The Impact of Accessibility on the Value of Offices

Abstract

Accessibility is becoming an increasingly important issue in the Netherlands, not only for policymakers but also for daily workers on the road and employers, who have to deal with a growing uncertainty of their staff being on time. Not only the access via roads is important; but also the unreliability of public transport (as experienced by passengers), and the lack of parking areas in many places contribute to the importance of accessibility in society.

Appendix A

The estimation of the Rail Service Quality Index (RSQI) of a station is based on the doubly constrained spatial interaction model, given as follows:

$$ {T_{{ij}}} = {A_i}{O_i}{B_j}{D_j}f(GJ{T_{{ij}}})g(GJ{T_{{ij}}}/{d_{{ij}}})\exp ({\xi_{{ij}}}) $$

(A1)

$$ {O_i} = \sum\nolimits_j {{T_{{ij}}}} $$

(A2)

$$ {D_j} = \sum\limits_i {{T_{{ij}}}} $$

(A3)

where ${T_{{ij}}}$ is the number of trips between stations $i$ and $j$; ${O_i}$ is the total number of trips originated in station $i$; ${D_j}$ is the total number of trips attracted by station $j$. ${A_i}$ and ${B_j}$ are the balancing factors which ensure that the constraints on origins and destinations (given by [2] and [3A3]) are met; $GJ{T_{{ij}}}$ is the generalized journey time between origin station $i$ and destination station $j$; ${d_{{ij}}}$ is the Euclidian distance between origin station $i$and destination station $j$; and ${\xi_{{ij}}}$ is the error component of the model which follows an independently and identically normal distribution. We specify the functions $f$ and $g$ as follows:

$$ f(GJ{T_{{ij}}}) = \exp \left(\sum\limits_{{c = 1}}^C {{\beta_c}DGJ{T_c}^{{ij}}}\right)$$

(A4)

$$ g(GJ{T_{{ij}}}/{d_{{ij}}}) = {\left( {GJ{T_{{ij}}}/{d_{{ij}}}} \right)^{\gamma }} $$

(A5)

where, $DGJ{T_c}^{{ij}}$ is a dummy variable, which is equal to 1, if $GJ{T_{{ij}}}$ falls in the generalized journey time category $c$and 0 otherwise. Thus, the doubly constrained gravity model we estimated is given by:

$$ {T_{{ij}}} = {A_i}{O_i}{B_j}{D_j}\exp \left( {\sum\limits_{{c = 1}}^C {{\beta_c}DGJ{T_c}^{{ij}}} } \right){\left( {GJ{T_{{ij}}}/{d_{{ij}}}} \right)^{\gamma }}\exp ({\xi_{{ij}}}) $$

(A6)

This equation can be linearized by taking the natural logarithm of both sides:

$$ \ln \left( {{T_{{ij}}}/{O_i}{D_j}} \right) = \ln {A_i} + \ln {B_j} + \left( {\sum\limits_{{c = 1}}^C {{\beta_c}DGJ{T_c}^{{ij}}} } \right) + \gamma \ln \left( {GJ{T_{{ij}}}/{d_{{ij}}}} \right) + {\xi_{{ij}}} $$

(A7)

The coefficient of the generalized journey time categories, the ratio of generalized journey time, and the balancing factors will be estimated from the above equation. Thus, in the estimation, the logs of the balancing factors in the equation represent the coefficients to be estimated. This requires that the logs of the balancing factors are multiplied by the dummy variable for the corresponding station. Therefore, the equation for the estimation is given as:

$$ \ln \left( {\frac{{{T_{{ij}}}}}{{{O_i}{D_j}}}} \right) = \sum\limits_{{\tilde{i} = 1}}^N {\ln {A_{{\tilde{i}}}}{S_{{\tilde{i}}}}} + \sum\limits_{{\tilde{j} = 1}}^{{N - 1}} {\ln {B_{{\tilde{j}}}}{S_{{\tilde{j}}}}} + \ln \left( {\sum\limits_{{c = 1}}^C {{\beta_c}DGJ{T_c}^{{ij}}} } \right) + \gamma \ln \left( {\frac{{GJ{T_{{ij}}}}}{{{d_{{ij}}}}}} \right) + {\xi_{{ij}}}. $$

(A8)

where, $N$ is the number of railway stations in the railway network; and ${S_{{\tilde{i}}}}$ and ${S_{{\tilde{j}}}}$ are dummy variables for departure station $\tilde{i}$ and destination station $\tilde{j}$. They assume the value 1 when $i = \tilde{i}$ and $j = \tilde{j}$, respectively, and 0 otherwise. Given the assumption on the error components above, (8) can be estimated using ordinary least squares (OLS). The estimated coefficients are then used in determining the Rail Service Quality Indices (RSQIs) for each station. The RSQI of any departure station $i$ is determined as the aggregation sum of the quality measures over all the destination stations ($j$’s). Thus, the RSQI of a given departure station is given by:

$$ RSQ{I_i} = \sum\limits_j {{{\hat{B}}_j}{D_j}\hat{f}(GJ{T_{{ij}}})\hat{f}(\frac{{GJ{T_{{ij}}}}}{{{d_{{ij}}}}})} = \sum\limits_j {{{\hat{B}}_j}{D_j}\exp \left( {\sum\limits_{{c = 1}}^C {{{\hat{\beta }}_c}DGJ{T_c}^{{ij}}} } \right){{\left( {\frac{{GJ{T_{{ij}}}}}{{{d_{{ij}}}}}} \right)}^{{\hat{\gamma }}}}}; $$

(A9)