Towards the analysis of urban livability in China: spatial–temporal changes, regional types, and influencing factors

Abstract

The increasing drift of urbanization and its impact on urban human settlements are of major concern for China cities. Therefore, demystifying the spatial–temporal patterns, regional types, and affecting factors of urban livability in China is beneficial to urban planning and policy making regarding the construction of livable cities. In accordance with its connotation and denotation, this study develops a systematic evaluation and analysis framework for urban livability. Drawing on the panel data of 40 major cities in China from 2005 to 2019, an empirical research was further conducted. The results show that urban livability in China has exhibited a rising trend during the period, but this differs across dimensions. The levels of urban security and environmental health are lower than those of the three other dimensions. Spatially, cities with higher livability are mainly distributed in the first quadrant divided by the Hu Line and Bole-Taipei Line. Cities in the third quadrant are equipped with the lowest livability. In addition, the 40 major cities can be divided into five categories, and obvious differences exist in terms of the geographical distribution, overall livability level, and sub-dimensional characteristics of the different types. Furthermore, the results of the System GMM estimator indicate that the overall economic development exerts an inhibiting effect on the improvement of urban livability in present-day China, but this logical effect exhibits obvious heterogeneity in different time periods and diverse city scales. Finally, there are also differences in the influencing direction and degree of specific economic determinants.

Appendix

This is the derivation for the calculation formula of the combined weight method. In Sect. 3.2, we have obtained the objective weight (w_1j) and the subjective weight (w_2j) of each indicator. Now, we need to calculate the combined weight (w_j) based on the w_1j and w_2j.

First, according to the relative entropy formula:

$${H}_{1}=\sum_{j=1}^{n}{w}_{j}\mathrm{ln}(\frac{{w}_{j}}{{w}_{1j}}), {H}_{2}=\sum_{j=1}^{n}{w}_{j}\mathrm{ln}(\frac{{w}_{j}}{{w}_{2j}})$$

(13)

The total relative entropy can be expressed as follows:

$$F={H}_{1}+{H}_{2}=\sum_{j=1}^{n}{w}_{j}\left({\mathrm{ln}w}_{j}-{\mathrm{ln}w}_{1j}\right)+\sum_{j=1}^{n}{w}_{j}\left({\mathrm{ln}w}_{j}-{\mathrm{ln}w}_{2j}\right), \sum_{j=1}^{ n}{w}_{j}=1$$

(14)

Then, according to the principle of minimum relative entropy, when the total relative entropy is minimum, w_j is the closest to w_1j and w_2j. Next, the minimum value of F can be calculated:

Assuming $\varphi \left({w}_{1},{w}_{1},\dots {w}_{n}\right)= {\sum }_{j=1}^{n}{w}_{j}-1=0$, we can construct a Lagrangian function:

$$L\left({w}_{1},{w}_{1},\dots {w}_{n},\lambda \right)=F\left({w}_{1},{w}_{1},\dots {w}_{n}\right)+\lambda \varphi \left({w}_{1},{w}_{1},\dots {w}_{n}\right)$$

(15)

Subsequently, according to the Lagrange Multiplier Method, we can get:

$$\left\{\begin{array}{c}\frac{\partial L}{\partial {w}_{j}}=1+\mathrm{ln}{w}_{j}-\mathrm{ln}{w}_{1j}+1+\mathrm{ln}{w}_{j}-\mathrm{ln}{w}_{2j}+\lambda =0\\ \frac{\partial L}{\partial \lambda }=\varphi \left({w}_{1},{w}_{1},\dots {w}_{n}\right)={\sum }_{j}^{n}{w}_{j}-1=0 \end{array}\right.$$

(16)

Arranging the first equation, we can get:

$${w}_{j}={e}^{\frac{\mathrm{ln}{w}_{1j}+\mathrm{ln}{w}_{2j}-\lambda -2}{2}}={e}^{\frac{-\lambda -2}{2}}\sqrt{{w}_{1j}\times {w}_{2j}}$$

(17)

Substituting Eq. (18) into Eq. (17), we can get:

$$\sum_{j=1}^{ n}{w}_{j}=\sum_{j=1}^{n}{e}^{\frac{-\lambda -2}{2}}\sqrt{{w}_{1j}\times {w}_{2j}}={e}^{\frac{-\lambda -2}{2}}\sum_{j=1}^{n}\sqrt{{w}_{1j}\times {w}_{2j}}=1$$

(18)

Therefore:

$${e}^{\frac{-\lambda -2}{2}}=\frac{1}{\sum_{j=1}^{n}\sqrt{{w}_{1j}\times {w}_{2j}}}$$

(19)

Substituting Eq. (20) into Eq. (18), we can know that F can obtain an extreme value when ${w}_{j}=\frac{\sqrt{{w}_{1j}\times {w}_{2j}}}{\sum_{j=1}^{n}\sqrt{{w}_{1j}\times {w}_{2j}}}$. Combined with the actual situation, this extreme value should be the minimum value.

In this way, we can get the final combined weight (w_j) of each indicator.