*2.1. Methodology*

URD is the synthesis metric of the city's ability to compete for external resources and the resource endowment. Here, the resource is a general concept involving all of the tangible and intangible necessities for urban development, such as land, water, labor, culture, policy, and so on. Previous pieces of literature have focused on the URD from the perspectives of urban competitiveness [33–37] and sustainability development [38–42]. Although these focuses can reflect the URD to some degree, they are more comprehensive conceptual frameworks which are not limited to the URD. Therefore, they cannot be used to analyze URD accurately and pertinently. Besides this, some scholars have conducted an in-depth analysis of the resources between different cities [43–47] and different industries [48–51] in urban agglomeration through the gravity model. The gravity model can reflect the resource competence ability of two cities exactly, but cannot reflect the resource competence ability of one city compared to all other cities. From the concept of URD, it can be said that industrial agglomeration is the external performance of URD, and URD is the internal motivation of urban industrial agglomeration. Therefore, this paper proposed a weighted comprehensive industrial agglomeration model (WCIA) to measure the city's URD. The WCIA is as follows:

(1) Spatial Gini coefficient

$$G\_i = \sum\_{j=1}^{n} G\_{ij} = \sum\_{j=1}^{n} \left(\mathbf{x}\_j - s\_{ij}\right)^2 \tag{1}$$

*Gi* is the total Gini coefficient of industry *i*; *Gij* is the Gini coefficient of industry *i* in city *j*; *xj* is the percentage of the total employment in city *j* compared to the total employment in an urban agglomeration. *Sij* is the ratio of industry *i* in city *j* to the total employment of industry *i* in an urban agglomeration. *Gi* = 1 indicates that the industrial agglomeration degree is high. Otherwise, *Gi* = 0 shows that the industrial distribution is balanced.

#### (2) Weight assignment

Suppose that there is an industry set of city *i Ei* = {*ei*1,*ei*2, ···*eim*} The Gini coefficient of industry *j* in city *i* at time *t* is recorded as *xtij* = (*t* = 1, 2, ··· *T*; *i* = 1, 2, ··· *<sup>m</sup>*). The decision sets are as follows:

$$X\_t = \begin{bmatrix} \mathbf{x}\_{t11} & \cdots & \mathbf{x}\_{t1m} \\ \vdots & \ddots & \vdots \\ \mathbf{x}\_{tm1} & \cdots & \mathbf{x}\_{tmm} \end{bmatrix} \tag{2}$$

According to the numerical properties of *xtij*, it can be divided into the positive index and negative index. In this paper, the range transformation method is used to normalize the positive index and negative index.

$$w\_{tij}^{+} = \frac{\mathbf{x}\_{tij} - \min\left(\mathbf{x}\_{j}\right)}{\max\left(\mathbf{x}\_{j}\right) - \min\left(\mathbf{x}\_{j}\right)}\tag{3}$$

$$w\_{tij}^{-} = \frac{\max\left(\mathbf{x}\_{j}\right) - \mathbf{x}\_{tij}}{\max\left(\mathbf{x}\_{j}\right) - \min\left(\mathbf{x}\_{j}\right)}\tag{4}$$

*v*+*tij* and *<sup>v</sup>*<sup>−</sup>*tij* are the positive normalization index and negative normalization index, respectively. *maxxj* and *m*i*nxj* are the maximum and minimum values of the *j*-th index. The weight of industry *j* of the city *i* in time *t* is

$$P\_{tij} = \frac{\upsilon\_{tij}}{\sum\_{j=1}^{n} \upsilon\_{tij}} \tag{5}$$

where 0 ≤ *vtij* ≤ 1; 0 ≤ *Ptij* ≤ 1. The entropy of industry *j* in time *t* is

$$\mathfrak{e}\_{t\dot{\jmath}} = -\left(1/L\_{n}n\right)\sum\_{i=1}^{n}P\_{t\dot{\jmath}}L\_{n}\left(P\_{t\dot{\jmath}}\right) \tag{6}$$

The weight of the Gini coefficient of industry *j* in time *t* is

$$w\_{tj} = \binom{1 - \varepsilon\_{tj}}{} \left/ \sum\_{k=1}^{n} (1 - \varepsilon\_k) \right. \tag{7}$$

#### (3) Urban resource degree (URD)

This paper combines the level of industrial agglomeration to form the overall concept of urban resources to reflect the city's resource endowment and its ability to compete for external resources. In Equation (8), *Ni* is the URD of city *i* at time *t*; *Gtij* is the Gini coefficient of industry *i* in city *j* at time *t*.

$$N\_{ti} = \sum\_{j=1}^{n} w\_{tj} G\_{tij} \tag{8}$$

#### *2.2. Materials and Indicators Selection*

The Shrinking City International Research Network (SCIRN) formally defined urban shrinkage as a city that has at least 10,000 residents, has experienced negative population growth for more than 2 years, and has undergone some structural crisis in economic structural transformation [52]. Since then, relevant research focused on urban shrinkage has achieved fruitful results. Oswalt defines urban shrinkage as cities that will lose a large number of residents, and stipulates that the annual population loss rate should be more than 1% [53]. After the establishment of the "China Shrinking Cities Research Network", scholars have systematically combed and summarized previous research and analyzed the development status of urban shrinkage in China. Zhang [54] and Long et al. [55] measured China's urban shrinkage through the data of the two national censuses in 2000 and 2010. Meanwhile, Zhang et al. judged China's shrinking cities as "one body, two wings and three dimensions" based on remote sensing data and geospatial data [56]. Liu et al. analyzed shrinking cities based on night light data [57].

Here, we can know that the academic community has not ye<sup>t</sup> reached a consensus on the criteria for the determination of urban shrinkage, but the generally agreed upon view is that the decrease in the urban population is the core feature of shrinking cities. Professor Wu Kang of Capital University of Economics and Trade comprehensively interpreted the definition of the shrinking city, and based on the urban population data of municipalities directly under the central government, provincial capital cities, prefecture-level cities and county-level cities from 2007 to 2016, the cities with a lower population in 2016 than in 2007 and negative population growth in three consecutive natural years were identified [58]. Results showed that 80 out of 660 cities meet the criteria for shrinking cities.

There are 24 shrinking cities (see Table 2) in the three provinces of Northeast China, accounting for 30% of the total shrinking cities. The three provinces in Northeast China are an old industrial base in China. In the 1930s, the most advanced industrial system in Northeast Asia was built, which once occupied 98% of China's heavy industrial base. In recent years, there has been a slowdown in the speed of economic development and the phenomenon of population outflow, resulting in a large number of shrinking cities. Northeast China is an important industrial agglomeration and economic development pioneer in China. However, there is a lot of urban shrinkage in these areas. It is worth exploring the deep-seated reasons for this phenomenon. Therefore, 24 shrinking cities in Northeast China were taken as research objects, and the URD was measured.


**Table 2.** Shrinking cities selected in Northeast China.

Data source: https://finance.sina.com.cn/china/gncj/2019-04-10/doc-ihvhiqax1466676.shtml (accessed on 1 october 2021).

#### *2.3. Data Source*

In China, there are 20 industry categories, 97 major categories, 473 medium categories and 1380 sub categories according to the *National Economic Industry Classification Standard* compiled by the National Bureau of Statistics. Given the research's purpose and operability, data-accessible, resource-intensive industries were selected as the sector indicators to measure the urban resource degree. Only the agglomeration of high-tech, high valueadded and resource-intensive industries can truly reflect the level of urban resources. To reflect the URD of cities, we selected the manufacturing industry; mining industry; scientific research and technical service industry; information transmission, software and information technology service industry; and financial industry. The relevant data are from China Statistical Yearbook, China Urban Statistical Yearbook, China Urban Construction Statistical Yearbook, China Energy Statistical Yearbook, and the Urban Statistical Yearbook, the regional statistical bulletin, and some network data from some provinces, municipalities, prefecture-level cities and county-level cities.

#### *2.4. Urban Resource Degree (URD)*

The URD of 24 cities in Northeast China from 2007 to 2016 is listed in Table 3.

**Table 3.** The URD of 24 cities in Northeast China from 2007 to 2016.


From Figure 1, the overall performance of the URD in Liaoning province is in the state of being basically stable, with a small fluctuation from 2007 to 2016. For the five prefecture-level cities, the URD of Fuxin was at a low level from 2007 to 2016, with a small fluctuation between 0.1 and 0.26. Besides this, Jinzhou's URD also remained at a low level. Except for 0.33 in 2012 and 0.42 in 2014, the other years were below 0.3. The URD of Fushun decreased significantly in 2013, and remained around 0.4 in the other years. After the comparison of 2007 to 2016, the overall performance of Fuxin, Jinzhou and Fushun's URD declined slightly in the past ten years. Instead, the URD of Anshan and Yingkou

was kept above 0.4, except in 2013, and presented a slight increase in the period. The URD of the only two county-level cities, Haicheng and Beipiao, of the seven shrinking cities in Liaoning Province changed greatly from 2007 to 2016. The URD of Haicheng experienced a grea<sup>t</sup> decline, a sharp rise, and then a substantial decline change: the URD of Haicheng (1) decreased from 0.256 to 0.047 in 2007–2009; (2) increased from 0.047 to 0.586 in 2009–2014; and (3) decreased from 0.586 to 0.162 in 2016. In contrast, the URD of another county-level city, Beipiao, was always the lowest in the seven shrinking cities in Liaoning Province. The changes of the URD are shown in Figures 2–4.

**Figure 1.** Changes of the URD of the shrinking cities in Liaoning.

**Figure 2.** Changes of the URD of the shrinking cities in Jilin.

**Figure 3.** Changes of the URD of the shrinking cities in Heilongjiang.

From Table 3, the URD in Liaoning shows a trend of rising first and then decreasing. The resource degree of the cities in Jilin and Heilongjiang fluctuates slightly at a relatively low level.

Figure 2 illustrates the changes of the URD in the six shrinking cities in Jilin. Although the URD changes in the six cities are different, the differences are gradually narrowing and tending to converge. It is worth noting that the six shrinking cities were in a state of less than 0.2, except for Tonghua and Baishan in 2008. Tonghua and Baishan are the only two prefecture-level cities of the six shrinking cities in Jilin. As shown in Figure 3, the URD of Tonghua and Baishan were at high levels from 2007 to 2009, which were much higher than those of the other cities in the period. The URD of the two cities reached peaks which were 0.313 and 0.245, respectively. However, after 2009, compared with other shrinking cities, the URD of Tonghua and Baishan no longer existed. In 2016, the URD of the two cities was 0.077 and 0.120, respectively, and the difference with other cities almost disappeared. As for Huadian, Shulan, Ji'an and Tumen, the URD of the four county-level cities was less than that of the two prefecture-level cities. As of 2016, the URDs of Ji'an and Huadian were 0.109 and 0.106, which increased by 0.076 and 0.033, compared with 0.034 and 0.073 in 2007. However, the URD of Tumen and Shulan decreased from 0.076 and 0.109 in 2007 to 0.07 and 0.062 in 2016, respectively.

In conclusion, the URD of the six shrinking cities in Jilin Province had a short-term upward fluctuation from 2007 to 2016, but the overall trend was downward. Besides this, the gap of the URD between the prefecture-level city and county-level city gradually narrowed. Tonghua and Baishan lost the advantages brought by their administrative levels.

In Figure 3, there are six county-level cities and five prefecture-level cities in Heilongjiang Province. Notably, although it has decreased over the years, the URD of Daqing is far higher than that of other shrinking cities in Heilongjiang Province. Besides this, the URD of other prefecture-level shrinking cities, e.g., Jixi, Jiamusi, Qiqihar and Hegang, had different changes in the periods. The URD of Qiqihar was between 0.2 and 0.33, and ranks the second among 11 cities, only next to that of Daqing. Unlike that of Daqing and Qiqihar, the URD of Jixi and Jiamusi fluctuated slightly from 0.08 to 0.22, and always ranked the third to sixth among the 11 cities. Besides this, the URD of the final prefecture-level shrinking city, Hegang, declined sharply after 2013, and was the last in the 11 shrinking cities in 2013, 2015 and 2016. Compared with the prefecture-level cities, the URD of the six county-level cities of Hailin, Bei'an, Zhaodong, Fujin, Nehe, and Ning'an were all ranked behind the five prefecture-level cities before 2012. However, after 2013, the URD of

Hailin, Bei'an and Zhaodong increased significantly, and they always ranked second to sixth among the 11 cities.

**Figure 4.** Spatial heterogeneity of the factors' influences on URD.

In summary, over time, the advantage of the URD of prefecture-level cities gradually weakened. On the contrary, the URD in county-level cities increased slightly, and the ability of cities to compete for and control resources increased.

#### **3. Factors That Influence the URD and how, from the Spatial Spillover and Spatial Heterogeneity Perspectives**

*3.1. Influence Factors*

In order to reflect various points of the previous pieces of literature from different perspectives, this paper conducted a literature review to extract the influence factors of URD. In order to avoid multicollinearity, this paper selects factors based on representativeness and the minimalist principle. We used the Factor Analysis Method (FAM) to reduce the dimension of 29 influences in Table 4. According to the relevant experience, the selected eigenvalues of the principal components must be greater than 1, and the cumulative variance contribution rate should be more than 80%. Therefore, given the results in 2007, 2011 and 2016, the top 10 principal components with cumulative variance contribution rates of 83%, 91% and 89% were selected. The rotating component matrix of the influencing factors of URD is shown in Table 4.

**Table 4.** Principal component rotation matrix of the influencing factors.


Factors: X1—R&D investment; X2—Number of patent applications; X3—Actual use of foreign capital; X4—SME registration application approval cycle; X5—House price to income ratio; X6—GDP per capita; X7—Disposable income per capita; X8—The total retail sales of social consumer goods; X9—Proportion of secondary and tertiary industries; X10—Investment in the fixed assets of the whole society; X11—Amount of public transportation per 10,000 people; X12—Road mileage per capita; X13—Hydropower supply capacity; X14—Proportion of the education expenditure to financial expenditure; X15—Number of secondary schools per 10,000 people; X16—Proportion of the medical expenditure to financial expenditure; X17—Number of hospitals per 10000 people; X18— Urban population density; X19—Per capita garden area; X20—Greening rate of the built-up

area; X21—Days of reaching air standards per year; X22—Industrial SO2 treatment rate; X23—Wastewater treatment rate; X24—Comprehensive utilization rate of solid waste; X25—Resource abundance; X26—Number of provincial cultural relic protection units per million people; X27—Number of cultural venues per capita; X28—Contributions per capita; X29—Average number of students in Colleges and universities per 10,000 people.

From Table 4, 29 influencing factors are divided into the following 10 principal components. The detailed information of the 10 principal components is listed in Table 5.


**Table 5.** Factors Affecting the URD.

#### *3.2. SSA and SHA for the Factors of URD*

To reveal the spatial spillover and spatial heterogeneity of the URD in the 24 shrinking cities, we used the Spatial Durbin Model (SDM) and Spatiotemporal Geographically Weighted Regression model (GTWR) to perform the SSA and SHA.

(1) SDM for SSA

> The SDM is as follows:

$$\begin{array}{l} y = \rho Wy + X\beta + W\overline{X}\gamma + \varepsilon\\ \varepsilon \sim N\left(0, \delta^2 I\right) \end{array} \tag{9}$$

where *ρ* is the marginal influence of the dependent variables of adjacent regions. *β* is the marginal effect of the independent variable on the dependent variable. *γ* measures the marginal effects of independent variables in adjacent regions on the dependent variables. *X* is a variable matrix of the independent variables.

(2) GTWR for SHA

Because the data may be non-stationary in time and space, the influence of the independent variable on the dependent variable is different in different times and regions; that is, there is heterogeneity in time and space. GTWR is an extended model of Geographically Weighted Regression (GWR), which embeds the time dimension into the regression model.

It takes into account the data changes of the URD of the shrinking cities in time and space. Therefore, GTWR is more in line with the actual situation.

$$Y\_i = \beta\_0(\mu\_{i\prime} \upsilon\_{i\prime} t\_i) + \sum\_k \beta\_k(\mu\_{i\prime} \upsilon\_{i\prime} t\_i) X\_{ik} + \varepsilon\_i \tag{10}$$

Here, *Yi* is the URD of city *i*, *μi* is the longitude coordinate of city *i*, *υi* is the latitude coordinate of city *i*, and *ti* is the time coordinate of city *i*. Therefore, (*μi*, *υi*, *ti*) is the spacetime longitude and latitude coordinates of city *i*. *β*0(*μi*, *υi*, *ti*) is the constant term, and *βk*(*μi*, *υi*, *ti*) is the independent variable regression coefficient. *Xik* is the *k*-th independent variable of city *i*. *εi* is the random error. The coefficient estimation of GTWR is as follows:

$$\hat{\beta}(\mu\_{i\prime}\upsilon\_{i\prime}t\_{i}) = \left[X^{T}\mathcal{W}(\mu\_{i\prime}\upsilon\_{i\prime}t\_{i})X\right]^{-1}X^{T}\mathcal{W}(\mu\_{i\prime}\upsilon\_{i\prime}t\_{i})Y \tag{11}$$

$$\mathcal{W}(\mu\_i, \upsilon\_{i\prime}, t\_i) = \text{diag}\left(\mathcal{W}\_{i1\prime}\mathcal{W}\_{i2\prime}\cdots\mathcal{W}\_{in}\right) \tag{12}$$

$$\mathcal{W}\_{ij} = \exp\left[\frac{\left(d\_{ij}^{ST}\right)^2}{h^2}\right] = \exp\left[\frac{\lambda\left[\left(\mu\_i - \mu\_j\right)^2 - \left(\upsilon\_i - \upsilon\_j\right)^2 + \mu\left(t\_i - t\_j\right)^2\right]}{h^2}\right] \tag{13}$$

*H* is the space–time bandwidth, which is selected according to the minimum crossvalidation (*CV*).

$$CV(h) = \sum\_{i} (y\_i - y\_l(h))^2 \tag{14}$$

#### *3.3. Data Source and Processing*

Part of the raw data comes from the China Statistical Yearbook, China Urban Statistical Yearbook, China Urban Construction Statistical Yearbook, China Energy Statistical Yearbook, Urban Statistical Yearbook, and some regional statistical bulletins and network data. Specifically, the R&D investment and social electricity consumption of the prefecturelevel cities are from China's urban statistical yearbook. Instead, in 2011–2016, the R&D investment and social electricity consumption of county-level cities are from China's urban statistical yearbook. In 2007–2010, the R&D investment of county-level cities is from the statistical yearbook of local provinces and the relevant statistical bulletin. The social electricity consumption is from the Power Industry Statistical Data Collection, the Statistical Yearbook of local cities, and related statistical bulletins. Besides this, the raw data of the built-up area are from the China Urban Construction Statistical Yearbook and Regional Statistical Yearbook. The SME registration application approval cycle and the contributions per capita were obtained from the Internet and field questionnaires. The housing price income ratio was calculated according to the average price of commercial housing and the regional per capita income.

a. House Price to Income Ratio

$$HPIR = \stackrel{TPH}{\quad} \bigg/ \begin{array}{c} \\ \\ \text{TIF} \end{array} \tag{15}$$

$$TPH = RAP \times PP \times PHP\tag{16}$$

$$TIF = PP \times PTI\tag{17}$$

*HPIR* is the house price to income ratio, *TPH* is the house price and *TIF* is the total annual household income. *RAP* is the residential housing area per capita, *PP* is the household size, *PHP* the average price per square meter, and *PTI* is the annual income per capita.

b Resource Abundance

The ratio of mining employees to the total number of employees is used to characterize the regional resource abundance.

c Hydropower Supply Capacity

The water and electricity supply capacity of each region is measured by the satisfaction degree of the residents with the local water and electricity supply.

d SME Registration Application Approval Cycle

Due to the large difference in the actual situation of each region, there is a gap in the registration approval process, integrated services, network information platform construction, and the scale and type of small and medium-sized enterprises. In order to facilitate the data collection and enhance the comparability of the data, this paper measures the SME registration approval cycle from the perspective of the interviewees' satisfaction, and collects the receipt of the SME registration approval cycle in each region by issuing questionnaires.

*3.4. Results*

In this paper, ArcGIS software and the GTWR plug-in were used to carry out the spatial-temporal weighted regression of URD in Northeast China Shrinking Cities (NCSC).

(1) Results for SSA

The test results of LM, Hausman and LR for the non-spatial panel data are shown in Table 6.


**Table 6.** Non-spatial panel model test of URD in Northeast China.

As shown in Table 6, the Hausman test is significantly positive. Therefore, we rejected the null hypothesis and selected the fixed effect model. The joint significance test LR time-fixed and space-fixed test results are 216.29 and 113.18, respectively. Therefore, LM (error), Robust LM (error), LM (lag), and Robust LM (lag) test of the space and time dual fixed model were selected to verify the specific form of the model. The results showed that there are spatial lag effects of both variables and error terms. That is, SDM is suitable to conduct the SSA. Table 6 is the results of the SDM for SSA.

In Table 7, the Wald test spatial lag and Wald test spatial error statistics passed the 1% significance test. Therefore, SDM cannot degenerate into SAR or SEM. The total effect, direct effect and indirect effect of SDM are listed in Table 8.

The direct effect, the indirect effect and the total effect of the influencing factors on the shrinking cities are shown in Figure 4.

a. The Direct Effect

From the direct effect perspective, TIA, GML, EDL, EDQ, PSC, US, MCQ have positive influences on the URD of the shrinking cities. Notably, EDL and EDQ have the greatest positive effects on URD, reaching 0.501 and 0.469, respectively. As we know, the development of EDL and EDQ requires the URD as the foundation. Therefore, it can be said that while URD promotes EDL and EDQ, economic development also has a significant role in promoting the URD. Besides this, the influence coefficient of TIA on URD is 0.401,

revealing that technological innovation is an important motivation for attracting resource accumulation. In addition, GML can enhance the charm of cities and create a friendly environment for the entry of external resources. However, EL and HCD have no significant effect on the URD of the shrinking cities. This reflects that the natural environment and the human environment do not work on the URD of shrinking cities. It is worthy of noting that RE is the only factor that has a negative impact on the URD of the shrinking cities in Northeast China. The influence coefficient is −0.244, and has passed the significance test of 1%. It shows that the better the resource endowment is, the more unfavorable it will be to the URD, i.e., the "resource curse" proposed by relevant research [59].



\* *p* < 0.1, \*\* *p* < 0.05, \*\*\* *p* < 0.01

**Table 8.** The total, direct and indirect effects of the SDM model of the URD of the shrinking cities in Northeast China.


\* *p* < 0.1, \*\* *p* < 0.05, \*\*\* *p* < 0.01

#### b. The Indirect Effect

From the indirect effect perspective, TIA, El, RE and HCD have significant positive indirect effects on the URD of shrinking cities. In other words, they have spill-over effects on URD. As we can see, the indirect effect of TIA on URD is 0.394, reflecting that the spill-over effects of technological innovation could improve the URD of the overall region. Instead, GML, EDL, EDQ, PSC and US have negative indirect effects on URD. That is, the negative spill-over effects of these factors would weaken the attraction of the shrinking cities for external resources, producing vicious competition.

#### (2) Results for SHA

In order to reveal the spatial heterogeneity of the factors' influences on the URD of the shrinking cities, GTWR is used to conduct the SHA. The results are shown in Figure 5.

**Figure 5.** Influential factors and mechanisms of shrinking urban resources in Northeast China. (**a**) The coefficients of different factors. (**b**) The direct and indirect effects of GML. (**c**) The direct and indirect effects of TIA, US and EL. (**d**) The direct and indirect effects of EDL, EDQ, PSC, HCD, MCQ and RE.

Figure 4 illustrates the spatial heterogeneity of the influencing factors on the URD of the 24 shrinking cities in northeast China. The influence of TIA, US, EL on URD gradually weakens from the west to the east, and the coefficients are between 0.8 and 1.4 for the western cities such as Anshan, Fushun, Fuxin and Jinzhou. Instead, the influence of EDL, EDQ, PSC, HCD, MCQ and RE gradually strengthens from the west to the east, and the coefficients are between 1.0 to 1.4 for the URD of Hegang, Jiamusi, and Fujin. Notably, the influence of GML on the URD of the shrinking cities in Northeast China showed a trend of gradually increasing from the northwest to the southeast. The URDs of Qiqihar, Daqing, and Bei'an are influenced least. Anshan, Fushun, and Tonghua are the most affected, and the influence coefficient reaches more than 1.0.

#### **4. Discussion and Policy Implications**

From the above results of URD and the spatial spillover effect and spatial heterogeneity of various factors for the URD of the shrinking cities in Northeast China, the overall characteristics are summarized as shown in Figure 5.

From Figure 5, given the SSA and SHA, the influences can be categorized into three types:


From the above findings, we proposed the policy implications as follows:

