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1 Land Use Change with Externalities in the Fringe of Jakarta Metropolitan: Spatial Tobit Model Rahma Fitriani, University of Brawijaya, Indonesia Eni Sumarminingsih, University of Brawijaya, Indonesia The Asian Conference on Sustainability, Energy and the Environment 05 Official Conference Proceedings Abstract Among many other factors, land use externalities became more significant factors which drive land use change. The theoretical land use change model with externalities indicates that the competing externalities contribute to the sprawled development pattern in an urban area. This theory is empirically supported by the result of a study of land use change in the fringe of Jakarta Metropolitan. There are some evidences that sprawl in this area has been driven by interaction of competing land use externalities. This type of development is considered inefficient. It gives more pressure to the conservation area and the productive agricultural sites in the southern fringe. It motivates this study to analyze the extent of those externalities and their role in shaping the recent development pattern based on spatial econometric models. The model will be useful to predict the effect of future land use change on the conservation area and productive agricultural sites. Two models are considered namely Spatial of Lag X (SLX) Tobit Model and Spatial Durbin (SD) Tobit Model. Two variables (density and area proportion of agricultural activity) at district level are used to capture the competing externalities (social and green externalities) of land use. The proportion of developed area per district serves as a proxy for the development land value. The model confirms the significant role of the spatial externalities on the development activities, even though only the social externalities that can extend locally. The natures of externalities are in line with predicted effect of land use change. Keywords: externalities, land value, sprawl, spatial model iafor The International Academic Forum

2 Introduction The fundamental concept underlying the essence of regional science has been determined by the importance of space. Among many other issues faced by cities and regions, land use change problem has been addressed by formulating empirical as well as theoretical model of human or agent spatial behavior. The theoretical model must be specified in a formal mathematical model, and validated based on the empirical model. In the empirical model, variables need to be given meaning in the context of available data and measurements. In this case, the data (e.g. land value, land use, density, distance to CBD, etc) must have spatial reference, so called spatial data. They are used further to estimate the model parameters, test the hypotheses and predict the effect of various scenarios under study. This is typically conducted based on a statistical or econometric methodology. The main characteristics of spatial data are spatial dependence and spatial heterogeneity. Spatial dependence is a functional relationship between situation in one space and situation elsewhere. In terms of land use change, it defines the situation in which land use type in one location depends on land use type in the nearby location. It is a fundamental concept due to the existing spatial interaction phenomena. On the other hand, spatial heterogeneity refers to variance changes across the spatial data sample. These spatial effects are the main interest of the analysis, but they may violate the Gauss Markov assumption in a standard OLS based econometric model. Therefore alternative estimation methods, such as maximum likelihood (ML) (Ord 975), quasi maximum likelihood (QML) (Lee 004), instrumental variable (IV) (Anselin 988), generalized method of moments (GMM) (Kelejian and Prucha, 998, 999) or Bayesian Markov Chain Monte Carlo Methods (Bayesian MCMC), are needed (Anselin 988; LeSage and Pace 009). Those techniques are considered to be the domain of spatial econometrics. The last method is particularly useful to deal with some problems (e.g. a heteroscedastic error structure, or a limited dependent variable) in which the standard methods cannot work properly, due to the characteristics of spatial data. The traditional monocentric city model from Alonso (964) is the initial model of land value, in which distance from CBD is the main determinant of land value. It predicts that the pattern of development will be the compact ring of developed land surrounds the CBD, followed by agricultural land in the outskirt of the city. Clearly, it does not explain very well the emergence of sprawl in many metropolitans around the world including Jakarta Metropolitan and its fringe area (BoDeTaBek: Bogor, Depok, Tangerang and Bekasi) (Douglass 000). Sprawl is the type of discontinuous pattern of urban development in the fringe of urban center. It is considered as an inefficient development activity, with higher costs than benefits. In the fringe of Jakarta, one of the costs is the premature conversion of productive agricultural sites or any conservation areas (Firman 004). A recent study (Fitriani and Harris 0) indicates that in this area, in addition to some other driving forces, sprawl has been mainly dictated by the interaction of two competing land use externalities: () social type of externality which represents the urban agglomeration, and () green type of externality which captures the preference for surrounding open space. The study shows that this type of development has increased the development value of the conserved and the productive agricultural sites in the southern fringe.

3 Even worse, the recent land use policy has not been enforced effectively, such that the environmentally important sites in this area have been converted for urban use (Firman 004). Consequently, the main Jakarta and the surrounding regions have suffered serious environmental problems, e.g. flood, water quality degradation (Douglass 005). Some studies indicate that the negative consequences of sprawl (Irwin and Bockstael 004; York and Munroe 00; Fitriani and Harris 0) can be reduced by applying proper land use policy (e.g. urban growth boundary, incentive based policy or zoning) based on the most dominant type of externalities. It is expected that the policy can reduce the development pressure on the sites which are environmentally sensitive. It motivates this study to analyse the extent of those externalities and their role in the recent development activities in the area based on a model of land value with externalities: Residential Choice of Location model with Externalities from Fitriani (0). It is clear that in the case of land value, spatial externalities which are the product of interaction of spatially distributed agents (households, farmers) (Caruso, Peeters et al. 007), lead to spatial dependency of land use between neighbouring locations. Therefore the significance of each type of externalities will be tested based on one of the spatial econometric models. Two spatial econometric models will be considered, namely Spatial Durbin (SD) Model and Spatial Lag of X (SLX) Model. Specifically for the case of Jakarta, since there is no formal land market, it is not possible to obtain land value explicitly in term of price. For that reason this study use per district development proportion as a proxy of land value. Unfortunately, this approach leads to the limited nature of the dependent variable, which motivates the use of SD Tobit Model and SLX Tobit Model. The result will be useful as a reference to formulate proper policies and predict their effect on the land value. Spatial Econometric Models: Spatial Durbin (SD) Tobit Model and Spatial Lag of X (SLX) Tobit Model for Limited Dependent Variable This section initially presents a general characteristics for spatial econometric models, which is then followed by a more specific approach in which the dependent variable is limited. The main difference between spatial model and other statistical models is that the used of location index for every unit of observation, describing their spatial arrangement geographically. The location index plays an important role in defining the neighbors in which a particular location has spatial dependencies on. The definition of neighbors has been translated into a spatial weight matrix W which describes the spatial arrangement. The spatial weight matrix is commonly formed based on one of the following schemes (i) spatially contiguous neighbors, (ii) inverse distances, (iii) length of shares borders, (iv) bandwith as the n-th nearest neigbhbor distance, (v) ranked distances, (vi) constrained weight, (v) all centrois within distance d, (vi) constrained weight for an observation equal to some constant (Elhorst 04). In this study, the spatial weight matrix will be formed based on the assumption that the externalities can extend to a certain radius (d). Beyond the specified distance, the effect of externalities will be diminished. The particular distance should be chosen based on the characteristic of land use change in the area under study. Fitriani and Sumarminingsih (05) determine the distance (d) specifically for the case of the

4 fringe of Jakarta Metropolitan, based on a semivariogram analysis. They conclude that the social externalities reach to a shorter distance than the green externalities. It motivates the use of different distances, i.e. different spatial weight matrices for each type of externalities. The two locations are considered neighbors if their distance is less than the specified distance (d). The ij th element of the non-normalized spatial weight n n matrix will be if observation j is neighbor to observation i, and 0 otherwise, with n as the number of region/observation under study. For the ease of interpretation, the normalized matrix (the elements of each column is sum to one) is commonly used. Two models representing the assumed types of spatial dependency are considered. First, it is assumed that land development value (Y) between locations interact globally. In this case the externalities (X) offered by a certain location have been capitalized into the land development value of its neighbors, which in turns have also affected the land development value of their neighbors. This might be due to the time dependence of land use decision or the exclusion of other spatially dependent explanatory variables (LeSage and Pace 009). It motivates the use of SDM, in which the interaction effects are captured by WX for the externalities and WY for the land development value, which is defined as follows: Y = ρ WY + X β + WX θ + ε (0.) Y = I ρw) ( X β + WX θ + ε). ( In (.) the magnitude of interaction effect for externalities and land development value are represented by θ and ρ respectively. The second assumption is that the interaction of land development value between neighboring locations, comes locally through the explanatory variable defining each type of externalities. In other words, the land development value of a particular location depends on the externalities offered by its neighbors. It leads to the use of (SLX) in which the interaction effects are captured by WX (LeSage and Pace 009), based on the following form: Y = X β + WX θ + ε. (0.) In (.) and (.) Y is the n vector of response variable, X is the n k matrix of k spatially independent explanatory variables including the constant term, X is the n k matrix of k spatially dependent explanatory variables and ε is the n vector of the error terms. The models defined in (.) and (.) assume that all dependent as well as independent variables are known for the entire sample. In a certain situation the sample is limited by censoring (Long 997). It occurs when the independent variables are observed for the entire sample, but the information of the dependent variable are limited. This type of dependent variable is called a latent variable (Y i *). For example, when per district development proportion (Y i *) is used as the proxy for land development value, it is only observed for a certain range of value (e.g. 0 Y i * ). The observed 0 value of Y i * also represents the unobserved negative values, which are censored at 0. On the other hand, the observed value of Y i * also represents the

5 unobserved greater than values, which are censored at. Therefore, Tobit model should be used instead. By still accommodating the assumed spatial dependencies, the SD Tobit model can be defined as (LeSage and Pace 009): 0, if Y* < 0 Y = ( I ρ W) ( Xβ + WXβ + ε ), if, if Y* > 0 Y* (0.3) and the SLX Tobit model as: 0, Y = Y* = Xβ + WXβ, if Y* < 0 + ε, if 0 Y* if Y* > (0.4) The models in (.3) and (.4) indicate that any change of an explanatory variable at location i affect not only the response at the same location (Y i *) but also the respone at other locations (Y j *, i j). In terms of marginal effect, for a general spatial econometric model, the two effects are called direct and indirect (or spillover) effects, respectively. Specifically for SD Tobit model in (.3) the direct and indirect effects because of the change of variable X, k,..., k k = are the diagonal elements and off diagonal elements of ( I ρw) β, respectively. The direct and indirect effects due to k the change of variable X k, k' =,..., k are the diagonal elements and off diagonal ' elements of ( I ρw) Wθ, respectively (Elhorst 04). Both effects are presented as k ' an average of elements which correspond to the desired effect. Since SLX Tobit model in (.4) is the version of (.3) when ρ = 0, the diresct effect will be simply β k (due to change of the spatially independent explanatory variables) and the indirect effect will be θ (due to the change of spatially dependent explanatory variables). In k ' addition to the significant test for the estimated parameters, the estimated indirect effects should also be used to test the hypothesis whether the spatial interaction is significant. Bayesian MCMC Estimators for Spatial Tobit Model Due to the limited nature of the available dependent variabel, this study uses SD and SLX Tobit Models. In a non spatial model, it is assumed that the limited dependent variable has a censored normal distribution, and use it to derive the estimators which maximize the likelihood (MLE). But, in the Spatial Tobit model, the spatial interdependence leads to the use of Multivariate Truncated Normal Distribution (TMVN). With this assumed distribution, MLE would require more technical difficulties as well as computational time. Therefore MCMC is proposed to handle the issues. In general, the observations are divided into two blocks, one block of n censored observations and another block of n observed observations. According to the defined models in (.) and (.3), the observations are censored if Y i *<0 or Y i *>. Whereas the observations falls into the observed block if 0 Y i *. An n vector of the censored observations is defined as Y * and an n vector of the observed observations is defined as Y. The conditional posterior distribution for the n censored observations is TMVN with certain mean and variance covariance:

6 Y µ Ω * * ( µ Ω ), ( Ψ ) Ψ ( Y µ ),, + ( Ψ ) Ψ Ω,,, * ~ TMVN, * = µ * = Ω,, with the following definitions for the SD Tobit model: Ω = Ψ = Ω µ = µ = σ ε [( I ρw) ' ( I ρw) ] ( I ρw) ( ), X β + WX β ( I ( X β + WX β ),, and for the SLX Tobit model: Ω = σ ε, Ψ = Ω µ = X β + WX β µ = X β + WX β The subscripts and are used to denote an n n matrix, such that for example Ω, is an n n sub matrix of Ω and Ω, is an n n sub matrix of Ω. In order to obtain the Bayesian MCMC estimators a Gibbs sampling procedure is applied. Using the initial values of the model parameters β, β, σ, and ρ, the assumed TMVN is used only to generate the censored observations Y *. The full sample Y* =( Y *, Y ) is then used to sample from the conditional posterior distribution for the remaining model parameters β, β, σ, and ρ, such that the first set of parameter estimates are found. It is used then to generate the censored observation for the second round, and so on. The procedure will stop until it converge at the required model parameter. The Study Area and Data Specification The study area covers the fringe of the Jakarta Metropolitan Area: Bogor Regency, Bogor Municipality, Depok, Bekasi Regency, Bekasi Municipality, Tangerang Regency and Tangerang Municipality. Each region has some districts at the lower administration level, leading to 83 districts in overall. District will be the unit of study. The map of the regions and the planned important urban centres is depicted in Figure. The spatial information of each district is extracted from the map of the study area provided by BIG (Geospatial Information Agency) Indonesia. The land use related variables of the districts are available from Regions in Numbers by BPS (Central Statistics Biro) Indonesia for situation in 00. The empirical model of land value for development in this study is based on the Residential Choice of Location with Externalities from Fitriani (0). In that theoretical model, land rent is a function of a vector of specific location characteristics (e.g. distance to the CBD (Dist i ), and neighbourhood land use externalities) and the development costs. The distance negatively affects land value, and conversely the neighbourhood land use externalities positively affect land value. Whereas the higher the development costs the lower the rent will be.

7 Since the land market in the area has been dominated by informal sector, information of land rent in terms of price is limited. Therefore, the development proportion per district (Dev i ) is used as a proxy for development rent or land development value. The small proportion of development in a district implies that the particular district is less likely to be developed or it has low development value. On the other hand, the higher the proportion of development in a district represents its potential for development or its high development value. Figure : The map of the study region: the fringe area of Jakarta metropolitan and the Planned urban centres. The proxy of development value is considered as a limited variable, since it is observed only for value in between 0 and. An observed 0 proportion of development in a certain district might also represent negative development value. On the other hand, an observed proportion of development in a certain district might represents a high intensity development. This type of development is the implication of a considerably high development value of the district. Two variables are used to capture the competing externalities of land use, indicated as the causes of sprawl development pattern in BoDeTaBek. They are density (000 people/km ) per district and proportion of land use for agricultural activity per district. Following the previous study (Fitriani and Sumarminingsih 05), density per district (Dens i ) is chosen as a proxy of social type of externalities since it represents the intensity of social interaction in a particular district. Whereas, each district proportion

8 of agricultural area (Agr i ), which defines per district amount of agricultural activity, represents the green type of externalities. This study differentiates the definition of neighbors for each type of externalities. It is motivated by the result of semivariogram analysis in Fitriani and Sumarminingsih (05), in which each type of externalities can be enjoyed by districts (neighbors) within radius 9 km and km respectively for green and social externalities. Therefore, the spatial weight matrix for the green externalities (W ) is designed such that every two districts will be neighbors if their distance is less then 9 km, whereas the spatial weight matrix for the social externalities (W ) is designed such that every two districts will be neighbors if their distance is less then km. In addition to W and W, a spatial weight matrix for the development proportion per district (Dev i ) is also defined. It is assumed that land development value in a certain location is affected by the land development value of neighboring districts. Rook Contiguity matrix (W) is used in this case, such that only border sharing districts are considered as neighbours. It is an matrix with as the ij-th element, if the i-th and j-th districts are neighbours, and 0 otherwise. Using this setting, the main diagonal elements are zeroes. Both matrices are used in their normalized forms. This study also uses the geographical condition, defined as:, if above 50% of district i is flat Geo i = 0, otherwise (hill, swamp or mountain area) as a proxy for the development costs. The mostly flat region (Geo i = ) is more suitable for development such that it is predicted to have higher development rent. Together with distance to CBD (Dens i ), they form an 83 3 matrix of spatially dependent explanatory variables (including constant): [ Dist Geo ] X =. Two spatial econometric models, with limited dependent variable, SD Tobit model in (.3) and SLX Tobit model in (.4) are considered. The simpler model is the second one. The model assumes that land development value in a certain location/district has been driven by its distance to the CBD and two competing externalities offered by its neighboring districts. This study differentiates the definition of neighbors for each type of externalities. It is motivated by the result of semivariogram analysis in Fitriani and Sumarminingsih (04), in which each type of externalities can be enjoyed by districts (neighbors) within radius 9 km and km respectively for green and social externalities. Therefore, the spatial weight matrix for the green externalities (W ) is designed such that every two districts will be neighbors if their distance is less than 9 km, whereas the spatial weight matrix for the social externalities (W ) is designed such that every two districts will be neighbors if their distance is less than km. Both matrices are used in their normalized forms. The SLX Tobit model in terms of the operational variables is defined as: 0, if Dev* 0 (0.5) Dev = Dev* = Xβ + W Aβ + W Densβ + ε, if 0 < Dev* < 3, if Dev*

9 On the other hand, SDM, in addition to all the above specifications, also assumes that land development value in a certain location is affected by the land development value of neighboring districts. Rook Contiguity matrix (W) is used in this case. In terms of the operational variables, the definition of SD Tobit model is: 0, if Dev* 0 Dev = Dev* = ( I ρ W) ( Xβ + WAβ + W Densβ + ε ), if 0 < Dev* <, 3, if Dev* (0.6) Results and Discussion The Bayesian MCMC estimators for both models are depicted in Table. Only for the SLX Tobit model, the t test for distance Dist to the CBD and neighborhood density Dens (social externalities), significantly affect land development value. While the effect of neighborhood agricultural activity Agr (green externalities) is not significant in all models. However, the result for every model confirms the individual effect predicted by theoretical land value model in which distance to the CBD negatively determine land development value (negative coefficient of Dist), the externalities exert positive effects on development land value (positive coefficients of Dens and Agr) and region with lower development costs (mostly flat) has higher development land value (positive coefficient of Geo). But, the structure of the assumed spatial models (in (4.) and (4.)) implies that each of the coefficient estimates does not represent the marginal effect of each explanatory variable. In fact, the marginal effect consists of the effect on the same location (direct) and the effect on other locations (indirect). Therefore the coefficient estimates cannot be used alone if the objective of the study is to analyze the significance of the spatial spillover or externalities. The empirical model of land development value assumes the existence of spatial spillover through its explanatory variables. This assumption can be tested based on the estimates of the indirect effects. The 95% and 99% confidence intervals of the indirect effect of each variable, provided by the Bayesian MCMC estimation procedure, will be useful for that purpose. The result in Table shows that, the SD Tobit model produces direct and indirect effects of all variables. But the confidence intervals indicate that only the direct and indirect effects of distance Dist that is different from zero. On the other hand the SLX Tobit model produces indirect effects of the neighborhood externalities variables (Dens and Agr), but only the effect of the neighborhood density Dens that is different from zero. The structure of SLX implies that even though the direct effect of distance to the CBD Dist on land development value is significant, it does not affect the neighbors land development value. One main question is, among the two assumed models, which model best describes the data. As mentioned earlier, the SLX Tobit model is nested in SD Tobit model, in which SLX Tobit model is the version of SD Tobit model when the when ρ = 0. The estimated coefficients in Table indicate that indeed that is the case, the estimated coefficient for development value spatial interaction ( ρ ) in SD Tobit model is not significant. Therefore SLX Tobit model is considered as a more representative model for the land development value with externalities in BoDeTaBek. The Bayesian Information Criterion (BIC) of the two models are in accordance with this choice. BIC is the measure of model fitness based on the residual sum of square of the model

10 and the number of explanatory variables. Therefore the better the model fit the data, the smaller residual sum of square will be. Furthermore the simplicity of the model is indicated by fewer explanatory variables used. In overall, the better the model the smaller the BIC is. In this case, based on the presented BICs of the two models in Table, SLX is indeed the better model. Table The Bayesian MCMC Estimators for SDM and SLX to Explain Land Development Value Variable SD Tobit Model SLX Tobit Model Constant (**) (0.0) (0) Dist (**) (0.04) (0) W. Dens (social (**) externalities) (0.7) (0) W. Agr (green externalities) (0.486) (0.4) Geo (*) (0.64) (0.097) ρ (0.0) - s Residual Sum of Square BIC ** Significant at 5%; * Significant at 0%; p value of the t-test in parentheses Direct Effect SD Tobit Model SLX Tobit Model Dist (**) (**) Dens (Social Externalities) Agr (Green Externalities) Geo (*) SD Tobit SLX Tobit Indirect Effect Model Model Dist (**) - Dens (Social Externalities) (**) Agr (Green Externalities) Geo ** Significant at % based on 99% confident interval; * Significant at 5% based on 95% confident interval Theoretically, sprawl exists when a development decision has been influenced by the equal need between the social externalities (to be surrounded by other development) and the green externalities (to be surrounded by open space). The coefficient estimates as well as indirect effects estimate of SLX Tobit model are the tools to discover the relative importance between the two types of externalities for the development decision, leading to sprawl in BoDeTaBek. In general the SLX Tobit model confirms that based on 00 land use data, the empirical land development value model of BoDeTaBek does not deviate from the theoretical model. Distance to CBD is negatively determined land development value. The further the location from the CBD is, the lower the land development value is. In addition to distance, the

11 empirical model indicates that the two competing types of neighborhood externalities positively determined the development land value. However, only the coefficient estimates of social externalities, which is significant, individually as well as indirectly. It gives some evidence that in BoDeTaBek, sprawl is indeed partly driven by interaction between the two competing externalities. The fact that SLX Tobit model is the chosen empirical model implies that the spatial externalities, especially the social externalities, offered by a certain district can be extended locally for its immediate neighbors. The new development in a certain location affects the land value of its immediate neighbors. The SLX Spatial Tobit model is then used to predict per district development proportion. The comparison between per district prediction and the current condition is depicted in Figure 4. By comparing per district agriculture proportion in Figure, and per district density in Figure 3, Figure 4 indicates that the rate of development will be faster for districts in proximity to urban centers, with mixed uses between agriculture activity and development. The local characteristic of social externalities explains this situation. The higher rate of development occurs as well in the southern fringe districts, near Bogor, which originally designated for conservation and water recharge area. Concluding Remarks The characteristics of land development value with externalities require the accommodation of spatial dimension to develop the empirical model. It is in the context of spatial econometric models. Among many spatial econometric models, when spatial spillover of land development value is assumed, SLX is the model which suits the situation for the case of BoDeTaBek. This study uses a limited type variable as a proxy for the development value, which leads to the application of SLX Tobit model. The coefficient estimates in the SLX Tobit model for the empirical land development value model of BoDeTaBek give some evidence for the contribution of the neighborhood externalities on land value, leading to sprawl. In this case, among the two competing externalities, the social externalities create more significant effect on the development value.

12 Figure : Per District Agriculture Proportion in the Fringe of Jakarta, 00 Data Figure 3: Per District Density in the Fringe of Jakarta, 00 Data

13 Figure 4: The Map of Development Prediction in the Fringe of Jakarta, 00 Data The knowledge regarding the local characteristic of the social externalities should be accommodated in the future development planning and policy. By accommodating this characteristic, the development pattern can be arranged more compactly, such that the new development can be concentrated on the nearby urban centre, and leave the as much as possible the conservation area in its current use. Moreover, any implemented policy in one district must be in line with the implemented policy in the neighboring districts.

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15 Irwin, E. G. and N. E. Bockstael (004). "Land use externalities, open space preservation, and urban sprawl." Regional Science and Urban Economics 34(6): LeSage, J. P. and R. K. Pace (009). Introduction to spatial econometrics Boca Raton, FL CRC Press. Long, J. S. (997). Regression models for categorical and limited dependent variables. Thousand Oaks, Sage Publications. Ord, K. (975). "Estimation methods for models of spatial interaction." Journal of the American Statistical Association 70(349): 0-6. York, A. M. and D. K. Munroe (00). "Urban encroachment, forest regrowth and land-use institutions: Does zoning matter?" Land Use Policy 7(): Contact