s2fieldsofstudy: Economics Business

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Local and spatial spillover effects of corporate financing costs on regional carbon emissions: evidence from Chinese listed firms

The signing of the Paris Agreement has raised concerns about global carbon emissions, which have detrimental consequences in terms of climate change. At the same time, the financing process for listed companies has begun to incorporate investigations into these firms’ carbon emissions. But the current impact of financing costs on firms’ carbon emissions has not been accurately assessed. There are large differences in endowments in different regions of China, and factors flow frequently among regions. To date, no empirical evidence has emerged to show the spatial effects of financing costs on carbon emissions. This study uses the STIRPAT model and a panel lag regression model for empirical testing. The results show that increasing financing costs will increase the burden imposed by carbon reduction efforts in various regions. Although this trend has obvious spillovers to surrounding areas, the location of the enterprise bears a more negative burden of externalities. Further analysis shows that reducing the financing costs of enterprises in economically developed regions can reduce both their carbon emissions and the damage to economic growth. These research conclusions can help policymakers shape carbon reduction activities through reducing corporate financing costs on the basis of regional development differences.

Introduction
Climate change is one of the major challenges facing the world today. Approximately, 51 billion tons of greenhouse gases is emitted into the atmosphere globally each year. As part of the effort to mitigate the damage caused by greenhouse gases such as carbon dioxide, the Paris Agreement, which was completed in December 2015, determined emission reduction plans and goals for all of its signatory states. In turn, countries around the world are now implementing large-scale cooperative actions to achieve carbon neutrality goals. The issue of carbon emissions is of great significance to the sustainable development of the world's resources and environment. According to research carried out by the International Energy Agency (IEA), the total carbon dioxide emissions of China-the world's second largest economyaccount for one-fourth of the world's total, so China plays an important role in addressing global carbon emissions and climate change. At the 75th United Nations General Assembly, China formally proposed a "dual carbon" goal, striving to reach its peak of carbon dioxide emissions by 2030 and to achieve a balance between "carbon emissions" and "carbon absorption" by 2060.
The development of the financial industry plays an important role in reducing carbon emissions. On the one hand, it provides a financing platform for enterprises; on the other hand, it provides a convenient channel for investment behavior. Through this mechanism, enterprises benefit from the pressure exerted by the financial industry to reduce R&D costs, promote green economic growth, and improve environmental quality. Traditional financial services do not consider the negative externalities brought about by corporate environmental behavior, but only focus on ways to maximize profits from the perspective of economic feasibility and financial returns. In the context of low-carbon goals, however, financial services take negative externalities into account in the process of measuring allocation efficiency, and they regulate the behavior of individuals and enterprises by adjusting the flow of funds.
In the Sustainable Development Goals report authored by Garroway and Carpentier, it is proposed that the key to helping countries achieve such goals is to improve deficiencies in financing (Sinha et al. 2021). The United Nations Global Compact has also pointed out that to accelerate countries' efforts to address climate change and achieve sustainable development, the most important consideration is to reposition the global capital market-a process that requires adjustment of corporate financing mechanisms. As part of this pursuit, stakeholders have begun to pay extensive attention to corporate carbon emissions, investment trends have shifted to favor green and low-carbon investments, and new financial instruments such as green bonds and ESG (environmental, social, and governance) funds have emerged one after another, further narrowing the financing channels open to the high-carbon energy industry and forcing enterprises to consider limiting their carbon emissions (Sinha et al. 2021).
In the study of carbon emissions, reducing the total amount of carbon emissions has been widely recognized as a desirable international goal, but there is controversy over the impacts of the financial industry on carbon emissions. Tamazian et al. (2009) asserted that the development of the financial industry can reduce corporate financing costs, enrich corporate financing channels, promote energy-saving production, and reduce carbon emissions by encouraging companies to innovate in regard to their production technologies. However, Işik et al. (2017) found that the development of the financial industry increased carbon dioxide emissions when studying the Greek problem. Sadorsky (2010) suggested that the development of financing avenues, especially the improvement of corporate financing capabilities, will motivate companies to seek out more investment projects, further expand the scale of their production and operations, and lead to increased energy consumption. In addition, Dogan and Turkekul (2016) found that financial development does promote economic development in the short term, but does not have a significant impact on environmental pollution. Thus, the evidence on how corporate financing affects carbon emissions remains contradictory. In addition, the conclusions reached vary according to the specific research context and may not relate to the decarbonization scenario posited in the current research.
In China, there are obvious differences in the level of economic development and resource endowments in various regions, and enterprises frequently conduct cross-regional flow of factors, leading to significant spatial effects on carbon emissions. Thus, if a unified national carbon reduction program is implemented, the rights and responsibilities associated with carbon emissions in various regions will not be equal-which may not only fail to curb carbon reduction, but also hinder the economic development of some regions. To account for this perspective, this study is based on the data of listed companies in China, combined with the data on the development of various regions in China; it also reflects the financing situations of enterprises with financing costs and discusses the previously mentioned spatial effects of carbon reduction in China.
Our research makes important contributions from three perspectives. First, most of the literature has ignored the externalities of financial services in the context of low-carbon target development, and few studies have addressed the impact of financing costs on carbon emissions. Our study refines the research perspective to the micro-enterprise level, focusing on the impact of corporate financing costs on regional carbon emissions. Second, our study breaks new ground by incorporating the spatial effects into the framework used for analyzing the impact of financing cost on regional carbon emissions. The STIRPAT model and a spatial lag regression model are used to study local effects and peripheral spillover effects. Finally, our research focuses on carbon emissions while simultaneously taking regional economic development into account and introduces a "regional decoupling index," which measures the process of breaking the link between economic activity and the environment, as a means to achieve a win-win situation for both carbon reduction and economic growth.

Effect of financing costs on carbon emissions
In prior research on carbon emissions, many scholars have focused on the famous environmental Kuznets curve (EKC) hypothesis, and some studies have considered the form of EKC exhibited by the manufacturing industry (Isik et al. 2019;Işık et al. 2019;Isik et al. 2021;Ongan et al. 2021) to study the relationship between carbon dioxide and other greenhouse gas or environmental pollutant emissions and economic growth and energy consumption. Noting the different performances of agriculture, forestry, and animal husbandry in the EKC hypothesis, one study concluded that considering the different impacts of the three was important to comprehensively implement measures to reduce carbon emissions . Some scholars proposed to incorporate production and consumption into the analytical framework to use the ecological footprint to measure the degree of environmental degradation Khan et al. 2021;Sharif et al. 2019). In addition to studying traditional industries, Ahmad et al. (2021) creatively proposed the heterogeneous effects of inward foreign direct investment (IFDI) on EKC performance. However, this line of research generally ignores the role of the financial industry.
Financial development is closely related to carbon emissions. As an allocation mechanism, finance not only promotes economic expansion and technological progress, but also plays a role in the choice of production factors, guiding capital and other production factors to stay away from industries with high energy consumption, high carbon emissions, and high pollution. The carbon emission rights and the carbon tax formed under the Coase property rights theory and the Pigou tax theory have resulted in the internalization of firm costs associated with such factors (Wei and Yang 2022). To help firms cope with the increasing carbon reduction costs they must bear, financial institutions need to support the firms by developing financial design systems that are compatible with the structure of the environment (Lin et al. 2021).
With the development of supportive financial factors, especially improvement in firms' ability to obtain credit, the firms will be able to seek out more investment projects and further expand the scale of their production and operations, which will in turn lead to an increase in their energy consumption (Sadorsky 2010). From consumers' perspectives, booming financial markets tend to stimulate domestic consumption, and this increase in demand for various household items then leads to greater energy consumption and environmental pollution through increased production (Zhang 2011). Xiong and Qi (2016), taking China as their research object, used the generalized method of moments (GMM) regression estimation method to draw the conclusion that the deterioration of air quality is closely related to the level of financial development-a revelation that prompted emission reduction policymakers in various regions began to pay more attention to the development of the financial field.
According to Porter's theory, firm financing is a key financial activity that can stimulate more investment in R&D by firms and encourage them to upgrade equipment or invest in new technologies that can reduce their carbon emissions (Petroni et al. 2019). At the same time, the external pressure of financing costs prompts firms to overcome their financing inertia and has a complementary effect with their internal production mechanisms that can further improve the carbon emission problem (Ambec & Barla 2002). In addition, according to information display theory, compared with regulatory policy measures, financing behaviors are mostly carried out in the trading markets, which are prone to information asymmetry and principal-agent problems, thereby affecting firms' carbon emission decisions. Thus, high financing costs may hinder firms from carrying out carbon reduction activities and reduce their enthusiasm for carbon reduction investments.
This line of theoretical analysis suggests that firm financing behaviors have both positive and negative effects on carbon emissions. To date, however, few studies have directly addressed the impact of financing costs on firm carbon emissions. He et al. (2012) found that when firms pursue financing for technological innovation activities, due to the confidential and proprietary nature of those technologies and the long payback period for investments, the problem of information asymmetry between investment and financing parties often arises, which leads to financing difficulties for firms. As a result, investment of capital in innovative activities such as carbon reduction may not be favored. Ge et al. (2018) showed that firms find it difficult to engage in green technology innovation, and their inability to do so leads to higher carbon emissions. Guariglia and Liu (2014) proposed that investments that aim to reduce carbon emissions are a part of the costs faced by firms, and suggested that firms have insufficient motivation to engage in environmental protection investments when under financing constraints. In addition, Zhang et al. (2019) pointed that managers, as trusted persons in business operations, tend to favor shortterm and high-yield projects when under performance pressure, while ignoring long-term investment projects geared toward the goal of carbon reduction. Moreover, as a result of their adoption of low-cost production methods, the carbon emissions of firms have greatly increased.
Based on the preceding arguments, we propose the following hypothesis: Hypothesis 1: financing costs have a significant positive impact on carbon emissions because the positive impact between the two is greater than the negative impact.

Spatial effects of firm behaviors on carbon emissions
Most studies on carbon emissions focus on the macrolevel, such as countries and regions, or on the mesolevel, such as industries. Tamazian et al. (2009) used country data to show that the development of the financial industry can reduce financing costs, enrich financing channels, and achieve energy-saving production by promoting innovative production technologies, ultimately reducing carbon emissions. Based on the panel VAR model, Gu and He (2012) found that deepening financial cooperation has, to some extent, reduced carbon emissions by tracking the relationship between availability of financing and carbon emissions in China's provincial-level regions for 30 years.
Firms are the main entities that shape market behavior as well as the main actors in regard to carbon reduction behavior. Refining the research perspective to the firm level, therefore, can address carbon emissions more specifically. Although microdata for firms are more diverse and less available than data on the level of regions or industries, some scholars have made innovative attempts at firm-level analysis. Wang and Ni (2016) used a questionnaire survey to collect carbon emission samples from 32 firms in Zhejiang Province, China, and applied the analytic hierarchy process (AHP) model to construct measurement indicators. However, limited by the small sample size, their research conclusions had regional differences. Shen et al. (2017) collected pollutant discharge fee data for 32 companies and carried out a study based on the homology of carbon dioxide and air pollutants. However, missing values and measurement errors have obvious influences on this process. Zhou et al. (2019) were able to expand the sample size by taking S&P 500 companies as the research objects and studied the carbon efficiency of firms by measuring their carbon emissions.
Notably, the preceding studies ignored the spatiality of carbon emissions caused by firm production. With the rise of spatial econometrics, spatial factors have become more widely incorporated into the analysis framework of carbon emissions. When Fisher-Vanden et al. (2004) studied the energy consumption intensity of Chinese industrial firms, they found that carbon dioxide and other gas emissions caused by energy consumption had a significant spatial effect. Khezri et al. (2022) used the spatial Durbin regression model to comprehensively study the possibility of financial development having direct and spillover effects on carbon emissions at the regional level. Their study found that financial development stimulated carbon dioxide emissions, while financial demand in adjacent regions played an important role in a country's total carbon emission. Using a spatial econometric model, Wang et al. (2021) found that the negative spillover effect of financial development is higher than the positive direct effect. In general, financial development has an adverse impact on carbon dioxide emissions in adjacent areas. Zhao (2003) used adjacency, distance, and gravity matrices to construct a spatial econometric model, finding that fixed asset investment in the financial industry can reduce the local carbon emission level by developing the financial market.
Large differences are evident in the level of economic development and resource endowments in various regions of China. Production factors of firms often flow across regions, such that firms demonstrate spatial dependence and spillover characteristics in the production process. But what are the spatial and temporal characteristics of companies' impacts on carbon emissions? Zhang and Dou (2016) used a dynamic spatial Durbin model to show that pollution emission intensity has a significant positive spatial correlation and spillover effect. In addition, some studies have found that there is a significant spatial autocorrelation of carbon emissions (Liu and Zhang 2019), and that the regional carbon reduction level is consistent with the development direction of financial efficiency. The key to the positive effect of firm financial development on emissions reduction, it seems, lies in the supervision of funds, not the absolute amount of funds invested (Huang et al. 2014). As yet, however, the literature on carbon emissions under the influence of financing costs remains lacking. To address this gap, our research incorporates the spatial factors into the analysis framework to study the previously mentioned problems.
Based on these arguments, we propose the following hypothesis: Hypothesis 2: carbon emissions are spatially correlated, and an increase in corporate financing costs will not only increase local carbon emissions but also have spatial spillovers to surrounding areas.

Decoupling analysis of firm-level and regional-level carbon reduction
According to the externality theory, a firm is a rational economic "person" whose purpose is to make a profit. Thus, when determining its goal level of carbon emissions, the firm weighs the carbon reduction cost against the carbon reduction benefit. If a one-sided emphasis on the carbon reduction goals fails to take into account the relevant economic development issues, it will lead to "abandonment of food due to choking." Promoting the normal operation of the firm under such circumstances will be difficult. At the same time, there are large differences in the level of economic development between regions. When studying carbon emissions, if only the absolute amount of carbon reduction is considered, it is easy to cause the main body of carbon reduction to engage in a carbon-reduction competition, which is inconsistent with each firm's actual level of development.
As an alternative approach, the Organization for Economic Co-operation and Development (2002) proposed decoupling theory as a vehicle to study the relationship between economic growth and carbon emissions. This theory generally focuses on the process of breaking the link between economic activities and the environment (Enevoldsen et al. 2007). Based on this theory and the preceding arguments, we propose the following hypothesis: Hypothesis 3: using regions in different "decoupling" states as the classification basis, there are significant differences in the local effects and spatial spillover effects of corporate financing costs on regional carbon emissions.
Using decoupling theory, some earlier studies have explored the dependence between carbon emissions and economic growth. In developing economies, economic development is still the primary focus, so the decoupling trend fluctuates greatly across these countries (Wu et al. 2018). In developed economies, a transition from weak decoupling to strong decoupling appears to be under way, which is gradually resulting in a good separation of economic development and carbon emissions (Wang and Su 2020). When applying decoupling theory, most studies have focused on the national level. In contrast, our research applies decoupling theory to the analysis of regional carbon emissions.
The Tapio decoupling index is used to describe the coupling relationship between regional economic growth and environmental impact (Yasmeen and Tan 2021); it avoids the use of a single absolute or relative measurement and, in turn, minimizes the deviation caused by high sensitivity or extremeness of such an indicator. The Tapio decoupling index is calculated as follows: where i is the region, C is the regional carbon emissions (in units of 10,000 tons), and GDP is the regional gross domestic product (in units of 100 million yuan).
In Eq. (1), represents the growth rate of carbon emissions, and represents the economic growth rate. Topio i represents the decoupling elasticity. The differences in the growth rates of the economy and carbon emissions fall into the categories shown in Table 1.

Data sources
Our sample comprises the annual data of Chinese listed companies from 1998 to 2018, with the data being obtained from the China Stock Market and Accounting Research (CSMAR) database. This database, which was created by China Shenzhen Shishma Data Technology Co., is an authoritative source for the study of China's economic and financial fields, and is used by many colleges and universities, independent research institutions, and government agencies. The provincial index data come from the China Statistical Yearbook for the years of interest. The carbon emission (1)

Explained variable
The carbon emission accounting data are based on the China Emission Accounts and Datasets (CEADs) accounting method. The specific calculation formula is as follows: where AD ij represents the consumption of fossil energy i in sector j (in units of 10,000 tons of standard coal). EF ij represents the emission factor, which we obtained by multiplying the combustion value per unit of fossil energy NVCi, the emissions of CO 2 per unit of combustion value CC i , and the proportion of oxygen O i . The formula for calculating EF ij is as follows:

Explanatory variables and control variables
The carbon emission accounting results were expressed in lnCE. Financing costs (lnPRO) were given in terms of the public company's share issuance premium (Bolton and Kacperczyk 2021). The age of the company (lnAGE) was calculated as the current year minus the year in which the firm was opened.
(2) The logarithm of the firm's operating income is used to represent firm size (lnSAC). The firm asset structure (lnSTR) was calculated as "(net fixed assets + net inventory)/total assets." The remaining provincial-level variables were obtained as follows. GDP per capita (lnA) was calculated by dividing the constant-price GDP by the population at the end of the year. Temperature (lnTEM) was represented by the annual mean temperature of the capital city of the province. The educational level (lnEDU) consisted of the proportion of the population with a high school education or above in the province relative to the population older than age 6. Population density, foreign direct investment, and the proportion of secondary industry were expressed as lnP, lnFDI, and lnT, respectively. The descriptive statistics for these variables are shown in Table 2.

Model construction
The STIRPAT model comprehensively considers the main factors affecting regional environmental changes, such as population, economic development level, and technical level; it is widely used in the study of regional behavior and regional environmental changes. Our study draws on the work by Ahmad et al. (2021), which was based on the STIRPAT model (Dietz and Rosa 1997), but extends this model to avoid the randomness of variable selection of carbon emissions influencing factors. Among these factors, the impacts of population, affluence, and energy intensity on carbon emissions have been confirmed in many studies. Our model was calculated as follows: where a is a constant and 1 − 10 represents the regression coefficient of each variable. Taking the natural logarithm of both sides of Eq. (4) to linearize, it results in the following equation: (4) where c is the region, i is the firm, t is the year, is the time fixed effect, is the industry fixed effect, and is the random error term. The remaining variables have the same meaning as in Table 2.
Carbon emissions not only depend on the specific region, but also are affected by the interaction of geographically adjacent regions (Zhao and Sun 2022). Taking into account the existence of spatial autocorrelation of carbon emissions, we used the following model used to study regional effects: where indicates the direction and extent of the impacts of carbon emissions on the local area, f irmControls it represents the control variable at the firm level, and areaControls ct represents the control variable at the provincial level. Wp ct is the spatial lag term, which reflects the carbon emission impacts of the surrounding area on the central area. It is calculated as follows: where W cd is the inverse geographic distance spatial weight matrix established according to the latitude and longitude of the region (if the research area is at the provincial level, the matrix is 30 × 30, excluding the data for Hong Kong, Macao, Taiwan, and Tibet). p dt represents the carbon emissions of region d in year t.
In addition to having local effects, carbon emissions may spillover to surrounding areas (the dependent variable in our study). Thus, we focus on the "spillover effect" of the local (5) clnCE ct = a + 1 lnPRO it + 2 lnAGE it + 3 lnSCA it + 4 lnSTR it + 5 lnA ct + 6 lnP ct + 7 lnFDI ct + 8 lnT ct + 9 lnEDU ct + 10 lnTEM ct + + + (6) The dependent variable is constructed as follows, representing the local spillover value of carbon emissions to the surrounding area: where Ŵ p ct still represents the spatial weight matrix, but differs in the direction of influence p ct represents the observed value for area c in year t.

Spatial correlation test
We first conducted a univariate spatial correlation test. The results of the Moran index (Moran's I) showed that in the study year, there was a significant positive spatial autocorrelation of carbon emissions in the province, meaning that the provincial carbon emissions show a significant "high-high, low-low" aggregation phenomenon. When we carried out sensitivity analysis based on the guidance provided by Anselin and Moreno (2003), the results (shown in Table 9 in the Appendix) confirmed the existence of spatial correlation.
In the global autocorrelation analysis of carbon emissions from 1998 to 2018 (see Table 3), Moran's I was positive, and all results passed the 5% significance test. Bivariate correlation analysis can fix one-way effects in space and time. Columns (3) and (5) of Table 3 describe how the carbon emissions of a province in 2009 (2018) were affected by the weighted average carbon emissions of neighboring provinces in 1998 (2009). This interactive influence can be seen as "inward spillover." Columns (2) and (4) (2018), which can be seen as "outward spillover." (8) Wp ct = 0 + 1 lnPRO it + 2 firmControls it + 3 areaControls ct + ε + ε + ε (9) Wp ct = n ∑ d=1 W dc p ct

Analysis of empirical results
This empirical research is divided into three parts. First, we used the fixed effects of the firm panel data to study the impacts of financing costs on local carbon emissions as the benchmark regression. Second, we studied the impacts of corporate financing costs on regional carbon emissions from the perspectives of local effect and spatial spillovers. Third, we performed robustness testing, heterogeneity testing, and endogeneity analysis.

Estimation results for the basic model
As shown in Table 4, we found a significant positive relationship between carbon emissions and financing costs. The regression results in columns (3) and (4) show that a 1% increase in financing costs increased regional carbon emissions by 0.0158% to 0.0165%. The regression results for the control variables were all significant at the 1% level. Specifically, we identified a significant negative correlation between greater firm age (lnAGE) and the level of carbon emissions. Firms with a longer history have more mature emission reduction facilities and tend to engage in long-term planning, which is conducive to the realization of emission reduction targets.
The expansion of firm scale (lnSAC) often leads to an increase in input factors such as energy, thereby increasing the production of carbon emissions. The regression results for the asset structure (lnSTR) showed that an increase in the firm's fixed assets led to an increase in its energy consumption, which in turn increased its carbon emissions.
Per capita GDP (lnA) had a negative relationship with carbon emissions, indicating that energy efficiency has a greater inhibitory effect on carbon emissions than does economic growth, and the "decoupling" of regional economies has achieved remarkable results. The impact of population density (lnP) on carbon emissions was significantly negative, suggesting that the impact of population size on carbon emissions becomes weaker as the industrial structure undergoes adjustments and energy efficiency improves. An increase in the proportion of secondary industries (lnT) with resource consumption as their main modes of production will inevitably promote a continuous increase in production-related carbon emissions. An increase in foreign direct investment (lnFDI) may also lead to increased carbon emissions by companies. Provinces with higher temperature (lnTEM) do not need heating in winter, so air pollution associated with heating sources is less likely; this was manifested in our results as a negative relationship between temperature and carbon emissions.

Local effects and spatial spillover analysis
After confirming the spatial correlation of carbon emissions, columns (1) and (2) in Table 5 report the use of Eq. (6) to examine the "local effects" of financing costs on carbon emissions. The estimated coefficient of financing costs on local carbon emissions was still significantly positive, indicating that an increase in financing costs led to an increase in carbon emissions. The regression coefficient of wlnCE was significantly positive, which suggests that regional carbon emissions do have significant spatial dependence. We proposed that the effects of financing costs on carbon emissions will be affected by carbon emissions in surrounding areas. The benchmark regression results actually included the externality of carbon emissions in surrounding areas. This was consistent with the regional aggregation of carbon emissions in the correlation test. In addition, the adjusted R 2 value was greater than that shown in Table 4, indicating that after incorporating the spatial correlation, the model better described the impacts of financing costs on regional carbon emissions.
Columns (3) and (4) in Table 5 report the use of Eq. (8) to test the "spillover effect" of carbon emissions. The results showed that financing costs had a "positive spillover effect" on carbon emissions, such that rising corporate financing costs not only increased local carbon emissions, but also created pressure to reduce emissions in surrounding areas. When the control variables (i.e., time and industry fixed effects) were added into the model, for every 1% increase in financing costs, carbon emissions from the company's location to the surrounding area increased by about 0.0136%. Thus, because it was affected by differences in development  levels and policy regulations in the various regions, the "spillover effect" of financing costs on carbon emissions was slightly smaller than the "local effect."

Robustness tests
As shown in Tables 4 and 5, when we controlled for the industry fixed effects, the regression coefficient of the core explanatory variables decreased, or even decreased significantly; this suggests that the impacts of financing costs on carbon emissions may tend to aggregate within a specific industry. Table 6 shows that the results were still robust when we excluded industries with higher financing costs from the regression. In addition, the significance and coefficient of the variables increased significantly, indicating that there were industry differences in the positive correlation between corporate financing costs and carbon emissions. We also considered whether the spatial weight matrix using geographic proximity might be affected by the number of neighbors-that is, the smaller the number of neighbors, the greater the influence of each neighbor. If there is only one neighbor, even if data are normalized, all of the weights will be assigned to this neighbor. Notably, in the context of our study, the area of the provincial administrative regions in the western region of China is larger than the area of the eastern provincial administrative regions. Using the radius distance spatial weight matrix would therefore result in too many neighbors in the eastern provincial administrative regions and fewer neighbors in the western provincial administrative regions. To account for this factor, we changed the threshold distance to use the K-order adjacent spatial weight matrix and set the number of neighbors to 4 based on the work of scholars who have studied China's provincial administrative regions (Jiang 2016;Li 2018). The regression results (shown in Table 10 in the Appendix) were still robust.

Heterogeneity tests
The decoupling index reflects the differences in the transformation of the economic structures in different regions. Based on the Tapio decoupling index we calculated earlier, we divided the study provinces into two samples: those with weak decoupling and those with expansive coupling. The estimation results in Table 7 show that regions in the state of "weak decoupling" exhibited a stronger positive effect of financing costs on carbon emissions, while regions in the "expansive coupling" sample showed the opposite (and insignificant) effect.
Regions in the "expansive coupling" sample included Inner Mongolia, Ningxia, and Xinjiang. These regions rely more on agriculture, animal husbandry, and other industries for economic development. Their financial markets are not perfect, and their economic growth and carbon emission growth are basically synchronized. Therefore, the impacts of financing costs on carbon emissions were not obvious in this sample. Table 6 Regression results after excluding some industries The values in brackets are standard errors; * , ** , and *** are significant under the conditions of 10%, 5%, and 1%, respectively  Regions in the "weak decoupling" sample had achieved remarkable results in reducing emissions. At the same time, the impacts of financing costs on their local carbon emissions were significant at the 1% level. When their financing costs increased by 1%, the impacts of local carbon emissions increased by 0.017%. Carbon emission spillover to the surrounding areas increased by about 0.0225% under this condition, a growth level higher than that seen in the benchmark regression. Thus, reducing the financing costs of firms in such areas promises to bring about a significant enhancement of the emission reduction effect.

Endogenous analysis
The higher carbon emissions of firms may affect those enterprises' financing costs, though this research mainly considers the endogeneity problem that may be brought about by mutual cause and effect. For example, companies that emit more carbon dioxide may face administrative penalties, including fines. Such fines become part of the company's costs. When information asymmetry is present, investors will reduce their investments in such companies, making it difficult for companies to obtain financing. When selecting the instrumental variables for endogenous treatment, we noted that local governments will support firms' emission reduction actions. If companies are actively seeking to reduce their carbon emissions, the government will tend to view them favorably-and may pass on this positive information to potential financing sources. Thus, having a good reputation can help companies obtain more bank credit and reduce their financing pressure.
Although bank lending does not directly affect local carbon emissions, it is a relatively good exogenous policy tool variable. Table 8 reports the empirical results after controlling for the endogeneity of bank credit at the end of each year. In essence, these data confirmed the robustness of our earlier results.

Discussion
Countries around the world and international social organizations alike have promoted the signing of a number of climate change-related agreements, driving the financial industry to gradually develop financing services to support carbon reduction. So, how will financing costs affect the results of carbon emissions?
First, we found that raising financing costs increases carbon emissions. Enterprises not only represent the demand side of funds, but also serve as the main drivers in green technology development. Financing costs affect corporate behavior, with that behavior reflecting the size of the environmental impacts that green funds can ultimately achieve (MacAskill et al. 2021). If the financing cost of enterprises is appropriately reduced, it will help the enterprises to internalize the costs of carbon emissions, on the one hand, and to obtain more capital investment for their preliminary green projects, on the other hand. Thus, lower financing costs will encourage the enterprises to actively carry out green technology research and development to ensure they can achieve carbon reduction and improve environmental quality (Bolton et al. 2020).
In addition, spatial economics asserts that there is a correlation between the economic geographic behavior of a spatial unit and the behavior of neighboring regions, which incorporates a certain degree of spatial dependence and correlation characteristics. Kang et al. (2016) have suggested that there are obvious spatial spillover effects of carbon emissions in China's provinces, and that ignoring the spatial factors will lead to wrong estimations of this model. Our research is the first to consider the inter-provincial transfer of carbon emissions in the study of the impact of corporate financing costs on regional carbon emissions. Our spatial autocorrelation analysis showed that there is, indeed, an obvious "agglomeration effect" in carbon emissions. Differing from the approach taken in the related literature, we specifically divided the spatial effect into two aspects-the impact on the local area and the impact on the surrounding area-which is similar to the direct effect and the indirect effect proposed by LeSage and Pace (2009). The spatial effect may have a time lag, so we took the time factor into account in the spatial correlation analysis and used a bivariate correlation analysis to fix the one-way effect in the space-time effect. This analysis revealed that raising financing costs increases carbon emissions, both locally and in the surrounding area.
On the one hand, high financing costs have created a threshold effect in regard to carbon emissions (Tamazian et al. 2009), such that only large-scale enterprises can afford the financing risks and use funds for carbon reduction activities. Enterprises that reject high financing costs have small production scales, imperfect supporting facilities, and production activities that are usually accompanied by high carbon emissions. On the other hand, adjustments in carbon emissions based on financial funding need to be matched with adjustments in industrial structure. Only by helping enterprises to promote the development of low-carbon industries can the low-carbon effect of financing be guaranteed (Hammond and Norman 2012).
Our results also suggested that lowering financing costs has a greater effect on local carbon reduction than on carbon reduction in surrounding areas. The scale of the economy, the speed of development, and the intensity of environmental regulation differ for each province, and all of these factors may, in turn, affect carbon emissions. Therefore, local adjustment of financing costs is needed to coordinate and work with other factors to achieve carbon emission targets. However, most of the surrounding areas are only affected by carbon emission spillover, so the degree of impact is small.
Finally, we relied on the "decoupling" indicator to measure the relative speed of economic development and carbon emissions. Our findings indicated that the difference in "decoupling" between provinces had increased over time. Most provinces switched from "weak decoupling" or "expansive coupling" to "weak decoupling" over the study period, a result consistent with Gao et al. (2021). Unlike similar studies, our research included a regression of samples based on different "decoupling" states, with the results showing that it is more effective to carry out carbon reduction activities by reducing corporate financing costs in areas with obvious "decoupling." This conclusion is consistent with the actual development of China's economy. On the one hand, China's provincial-level regions have large differences in area and population; on the other hand, due to the slow industrialization process of the less-developed provinces in western China, carbon emissions are relatively low there. By comparison, the eastern provinces have geographic advantages and have realized dividends from the national carbon reduction policy, and their economic development started earlier, resulting in a large amount of carbon emissions during the development process. In these provinces, firms tend to find it more beneficial to carry out targeted carbon reduction activities (Hu et al. 2017).

Conclusions
Across the world, shocks such as global warming, environmental pollution, and energy consumption ultimately affect all financial market participants and individual investors (Sharif et al. 2020). Corporate financing behavior in financial markets is also closely related to regional carbon emissions. This study used data from Chinese listed companies to refine the research on carbon emissions on the microlevel, established a panel fixed effect model and a spatial lag regression model, and empirically analyzed the impacts of corporate financing costs on regional carbon emissions. The results yielded three important lessons.
First, an increase in corporate financing costs will increase regional carbon emissions. Firm age, firm scale, asset structure at the firm level, economic development level, economic structure, foreign direct investment level, population density, environmental climate, population quality, and other factors at the regional level have significant effects on regional carbon emissions at the statistical level.
Second, after incorporating the spatial factor, it appears that the effects of corporate financing costs on carbon emissions in the local region are subject to the "spillover" of carbon emissions in the surrounding areas (local effect), and an increase in carbon emissions in the local region will also "spillover" to the surrounding areas (spillover effect). The role of the "local effect" is greater than that of the "spillover effect." Third, the "local effects" and "spillover effects" in "weak decoupling" regions are significantly greater than those in "expansive coupling" regions. In other words, reducing the financing costs of firms in "weak decoupling" regions can achieve more significant carbon reduction outcomes.

Policy implications
Based on the preceding conclusions, the following suggestions are put forward. First, to achieve carbon reduction goals, it is important to reduce financing costs for firms that seek to carry out low-carbon activities. It is also recommended to improve the adaptability of corporate financing and corporate low-carbon practices. Vigorously reducing the financing costs of firms, especially by providing more complete financing channels for firms that carry out environmental governance, pollution reduction, and carbon reduction efforts, and effectively dealing with problems such as information asymmetry in the financial trading market will enhance the likelihood of reaching the desired emission levels.
Second, governments and enterprises need to build a spatial linkage mechanism that supports regional carbon reduction. Areas with serious carbon emissions should effectively cut off the sources of carbon emissions based on traceability analyses, while simultaneously aiming to avoid asymmetry between carbon emission rights and carbon reduction responsibilities. The significant inter-provincial transfer of carbon emissions highlights that achieving carbon reduction goals will require multiregional coordination, and specific carbon reduction targets should be formulated according to the economic development status of different regions.
Finally, measures to reduce regional carbon emissions by reducing corporate financing costs should be implemented mainly in "weak decoupling" regions. Our empirical analysis results indicate that reducing the financing costs of firms in "weak decoupling" areas can effectively avoid hindering the economic growth of firms that undertake carbon reduction efforts while still reducing overall carbon emissions. Therefore, reducing financing costs in "weak decoupling" regions can achieve a win-win goal-reducing carbon emissions while still supporting economic growth.

Limitations
This study, like all research, has some shortcomings. First, the impact of the COVID-19 pandemic on the study's conclusions was not considered. The pandemic has had a huge impact not just on the global economy, but also on financial market activities (Sharif et al. 2020). Measuring global economic policy uncertainty showed that these perceived uncertainties may affect consumption and investment, thereby reducing the overall scale of economic activity (Işık et al. 2020). This may have some influence on the conclusions of this study. Of course, the publication of data takes time, and relevant data for the pandemic period were not available during the research phase of the study. Moreover, if such data had been available and were combined with the annual data for non-pandemic years, it would inevitably lead to biased estimates. Thus, follow-up studies should consider updating the content of the data and adopt causal identification methods such as differences-indifferences (DID) analysis to eliminate the impacts of the pandemic and other factors before conducting research.
In addition, we constructed the spatial weight matrix only from the perspective of geographic proximity. In reality, the correlation between regions has complex associations. Future research might consider constructing a spatial weight matrix based on economic distance and other aspects-that is, assigning greater weights to spatial units with similar levels of economic development-so as to more accurately describe the relationship between spatial units.
Author contribution Yubo Zhao contributed to conceptualization, supervision, and writing-review and editing. Shijing Zhu was involved in data collection, data processing, methodology, and writing. Gui Zhang helped in supervision and resources.

Data availability
The data used to support the findings of this paper are available from the corresponding author upon reasonable request.

Declarations
Ethical approval Not applicable.


ICT in Agriculture: Creating SMART Farmers

Agriculture is the backbone of any country and India is blessed to have agriculture as the main occupation of a large population. The varied geographical terrain of India provides an opportunity for year long production of crops. With the onset of technical revolution in all the areas of life, all over the world, agriculture is not untouched. The developments in ICT has revolutionized agricultural operations many folds. Be it the meteorological information, soil health, seed health, fertilizer application or even the insect attack on the crops, all are being regulated by the ICT applications in one form or other. Our today’s farmer is well informed about the use of new technologies in agriculture and is very efficiently utilizing the information in an intelligent way. All these are irrespective of the region, season, crop, place or the location. The use of Information Technology has made our farmers SMART, i.e., they are Self Monitoring, Analyzing and Reporting through the use of adequate Technology. The use of proper IT tools has given both the scientists and farmers a suitable platform to interact more frequently and on time. The scientists are using ICT tools to reach the farmers on their fields and our farmers has brought their knowledge to the labs for further growth and development in the field of agriculture. The present paper is a review on the current ICT applications which is making our farmers SMARTER and self reliant. There are many initiatives of government and private organizations to bring our farmers closer to the technologies developed for their benefit. The current paper is an attempt to visualize the efforts made by scientists and technologists in the field of information and Technology for the benefit of farmers and towards the end it conceptualizes the application of ICT and its use by our farmers.

Introduction
Timely and reliable information related to agriculture acts as a magic for agriculture and farmers. There are many telecom devices and services for supporting our farmers today. Computers, mobile phones, television are a few of them. Rapid growth in the field of information and technology has initiated a revolution in the field of agriculture also.
Instant communication, swift exchange of information as well as the ease of adoption has made ICT tools 'must' for agriculture development.
Globalization of agriculture and related products, bumper production and demand of produce has widened the spectrum of agriculture. Today agriculture is not limited only to production and practices of crops but it also includes quality processing, packaging, marketing and even the exports. It not includes only the large land holders but the marginal and small farmers are also a part of it. ICT has brought them together on one platform and they are collectively contributing towards the development of the country.

Digital Revolution in India and Agriculture
Computers, World Wide Web, pagers, cellular phones, satellite networks and many more introduced and boosted digital revolution all over the world. Digital revolution in India is dated around 1980's when computers were introduced and with the launch of internet and satellite communication the whole system welcomed digital revolution and got involved. Computer education was introduced in school and university education, digitization of banks, transport, laboratories and more, marked the revolution. Use of television, radios for broadcast, telephones for communication were all revolutionized and the whole world got 'linked' in one way or other.

ICT Initiatives in India
The introduction of Information and Communication Technology tools revolutionized the Indian economy at a faster pace and there was a steep rise in the exchange of thoughts, ideas and techniques. Although ICT tools were not new to any community all over the world and the exchanges took place through telephones, telegraphs and other modes of communication, however introduction of satellite communication and internet brought the wide spread community much closer at a faster pace. The traditional agriculture has been reformed and revolutionized with the use of digital technology and it has definitely changed the scenario of Indian agriculture making it more sustainable and profitable. 1 The technology has proved to be beneficial in disseminating right information, at the right time which stands helpful for farmers in choosing the farming operations at the appropriate time.
Many International and National agencies, Departments, organizations, institutes are involved in collection, evaluation and processing of data logically through electronic modes. The speedy analysis of data, logical evaluation and effective dissemination of information at the right place and time has benefitted farmers in controlling diseases, evaluating cropping systems, processing and marketing of their crops. 2 The technology is assisting our farmers in judging the health of soil, suitable selection of crops, time of sowing and harvesting including many other on-farm operations like irrigation, insect-pest control etc. ICT tools are helpful in spreading the information on weather conditions, disease outbreaks, swarm and locust issues and many more which makes the farmers alert and aware before hand.
ICT has three major roles to play viz., Education, Awareness and Dissemination. It very efficiently covers all aspects of a farmers' life. Crops, livestock and poultry, health and nutrition related issues of family members, all are very conveniently covered by ICT.

Education
Varied type of ICT tools including computers, mobile phones, television, radio etc can be used to educate the community through films, stories, discussions, e-books, e-messages and many more. These tools can be used to spread the information amongst the related community on symptoms of diseases, insect-pest infestation, processing and preservation operations, fertilizer applications, irrigation tools, storage techniques and some aspects related to livestock and poultry operations. This information will make the farmers educated on various aspects and will make him ready to deal with such problems before hand.

Awareness
Various ICT tools are helpful in creating awareness amongst farmers on different aspects like health issues of their livestock and birds, availability of suitable seed varieties, soil conditions, extreme weather conditions, expected outbreaks and its control, processing and preservation operations, marketing opportunities and many more. An alert and aware farmer is capable to taking timely decisions and this will help him to reap his profit.

Dissemination
Proper selection of ICT tool for disseminating information will help in spreading the wise words amongst the community at a faster pace in a short time. This could be helpful in controlling insectpest, diseases, problems like water-logging, floods, drought etc. A prior spread of information on healthhygiene of livestock, availability of new varieties, seeds centers, fertilizers etc will help farmers to manage their crops and livestock in better way and keep them ready for the forth coming issues.

1.
These can be best tools for disseminating agriculture related information on a wider front in a short time 2.
As an awareness and education tool 3.
As an alerting tool 4.
For creating online farmer groups to carry out discussions and other exchange of information 5.
For generating real time pricing and marketing information 6.
For popularizing Government schemes and programmers 7.
As a tool to support agri-clinics and agri-finance systems 8.
As a tool for connecting to agri business units and outlets 9.
For providing real time information on new technologies on insect-pest control, irrigation and other related practices 10.
As a tool for one to one contact of farmers and scientists or experts, all over the world, for success stories.

ICT Initiatives for Farmers
ICT has been able to support farmers by giving them exposure to exchange their experiences, practices, doubts and ideas using electronic medium. 3 Simple agriculture has now been transformed to e-Agriculture and that too is not only limited to rich or large land holders but it has entered the households of small, marginal and poor farmers as well. Many agriculture specific applications are targeting small holders with major two objectives: 1.
Empowering small and marginal stakeholders with assets and services to enhance their productivity and incomes and to improve their livelihoods by ensuring food security.

2.
To exploit all the possibilities of ICT to match the rapidly changing global markets.
ICT is a boon to both public and private sector players who are continuously working towards finding out effective solutions to address both the long term and short term challenges being faced by farmers. 4 Public and private sector actors have long been searching for effective solutions to address both the long-and short-term challenges in agriculture, including how to answer the abundant information needs of farmers. ICT is one of these solutions, and has recently unleashed incredible potential to improve agriculture in developing countries specifically

Some of the initiatives of farmers' interest include: Crop Specific Applications
Some of the mobile and computer based applications for farmers dealing in specific crops include (icar.gov.in):

Ikshu Kedar
Application developed by IISR Lucknow, is a beautifully designed app to support sugarcane farmers. The app suggests the date of irrigation in sugarcane crops as per prevailing environmental conditions. Also the app suggests certain precautions and other related advisories for different types of soils that otherwise affects the sugarcane crops.

Farm Tree
Developed by ICAR-CAFRI, Jhansi, Uttar Pradesh, this is one of the beautifully designed and technically sound mobile app. It not only supports the tree growing farmers but is also knowledgeable for the use by scientists, students and other professionals. It is a well decorated app with all essential technical details of planting a nursery to potential utilization of produce received from a tree.
There are some other apps for specific crops like cashew, banana, cotton, tobacco, various fruit crops including mango, sapota, herbs of different kinds and even the flowers like orchids, tubrose etc are helpful for farmers. Some of these are also available in their own regional language.

Livestock Specific Applications
Some of the computer based or mobile based apps are designed specifically for livestock care and maintenance. To name a few from ICAR organization includes; Buffalo Nutrition, BHealth and others.
Other animals covered include cattle, sheep, goat, pig, poultry and fish. Some of these apps are available in both Hindi and English language. These apps have vaccination schedule, disease symptoms with diagnosis and treatment, gestation calendar, rationing tips and suggestions. Also, the processing, marketing and food safety concerns are an essential part of some of these applications

E-Learning Applications
Having knowledge and learning more is essential for continuous growth and development. Some of the fully devoted portals and applications are also designed and made available for farmers who want to learn and explore more and more opportunities in their traditional agricultural practices.

E-Krishisiksha
is one such portal devoted to e-learning. The portal has lots and lots of e-contents for training and learning through reading. Farmers can explore new opportunities in the guidance of experts and the e-content on various topics supports their queries from time to time which can be accessed any where any time.
Krishi a fully devoted knowledge based research information system for innovation in agriculture. It is a type of repository of ICAR research data for knowledge management E-Krishimanch is a query management system which is like a scientist-public interface. Here farmers can directly to the subject experts and get their queries solved at the earliest.
Similar types of apps like Kisan Mitra are also available in Gujrati language and Krishi Gyan is also a regional language app.
Some of the apps for the benefit of farmers are available on the portal of Department of Agriculture and Cooperation and Farmers Welfare, Ministry of Agriculture and Farmers welfare, GoI. These include; Kisan Suvidha deals with all types of issues of farmers and farming community.
Pusakrishi is a helpful app to promote agri-business ventures including commercialization of technology and the market ready technology.

M-Kisan
shares advisories by expert which are both season and crop specific. Also it is a platform for sharing programme launched by Government for the benefit of farmers. It is a SMS based app and constantly updates the farmers.

Kisan Call Centre (Kcc)
It is a telephone based app. Experts from different fields respond to the queries of farmers on telephone.
Shetkari Masik Android App is a type of monthly magazine in digital form. It contains articles, advisories and related information from the experts for the farmers. Being a monthly circular it is convenient for farmers to keep themselves updated with the latest development in the field of agriculture.

Farm-O-Pedia
is also a digital information portal. It has lots of information for our farmers on package and p r a c t i c e s o n a l m o s t a l l t y p e s o f c r o p s , weather conditions, soil health, animal health, food processing, storage practices and many more.

Bhuvan Hailstorm App
is specifically designed to alert farmers in the areas of extreme weather conditions. It alters farmers on expected hailstorm conditions. Also the app is specifically designed to ascertain the losses incurred by farmers due to these bad weather conditions. It has an inbuilt GPS and camera system which locates the field of farmers and clicks photo graphs. This data is immediately transferred to the portal for further analysis and can be used for claims.

Agri Market
is a synonym to its name and is helpful for farmers in selling their produce at MSP's directly. The portal continuously flashes the current prices of the crops.
The farmer can directly approach the nearest market using the GPS locator and sell his produce.
Some of the private firms, non-government organizations, civil society organizations, research groups are also working for farmers and making them more techno-friendly and smart by innovating specific apps, viz; There are many more applications and portals for the benefit of farmers. Some of them are in regional languages

Creating SMART Farmers
Traditionally, Indian farming was based upon the indigenous knowledge our farmers had from their forefathers and other fellow farmers. However those who revolutionized farming followed advice of their friends, input dealers, visitors and others which were sometimes not as successful as it had to be. With the advancement in science and technology some of the practices in traditional agriculture improved and our farmers adapted it beforehand. But still the output was not at par. With the introduction of ICT tools the communication and dissemination of information moved at a faster pace and the developments in the field of science and technology were also geared up. The information related to agricultural practices reached our farmers directly from the experts in the field.
Introduction of in-hand ICT tools including mobiles, smart phones, computers made our farmers SMART, i.e., they are Self Monitoring, Analyzing and Reporting through the use of adequate Technology. 5 They are now able to decide on the cropping pattern, seed selection, application of fertilizers, insect pest and disease management, processing, marketing etc, With the timely dissemination of information related to agriculture they can Self Monitor their crops, they are able to Analyze cropping conditions including soil health, weather conditions, water availability and more and Report the results using suitable Technology. Farmers have become self reliant and informed. ICT tools have brought laboratories to the farmers' field and today a real time data can be assessed to modify the cropping pattern inorder to enhance the output. Adaptation of techniques related to Precision farming, micro-irrigation, fertilizer application, soil health, seed health, livestock, integrated farming practices and more, today's farmer is smart enough to deal with it. ICT applications have generated authentic database on weather forecast, soil health, crop cultivation practices, processing, marketing, storage and many more to help our farmers. 6

Conclusion
Agriculture is the backbone of Indian economy and needs to stay updated with new technologies from time to time. ICT tools have proved to be very helpful in updating the data base and disseminating the related information to our farmers. They have empowered our farmers by providing right information at the right time to the right person. It has reduced the gap between the learned scientific community and the traditional farmers. Today they are working in coordination with each other by using appropriate ICT technologies and achieving the growth targets at a faster pace.

Acknowledgement
Author is thankful to Jawaharlal Nehru Krishi Vishwa Vidyalaya, Jabalpur and Bhabha University, Bhopal for helping in conceptualizing and presenting the work during the International conference on 'Emerging Trends in Multi Disciplinary Research' during August, 2021.

Funding
The author(s) received no financial support for the research, authorship, and/or publication of this article.

Conflict of Interest
There is no conflict of interest with this manuscript.


Research on Longevity Risk and Its Relevant Issues

. China entered an aging society as early as 1999. With the constant improvement of death rate increasing average life expectancy and rapid decline of fertility rate, the aging problem is more and more serious, and the longevity risk in China’s pension system is increasingly emerging. This inevitably brings new challenges for insurance companies, pension fund and government. Therefore,many scholars at home and abroad carry out diverse research on issues caused by longevity risk, mainly including mortality prediction model and longevity risk measurement. The paper analyzed the longevity risk from the aspect of its identification, measurement and management, and preliminarily explored the financial derivatives and the management strategies to defuse longevity risk in order to offer relevant experience reference for further studies.

Introduction
With the rapid development of economic society and continuous improvement of medical technology and people's health consciousness, the death rate has dropped significantly and the birth rate continued to fall, which leads to increasing aging population and the decline of fertility and death rate. What's worse, the adjustment and configuration of resources may generate a series of macroeconomic effect and inevitably bring aging problem including higher social security payments for the elderly, the decline of working-age population, shortage of labor supply, increasing labor costs and so on, which will affect the long-term development of China's economy.
Increasing life expectancy has become a common phenomenon around the world. According to the National Bureau of Statistics, the average life expectancy of Chinese people rose from 67.8 years in 1981 to 76.7 years in 2017, an increasing of 10 years in less than 40 years. Over the long term, human life expectancy has been steadily rising and the longevity risk brought by it cannot be ignored. Longevity risk makes a profound influence on insurance industry, pension system and social security system in all countries: longevity risk makes the balance of payments of pension security system unsustainable under the background of high fertility and low life, brings heavy financial burden for government, and makes the social security fund face a huge gap that will have a negative effect on the development and improvement of social security. Therefore, studies on longevity risk have been paid more and more attention at home and abroad. Blake and Burrows (2001) creatively proposed that survival bonds could be used to avoid longevity risk. Subsequently, in order to further measure longevity risk, many related researchers conducted studies from the prediction model of mortality and pricing method of longevity risk. At present, how to deal with and control longevity risk in the future, not only to solve the government's solvency dilemma, but also to promote economic growth, is also a problem that needs to be considered thoroughly. This paper reviews the existing studies on longevity risk and its related issues in order to provide references and suggestions for further research.

The Concept of Longevity Risk
Longevity risk means that the average actual life expectancy of the population in the future is higher than the expected life expectancy. It is caused by the uncertainty of the long-term trend of mortality. According to the existing foreign research literature, longevity risk is usually understood from individual and overall levels (MacMinn, Brockett and Blake, 2006;Stallard, 2006). Longevity risk at the individual level refers to the possibility that an individual's actual life expectancy in the future may be higher than that of currently expected, which leads to a gap in income and expenditure as a result of inadequate financial provision for retirement. Individual longevity risk can be dispersed, which can be managed through participating in endowment insurance plans and purchasing annuity products. Longevity risk at whole level usually refers to the fact that the actual future payment of an insurance plan, such as the pension annuity insurance plan of an insurance company, the social insurance plan of the government and the pension insurance plan of an enterprise, may be higher than the predicted payment based on the current estimate of the future average life expectancy. Such aggregated longevity risk cannot be dispersed according to the law of large numbers and shows systemic risk characteristics (Milevsky, Promislow and Young, 2006; Cairans, Blake and Dowd, 2006b). Mikaelson and Mulholland (2014) estimate the potential scale of the global longevity risk market for pension liabilities is between $60 trillion and $80 trillion. Pigott & Walker (2016) also estimates longevity risk in the private sector is around $30 trillion.
Many authors have proposed models to assess and hedge longevity risk and its impact on pension funds or life insurance. Antolin (2007) (2019) proposed a random mortality model with age-related drift and volatility, and they derived an analytical formula for the price of longevity derivatives. Hari and other people (2008) analyzed the importance of longevity risk to the solvency of pension annuity portfolios and distinguished two types of death risk: micro longevity risk which quantifies the risk associated with uncertainty about the time of death, while macro long-term longevity risk which is due to uncertain future survival probability.

The Measurement and Pricing of Longevity Risk
The measurement of longevity firstly cannot succeed without the prediction of mortality. Stallard (2006) pointed out that existing population data and mortality models have provided necessary conditions for the prediction of mortality, so that longevity risk can be quantified. Therefore, how to accurately estimate future mortality or survival rate is the key to longevity risk measurement and the basis of longevity risk management.

The Prediction of Mortality
Mortality models have a long history. Since Nepertz published his law of mortality in 1825, various mortality models have been proposed and introduced. Most mortality prediction methods are extrapolative, taking advantage of the common regularity in age patterns and trends over time. This method includes inference from traditional and relatively simple synthetic measurements, such as the Lee-Carter method. Lee and Carter (1992) first applied the stochastic discrete model to estimate life expectancy. This model is not only simple and easy to use, but also can obtain relatively accurate mortality and population prediction data. However, it is a single-factor model, which does not consider the birth year effect that may lead to inaccurate fitting of historical data. In addition, the original Lee-Carter model lacks smoothness in estimating the age effectβx. Therefore, many subsequent researches have improved the Lee-Carter model to solve these problems. Renshaw& Neuil (2010) also studied and extended the continuous random model. In addition, if a mortality prediction method (CMI) using penalty Splines (P-splines) is popular in the UK, and this model can obtain a high overall fitting degree, so that it has been proved to be effective. Hyndman and Ullah proposed a Functional Demographic Model in 2007, which predicted mortality rate by age based on functional data analysis and non-parametric smoothing and steady statistics.

Pricing Methods of Relevant Derivative Products
Due to the incomplete market and unreliable mortality data, longevity risk and related derivatives can not be priced by using non-arbitrage analysis method that we usually use. According to existing literature, following pricing methods are mainly used for longevity risk:

Wang Transformation
In 1991, Venter proposed the method of Distortion of Distribution, that is, risk is priced by the losing distortion of distribution. In 2000 and 2002, Wang applied the distortion of distribution method to the pricing of financial and insurance risk respectively, and proposed a new transformation method, where normal distribution and T-distribution are used to replace the above transformation function, namely single-factor and two-factor Wang transformation. Compared with CAPM model and Black-Scholes share option pricing formula, it is concluded that Wang transformation can copy CAPM model and Black-Scholes share option pricing formula. Lin and Cox (2005) first used Wang transformation to price survival bonds and obtained the market price of longevity risk. Cox, Lin and Wang (2006) studied the pricing of survival bonds and death risks issued by Swiss insurance company and showed that this method could be applied to the pricing of mortality index derivative securities.

The approach of Risk-Neutral
According to the theory of financial economics, in an incomplete securities market, assuming that there is no arbitrage opportunity, there is at least one risk measure that can be used to determine the fair price of securities, which is called risk-neutral measure Q, and it corresponds to the actual probability measure P. Milevskyand Promislow (2001) used the risk-neutral assessment method to price q forward contracts and believed that as long as an appropriate risk-neutral measure was selected, parameters such as mortality model jump and risk market price could be obtained, so that q forward contracts could be priced. In 2015, Yang et al considered parameter error, process error and model error from an overall perspective through modified semi-parametric re-sampling method, and found that model selection has an important impact on risk-neutral assessment.

Instantaneous Sharpe Ratio
This method was firstly proposed by Milevsky, Promislow and Young (2005), assuming that the party holding non-dispersible longevity risk needs to get risk premium return, then the party has multiple (instantaneous Sharpe ratio) standard deviation combinations, the risks of small samples have been dispersed, and the standard deviation is derived from an assumed mortality changing process. Additional studies include Young (2008) and Bayraktar et al (2009). The Sharpe ratio (SR) is the most important parameter in this method and represents the risk premium required to assume an asset. In contrast to the Wang transformation, the Sharpe ratio is a pre-set exogenous parameter, while the risk market price is an endogenous variable derived by calculating the market annuity price.

Other methods
Chen et al studied the stability of the above three kinds of longevity risk pricing method in 2010, and compared the relationship and difference of the three methods through the theoretical analysis and mathematical reasoning. It shows that that the smaller the sensitivity absolute value is, the steadier the method is. Risk-neutral evaluation and sharp rate method are beneficial to the operation of shortterm bonds, and Wang transformation method is more suitable for long-term bonds. After comparative analysis of Wang transformation and risk-neutral assessment method, Li proposed to use maximum entropy method as an alternative method to price mortality linked securities, and believed that the advantage of this method is that it doesn't require any subjective judgment of users. In

Financial products design based on Longevity risk
Besides the traditional risk retention, reinsurance and annuity methods to disperse the risk, longevity risk can also be securitized and transferred to the capital market. Longevity risk securitization refers to the construction and issuance of financial products and derivatives connected with longevity risk through the capital market, and the product income is linked with mortality or survival rate. The risk of both sides achieves the segmentation and standardized of risk by means of securitization, and the longevity risk is transferred to the capital market. Compared with traditional longevity risk, longevity risk securitization does not only provide additional market capacity, sufficient liquidity and transparency, but also bring price discovery and information asymmetry decline. The more participants there are in the capital market, the more risk will be spread and it is easier to manage risk. The existing securities related to longevity risk generally include longevity bond, longevity swap, longevity option, longevity futures, Q forward and so on.

Longevity bonds (LBs)
Longevity bonds (LBs) are bonds that coupons or principal are linked to the survival probability of a specified group of people. The longevity risk of pension funds or annuity insurance companies is transferred to investors in the capital market, so as to achieve the purpose of dispersing the risk. In November 2004, the European Investment Bank (EIB) issued an EIB longevity bond with an amount of 540 million pound, which was the first continuous longevity bond. However, because this longevity risk didn't attract enough investors, it eventually failed to issue in the market. Blake et al. (2006) and Biffis and Blake (2009) discussed in depth the issuance arrangement and the reasons for the failure, and summarized that EIB longevity bonds cannot fully hedge the longevity risk faced by pension funds for a long time, cannot cover the longevity risk of different ages and genders, and the high threshold of bond investment can't attract enough investors to buy.

Longevity swaps
Longevity swaps are financial derivatives based on the future survival index of specific target groups. The original theoretical exploration of longevity risk swap contract began with Lin and Cox (2005).Then Dowd and others proposed vanilla survivor swaps in (2006). If one party trades fixed cash flows for floating cash flows of the other, it is commonly known as a longevity swap.
Compared with Longevity bonds, Longevity swap has the advantages of low issuance cost, high clause flexibility and easy hedging. Therefore, its prospect of market development is better than that of longevity bonds. The world's first capital market-based longevity swap took place in July 2008. It was conducted by J.P. Morgan and Canada life in the UK (transaction risk, 2008). Longevity risk was transferred from Canada life to J.P. Morgan and then directly transferred to investors. This transaction brought investors in the capital market into the longevity market for the first time. Barrieu and Albertini (2009) elaborated longevity risk and J. P. Morgan's longevity risk transaction.

Longevity futures, options
Longevity future is a standardized contract of the object closely related to mortality. According to the different objects, it can be divided into annuity futures, longevity bond futures and survival index futures. Among them, the futures market of longevity bonds shows high price transparency, strong volatility, and strong demand for hedging and speculation.
The same or similar underlying assets as longevity options can be chosen as longevity futures. Annuity insurance companies obtain the right to buy and sell basic assets at a certain price in the future by paying option fees. There is a non-linear relationship between option return and the price or index change of underlying assets, which can effectively manage the adverse impact in changes of contract underlying assets after the purchase of options. Futures are usually standardized contracts, and the contract form of options is flexible. Blake, Cairns and Dowd(2006) preliminarily studied the longevity futures and options.

Q-forward
Q forward is a simple capital market tool used by pension funds and insurance companies to hedge longevity risk and death risk. It is a forward agreement based on the life metrics mortality index compiled and released by J. P. Morgan. Both parties agree to exchange the contract for calculating cash flow based on the actual (floating) mortality and agreed (fixed) mortality of a specific population at a certain point in the future, and replace the uncertain future real mortality with the determined current expected mortality. Annuity insurance company and J.P. Morgan are the payers of actual floating mortality and expected fixed mortality respectively. The expected fixed mortality rate can be calculated according to the mortality time series model when the Q forward contract is signed, and the actual floating mortality rate is determined by actual life metrics mortality index when the contract expires. At maturity, only one party pays the net cash amount according to the relative level of expected fixed mortality and actual floating mortality. If longevity risk occurs, the actual mortality on the maturity date of the Q forward contract is lower than the fixed mortality, and the annuity insurance company obtains net cash inflow, so it can make up its operating loss caused by paying too much annuity (Coughlan et al., 2007). Q forward contract has good flexibility. Annuity insurance companies can dynamically adjust the degree and direction of hedging transactions according to new information, so it can also be used as an important basic component of other longevity risk financial derivatives, which helps to improve the liquidity of longevity risk market (Biffis and Blake, 2009; Deng et al., 2012).

Macroeconomic effects of longevity risk
Macroeconomic impacts caused by longevity are major practical problems in current economic development. While benefited from a long life, individuals and society also need to seriously consider how to reasonably adjust and allocate the economic resources caused by longevity, which will produce a series of macroeconomic effects.
First of all, the extension of life cycle makes people face a longer period of old age, and there may be a risk of insufficient pension resources. However, rational actors have the ability to coordinate life cycle resources. They will fully consider the impact of the extension of life expectancy, and adjust their life cycle behaviors such as consumption, savings and retirement accordingly. This will affect the accumulation of material capital, labor supply and employment, thus affecting macroeconomic growth. Secondly, the extension of life expectancy also means that individuals can prolong their years of education, so as to enjoy the high returns of human capital investment in the future, but at the same time, they also have to pay more investment costs, which will change the educational investment behavior of families and individuals, thus affecting the accumulation of human capital. Thirdly, the impact of longevity risk will also make the payment balance of the old-age security system established under the background of high fertility and low life difficult to sustain, which will bring a heavy financial burden on the government. The social security fund may face a huge gap, which will have an adverse impact on the development and improvement of social security.
Life extension will also have an important impact on pension revenue, expenditure and the safe operation of the pension security system. According to various existing estimates, under the impact of longevity risk, the gap between pension revenue and expenditure will continue to expand. Sin (2005) believes that China's social security pooling account has been unable to make ends meet, and there will be a deficit in the social security individual account from 2032 to 2050. The dual payment pressure of individual account and pooling account exist in the pension system. The reform of pension security system to deal with longevity risk has also attracted much attention. At present, a large number of studies mainly focus on the economic effect or economic efficiency of pay as you go system and fund accumulation system. Samuelson (1958), diamond (1965), Aaron (1966) and others believed that the introduction of pay as you go pension insurance system can improve the level of social welfare. Feldstein (1985), Alba & Kotlikov (1987), Kotlikoff (1996), Lassila & Valkonen (2001) and other scholars analyzed the macroeconomic effects and welfare level of the fund accumulation system, argued that the fund accumulation system could solve the shortage of the pay as you go system, and suggested reforming the old-age insurance system. Some scholars also suggested that China is more suitable for the partial fund accumulation system -"combination of unified accounts". For example, Liu Zunyi (2003) proposed that China should design an old-age security system combining social basic pension and individual account accumulation; Williamson & Deitelaum (2005) believed that China's "unified account combined" pension insurance is a correct direction of reform, but it will be restricted by regional segmentation, income gap and system. Considering the reform of old-age insurance in dealing with the risk of longevity, although the existing literature has conducted various and multi angle research on China's old-age insurance system, the opinions of scholars are still controversial. The reform of the old-age security system should absorb the advantages of the old-age insurance system with accumulation function and the old-age security system with redistribution function at the same time, which can not only solve the government's payment dilemma, but also promote economic growth and take into account social equity, which is the focus of researchers and the basis of system design. The reform of China's oldage security system should also follow these basic principles.

Policy suggestions to deal with longevity risk
At present, the academic community has made some achievements in the understanding, estimation and management of longevity risk, but at the same time, we should see that there are many deficiencies in the research of longevity risk. For example, although various and multi-angle research has been conducted on China's old-age insurance system, the opinion of scholars are still controversial. In view of the relatively rough statistical data of population death in China, it is urgent to improve the existing mortality modeling methods to obtain accurate prediction data. In addition, the research on longevity risk securitization is still in the stage of introducing overseas theoretical development trends and practical experience, and there is a lack of in-depth research on China's securitization.
Longevity bonds have failed to be issued many times, and the advantage of transferring longevity risk through capital market management tools is not apparent.
In the face of the increasingly serious risk of longevity, all parties need to improve their understanding. First, relevant government agencies need to strengthen the financial knowledge to educate people, gradually recognize the existence of longevity risk, study the longevity risk existed in various risk subjects as soon as possible and formulate countermeasures. In addition, the government should provide financial and legal support for insurance companies to build longevity risk asset securitization products and develop longevity risk capital market. Second, the banking and insurance regulatory authorities should pay attention to the significant impact of longevity risk on the solvency of the overall insurance industry, clarify the products and departments that is involved in longevity risk in the insurance industry, measure the corresponding risk degree, and formulate reasonable longevity risk solvency capital indicators. At the same time, regulatory authorities also need to formulate a long-term mechanism for longevity risk supervision, improve the supervision system, speed up the revision of actuarial methods, and reduce the risk losses caused by unreasonable actuarial methods. Third, insurance companies need to actively develop corresponding products to create market demand and attract investors. The insurance industry and government pension institutions need to strengthen cooperation, including longevity risk identification, data sharing, mortality prediction and risk management. Only with the joint cooperation of all stakeholders can the increasingly serious longevity risk be alleviated and solved. Fourth, for individuals, Chinese people need to study more financial management knowledge, understand the longevity risk, allocate their personal assets reasonably, and manage their longevity risk by purchasing financial derivatives of longevity risk.
To make a long story short, How to effectively manage this new and increasingly serious social risk still has a long way to go. Although China's longevity risk management faces problems such as insufficient understanding of longevity risk, lack of data, difficulty in estimation of mortality, fuzzy insurance supervision and single risk management mode, if all parties related, including the government, insurance companies, individuals and other relevant departments work together to solve the existing problems, the increasingly serious longevity risk is expected to be effectively managed.