3.1 Study area overview.
Shaanxi Province is located in the hinterland of China, in the middle reaches of the Yellow River, with a total area of 205,600 square kilometers. It is divided into three natural regions by the North Mountains and Qinling Mountains: the north is the Loess Plateau area, the middle is the Guanzhong plain area, and the south is the Qinba Mountain area. As one of the provinces with relatively high level of economic development in western China, the GDP of Shaanxi Province reached 2,980.98 billion RMB in 2021, agricultural production is stable, and the situation of animal husbandry is improving. Industrial production is stabilized and consolidated, and enterprise benefits grow rapidly, the service industry grows rapidly and its operating revenue remains stable.
At the end of 2021, the urbanization rate of Shaanxi Province reached 63.63%, narrowing the gap with the national average urbanization rate of 64.72%. In 2012, the urbanization rate of Shaanxi Province was only 50.02%. In the past decade, the urbanization rate of Shaanxi Province increased by 13.61%, and the average annual urbanization growth rate reached 1.36%. During the 13th Five-Year Plan (2016–2020), the urbanization level of Shaanxi Province rose steadily. The urbanization rate of permanent residents in Shaanxi Province was 53.92% in 2015, and rose to 62.66% in 2020, an increase of 8.74 percentage points. According to the theory of "S" type urbanization development stages, the urbanization level of Shaanxi Province is between 30% and 70%, which is in the acceleration stage. The strong industrial foundation of the cities, the obvious enhancement of economic strength, and the significant increase of agricultural labor productivity make a large number of rural people live in the cities.
3.2 Selection of evaluation indexes and data processing.
This paper adopts a combination of objective and subjective research method, namely "comprehensive evaluation method combining principal component analysis (PCA) with analytical hierarchy process (AHP)", to make up for the shortcomings of a single method. The comprehensive evaluation method not only reduces the uncertainty of subjective factors, but also improves the accuracy and utilization rate of original information. In this paper, the weights of PCA and AHP are respectively determined as 0.5 by referring to the practice of Cao [42] .
According to the definition of land urbanization and population urbanization, as well as the geographical situation, economic and urbanization development characteristics of Shaanxi Province, this paper selected two variables on the objective layer, namely, land urbanization and population urbanization; seven variables on the criterion layer, namely, land structure, land input, land output, population composition, industrial structure, quality of life, lifestyle; twelve variables on the plan layer, namely, urban built-up area, regional average fixed asset input, regional average real estate investment, regional average output value of the secondary and tertiary industries, regional average fiscal revenue, proportion of non-agricultural population, proportion of workers in the secondary and tertiary industries, proportion of output value of the secondary and tertiary industries in GDP, per capita consumption expenditure of urban residents, per capita disposable income of urban residents, number of hospital beds per 10,000 people, and number of private cars per 100 urban households. All these constitute the comprehensive evaluation and coordinated development indexes of Shaanxi Province`s urbanization.
Among them, the variable "urban built-up area" refers to the actual urbanized land area in the urban area of Shaanxi Province during the research period, and the unit is square kilometers. The variable "regional average real estate investment" is obtained when the real estate development investment in Shaanxi Province is divided by the urban built-up area, and the unit is 100 million RMB yuan/square kilometer. The variable "regional average fiscal revenue" is obtained when the fiscal revenue of Shaanxi Province is divided by the urban built-up area, and the unit is 100 million RMB yuan/square kilometer.
The variable of "regional average fixed asset input" is obtained when the fixed assets input of the whole society of Shaanxi Province is divided by the urban built-up area, and the unit is 100 million RMB yuan/square kilometer. The variable of "regional average output value of secondary and tertiary industries" is obtained when the sum of secondary and tertiary industries is divided by the urban built-up area of Shaanxi Province, and the unit is 100 million RMB yuan/square kilometer. The variable "proportion of non-agricultural population" is obtained when the non-agricultural population is divided by the total population of Shaanxi Province at the end of the year (unit: %). The variable "proportion of workers in the secondary and tertiary industries" is obtained when the sum of the number of employed people in the secondary and tertiary industries is divided by the total number of employed people in Shaanxi Province (unit: %). The variable "proportion of output value of the secondary and tertiary industries in GDP" is obtained when the sum of output value of the secondary and tertiary industries is divided by the gross product of Shaanxi Province, and the unit is %.
The units of the variables of "per capita consumption expenditure of urban residents" and "per capita disposable income of urban residents" are both RMB yuan. The variable "number of hospital beds per 10,000 people" is obtained when the number of beds in health institutions is divided by the total population at the end of the year, and the unit is bed." Considering the availability of data and the feasibility of statistical treatment, this study selected the sample data from 2008 to 2020, and the relevant data were all from Shaanxi Statistical Yearbook 2021 and China Statistical Yearbook 2021. (See Table.1)
Table 1
Comprehensive evaluation index system of new-type urbanization in Shaanxi Province
Objective layer | Criterion layer | Index layer | Index formula and unit |
land urbanization | Land structure | Urban built-up area | square kilometers |
Land input | Regional average fixed asset input | 100 million RMB yuan/ square kilometer |
Regional average real estate investment | 100 million RMB yuan |
Land output | Regional average output value of the secondary and tertiary industries | 100 million RMB yuan |
Regional average fiscal revenue | 100 million RMB yuan/square kilometer |
population urbanization | Demographic structure | Proportion of non-agricultural population | % |
Industrial structure | Proportion of workers in the secondary and tertiary industries | % |
Proportion of output value of the secondary and tertiary industries in GDP | % |
Quality of life | Per capita consumption expenditure of urban residents | RMB yuan |
Per capita disposable income of urban residents | RMB yuan |
Mode of life | Number of hospital beds per 10,000 people | - |
Number of private cars per 100 urban households | - |
In order to exclude the influence caused by dimension and order of magnitude, this paper normalizes the indicators of the plan layer, and the calculation formula is: \({Y}_{i}=\frac{{X}_{i}-{X}_{min}}{{X}_{max}-{X}_{min}}\). Where Yi is the normalized value, Xi is the original observed value of the ith index, Xmin is the minimum value, and Xmax is the maximum value.
3.3 Evaluation of coordination level between land and population urbanization.
Establish a multi-index weighted comprehensive evaluation model based on AHP. The following model can be constructed according to the solution to solving the problem with AHP and the content of the research topic. At the same time, the weight of index layer is determined by constructing judgment matrix, hierarchical ranking and consistency checking calculation.
$${A}_{k}=\sum _{i=1}^{n}{Y}_{i}\times {W}_{i},i=\text{1,2}\dots k=\text{1,2},3 or k=\text{1,2},\text{3,4}$$
Where Yi is the quantified value of the ith index, Xi is the weight of the ith index, and Ak is the score of the criterion layer index.
$$A=\sum _{k=1}^{v}{A}_{k}\times {N}_{k},k=\text{1,2},3 or k=\text{1,2},\text{3,4}$$
1
Where Ak is the score of the criterion layer index, Nk is the weight of the kth criterion layer index, A is the target layer index score.
Firstly, we pass judgments on the relative importance of each factor at each level in the form of 1–9 values, and construct pairwise judgment matrix R. Secondly, we conduct single-level ranking and consistency check. We calculate the eigenvalues and eigenvectors of the judgment matrix, that is, calculate the eigenvalues λmax and the eigenvectors S under the condition of RS = λmaxS, and then take the normalized eigenvectors as the weights of the elements at this hierarchy for the membership elements. In order to test the consistency of the judgment matrix, it is necessary to calculate its consistency index CI, where \(CI=\frac{{\lambda }_{max}-n}{n-1}\), and compare CI with the average consistency index RI. The corresponding values of each order in RI, which are given in the fixed values of AHP, are omitted here. Finally, we carry out the total hierarchy ranking and consistency test. We calculate the importance weight of the factors in this hierarchy for the previous level, using the results of the single ranking of all the levels in the same hierarchy, and the final calculated result is the comprehensive evaluation index. The consistency index \(CR=\frac{\sum _{i=1}^{n}{a}_{i}{CI}_{i}}{\sum _{i=1}^{n}{a}_{i}{RI}_{i}}\), where CIi is the consistency index of single ranking, and RIi is the corresponding average random consistency index.
Construct the mathematical model of PCA. PCA uses the idea of dimensionality reduction to transform multiple indicators reflecting a certain problem into a few indicators that almost cover the information used. The mathematical model is as follows:
$$\left\{\begin{array}{c}{H}_{1}={D}_{1}^{T}Y={D}_{11}{Y}_{1}+{D}_{12}{Y}_{2}+\dots +{D}_{1P}{Y}_{P}\\ {H}_{2}={D}_{2}^{T}Y={D}_{21}{Y}_{1}+{D}_{22}{Y}_{2}+\dots +{D}_{2P}{Y}_{P}\\ \dots \\ {H}_{P}={D}_{P}^{T}Y={D}_{P1}{Y}_{1}+{D}_{P2}{Y}_{2}+\dots +{D}_{PP}{Y}_{P}\end{array}\right.$$
From the system of linear equations, we can get:
$${V}_{ar}\left({H}_{i}\right)={V}_{ar}\left({D}_{i}^{T}Y\right)={D}_{i}^{T}\sum {D}_{i},i=\text{1,2},\dots ,p$$
$$Cov\left({H}_{i},{H}_{j}\right)=Cov\left({D}_{i}^{T}Y,{D}_{j}^{T}Y\right)={D}_{i}^{T}\sum {D}_{j},j=\text{1,2},\dots ,p$$
The constraint conditions are:
$$\left\{\begin{array}{c}{D}_{i}^{T}{D}_{i}=1\\ maxVar\left({H}_{1}\right)={D}_{1}^{T}\sum {D}_{1}\\ Cov\left({H}_{i},{H}_{i+1}\right)={D}_{i}^{T}\sum {D}_{i+1}=0\end{array}\right.$$
The principal components with eigenvalue greater than or equal to 1 are extracted by corresponding calculation, and the component matrix is Ki and the eigenvalue is λi, then the eigenvector is \({R}_{i}=\frac{{K}_{i}}{\sqrt{{\lambda }_{i}}}\) and the principal component score is:
$${B}_{i}={R}_{i1}{Y}_{1}+{R}_{i2}{Y}_{1}+\dots +{R}_{i12}{Y}_{12}$$
Through the above calculation, the comprehensive score of principal components can be obtained as:
$$B=\frac{{B}_{1}{\lambda }_{1}+{B}_{2}{\lambda }_{2}+\dots +{B}_{i}{\lambda }_{i}}{{\lambda }_{1}+{\lambda }_{2}+\dots +{\lambda }_{i}}$$
2
In summary, the comprehensive weighted evaluation score of urbanization based on AHP and PCA is as follows:
Calculation of coordination level. By referring to the previous research results on coordination [43, 44], this paper defines the coordination level of land urbanization and population urbanization as follows:
$$CL=\frac{\left|L+P\right|}{2\sqrt{{L}^{2}+{P}^{2}}}$$
4
Where L represents the comprehensive evaluation score of land urbanization on the objective layer, P represents the comprehensive evaluation score of population urbanization on the objective layer, and CL represents the coordination index between land urbanization and population urbanization. When the absolute values of L and P are equal and their signs are opposite, CL = 0, indicating that land urbanization and population urbanization are completely inconsistent. When L and P are equal, CL = 1, indicating that land urbanization and population urbanization are completely coordinated. Other situations fall between the two, and with the sustained increase of the coordination index, it indicates that the coordination level of land urbanization and population urbanization is increasing. Based on the division criteria of coordination index by Wang [45], this paper divides the measurement criteria of coordination degree as shown in Table 2.
Table 2
Classification of coordination indexes between land urbanization and population urbanization
CL | Type of coordination | The magnitude of L versus P | Subtype of coordination |
0.9<CL<1 | highly coordinated | L>P | Population urbanization lags behind |
L<P | Land urbanization lags behind |
0.8<CL ≤ 0.9 | basically coordinated | L>P | Population urbanization lags behind |
L<P | Land urbanization lags behind |
0 ≤ CL ≤ 0.8 | uncoordinated | L>P | Population urbanization lags behind |
L<P | Land urbanization lags behind |
3.4 Evaluation of imbalanced development risk between land and population urbanization.
Risk identification is a complex, sustained and long-term process of measuring and processing risks by collecting information about risk factors, risk accidents and loss exposure. It mainly includes four aspects: discovering and perceiving risk sources, predicting hazards and attaching importance to risk exposure. At present, there are six main risk identification methods: risk loss list, field investigation, financial statement, flow chart, cause-effect diagram and fault tree [46]. This paper mainly uses "field investigation and risk loss list" to identify the development risk of "land urbanization and population urbanization" in Shaanxi Province. In the process of urbanization development, the exposure of risks is more likely to affect the livelihood of people at the bottom of the society. Therefore, mining risk factors through field investigation and discovering potential risks is conducive to obtaining first-hand data from the bottom up and ensuring the scientific and comprehensive risk identification. The risk list can help clarify the risk identification ideas in advance and avoid missing important risks. The combination of the two methods is conducive to a more comprehensive and accurate risk identification.
Risk assessment methods are mainly selected according to the types and characteristics of risks, which generally include qualitative and quantitative analysis dimensions. Qualitative analysis methods mainly include Delphi method, qualitative decision tree method, SWOT analysis method and good or bad evaluation method. Quantitative analysis methods mainly include data envelopment analysis, efficacy coefficient method, factor analysis and mutation progression evaluation method, etc. [47] These two analytical methods have their own advantages and disadvantages. Generally, in order to effectively evaluate the risks, scholars will adopt the comprehensive evaluation method combining the two methods, such as fuzzy comprehensive evaluation method, AHP and analytic network process (ANP). ANP can effectively reflect the coupling relationship and feedback mechanism between different factors on the basis of experience summary and scientific prediction, and is suitable for decision analysis of complex problems. The unbalanced development risk subjects of land urbanization and population urbanization have diversified characteristics and wide influence, and there is certain dependence between risk factors. Therefore, this research conducts risk assessment by ANP.