Takahisa Yokoi

Japanese Regional Amenity Evaluation Considering Spatial Effects with Simultaneous Spatial Autoregressive Models

Empirical analyses on urban/regional amenity began in the 1980s. These economic researches measured the “quality of life index” (QOLI) of cities and regions. The endogenous variables, rent, wage and population, were explained by social and economical attributes as well as some amenity attributes of regions. Simultaneous equation models were estimated and regional levels of amenity were evaluated from the estimated coefficients.In the literature regarding amenity evaluation, interregional spatial interactions and interregional spatial effects have not been sufficiently considered, however. With progress of the motorization, and expansion of the high-speed public transportation network, interregional commuting and consumer activity between areas became common. Existing researches on the measurement of regional amenities are insufficient from this viewpoint. We will be able to evaluate the regional quality of life more precisely if we employ a model in which spatial influences between regions are considered. One of the techniques for modeling such influences is spatial autoregressive models. The technology has been well established in recent decades.There has been some research regarding amenity evaluation which considers interregional spatial influences using a simplified single equation model. We cannot ignore interdependencies between endogenous variables, however. We think that a simultaneous equation system should be adopted.In this paper, we formulate econometric analyses using simultaneous spatial autoregressive models. We combine simultaneous equation systems for the endogenous variables, and consider spatial influences using a spatial autoregressive model. In this research, we use data regarding cities and regions in Japan. The amenity variables, which we evaluate, concern living, education, safety, industrial accumulation, air pollution, and natural conditions.

Simulation Study on Estimation Bias in Spatial Lag Model from Omitted Variable Correlated with Regressors

In this research, the omitted variable problem in a spatial autoregressive model is analyzed by simulation. We examine the performances of estimators when an omitted variable is correlated with explanatory variables. In the literature, theoretical aspects of estimating spatial autoregressive models have been discussed including the spatial error model for the spatially autocorrelated omitted variable. Regarding the ideal case of the spatial lag model, in which there is not an omitted variable correlated with regressors, there have been theoretical discussions of consistency and simulation analyses on the small sample property of the estimator. In the case of real data, some important variables may not be available and most socioeconomic variables are mutually interdependent. Consequently, the performance of estimation methods should be verified in such cases. In this research, we compared three estimation methods for the spatial lag model, namely, maximum likelihood (ML), spatial two-stage least squares (S-2SLS), and the general method of moments (GMM), by using two definitions of the root mean square error. Our simulation results show that the S-2SLS estimator is strongly affected by the omitted variable under certain conditions.

Division of Weight Matrix Based on Pair-Distances and Resulting Nonlinear Spatial Dependency in Spatial Autoregressive Models

In spatial autoregressive models, spatial autocorrelations in the dependent (or omitted) variable are modeled. Dependency is measured under known spatial structures, typically represented as a spatial weight matrix (W). For ordinal spatial autoregressive models, a unique W exists, and the strength of influence of the variable (or autocorrelation) is expressed through this matrix. Elements of W are obtained as a monotonically decreasing function of distance between points within the solution space. Since the coefficients of W are a measure of the autocorrelation, the model is a linear function of the dependency. In actual situations, for example, locational or tax competition, highly complex interdependency may exist. Simultaneously, the model may exhibit negative autocorrelation at short distances, caused by substitution effects, and positive autocorrelation at long distances, caused by complementary effects. In this paper, we discuss realistic models by dividing spatial terms. The resulting nonlinear dependency function is represented through the coefficients of a pair of spatial weight matrices. As an example, we formulate land price models for all prefectures in Japan. From comparisons between the conventional ordinal one-weight-matrix model and the proposed two-weight-matrices model, we established that the latter may produce lower information criterion values. Our results show that division of spatial terms is important for extending the variability of spatial autoregressive models.