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) .
from functional restrictions. Model A3 eases the functional restrictions even further such that all parameters in can vary by proximity orders and types of station; thus, has no room to intervene. In both extended models, a greater J is associated with more parameters, whereas the number of parameters does not go beyond six in Model A1. Table 11 describes estimation results for Model A2. The results of the model with J = 4 or more are not shown in the table because these maximum likelihood estimates fail to converge. We suspect that and some of are no longer statistically different from zero for j = 4, preventing the parameters from being identified. << insert Table 11, here >> 12 shows results for Model A3. We are also unable to estimate the models with J = 4 or more. By construction of this model, and cannot be identified if is zero. We suspect that is close enough to zero. << insert Table 12, here >> Next, the following two models are examined as extensions of Model B1: Model B2 Model B3 As with the previous cases, only ’s in Model B2 are generalized from Model B1, and Model B3 allows all parameters to vary by proximity orders and qualitative characteristics. We employ OLS for Model B3, which now turns to be a linear function. Table 13 shows the results for Model B2. In contrast to Model A2, we are able to obtain results for all J from 1 to 9, because the parameters are independent of one another in this model. We observe that and are close to zero, as with the results for Model B1. << insert 13, here >> In [13-5], = 0.22 means that the effect of the second closest station with a new line is 22% as significant as the effect of the closest station. It turns out that is the only weighting parameter with a significant sign. = 0.41 implies that the rent is higher by 4,100 yen ($41) for a housing unit with , and compared with the rent of a housing unit with , and . If we assess the rental difference by using the mean distance to the second closest station (0.93 mile) and , the rental gap will be approximately 1,300 yen ($13).
SRC 0.07 0.26 0 1 Others 0.01 0.11 0 1 Steel 0.26 0.44 0 1 Wooden 0.22 0.42 0 1 Table 5. Basic statistics (distance, number of lines, new-line dummy) Variable Mean SE Minimum Maximum Distance: d(j) d(1) 0.56 0.36 0.01 2.62 d(2) 0.93 0.43 0.13 3.06 d(3) 1.20 0.49 0.26 3.55 d(4) 1.42 0.54 0.38 3.69 d(5) 1.59 0.56 0.49 3.85 d(6) 1.75 0.60 0.52 4.14 d(7) 1.89 0.63 0.60 4.42 d(8) 2.03 0.66 0.69 4.65 d(9) 2.16 0.69 0.82 4.79 Number of lines: q(j) q(1) 1.45 0.93 1 10 q(2) 1.42 0.97 1 12 q(3) 1.38 0.90 1 12 q(4) 1.42 0.95 1 12 q(5) 1.43 0.93 1 12 q(6) 1.46 1.02 1 12 q(7) 1.47 1.16 1 12 q(8) 1.46 1.15 1 12 q(9) 1.49 1.16 1 12 New-line dummy: D1(j) D1(1) 1 0 1 1 D1(2) 0.51 0.50 0 1 D1(3) 0.44 0.50 0 1 D1(4) 0.41 0.49 0 1 D1(5) 0.35 0.48 0 1 D1(6) 0.31 0.46 0 1 D1(7) 0.30 0.46 0 1 D1(8) 0.29 0.45 0 1 D1(9) 0.27 0.44 0 1 Table 6. Model A0: Traditional accessibility measure [6-1] [6-2] [6-3] [6-4] [6-5] J = 1 2 3 5 9 Parameters in the proximity measure