In the following section, we demonstrate two types of measures. The first type is the traditional accessibility measure with some minor modifications to the conventional accessibility measure used in previous studies, so that it fits within the context of point-to-point spatial analysis. The second type is a proposed proximity measure that also accounts for the third assumption (A3). In Section 3, we illustrate an application of the relationship between the housing rental value and the clustering of train and subway stations in Tokyo, Japan. In general, addressing a greater number of neighbor stations in an empirical model should be associated with a better estimation result if the model is correctly specified. However, we observe in the application that the traditional accessibility measure worsens the estimation result when the information of a greater number of stations is addressed in the model. This result is due to the incorrect functional specification of the spatial effect by failing to account for the third assumption (A3). The proposed measure solves this issue, and the estimation result improves with the number of stations considered in the model. Although all existing empirical studies on hedonic housing price analysis in Tokyo, to our knowledge, have taken only distance to the nearest station into account, our result shows that at least the first three closest stations need to be addressed to obtain a better estimate of the housing value in Tokyo, whereas including more than the five closest stations in the model does not improve the prediction. More importantly, this study reveals that both distances to sites and the order of proximity to each site can be a vital factor of the spatial effect, and ignoring this factor could result in a significant estimation bias. Some additional examinations with generalized proposed proximity measures are discussed in Appendix 2. Finally, Section 4 offers conclusions from the 2. Traditional accessibility measure and proposed proximity measure Traditional accessibility measure As discussed earlier, the intention of previous studies adopting an accessibility measure for the hedonic approach is to take into account the polycentric urban structure by constructing a measure of accessibility from one region to employment opportunities in other regions. Therefore, the first part of this section makes some minor modifications to the conventional accessibility measure used in previous studies to fit within the context of point-to-point spatial analysis. See Appendix 1 for further discussion on the conventional accessibility measure. Let us use a subscript to refer to the housing unit and to indicate the closest site from i ith jth housing Then, the traditional accessibility measure redefined for our study is specified as i. follows: (3) .
In the following section, we demonstrate two types of measures. The first type is the traditional accessibility measure with some minor modifications to the conventional accessibility measure used in previous studies, so that it fits within the context of point-to-point spatial analysis. The second type is a proposed proximity measure that also accounts for the third assumption (A3). In Section 3, we illustrate an application of the relationship between the housing rental value and the clustering of train and subway stations in Tokyo, Japan. In general, addressing a greater number of neighbor stations in an empirical model should be associated with a better estimation result if the model is correctly specified. However, we observe in the application that the traditional accessibility measure worsens the estimation result when the information of a greater number of stations is addressed in the model. This result is due to the incorrect functional specification of the spatial effect by failing to account for the third assumption (A3). The proposed measure solves this issue, and the estimation result improves with the number of stations considered in the model. Although all existing empirical studies on hedonic housing price analysis in Tokyo, to our knowledge, have taken only distance to the nearest station into account, our result shows that at least the first three closest stations need to be addressed to obtain a better estimate of the housing value in Tokyo, whereas including more than the five closest stations in the model does not improve the prediction. More importantly, this study reveals that both distances to sites and the order of proximity to each site can be a vital factor of the spatial effect, and ignoring this factor could result in a significant estimation bias. Some additional examinations with generalized proposed proximity measures are discussed in Appendix 2. Finally, Section 4 offers conclusions from the 2. Traditional accessibility measure and proposed proximity measure Traditional accessibility measure As discussed earlier, the intention of previous studies adopting an accessibility measure for the hedonic approach is to take into account the polycentric urban structure by constructing a measure of accessibility from one region to employment opportunities in other regions. Therefore, the first part of this section makes some minor modifications to the conventional accessibility measure used in previous studies to fit within the context of point-to-point spatial analysis. See Appendix 1 for further discussion on the conventional accessibility measure. Let us use a subscript i to refer to the ith housing unit and to indicate the jth closest site from housing i. Then, the traditional accessibility measure redefined for our study is specified as follows: (3) .
20170502-econo-sadayuki-wp-draft22.docx