Impact of China’s Provincial Government Debt on Economic Growth and Sustainable Development

Macroeconomic stability is the core concept of sustainable development. However, the coronavirus disease (COVID-19) pandemic has caused government debt problems worldwide. In this context, it is of practical significance to study the impact of government debt on economic growth and fluctuations. Based on panel data of 30 provinces in China from 2012 to 2019, we used the Mann–Kendall method and Kernel Density estimation to analyze the temporal and spatial evolution of China’s provincial government debt ratio and adopted a panel model and HP filtering method to study the impact of provincial government debt on economic growth and fluctuation. Our findings indicate that, during the sample period, China’s provincial government debt promoted economic growth and the regression coefficient (0.024) was significant. From different regional perspectives, the promotion effect of the central region (0.027) is higher than that of the eastern (0.020) and western regions (0.023). There is a nonlinear relationship between China’s provincial government debt and economic growth, showing an inverted “U-shaped” curve. Fluctuations in government debt aggravate economic volatility, with a coefficient of 0.009; tax burden fluctuation and population growth rate aggravate economic changes. In contrast, the optimization of the province’s industrial structure and the improvement of the opening level of provinces slow down economic fluctuations.


Introduction
The coronavirus disease  pandemic has extensively impacted the economy of countries worldwide, leading to prominent government debt problems [1]. According to estimates by the Congressional Budget Office (CBO) of the United States (US), because of the pandemic, the US federal government debt ratio rose to 126% in 2020 and continues to rapidly rise (Date sources: https://www.cbo.gov/publication/57635, Washington, DC, U.S. accessed on: 31 August 2021) [2]. Furthermore, the data released by China's National Bureau of Statistics suggest that China's government debt balance in 2020 was 46.55 trillion yuan, and that the government debt ratio was 45.82%. As of the end of December 2020, the national local government debt balance was 25.66 trillion yuan-a year-on-year increase of 20.44%-but the issue of sustainability of local government debt is very urgent (Date sources: http://www.gov.cn/xinwen/2021-01/26/content_5582612.htm Beijing, China. accessed on: 31 August 2021). In recent years, the scale of local government debt in China has shown a trend of continuous expansion, which has had a profound impact on macroeconomic stability and fiscal sustainability [3][4][5]. The local government debt has a positive impact on promoting investment and enhancing the vitality of the local economy [6][7][8]. Furthermore, China's economy has been seriously affected by COVID- 19. In order to quickly restore the social and economic order, China implemented economic stimulus policies by issuing government bonds and other forms of financing. The phenomenon of rapid increase in government debt risks has begun to frequently occur throughout the country, which has aroused panic among the people and caused widespread concern in society [9].
Since the post-Keynesian era, government debt and GDP, as well as the relationship and fluctuations between them, are important components of macroeconomic theories [10,11]. There have been endless debates among various schools of thought about whether government debt expansion can effectively promote economic growth in the long term [12,13]. Some scholars believe that government borrowing will weaken its ability to formulate relevant countercyclical policies in response to economic crises, which will cause the government to do nothing in the face of economic fluctuations, thereby affecting the stability of the entire economy and society [14,15]. Furthermore, scholars have proposed that, when government issues additional public bonds and implements fiscal deficit policies, it can effectively expand domestic demand and promote regional economic development [16][17][18]. In addition, others have demonstrated that the effects of raising debts and levying taxes on finance are the same, and that the behavior of local governments raising debt will not affect social resources, investment, labor supply, and other factors, which proves the neutrality of debt [19][20][21][22].
Evaluating relevant research conducted from an empirical perspective, we found that empirical results were very different owing to the different theories and data referred to in discussions concerning these matters. On the one hand, some scholars used the panel regression of a time series to draw the conclusion that government debt promotes economic growth. They mainly studied the debt and economic development of Southeast Asian countries and found that, in most Southeast Asian countries, government debt has an obvious positive effect on economic growth [23]. Others showed that government debt can promote economic development to a certain extent in both the short and long term [24]. On the other hand, some scholars have confirmed that the influence of government debt on economic growth is unfavorable. Cohen [25] proposed using the ratio of government debt to regional GDP to represent the degree of dependence of the local economy on government debt. His research showed a negative correlation between government debt and economic growth. Elmeskov and Sutherland [26] conducted research from a long-term perspective and suggested that excessive government debt would seriously affect public savings. Their research data showed that, for every 1% increase in the total government debt, the total gross domestic product (GDP) of the region under stable output will be reduced by 10%. At the same time, Woo and Kumar [27] pointed out that government debt led to a decrease in investment and labor. Slowdown in productivity growth is the root cause of this phenomenon.
With the enrichment of empirical tools and data sources, many scholars have found that there is a nonlinear relationship between government debt and economic development. Some scholars used empirical research to find that the relationship between government debt and economic growth is "U-shaped" [28]. However, other scholars have different views, such as Checherita-Westphal and Rother (2011) [29], who selected 12 Eurozone countries as their research sample. They found that there is a clear threshold effect between government debt and economic growth, and that the relationship between them is a typical inverted "U-shaped". Many scholars have conducted similar studies correspondingly [30][31][32][33], others believe that there is not only a threshold effect between debt and economic growth, but also a more complex relationship [34][35][36].
For China, China's government debt-to-GDP ratio is lower than that of most large, developed economies [37], and government debt scales have not reached their respective thresholds [38]. However, there is a lack of research on China's provincial government debt. In recent years, China's provincial government debt has risen every year, and the debt ratio of some relatively backward provinces has reached the risk warning point. Many scholars [39][40][41] used a panel data model to study the relationship between government debt and corporate leverage and found that there is a negative relationship between the two. Some of them [42] used a fixed effects model and panel data from 2006 to 2015 to study the impact of land hoarding and prices on the scale and risk of local government debt. Subsequently, they found that both the scale and the price of land had a positive impact on the scale and risk of urban investment bonds (UIB). In terms of different regions, only the eastern region showed a significant correlation between land assets and the UIB. Other scholars [43] used economic fluctuations, local debt risks, and bank risk-taking variables to construct an econometric model and found that both economic changes and local government bond risks have a significant positive impact on bank risks and a negative correlation with regional economic growth. The authors of [44] researched China's local government financing platform (LGFV) and found that there is an inverted "U-shaped" relationship between the diversification of LGFV and local economic growth.
Based on sustainable development theory, we used the Mann-Kendall method and Kernel Density estimation to analyze the evolution of China's provincial government debt ratio and adopted a panel model to study the impact of provincial government debt on economic growth and fluctuations. Because of the opaqueness of local hidden debts before the "New Budget Law" was promulgated and implemented, related debts were difficult to obtain. The data of previous studies lacked timeliness and guidance for the implementation of current policies was limited. Therefore, compared with previous studies, our study mainly contributes to the existing literature in several ways. First, we considered provincial government debt as the research object, which could make the research on economically sustainable development more in-depth and specific. Our study explores the sustainability of China's provincial government debt and depicts the temporal and spatial evolution of the provincial government debt ratio from 2009 to 2020. Second, our research overcomes the limitations of the availability of local debt data, updates the research data to the latest, extends the perspective to the impact of local government debt on economic growth and volatility, builds an empirical model to verify them, and analyzes nonlinear relationships and regional differences. Third, we tested other influencing factors and proposed specific suggestions to improve the sustainable economic growth of different regions and provinces.
The remainder of this paper begins with Section 2, which introduces the research concept of this article and includes study ideas, methods, and data. Section 3 presents the trend analysis, provides empirical results and robustness tests, and provides an analysis. Section 4 discusses the empirical results and propose methods for sustainable development under COVID-19. Section 5 includes the conclusions, policy implication and limitations.

Study Idea
First, we determined the methods for studying the economically sustainable development of China's provinces, constructed econometric models, and analyzed the variables and data needed for the study.
Second, we used geographic information system (GIS) tools and kernel density estimation to show the dynamic distribution of China's provincial government debt ratio from 2009 to 2020. By using a Mann-Kendall test, we analyzed the trend of China's provincial government debt ratio from 2009 to 2020. In terms of empirical testing, we used econometric methods to determine the impact of provincial government debt on economic growth and fluctuations and analyzed nonlinear relationships and regional differences.
Finally, based on the results of the empirical analysis, we proposed specific policy recommendations for the eastern, central, and western provinces in China and explored research deficiencies and improvement methods.

Kernel Density Estimation
We used kernel density estimation to describe the evolution trend of China's provincial government debt ratio and analyzed the status quo of sustainable development of government debt in various regions of China.
As a non-parametric method, kernel density estimation has weak model dependence and strong robustness (Mariani and Vaden, 2010) [45]. This has become a common method for analyzing spatial imbalances. This method usually assumes that the density function of random variable X is: The kernel density function, as a smooth transition function or weighting function, usually satisfies: where N represents the number of observations, X i represents the independent and identically distributed observations, x represents the average value, k represents the kernel density, and h represents the bandwidth. The larger the bandwidth, the smoother the estimated density function curve and the lower the accuracy of the estimation; in contrast, the smaller the bandwidth, the less smooth is the density function, but the estimation accuracy is higher.

Econometric Methodology
Many scholars have adopted the most cutting-edge models and empirical methods to study the problem of government debt, such as the dynamic debt stabilization game model [46] and Python toolkit [47]. Based on the applicability of our study, following the classic research on government debt [9,11,48,49], we applied a panel data approach to examine the impact of local government debt on economic growth, namely, whether there was a threshold effect and the impact of local government debt on economic volatility, starting at the provincial government level. First, the impact of government debt on economic growth was examined by constructing a panel model, as follows: Second, we used the quadratic curve analysis method to bring the quadratic term of government debt variables into the econometric Model (4), as follows: Finally, the impact of local government debt on economic volatility was studied using the Hodrick-P rescott (HP) filter method to measure economic volatility; accordingly, a panel model was constructed as follows: where lnGDP is the dependent variable that represents the natural logarithm of provincial real GDP and GDPFlu is the dependent variable that represents the fluctuating term of the natural logarithm of provincial real GDP. As an independent variable, lnDebt is the natural logarithm of provincial government debt size, lnDebt 2 is the quadratic term of the natural logarithm of government debt size, and DebtFlu is the fluctuating term of the natural logarithm of provincial government size. Controls and ControlsFlu represent the set of control variables of Models (3) to (5), respectively. Province i and Year t are province and year fixed effects, respectively, which help mitigate issues from omitted variable bias. The symbol ε represents the estimated error item; the terms i and t denote the province and time, respectively. In the empirical process, the first-order lag term of the independent variable was used for the regression. The reasons are as follows: (1) The data selected to measure the level of government debt are the balance of government debt at the end of each year, and the balance at the end of the year will generally affect government spending in the second year and have an impact on provinces' GDP. Therefore, the impact of government debt on economic growth generally has a time lag [50,51]. (2) Using the first-order lag term of the independent variables can alleviate the endogeneity problem to a certain extent.

Research Data
The specific calculation methods and data sources of the variables are listed in Table 1. (1) Dependent Variables: Economic growth: lnGDP To eliminate the effect of inflation, 2009 was used as the base period to measure economic growth by calculating the real GDP of each province by taking the natural logarithm of each province's nominal GDP collected for 2009 and the provincial GDP index for the period of 2010 to 2020 [52].
Economic fluctuations: GDPFlu We chose the HP filtering method to deal with economic fluctuations. The HP filtering method approach can separate the trend items in the time series variables in a smooth sequence, so the time series data are divided into two parts: a smooth trend item and a periodic fluctuation item [53].
In data processing, HP filtering is performed on the natural logarithm of actual GDP. The trend item obtained after the HP filtering of the time series of the total output can be used to represent the potential output, the fluctuation item represents the output gap, and the time series of the output gaps can reflect economic changes. The decomposition process is the minimization process of solving Equation (6).
In Formula (6), lnGDP represents the total output level, and lnGDP t * represents the actual potential output. The decomposed trend item is obtained by calculating the HP filter, which is the actual potential output lnGDP t *. Next, the cyclical fluctuation part of economic growth is obtained by removing the trend item-that is, the output gap (lnGDP t -lnGDP t *). This result can be used to represent the cyclical fluctuation of the GDPFlu economy. The smoothing parameter λ in Formula (6) is set to 100, according to the value of regarding the annual data [54]. This study calculated the natural logarithm of the scale of local government debt, performed HP filtering, set the smoothing parameter λ to 100, and considered the volatility term as an indicator to measure the volatility of government debt.
(3) Control Variables Level of urbanization: Urb measures the level of urbanization using the urbanization rate of each province [55]. Industrial structure: Indus. This study used the share of the tertiary sector in the province's GDP to measure the degree the industrial sector's sophistication [56]. Population growth: Pop; represents a measure of the province's natural population growth rate. Opening level of provinces: Open, following [57], is the ratio of total provincial exports and imports to a province's GDP per year, used to measure the degree of a province's openness. Level of financial expenditure: Gov, this study used the ratio of province's general public budget expenditure to its GDP to measure the level of local general public budget expenditure [58]. Local general public budget expenditure includes general public services, public security expenditures, local overall social undertakings expenditures, and so on. Level of province's tax liability: Tax; in this study, the ratio of provincial government's annual tax revenue to nominal GDP was used to measure the tax burden level in each province. Province's human capital levels: Edu. We chose the years of formal education per capita in each province to measure this indicator [59].
The descriptive statistics of the variables are presented in Appendix A. We used Eviews 10.0 ® and Stata 16.0 ® for data calculation, statistical analysis, and regression analysis.

Empirical Results
We divided China's 30 provinces into three regions: East, Central, and West. Among them, there are 11 provinces in the eastern region: Beijing, Tianjin, Hebei, Liaoning, Shanghai, Jiangsu, Zhejiang, Fujian, Shandong, Guangdong, and Hainan. The eight provinces in the central region are Shanxi, Jilin, Heilongjiang, Anhui, Jiangxi, Henan, Hubei, and Hunan. Furthermore, the 11 provinces in the western region are Inner Mongolia, Guangxi, Chongqing, Sichuan, Guizhou, Yunnan, Shaanxi, Gansu, Qinghai, Ningxia, and Xinjiang. Because the sample data volume in Tibet was too small and it was difficult to obtain accurate data, it was not within the scope of the sample selection in this study. In the text, we abbreviated the provincial government debt ratio as the PDR (Provincial government debt ratio: The ratio of the provincial government debt balance at the end of the year to province's GDP of the year. It is an indicator that measures the carrying capacity of the province's economic scale on government debt or the dependence of province's economic growth on government debt. Internationally, the debt ratio of 60% stipulated in the Maastricht Treaty is usually used as the reference value of the government debt risk control standard), and the indicator would be used for robustness testing. We calculated the PDR of 30 provinces from 2009 to 2020, as shown as in Appendix B.

Temporal Evolution
We used ArcGIS 10.C S ® to draw PDR distribution map. Figure 1A-D show the changing trend of China's PDR in 2009, 2012, 2016, and 2020. It divides the PDR in China's 30 provinces into four categories, from low to high. Notably, the darker the red color, the higher the PDR in that year. The data of the PDR originates from Wind database and manual calculation by authors.  Figure 1E shows the mean value of the PDR from 2009 to 2020; the darker the red, the higher the mean value, where Guizhou Qinghai and Yunnan have the highest average value and a heavy debt burden; Guangdong Henan and Shandong have the lowest average value, and the debt pressure is relatively light. As shown in Figure 1F, the Mann-Kendall method was used to measure the trend value of the PDR in each province. The first interval is green, indicating that the PDR has a downward trend; the second range is light red, indicating that the PDR has an upward trend; and the third range is dark red, indicating that the PDR shows a significant upward trend. We found that the most developed regions

Spatial Evolution
We used MATLAB R2021 ® to make the nuclear density distribution map of PDR of whole country, eastern region, central region, and western region from 2009 to 2020.
As shown in Figure 2, the main peak of China's overall PDR tended to shift to the right and the peak increased after the main peak became shorter. After 2013, the peak increased, the bandwidth increased to a certain extent, and there was a right tailing trend with greater ductility. Overall, China's overall PDR shows a continuous upward trend with obvious inter-provincial differences-but a downward trend, nonetheless, especially after 2013. The provinces with a higher index widen the domestic differences, but the provinces with a lower PDR have a catch-up effect, and the differences between regions begin to narrow.
The main peak of the PDR in the eastern region shifted to the right and the peak height increased after a certain decline. The decline was more obvious from 2009 to 2013. Specifically, the bandwidth showed a continuous shrinking trend; there was a right tailing phenomenon, and the ductility increased. It can be seen that the PDR level in the eastern region shows little difference and change. In recent years, the gap between provinces with a high PDR and provinces with a low PDR has gradually narrowed and the PDR level in the region is relatively stable. The main peak of the PDR in Central China tends to shift to the right after a small range, and the peak obviously fluctuates in stages. There is an obvious downward trend from 2009 to 2013 and an obvious upward trend from 2014 to 2020. The bandwidth shows a certain expansion trend as there is a right tailing phenomenon and the ductility decreases. The level of PDR in the central region shows an overall difference, the change is small, and there is an obvious polarization effect. The provinces with high levels of PDR continue to grow, while the provinces with low levels of PDR grow slowly.
The main peak of the PDR in the western region has a small and rapid increasing trend. Accordingly, the decline is stable and there is rapid growth, and the peak height has obvious fluctuations. This is mainly manifested in a slight decline from 2009 to 2013, a small increase from 2014 to 2018 as the bandwidth continued to shrink from a right tailing trend, and the ductility decreased. Therefore, it is still necessary to focus on the problem of high PDR in areas with backward economic development in order to further improve the sustainability of government debt in the region.

The Influence of Government Debt on Economic Growth (1) Benchmark regression
To test whether provincial government debt has an impact on economic growth, Model (3) needed to be regressed. Before the regression, there was an F test of the panel data. This showed that the p value of the F statistic is less than 0.01, which proves that the fixed effect of the sample data of the model is extremely obvious; Hausmann's test has a p value of 0.0000, strongly rejecting the null hypothesis, and confirms the use of fixed effects, and that provinces and years are fixed in the regression. As shown in Figure 3  As shown in Table 2, according to Model (3), Column (1) describes fixed effect regression of 30 provinces, the dependent variable is L1-lnDebt, and L1-lnDebt has a positive impact on lnGDP and passes the 1% significance test. That is, provincial government debt can significantly promote economic growth. The coefficient is 0.024, which means that, when the provincial government debt increases by 1% point, the real GDP will increase by 0.024% points. Among the control variables, Urb, Indus, and Edu significantly increased lnGDP and passed at least 1% significance level test. Open and Tax have a negative impact on lnGDP and passed the 1% significance test. The impact of Pop on lnGDP is negative and passed at least a 10% significance level test. Notes: L1-lnDebt and L1-lnDebt2 are first-order lag term of the independent variables, in order to alleviate the endogenous problem of the model, the independent variables are processed by lag first-order, t-statistics are in parentheses. *** p < 0.01 and * p < 0.1.
In the three major regions, L1-lnDebt is positively significant for lnGDP and passes at least a 1% significance level test. The eastern region has the lowest impact coefficient of 0.020, and the central region has the highest impact coefficient, reaching 0.027. The influence coefficient of the western region is 0.023, which is slightly lower than the overall level of 0.024. From the perspective of control variables, in the eastern region, Urb, Indus, and Edu all significantly promote lnGDP and pass the 1% significance level test. On the contrary, Open and Tax have an inhibitory effect on lnGDP; specifically, Open passes the 1% significance test, and Tax passes the 10% significance test. In the central region, Urb, Gov, and Edu have a significant positive impact on lnGDP as they all pass the 1% significance test. Notably, Indus, Open, and Tax hinder the growth of lnGDP; among them, Indus fails the significance test, Open passes the 1% significance test, and Tax passes the 5% significance test. In the western region, Urb and Edu have a significant promoting effect on lnGDP and they all pass the 1% significance test. Finally, Pop, Gov, and Tax inhibit the growth of lnGDP, but they all fail the significance test.

(3) Further study
To examine the nonlinear relationship between the debt scale and economic growth, we conducted an empirical regression on Model (4). As shown in Table 2, according to Model (4), Column (5) describes the fixed effect regression of 30 provinces. The corresponding dependent variables are L1-lnDebt and L1-lnDebt 2 , and they are both significant at the 1% level. This shows that there is a nonlinear relationship between China's provincial government debt and economic growth, showing an inverted "U-shaped" curve. This is similar to the findings of others, such as Bailey et al. (2021) [39] and Wei et al. (2021) [60]. Based on the quadratic axis of symmetry, the axis of symmetry of the government debt L1-lnDebt can be calculated as 6.684. From descriptive statistics, because 6.684 is within the value range of L1-lnDebt, and the provincial data year corresponding to the value is 2010, we say that, when the value of L1-lnDebt is 6.684, the threshold is reached; at this time, local government debt has the greatest positive impact on local economic growth. It can be seen from Figure 4 that the growth rate of China's GDP in 2010 reached 10.640%, the highest point from 2009 to 2020, which simultaneously confirmed the threshold effect.

The Influence of Government Debt on Economic Growth Fluctuations (1) Benchmark regression
To test whether provincial government debt has an impact on economic fluctuations, Model (5) was regressed. Before regression, the F test of the panel data was performed, and the result showed that the F statistic p value was 1, which confirmed that the model was not suitable for fixed effects. The LM test was performed, and the result showed that the p value was 1, which confirmed that the model was not suitable for random effects. After the F test and LM test, we used mixed regression to conduct an empirical analysis on Model (5). Figure 5   As shown in Table 3, according to Model (5), Column (1) describes fixed effect regression of 30 provinces. The dependent variable corresponding to Column (1) is L1-DebtFlu. Accordingly, it can be seen that L1-DebtFlu has a positive impact on GDPFlu and passes the 10% significance test. That is, provincial government debt volatility can significantly promote economic growth volatility. The coefficient is 0.009, which means that, when the provincial government debt volatility increases by 1% point, the real GDP volatility will increase by 0.009% points. Among the control variables, UrbFlu, PopFlu, GovFlu, TaxFlu, and EduFlu have positive impacts on GDPFlu; among them, PopFlu passes the 5% significance test, and TaxFlu passes the 1% significance test, but the remaining variables fail to pass the significance test. In contrast, IndusFlu and OpenFlu have a significant inhibitory effect on GDPFlu, and they all pass the 1% significance test.
(2) Regional Fluctuations analysis As shown in Table 3, Columns (2), (3), and (4) of Table 2 describe mixed effect regression of the eastern provinces, central provinces, and western provinces, respectively. The independent variable corresponding to Columns (2) through (4) is L1-DebtFlu. Based on Columns (2) and (3), in the eastern and central regions, L1-DebtFlu in provincial government debt has no significant impact on GDPFlu. Among them, the coefficient in the eastern region is positive, the coefficient in the central region is negative, and the absolute values are both small. This shows that the eastern and central regions have done a relatively good job in controlling government debt risks and the influence of government debt fluctuations on economic changes can be eliminated. Column (4) shows that, in the western region, the influence coefficient of L1-DebtFlu is significantly positive and passes the 5% significance test; moreover, the coefficient is 0.016, and the absolute value of the western region is higher than the overall national level. This shows that the volatility of provincial government debt in the western region has greatly aggravated economic volatility and caused unstable economic operations. Notes: L1-DebtFlu is first-order lag term of the independent variable; in order to alleviate the endogenous problem of the model, the independent variable is processed by lag first-order, t-statistics are in parentheses. *** p < 0.01, ** p < 0.05, and * p < 0.1.

(3) Robustness test
To ensure the reliability of the regression results, this study adopted the independent variable substitution method and used the government debt ratio to replace the natural logarithm of the government debt scale to measure the government debt level. The province's government debt ratio in the current year was attained by calculating the ratio of government debt this year to the province's GDP. Amplify 100 times and perform HP filter processing and retain its fluctuation term as a new explanatory variable. The results of the robustness tests are presented in Table 4.
The independent variables corresponding to Columns (1) through (4) in Table 4 are L1-DRFlu. The dependent variables in Table 4 are the same as those listed in Table 3. The regression results in Column (1) of Table 4 show that the independent variables are significant and that the regression coefficient is 0.008 and is significant at the 10% level. This supports the regression results in Table 4 that provincial government debt volatility can significantly promote economic growth volatility. However, compared with the regression results in Column (1) of Table 3, the regression coefficient is lower, indicating that government debt ratio volatility is less sensitive to economic growth volatility. Columns (2) to (4) of Table 4 describe the eastern, central, and western regions, respectively. After adjusting for the independent variables, the sign and significance of the regression coefficients of the independent variables did not change. This shows that the influence of government debt on economic fluctuations is not affected by the form of the independent variable and the model is robust. Notes: L1-DRFlu is first-order lag term of the independent variable; in order to alleviate the endogenous problem of the model, the independent variable is processed by lag first-order, t-statistics are in parentheses. *** p < 0.01, ** p < 0.05, and * p < 0.1.

Discussion
Based on sustainable development theory, we adopted the fixed effect model to analyze the impact of China's provincial government debt on economic growth and conducted regional heterogeneity analysis. Then, we introduced the square term of government debt into the model to verify the "nonlinear relationship" of the impact of China's government debt on economic growth and judged whether there is a threshold effect showing "U" or inverted "U" relationship between them. Finally, we conducted HP Filtering on all variables to further test the impact of China's provincial government debt on economic fluctuations and completed the robustness test.
We can see from the above empirical results that, on the one hand, China's provincial government debt promoted economic growth, Dey et al. [61] had the same view, and the regression coefficient (0.024) was significant. From different regional perspectives, the promotion effect of the central region (0.027) is higher than that of the eastern (0.020) and western (0.023) regions. This is consistent with the conclusion of [62]. Theoretically, there is a nonlinear relationship between China's provincial government debt and economic growth, showing an inverted "U-shaped" curve; however, ref. [63] presented nonlinear characteristics, rather than an inverted "U-shaped" relationship.
On the other hand, the variation in government debt aggravates economic fluctuations, and the regression coefficient (0.009) is significant. The regression coefficients of the eastern and central provinces are not significant; however, the regression coefficient of the western provinces (0.016) is larger and more significant than that of other regions. Tax burden fluctuations and population growth rates aggravate economic changes. In contrast, the optimization of provincial industrial structure and improving provincial opening level can slow economic fluctuations. This is similar to the viewpoint of [64].
We discovered that China's provincial government debt has a significant positive impact on economic growth. Moreover, debt volatility contributes to regional economic volatility. For example, owing to the effect of COVID-19, Hubei's GDP in 2019 was 4582.831 billion yuan, with an annual growth rate of 7.5%. However, by 2020, the provincial GDP was 4344.346 billion yuan, representing a year-on-year decrease of 5.0%-its economy has significantly declined. To speed up recovery and stabilize employment, the Hubei Provin-cial Government has increased its borrowing efforts. In 2020, the debt balance of Hubei Province was 1494.933 billion yuan, an increase of 85.934% year-on-year, and the provincial government debt ratio increased by 96.141% year-on-year. If the government does not borrow to increase investment and stabilize economic growth, Hubei's economy will experience more severe fluctuations and decline.
In short, China's provincial government debt has increased significantly under COVID-19. Owing to the slow economic recovery, the debt ratios of certain provinces such as Qinghai and Guizhou remain high, and there is even the possibility of debt crises. Therefore, we need to further explore how the economy can sustainably develop if the new coronavirus epidemic becomes a normal facet of the economy. First, the government must maintain macroeconomic stability and a stable level of government debt, and ensure that no debt crisis occurs. Second, the developed provinces in the east should assist the backward provinces in the west by providing horizontal fiscal expenditures to ensure that all provinces can overcome these difficulties. Third, the coronavirus highlights the ecological environment's importance. To maintain sustainable economic development, the government must increase investment in environmental protection; guide government debt to invest in green environmental protection industries and the green economy; and achieve sustainable economic development through green innovation. Finally, China in 2020 GDP growth rate has dropped by half because of the impact of COVID-19. The influence of COVID-19 has greatly restricted international trade and personnel movement; in order to revive the China's provincial economies, the government should increase the stimulation of domestic demand and simultaneously develop a combination of online and offline methods to promote product sales.

Conclusions
This study examines the impact of local government debt on economic growth and fluctuation, which has important research value. In the context of COVID-19's impact, local governments have increased borrowing, which has stimulated the economy; but local government debt also impacts local economic fluctuations. For example, when the government debt ratio is too high to repay debt, it will cause a debt crisis and have a disastrous impact on sustainable economic development. The data used here are more complete than those of previous studies and have been updated to 2020, which tests the impact of China's provincial government debt on economic growth and sustainable development with COVID-19. We build an empirical model to test the different impacts and regional differences in the scale of provincial government debt on economic growth and fluctuations. In addition, we verify the non-linear relationship between provincial government debt and economic growth.
From a national perspective, analyzing local government debt's impact on economic growth shows that such debt promotes economic growth, with a coefficient of 0.024. From the perspective of regional heterogeneity, the coefficients for the eastern and western regions are 0.020 and 0.023, respectively, and the role of government debt in promoting economic growth is significantly lower than the national level. The coefficient in the central region is 0.027, and the contribution of provincial government debt to economic growth is higher than the national level.
We empirically conclude that there is a nonlinear relationship between China's provincial government debt and economic growth, which shows an inverted "U-shaped" curve. There may be a theoretical threshold effect between local government debt and economic growth. When the threshold is reached, local government debt has the greatest positive impact on local economic growth. During the sample period, the maximum value of China's economic growth rate corresponds to the threshold point, confirming the above conclusion.
Regarding the impact of local government debt on economic fluctuations, from a national perspective, government debt volatility aggravates economic volatility with a coefficient of 0.008; however, in the eastern and central regions, its impact on economic shifts is not significant. In China's western region, the fluctuation of provincial government debt significantly aggravates changes in the local economy and causes unstable economic operations.
Thus, this study results are important. We propose a new perspective for China's local debt research; that is, China's regions should use government debt to manage the impact of the coronavirus pandemic, prevent risks in debt expansion, alleviate economic fluctuations, and ensure economic and social stability throughout China. This operation has a certain reference significance.

Policy Implication
This study reveals relevant policy implication. The economic development level in the eastern region is leading the country in this category. With strong debt management capabilities and relatively complete market systems, under normal circumstances, the market's self-adjustment mechanism should be relied upon, and it is not appropriate to extensively intervene [65]. The central region's economic endowment is insufficient, its economic foundation is weak, and the industrial structure remains imperfect. This requires actively promoting the reform of the government debt management system as well as rendering scientific and reasonable debt investment decisions. We recommend promoting the upgrading of the industrial structure in general and the entire market through the development of the characteristic economy in order to drive the regional economy's sustainable and coordinated development.
The degree of marketization, industrial structure, and economic development efficiency in the western region are far from those of the country's other two regions. The backward development concept for GDP should be abandoned, and a sound mechanism for evaluating government debt should be established. Government debt's role in promoting the economy and encouraging social capital within public investment should be emphasized. There should also be an appropriate increase in social capital's participation in areas of people's livelihoods, such as science, education, culture, and health.

Limitations
Several important limitations of this study warrant discussion. On the one hand, the sample data volume of this study is not rich enough, because only 30 provincial governments were studied, resulting in an insufficient sample size. In the future, we expect public disclosure of government debt data at the municipal and county levels; alternatively, we can use quarterly data from provincial units to expand the sample size. On the other hand, this study examined the impact of the scale of government debt on economic growth and fluctuation. However, in practice, the influence of different flows of government debt funds on economic growth is obviously different. In future research, we can consider subdividing government debt variables, studying the different effects of government debt flowing into different fields or industries on economic growth, analyzing the corresponding mechanism, and exploring specific ways to improve government debt's sustainable development.
Author Contributions: W.Y. and Y.W. designed this manuscript. Z.Z. wrote this manuscript. P.D. and L.G. collected the data and made scientific comments on this manuscript. All authors have read and agreed to the published version of the manuscript.

Conflicts of Interest:
The authors declare that they have no known competing financial interests or personal relationships that could have influenced the results reported in this paper. Notes: shows the statistical information of the variables adopted in this paper. When calculating the control variables involving the ratio, we take the value before the percentage sign, that is, enlarge the ratio by 100 times before regression.