## 4 Analysis and Results
Column (1) in Table 5 shows that a one unit increase in the market access of Seoul is associated with a 0.7 unit increase in the dependency of other cities on it, while columns (2) to (5) suggest that improved accessibility would reduce the attraction of each non-Seoul city, and this effect is more substantial for Deajon and Gwangju. This finding is consistent with our expectation that socioeconomically disadvantaged areas would lose more urban functions with the improvement of accessibility relative to developed areas. In addition, as the change of \(\theta\) could induce the change in market access, and the market size can be represented by GDP or population. For the consideration of robustness, we further choose different values of \(\theta\) accompanied by GDP and population as the market size, respectively, according to the research of [PERSON] (2017) [41] and [PERSON] (2019) [42]. Specifically, we constructed another five market access indicators as \(ma2x\) (1, population), \(ma3x\) (2.75, population), \(ma4x\) (2.75, GDP), \(ma5x\) (3.6, population), and \(ma6x\) (3.6, GDP). The former value in parentheses denotes different \(\theta\)--the latter indicates different sets of market size. We re-estimated Equation (2) with these alternative independent variables and the results, reported in Table 6, suggest that our main findings are robust to these alternative calculations as well. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & **(1)** & **(2)** & **(3)** & **(4)** & **(5)** \\ \hline
**Models** & **Model 1** & **Model 2** & **Model 3** & **Model 4** & **Model 5** \\ \hline ma1x & 0.7245 * (0.2284) & \(-\)0.0101 (0.0536) & \(-\)0.0679 (0.0292) & \(-\)0.0877 ** & \(-\)0.1451 *** \\ Inecopopr & \(-\)2.2998 (2.4783) & \(-\)2.1903 (2.3531) & (1.1651) & (1.7767) & (1.1750) \\ enterm & 56.6395 *** (5.2681) & \(-\)17.0541 (34.3528) & (47.7476) & (20.9843) & (10.2972) \\ Inuniver & \(-\)0.6220 (1.0777) & 0.5729 (1.3678) & 1.4035 (1.3002) & \(-\)0.6414 (0.4403) & \(-\)1.6614 (0.8283) \\ Ingland & 0.7063 * (0.2788) & 0.9561 * (0.3210) & 0.0891 (0.1883) & \(-\)0.9684 (0.4658) & \(-\)0.1415 * \\ Inteachp & \(-\)0.0171 (0.1074) & \(-\)0.3890 (0.7213*) & 1.2206 *** (0.4140) & (0.4618) (0.5641) & (0.2902) & (0.1098) \\ Incpi & 1.2202 (0.7605) & \(-\)10.6831 (0.3824) & 0.9688 (0.5079) & (4.7883) \\ Inbed & \(-\)0.1988 (0.2413) & 0.1739 (0.4128) & \(-\)0.6191 *** (0.1017) & (0.2755) (0.1689) & (0.1896) & (0.1008) \\ Indtravel & \(-\)0.9590 (0.4829) & 44.8464 (0.9061*) & 0.0036 (0.4903) & \(-\)1.1955 (0.4829) & \\ Time control & Y (0.4829) & (33.3957) & (0.2859) & (0.4390) & (2.4965) \\ Time control & Y (0.4829) & Y (0.4829) & Y (0.4829) & Y (0.4829) & Y (0.4829) & Y (0.4829) \\ City control & Y (0.4829) & Y (0.4829) & Y (0.4829) & Y (0.4829) & Y (0.4829) & Y (0.4829) \\ Constant & 7.5511 (10.2808) & \(-\)232.5805 (169.2619) & (8.5216) & (7.0936) & (3.2043) \\ Observations & 68 (0.4829) & 0.5294 (0.4586) & 0.6085 (0.4705) & 0.4705 \\ \hline \hline \end{tabular} Notes: Robust standard errors in parentheses, *** \(p<0.01\), ** \(p<0.05\), * \(p<0.1\). We set the \(\theta\) as 1 and GDP as the market size.  
\end{table} 
Table 5: Results with market access.