the demand curve D 1 ( E) in Figure 3 between two levels of the environmental attribute, say E 1 and E 2, represents the change in the consumer surplus caused by the change in this attribute. Once the demand function D 1 ( E) has been estimated, the change in the consumer surplus is calculated as the definite integral of D 1 ( E) with respect to the quantity of the environmental good between E 1 and E 2. By aggregating all individuals consumer surpluses we obtain the overall value of the environmental improvement. 3. The Spatial Issue when Estimating The Hedonic Price Model (HPM) According to the literature, there are many issues when estimating hedonic price models, such as the selection of dependent and independent variables, omitting 6

7 important variables, the problem of multi-collinearity, the choice of proper functional form, the problems for identification of the implicit inverse individual demand function, etc. However, the purpose of this article is to emphasize that HPM analyses are inherently spatial. This is because housing prices contain obviously spatial structure, such as that high price houses are usually concentrated in similar locations or areas, at nearby houses enjoy similar neighborhood characteristics, and that house prices influence each other when houses are on adjacent locations. In the literature, these spatial phenomena are called the spatial dependence or spatial (auto)correlation. Spatial correlation becomes an efficiency issue in estimation that may lead to incorrect tests of hypotheses results. Hence, in this paper, we only focus our discussion here on the importance of spatial effects, and, in particular, of spatial dependence on the efficiency and consistency of the hedonic model estimates, which has only very recently started to receive some attention (e.g., Pace, et al., 1998). As has by now been amply demonstrated, the neglect of spatial considerations in econometric models not only affects the magnitudes of the estimates and their significance, but may also lead to serious errors in the interpretation of standard regression diagnostics such as tests for heteroskedasticity (Kim, et al., 2003; Anselin, et al., 1998;). The questions that follow are: (1) how to incorporate the spatial dependence into the hedonic price model; (2) how to apply the spatial hedonic approach properly to address good statistical characteristics? For these questions, we follow the literature and present two basic spatial regression models as well as the various estimation methods. Two kinds of spatial regression model are the spatial-lag model and the spatial error model. ❶ In a spatial-lag model, both the direct effect (the standard explanatory variables of housing and neighborhood characteristics) and indirect effect (the spatially weighted average of housing prices in a neighborhood affects the price of each house) of a neighborhood s housing characteristics are captured through a spatial multiplier 1 (Kim, et al., 2003). In other words, based on the traditional (non-spatial) hedonic price equation, the spatial-lag model adds the spatially weighted average of housing prices into the explanatory variables set. The spatial-lag model provides the only way to obtain a consistent estimator for the parameter needed to carry out the spatial filtering (Anselin, et al., 1998). ❷ In contrast, in a spatial error model, spatial 1 The spatial multiplier is equal to the sum of each row of the [ ] 1 I ρ W matrix. where I is a n n identity matrix, ρ is a spatial autocorrelation parameter, W is a n n spatial weight matrix. n is the sample size. More details are presented the following sections. 7

8 autocorrelation is assumed to arise from omitted variables that follow a spatial pattern (Kim, et al., 2003). In other words, the error term of the hedonic price equation tends to be spatially autocorrelated. The spatial error model is only to deal with the problem of non-spherical error variance covariance matrix. In terms of the estimation methods, ❶ for the spatial-lag model, the ordinary least-squares (OLS) estimators are biased and inconsistent, and instead maximum-likelihood (ML) estimation or instrumental variables (IV) estimation needs to be employed to obtain consistent estimators. The IV estimation is equal to the spatial two-stage least-squares estimates (S-2SLS) that are based on the use of the spatially lagged explanatory variables as instruments that are robust to non-normality and consistent, but not necessarily efficient (Kim, et al., 2003). ❷ About the spatial error model, the OLS estimator remains unbiased for the regression coefficients, but is no longer efficient (Hill, et al., 2001; Anselin, 1988). Estimation must be based on either maximum likelihood (ML) or on a generalized moments (GM) approach. As usual, ML estimation requires an assumption of normality, which is not needed for the generalized moments approach (Kim, et al., 2003). We list the clear situations about the two basic spatial hedonic price models in Table 1. Table 1 Two basic spatial hedonic price models and the different estimating methods Assumptions Nearby or neighboring observations of housing prices Hedonic price equation omits one or more very spatial variables partially explain local housing price Appropriate Model Spatial Lag Model (Consistent) Spatial Error Model (Most efficient) OLS Biased and inconsistent Unbiased, but no longer efficient ML Consistent, but needs normal error term Unbiased, but needs normal error term IV (S-2SLS) a Consistent -- GM -- Efficient, and doesn t need normal error term a spatial two-stage least-squares estimates (S-2SLS) 4. Data and Variables In this paper, the study area is Taipei city. The housing data (price and address) and 8

9 structural characteristics use in this study are true traded price data that derive from the private real estate agency companies. The neighborhood characteristics and environmental characteristics of the housing sample were surveyed data that derive from using geographical information systems (GIS). The sample covered all 12 districts in Taipei city, and a total of 2,427 individual houses were used in this study. The following housing characteristics were selected as explanatory variables except the PRICE variable (Table 2). In our empirical model, we selected 8 variables to capture the neighborhood characteristics (or spatial structure). These were the Euclidean distances of a housing to the nearest mass rapid transit station, central business district, the railway station, the nearest hospital, the nearest school, the nearest wastedump, nearest electric power transformer station, and if the districts of house within city core or not. Besides, 5 variables are selected to indicate the structural characteristics of the house, they are total floor space of house, number of rooms, bathrooms, age of house, and if the house is allowed to be commercial use. Finally, the last three variables are green (environmental) variables that included total area of green space within a radius of 500m of a house, the Euclidean distances of a housing to the nearest park, and the green cover rate of district that the house is located on. Their inclusion in the price equation allows us to estimate the influence of urban green areas on the housing market value. Table 2 Definition for variables Variable Definition Unit Expected sign PRICE Property value of owner occupied house 10,000NT a ACSMRT Accessibility to the nearest MRT station (Euclidean distance) meter (-) ACSCBD1 Accessibility to the CBD (Tian-mu) (Euclidean meter (-) distance) ACSTATION Accessibility to the railway station (Euclidean distance) meter (-) ACSHPT Accessibility to the nearest hospital (Euclidean meter (-) distance) ACSSCH Accessibility to the nearest school (Euclidean meter (-) distance) ACSDUMP Accessibility to the nearest waste dump meter (+) (Euclidean distance) ACSEPTS Accessibility to the nearest electric power transformer station (Euclidean distance) meter (+) DCORE Dummy variable equals one if the district of the 0/1 (+) 9

10 house is city core, else zero TFLSP Total floor space of house ping b (+) NMRMS Number of rooms number (+) NMBATH Number of bathrooms number (+) HSAGE Age of house year (-) DBUSINESS Dummy variable equals one if the house is allowed to be in commercial use, else zero 0/1 (+) TAGREEN Total area of green space within a radius of 500m of the house hectare (+) ASCGREEN Accessibility to the nearest park (Euclidean distance) meter (-) GREENCR The green coverage of the district within which % (+) the house is located. a NT is the Taiwan currency; $US1 is approximately 31.2 NT. b Ping is a Taiwan unit for area; 1 ping is approximately m 2. Descriptive statistics of all variables (dependent and explanatory) in the hedonic price equation are provided in Table 3. The sample is broadly representative of the inside and outside characteristics of housing. The average house has 33 pings, 3 numbers of room, 2 numbers of bathroom, and is 14 years old. The average sales price of house is 7870 thousand NT$, the minimum price is 1320 thousand NT$, the maximum price is thousand NT$. In terms of neighborhood characteristics, the average distance to MRT station is 1246 meters, to CBD 2 is 8906 meters, to railway station is 4780 meters, to hospital is 844 meters, to school is 364 meters, to dump is 1687 meters, to electric power transformer station is 699 meters. Approximately 43% sample are located on core district of Taipei city, 10% sample are allowed to be commercial use. In terms of environmental characteristics, the average green area (park and green land) within a radius of 500m of sample is 3.36 hectare; the average distance to the nearest park is 178 meters; and the average green cover rate of Taipei city is 6.64%. Table 3 Summary statistics for variables Variable Minimum Maximum Mean Std. dev. PRICE ACSMRT ACSCBD ACSTATION ACSHPT As most of people s consideration, Taipei is a multi-cbd city. However, in our study, we select only one CBD (Tian-mu) to measure its accessibility. This is because that Tuan-mu CBD is different from most CBD of Taipei city that covered in spatial area of MRT stations 10

11 ACSSCH ACSDUMP ACSEPTS DCORE TFLSP NMRMS NMBATH HSAGE DBUSINESS TAGREEN ACSGREEN GREENCR The sample size is Empirical Models The relationship between the selling price and the characteristics of the housing can take several models. In the present work, three specifications are considered. First, we estimate the traditional (non-spatial) hedonic price model by means of OLS procedure. The result of estimation is the basis in comparison with the spatial hedonic model. In addition, following the discussion of literature, we consider two basic ways to incorporate spatial effects into a regression model: the spatial-lag model and the spatial error model. All spatial analyses are carried out by means of the SpaceStat software (developed by Anselin), Version For technical details on the construction of spatial regressions, see Anselin, Due to our main focus is on the spatial econometric aspects of the analysis, so we do not provide a detailed analysis of the role of the functional form. We will therefore only consider the results for the estimation of a semi-log specification. In the next section, firstly, we will introduce the foundations of spatial hedonic model and our empirical model specification. Secondly, we report the estimation result. Finally, we illustrate the important information about the estimation result and our argumentative basis. 5.1 The spatial error model This model is based on the assumption that there is one or more omitted variable in the hedonic price equation and that the omitted variable(s) vary spatially. Hence, it is 11

12 a special case of a regression specification with a non-spherical error variance covariance matrix (Kim, et al., 2003; Greene, 2003). Due to this spatial pattern in the omitted variables, the error term of the hedonic price equation tends to be spatially autocorrelated (Kim, et al., 2003). In contrast to the lag model, the spatial error model is appropriate when there is no theoretical or apparent spatial interaction and the modeler is interested only in correcting the potentially biasing influence of spatial autocorrelation, due to the use of spatial data. In other words, the interest focuses on obtaining the most efficient estimates for the coefficients in the hedonic model and in ensuring that inference is correct (Kim, et al., 2003). Our empirical hedonic spatial error model is: ln P = X1ß 1 + X2ß 2 + X3ß 3 e = λ We + u + e spatial dependence is present in the error terme, P is the vector of housing price, X 1 is a matrix with observations on structural characteristics, X 2 is a matrix with observations on neighborhood characteristics, and X 3 is a matrix with observations on environmental quality variables, λ is the spatial autoregressive coefficient, W is a n n spatial weight matrix (where n is the number of observations), and u is assumed to be a vector of i.i.d. errors. (3) In terms of spatial weight matrix, our analysis needs a weights matrix for all households. In other words, we need a spatial weight matrix. The element of spatial weight matrix W is W ij, which is the proximity of locations between point i and point j. In our empirical model, we use the Euclidean distance between point i and point j. Since we assume that attribute values (e.g., housing prices) of points follow the first law of geography 3, so the expected sign of spatial autoregressive coefficient is negative. With the distance matrix, we give larger weights to points that are far apart and smaller weights to points that are closer together (Lee & Wong, 2001). For the software (SpaceStat) requirement, we convert the non-standardized matrix that we constructed from the Euclidean distance to row-standardized form (i.e., such that the row elements for each observation sum to 1). Table 4 offers the estimation of the Eq. (3) by maximum-likelihood (ML) and generalized moments (GM) procedure, but the ordinary least squares (OLS) procedure is only used for traditional hedonic price function for comparison with the results of spatial error model. 3 The first law of geography (Tobler, 1970): everything is related to everything else, but near things are more related than distant things. (All things are related, but closer things are more related.) 12

13 Table 4 Estimation results of spatial error regression a Variable OLS ML GM CONSTANT *** ( ) *** ( ) *** ( ) ACSMRT E-05** (1.339E-05) E-05 ( E-05) E-05** ( E-05) ACSCBD E-05*** (3.646E-06) E-05*** ( E-06) E-05*** (3.132E-06) ACSTATION E-05*** (5.481E-06) E-05*** ( E-06) E-05*** ( E-06) ACSHPT E-05 (2.160E-05) E-05 ( E-05) E-05 ( E-05) ACSSCH 5.126E-05 (5.892E-05) E-05 ( E-05) E-05 ( E-05) ACSDUMP 6.017E-05*** (1.464E-05) E-05*** ( E-05) E-05*** ( E-05) ACSEPTS 2.944E-05 (2.521E-05) E-05 ( E-05) E-05 ( E-05) DCORE ( ) ( ) ( ) TFLSP *** ( ) *** ( ) *** ( ) NMRMS *** ( ) *** ( ) *** ( ) NMBATH ** ( ) * ( ) * ( ) HSAGE ( ) * ( ) * ( ) DBUSINESS *** ( ) *** ( ) *** ( ) TAGREEN ( ) ( ) ( ) ASCGREEN ** ( ) * ( ) ** ( ) GREENCR ** ( ) *** ( ) ** ( ) λ *** ( ) *** -- R Likelihood a N = 2427 ***Significant at 1%, **significant at 5%, *significant at 10%. ( ): Standard error, R 2 for all models other than OLS is pseudo-r 2 13

14 One set of estimates for the traditional hedonic model and two sets of estimates for the spatial error model are listed in Table 4. The ML estimates assume normality, which may not be appropriate in this case 4. The OLS and ML estimates are provided for comparison purposes. Firstly, we focus on the OLS estimates and diagnostics for testing the basic properties of this original equation. The model achieves a reasonable fit (R 2 =0.4) and all estimated coefficients have the expected sign, except for ACSSCH variable, which is positive, but not significant. And there is no problem of multi-collinearity, according to its variance-inflating factor (VIF) value for each variable is less than 3, and the condition index (CI) value for all variables is less than 30 (Gujarati, 2003, p.362). But the Jarque Bera test suggests that the error terms violate normality at a significance level, therefore, the OLS and ML regression may not be shown the correct result. In contrast, the spatial error model that is based on GM procedure doesn t need the assumption of normality as well as has corrected the error terms which include the spatial effect. Secondly, we compare the OLS result with GM, and focus the discussion on efficient aspect of estimation. The estimates provided by the two methods are very similar other than NMBATH variable, but the significant level of coefficients has some difference. Let us focus on that three green variables, the TAGREEN of GM is more insignificant than OLS regression. But the ASCGREEN and GREENCR of GM are more significant than OLS regression. This seems that GM method of spatial error model is able to distinguish the differences more efficiently between significant variables and insignificant variables 5. Finally, both the spatial autoregressive coefficient (λ ) of ML and GM are very significant and same with our expect sign. This indicates that the error terms include the phenomenon about spatial dependence indeed. 5.2 The spatial-lag model The spatial-lag model implicitly assumes that the spatially weighted average of housing prices in a neighborhood affects the price of each house (indirect effects) in addition to the standard explanatory variables of housing and neighborhood characteristics (direct effects) (Kim, et al., 2003). The spatial-lag model is particularly appropriate when there is structural spatial interaction in the market and the modeler is interested in measuring the strength of 4 A Jarque Bera test in the OLS regression suggests that the third and fourth moments of the error terms violate normality at a significance level of less than Most significant variables become more significant, and HSAGE variable changes from insignificant to significant. 14

15 that relationship. However, it is equally relevant when the modeler is interested in measuring the true effect of the explanatory variables, after the spatial autocorrelation has been removed, similar to a first-difference approach in time series (Kim, et al., 2003). Our empirical spatial-lag hedonic housing price model can be written as follows: ln = ρ W lnp + X ß + X ß + X ß e (4) P where P is the vector of housing prices, ρ is a spatial autocorrelation parameter, W is a n n spatial weight matrix (in our empirical process, it is same with the spatial weight matrix of spatial error model), X 1 is a matrix with observations on structural characteristics, X 2 is a matrix with observations on neighborhood characteristics, and X 3 is a matrix with observations on environmental quality variables, with e assumed to be a vector of independent and identically distributed (i.i.d.) error terms. Table 5 offers the estimation of the Eq. (4) by maximum-likelihood (ML), instrumental variables (IV or S-2SLS) and S-2SLS robust procedure. The result and the role of OLS estimation are same as the Table 4. 15

16 Table 5 Estimation results of spatial lag regression a Variable OLS ML S-2SLS (IV) S-2SLS robust ρ *** ( ) *** ( ) *** ( ) CONSTANT *** ( ) *** ( ) *** ( ) *** ( ) ACSMRT E-05** (1.339E-05) E-05* ( E-05) E-05 ( E-05) E-05*** ( E-006) ACSCBD E-05*** E-05*** E-05*** E-05*** (3.646E-06) (3.8997E-06) ( E-06) ( E-06) ACSTATION E-05*** E-05*** E E-06 (5.481E-06) ( E-06) ( E-05) ( E-06) ACSHPT E-05 (2.160E-05) E-06 ( E-05) E-06 ( E-05) E-05 ( E-05) ACSSCH 5.126E-05 (5.892E-05) E-05 ( E-05) E-05 ( E-05) ** ( E-05) ACSDUMP 6.017E-05*** E-05*** E-05*** E-05** (1.464E-05) ( E-05) ( E-05) (1.1939E-05) ACSEPTS 2.944E-05 (2.521E-05) E-05 ( E-05) 2.921E-05 ( E-05) E-06 ( E-05) DCORE ( ) ( ) ( ) ( ) TFLSP *** ( ) *** ( ) *** ( ) *** ( ) NMRMS *** ( ) *** ( ) *** ( ) *** ( ) NMBATH ** ( ) * ( ) * ( ) * ( ) HSAGE ( ) * ( ) * ( ) ( ) DBUSINESS *** ( ) * ( ) *** ( ) *** ( ) TAGREEN ( ) ( ) ( ) * ( ) ASCGREEN ** ( ) * ( ) ( ) * ( E-05) GREENCR ** ( ) ** ( ) ** ( ) *** ( ) R Likelihood a N = 2427 ***Significant at 1%, **significant at 5%, *significant at 10%. ( ): Standard error, R 2 for all models other than OLS is pseudo-r 2 16

17 Three sets of estimates for the spatial-lag model are listed in Table 5. The OLS and ML estimates are provided for comparison purposes. The reason is same with spatial error model above. According to the estimation results, we get several important discussion points. First, three sets of estimates for the spatial-lag models indicate a strong negative and significant spatial autoregressive coefficient ( ρ ), suggesting a great spatial similarity in housing prices. Second, both ML and S-2SLSmodels suggest a high degree of heteroskedasticity 6, which may affect the efficiency of the estimates. To take this into account, our final estimate uses a heteroskedastic robust form of the S-2SLS estimation. Third, in our application, the ACSMRT is a very important variable, which contains most spatial structure of Taipei city. In the S-2SLS robust procedure, the ACSMRT is significant, but in the S-2SLS procedure, the ACSMRT is insignificant, even though the S-2SLS is robust to non-normality and consistent. This would remind us, the heteroskedasticity problem must be dealt with carefully. Fourth, relative to the OLS results, when we use the S-2SLS robust procedure, the TAGREEN variable changes from insignificant to significant, the GREENCR variable becomes more significant, but the ASCGREEN variable becomes slightly less significant for the S-2SLS robust. Finally, ACSSCH and GREENCR variable coefficients are larger in absolute values, but all the other coefficients are smaller (relative to the OLS results). Such result suggests that the presence of spatial autocorrelation in this model would tend to inflate the coefficients of the housing characteristics in OLS estimates that ignore the spatial effects. In other words, the high degree of spatial similarity in the green variables levels among neighboring housing units, reduces the estimated contribution of green variables to the explanation of housing values at each individual location. When estimating the marginal benefits of green variables improvement, such spatial multiplier effects must be considered explicitly (Kim, et al., 2003). 6. Marginal Benefit Estimates Based on the above hedonic price theory, the derivative of the hedonic price equation with respect to each explanatory variable is its marginal implicit price (i.e. Equation (2)). In the Rosen s second-stage estimation, the marginal implicit price can be regressed on the observed quantities of the environmental attribute and some socioeconomic characteristics of individuals, under some restrictions, could allow the identification of the implicit inverse individual demand function that we can calculate the benefit (consumer surplus) of environmental improvement (Markandya, et al., 6 Heteroskedasticity is suggested by a highly significant Koenker Bassett test ( α < 0.001). 17

18 2002). Unfortunately, we have a lot of difficulties in getting the socioeconomic characteristics of households in Taiwan. Hence, in the current presentation, we only calculate the marginal implicit price, that can be interpreted as the marginal WTP, assuming the housing market is in equilibrium. According to the literature, a traditional hedonic property-value model may lead to a biased or at least imprecise estimate of the benefits of a housing characteristic change if spatial autocorrelation of housing value is present (Kim, et al., 2003). Hence, we calculate the mean marginal WTP of traditional linear model and spatial lag model respectively, and compare the results to illustrate the difference in these estimated benefits. Since our empirical model is semi-log functional form, we can derive the mean marginal WTP equation of the two models straightforward by from the basic mathematical exercise. The results can be written as follows: The mean marginal WTP of traditional linear model (OLS) is calculated by the following equation: β E ( OLS ) P (5) The mean marginal WTP of spatial lag model (S-2SLS) is calculated by the other following equation: 1 1 ρ β E ( S 2SLS ) P (6) where β E is the coefficient of the particular environmental variable, P is the sample mean of housing value, ρ is a spatial autocorrelation parameter. For the convenience of calculation, when we estimate the benefit of spatial lag model, we choose another spatial weight matrix which is base on our original distance matrix but convert to the inverse squared distance matrix (i.e. 2 1 distance ), such that the spatial autocorrelation parameter be conformed the assumption of Equation (6) (i.e. 0 < ρ < 1, ρ = ) (Kim, et al., 2003) 7. 7 Since our spatial lag model is: lnp = ρ WlnP + Xß + e l np = [ I ρw] Xß + [ I ρw] e where [ I ρ W] 1 is an (n n) inverse matrix, and the sum of each row of [ W] 1 ( 1 ρ) I ρ is 1, which would be the spatial multiplier if a unit change were induced at every location. Note that this result only holds for W matrices with row sums less than or equal to one and for ρ in the proper parameter space, i.e., 0 < ρ < 1.

19 Table 6 Mean marginal WTP for different green variables unit: NT a /per household Variables OLS S-2SLS TAGREEN 13,852 14,431 ASCGREEN (decreasing distance) 1,724 1,739 GREENCR 58,557 63,730 a NT is the Taiwan currency; $US1 is approximately 31.2 NT. The estimated mean WTP for marginal improvement in different green variable for OLS and S-2SLS models are given in Table 6 8. Based on the housing value are inherently spatial autocorrelation, we assume the OLS estimates are biased, and the marginal benefit of spatial lag model (S-2SLS) is higher than OLS. According to above, we believe the traditional hedonic model that use the estimates of OLS, would result in an underestimation of the benefits of an improvement of environmental variable. 7. Discussion and Conclusions In this paper, we attempt to incorporate the spatial-lag model and spatial error model into the hedonic price method, because of HPM analyses are inherently spatial, not only because of the dependent variable (housing price) but also the explanatory variables (e.g., accessibility to the MRT, CBD, and other external environmental characteristics). If the real world is exactly spatial and our empirical model ignores the spatial effect, the econometric model not only will be affected by the magnitudes of the estimates and their significance, but may also be led to serious errors in the interpretation of standard regression diagnostics. The spatial-lag model emphasizes the true effect of the explanatory variables, after the spatial autocorrelation has been removed, and to measure the strength of spatial interaction relationship. In contrast, the spatial error model focuses on obtaining the most efficient estimates for the coefficients in the hedonic model and in ensuring that inference is correct. Although each of the two spatial models has a different economic interpretation, for the comparison purposes, we still estimate the spatial-lag model by ML, S-2SLS, S-2SLS procedures and the spatial error model by ML and GM procedures respectively, and compare with the OLS procedure for traditional (non-spatial) hedonic model. 8 In the Table 6, the calculation results are based on an assumption that the green variables are independent for each other. In other words, when we change the value of one variable, the other two variables value will not be change following the first one. 19

20 According to our empirical results, we want to point out some important information as follows. (1) The urban green areas had a significant impact on housing prices. (2) In terms of estimation efficiency (compare OLS with GM procedure), the GM procedure of spatial error model is more efficient than OLS procedure of traditional hedonic model. In the spatial error model, most significant variables become more significant, most insignificant variables become more insignificant, and some variables change from insignificant to significant. (3) In terms of the true estimates (compare OLS with S-2SLS robust procedure), relative to the OLS results, most coefficients of spatial-lag model by S-2SLS robust procedure are smaller in absolute values. Such result suggests that the presence of spatial autocorrelation in this model would tend to inflate the coefficients of the housing characteristics in OLS estimates that ignore the spatial effects. And the spatial-lag hedonic model deals with neighborhood effects that cannot be captured by non-spatial techniques, the spatial-lag hedonic model also avoids the econometric problems of biased and inconsistent estimators when spatial dependence is present but ignored. (4) In terms of the marginal benefits, relative to traditional hedonic model, the estimated mean WTP for marginal improvement in different green variables for spatial-lag model are higher. For this empirical result, we tend to support a conclusion that using the traditional (non-spatial) hedonic model would result in an underestimation of the benefits of an improvement in the urban green area variables. In our empirical application, we do not deal well with the time dimension that is an important issue for our data set quality and selection of explanatory variables. Future studies may extend the spatial-lag model to allow the use of more flexible functional forms and compare their results. In addition, we want to calculate the true consumer surplus for different improvement programs, and not just the mean marginal WTP. References Alper, J. (1993), Protecting the Environment with the Power of the Market, Science, 260: Anselin, L. (1988), Spatial Econometrics: Method and Models, Boston: Kluwer Academic Publishers. Anselin, L. (1992), SpaceStat Tutorial: A Workbook for Using SpaceStat in the Analysis of Spatial Data, National Center for Geographic Information and 20

21 Analysis, University of California, Santa Barbara, CA. Anselin, L., and A. Bera, (1998), Spatial dependence in linear regression models with an introduction to spatial econometrics, in: A. Ullah, D. Giles (Eds.), Handbook of Applied Economic Statistics, Marcel Dekker, New York, p Bastian, C.T., D.M. McLeod, M.J. Germino, W.A. Reiners and B.J. Blasko, (2002), Environmental amenities and agricultural land values: a hedonic model using geographic information systems data, Ecological Economics, 40, p Freeman, A.M. III (1993), The Measurement of Environmental and Resource Values: Theory and Methods. Washington DC: Resources for the Future. Greene, W. H. (2003), Econometric Analysis (5th edition), NY: Prentice-Hall International Inc. Gujarati, Damodar N. (2003), Basic Econometrics (4th edition), NY: McGraw-Hill, Inc. Hill, R.C., William E.G. and George G.J., (2001), Undergraduate Econometrics, NY: John Wiley & Sons, Inc. Kim, Won Chong, Tim, T. Phipps, and Luc Anselin, (2003), Measuring the benefits of air quality improvement: a spatial hedonic approach, Journal of Environmental Economics and Management, 45, p Lee, J., and David, W. S. Wong, (2001), Statistical Analysis with ArcView GIS, New York: John Wiley & Sons, Inc. Markandya, A., P. Harou, L.G. Bellù and V. Cistulli, (2002), Environmental Economics for sustainable Growth: A Handbook for Practitioners, Cheltenham: Edward Elgar. Morancho, A. B. (2003), A hedonic valuation of urban green areas, Landscape and Urban Planning, 66, p Pace, R.K., R. Barry, and C.F. Sirmans, (1998), Spatial statistics and real estate, Journal of Real Estate Finance and Economics, Vol.17:1, p Rosen, S. (1974), Hedonic prices and Implicit Markets: Product Differentiation in Pure Competition, Journal of Political Economy, 82(1): Sengupta, S. and D.E. Osgood (2003), The value of remoteness: a hedonic estimation of ranchette prices, Ecological Economics, 44, p Tobler, W.R. (1970), A computer movie simulating urban growth in the Detroit region, Economic Geography, 46 (Supplement):