Based on the financial data for Chinese A-share companies listed in the Shanghai and Shenzhen stock exchanges and the corporate social responsibility (CSR) score data published in the Hexun website‡from 2010 to 2019, we carried out an empirical study and found that CSR fulfilment helps to restrain debt risk faced by firms, and that product-market competition can promote the inhibitory effect of CSR fulfilment on debt risk. The further study found that CSR fulfilment of monetary capital layer and human capital layer on debt risk will be significantly stronger than that of social capital layer.
China’s rapid economic growth over the past 40 years has brought about remarkable results, not least in making it one of the fastest growing economies among the countries of the world. In the past, China’s economic growth was achieved by relying on the high household savings rate and the high investment growth rate, and all this was due to the high debt operation. Also, in recent years, China’s debt risk has been exposed due to a series of changes in the macroeconomic environment, for example, the disappearance of demographic bonus, the slowdown of economic growth rate, overcapacity, financial crises and so on; further, default events such as city investment debt and China Aviation Oil have also emerged in quick succession, resulting in an adverse impact on the debt risk. Unless stringent precautionary measures are implemented, the debt risk will be released in a short time, which is likely to evolve into a systemic financial risk and harm the real economy of China. Therefore, scientific management and control of corporate debt risk is not only conducive to the long-term development of firms but also helps to build a barrier to prevent and resolve major financial systemic risks at the micro level; further, it has become a matter of consensus among all sectors of society that this scientific approach is imperatively necessary given the incumbent position of debt risk in China. Most of the existing studies in the literature investigate the causes of corporate debt risk based on three factors: corporate characteristics, internal corporate governance and external macro environment. The fulfilment of corporate social responsibility (CSR) helps to enhance corporate reputation, obtain the support of stakeholders and gain competitive advantage in the fierce product-market competition. It has a positive impact on corporate profitability and cash flow, and ultimately affects the debt risk faced by firms. However, few scholars have conducted in-depth research on the relationship between CSR and debt risk based on the Chinese background. With the advent of the ‘new normal’, the degree of industry competition and the firm behaviour in China’s product market show new characteristics. The fierce market competition has greatly affected companies’ internal financing ability and profit space. In order to obtain external funds at lower cost, managers must release more signals to the market to alleviate the information asymmetry with stakeholders, and establish a good social image and market image for firms through the fulfilment of CSR [1]. The impact of degree of competition in the product market on the relationship between CSR fulfilment and debt risk is worthy of further exploration.
The possible marginal contributions of this paper are as follows. First, it helps managers to further identify the influencing factors of debt default risk, and enriches the literature research in the field of CSR and debt risk. Second, for the first time, this paper brings CSR fulfilment, product-market competition and debt risk into the same research framework, and this arrangement provides a feasible way to deeply analyse the internal relationship prevailing among them. Third, this paper further explores the effect of the stratified influence mechanism of CSR fulfilment on corporate debt risk, and also, an understanding of this causative phenomenon is helpful for policy makers to reasonably guide CSR fulfilment and helps to prevent and resolve systemic financial risks, which has certain practical and theoretical significance.
The rest of this paper is organised as follows. The second part is the literature review and research hypothesis. The third part is the research design. The fourth part is the empirical analysis. The fifth part is a furtherance of the analysis. The last part contains the conclusion and policy suggestions.
This paper reviews the research achievements of domestic and foreign scholars in recent years. It is found that there are four main reasons that can explain why the fulfilment of social responsibility has a negative impact on debt risk: reducing the cost of debt financing, extending the debt maturity and reducing the strictness of debt contract, and improving the credit rating so as to have a restraining effect on debt risk. First, in terms of reducing the cost of debt financing: Goss and Roberts [2] conducted a sample survey of 3996 corporate loans in the United States, and found that the loan interest rate of firms with better CSR is 7–18 basis points lower than that of firms only focusing on CSR. Second, in terms of extending debt maturity and reducing the strictness of debt contracts, Shi and Sun [3] found that the more firms invest in CSR, the less restrictive the clauses in their debt contracts. Third, in recent years, studies have focused more on the relationship between CSR and credit rating. Attig et al. [4] showed that credit rating agencies tend to give higher credit ratings to firms that perform well in social responsibility. The studies mentioned above all lend credence to the view that firms playing an active part in CSR can obtain the benefit of reduced debt risk owing to their good corporate image, lower debt financing cost, more relaxed credit conditions and higher credit rating. According to this inference, we deduce the first research hypothesis:
H1: The fulfilment of CSR can inhibit the debt risk faced by firms.
With the advent of the ‘new normal’, the degree of industry competition and the firm behaviour in China’s product market show new characteristics. On the one hand, product-market competition urges firms to seek better internal governance; a highly competitive market will force firms to reduce product costs, seek lower financing costs, improve internal governance [5] and reduce the degree of information asymmetry [6]. On the other hand, fierce competition in the product market will aggravate firm risk. Wu Haomin et al. [7] show that the significant increase of idiosynthetic risk of listed companies in China is attributable to the intensification of product-market competition. Han Zhongxue and Zhou Tingting [8] found that for all manufacturing listed companies in China, product-market competition has a significant predatory risk effect on cash holdings. Competition is one of the most urgent problems for firms to face when they are established in the market. To some extent, firms’ fulfilment of CSR is affected by the competitors’ CSR input level. When stakeholders evaluate the fulfilment of CSR, they will also refer to the competitors’ degree of CSR fulfilment in the same industry. Thus, we propose the second hypothesis of this paper:
H2: The degree of product-market competition regulates the relationship between CSR fulfilment and debt risk.
This paper extracts data for the Chinese A-share listed companies in the Shanghai and Shenzhen stock exchanges from 2010 to 2019 as research samples, and carries out the following processing steps:
Remove the samples of listed companies with abnormal trading status such as ST, *ST, Pt, etc. Exclude samples with missing main variables. Exclude listed companies belonging to the financial and insurance sectors. To avoid the influence of extreme outliers, conduct winsorization to achieve tail reduction on all continuous variables at the level of 1%.
Through the steps outlined above, annual observations of 23,660 companies were finally obtained. The CSR data used in this paper were obtained from the CSR rating database Hexun, and the financial data from the CSMAR database.
In order to test hypothesis 1, we design model 1, which is represented as follows:
In the above model, the main explanatory variable is CSR, which is the comprehensive score of CSR published by Hexun from 2010 to 2019. The rating system integrates the CSR fulfilment in five aspects: shareholder, employee, rights and interests of suppliers, customers and consumers, environment and social of listed Companies. The full score is 100; the higher the score, the better is the fulfilment of CSR.
FDR is used as an explained variable to measure the debt risk of firms. According to previous studies, there are mainly two ways to estimate the debt risk of firms. The first approach is to use accounting data to measure the debt risk, and the second way is to measure the debt risk by combining market data and accounting data. Z_score [9] and O_score [11] are among the commonly used accounting data estimation methods. Estimation methods based on the combination of market data and accounting data include the default option model mentioned by Black and Scholes [12], the KMV model used by Merton [13] to measure default distance and a simple risk model mentioned in the study of Shumway [14]. In the past, a large number of studies in the literature used the combination of market data and accounting data to predict the debt risk of firms [15, 16]. However, when Agarwal and Taffler [17] conducted cross-border analysis, they found that the Z_score model was superior to risk-based and market-based prediction models in the accuracy of debt risk prediction. In a recent study, Altman et al. [18] confirmed the effectiveness of Z_score as a predictor of debt risk. Based on the above inferences drawn from the literature, this paper uses a forecasting model based on accounting data to estimate the debt risks faced by firms.
In model 1, FDR is the explained variable to measure the debt risk of firms. We mainly use two accounting measurement methods to predict the debt risk of firms, namely Z_score [19] as calculated by model 2 and O_score [11] as calculated by model 3.
The higher the calculated value of Z_score, the better the financial status and the lower the debt risk of the firm. For the sake of explanation, Z_score has been negative in the follow-up empirical test.
In model 3, logTA
Based on model 1, model 4 is designed to test hypothesis 2, as under:
In model 4, the explanatory variable is the cross product of CSR and HHI, where HHI is the degree of market competition. Based on the method suggested by Peress [20], the present study uses the Herfindahl–Hirschman index (HHI) to portray the degree of industry competition. Among others, one calculation formula used for HHI is the following:
In models 1 and 4, we also include the following sets of control variables, which probably affect FDR. Firm’s characteristics variables: firm’s scale (Size), firm’s age (Age). Firm’s financial characteristics variables: profitability (ROA), cash flow volatility (VCF), management expense ratio (Overhead), non-debt tax shield (NDT), market-to-book ratio of equity (MTB), whether there is a dividend payout during the current year (Div), noncurrent assets to total assets ratio (PPE), shareholding ratio of the top five shareholders (Lncon), growth rate of operating income (Growth) and stock returns (RET). Board characteristic variables: Ratio of independent directors (Indratio), CEO duality (Duality). We also control for ∑Industry (∑Year), which is a set of industry (year) dummy variables. Definitions of other relevant main variables are shown in Table 1.
Variable definitions
Explained variables | FDR | Z_score as calculated in model 2. |
O_score as calculated in model 3. | ||
Explanatory variables | CSR | CSR score is obtained from the CSR reports of listed companies published in Hexun. |
Control variables | Size | Natural logarithm of total assets at the end of the year. |
ROA | ROA is equal to pretax operating income divided by total assets. | |
Age | Age is equal to inspection year minus listing year. | |
VCF | Three year volatility of the ratio of cash flow to total assets at the end of the year. | |
Overhead | Overhead is the management expense that happened during the current year divided by total assets. | |
NDTS | NDTS is the ratio of current year depreciation and amortisation to total assets. | |
MTB | MTB is the growth rate of firms, and it is the ratio of the market value of equity at the end of the year to the book value of equity at the end of the year. | |
Div | Div represents weather the enterprise has had dividend payouts in the current year; if yes it takes the value of 1 and 0 otherwise. | |
PPE | The ratio of total noncurrent assets to total assets. | |
Lncon | Lncon is the combined shareholding of the top five shareholders. | |
Growth | Growth is the growth rate of operating income that equals change in sales revenue of the current year compared to the previous year, and then divided by the previous year’s operating income. | |
RET | RET is the firm’s average monthly stock return during the year. | |
Indratio | The proportion of independent directors to the total number of directors. | |
Duality | Duality is a dummy variable that equals 1 if chairman and the general manager are in one position and 0 otherwise. |
CSR, corporate social responsibility; MTB, market-to-book ratio of equity; NDTS, non-debt tax shield.
Table 2 presents descriptive statistics of the main variables. Altman [19] pointed out that when the Z_score is >2.99, it means that the financial status of the firm is in good health and the probability of debt risk is low. When Z_score is <1.81, it indicates that the firm has latent debt risk. When Z_score is between 1.81 and 2.99, it is called the ‘grey area’, which indicates that the financial situation of firm is in an unstable state. The main variable that is explained in this paper, Z_score, has a mean value of 6.7777, the maximum value is 55.5422 and the minimum value is 0.1785; further, the 25% percentile is 2.0313, the median value is 3.7837 and the standard deviation is 8.8820. O_score’s mean value is −11.5968, the maximum value is −5.0486 and the minimum value is −27.3073; further, the 25% percentile is −13.3983, the median value is −10.7945 and the standard deviation is 3.9466. This shows that the debt risk faced by different firms is quite different, and that at least 25% of firms are faced with debt risk. The full score of CSR fulfilment published in the Hexun database is 100. According to these data, the average and median value of CSR are 24.8365 and 22.1300, respectively, with the maximum value of 74.5200 and the minimum value of −3.1500, indicating that the degree of CSR fulfilment in China needs to be further improved. With regard to firm characteristics, the mean value of Size is 22.1602, the mean value of ROA is 0.0394, the mean value of VCF is 0.0453, the mean value of Growth is 0.1967 and the mean value of PPE is 0.2186, which indicates that the firms in this sample have a large proportion of fixed assets, low asset profitability and weak solvency, and face a certain level of default risk.
Descriptive statistics
Z_score | 23660 | 0.1785 | 6.7777 | 2.0313 | 3.7837 | 7.4065 | 8.8820 | 55.5422 |
O_score | 23660 | −27.3073 | −11.5968 | −13.3983 | −10.7945 | −8.8855 | 3.9466 | −5.0486 |
CSR | 23660 | −3.1500 | 24.8365 | 16.5800 | 22.1300 | 27.8000 | 16.0305 | 74.5200 |
Size | 23660 | 19.7510 | 22.1602 | 21.2268 | 21.9870 | 22.8968 | 1.2861 | 25.8845 |
ROA | 23660 | −0.2157 | 0.0394 | 0.0147 | 0.0368 | 0.0657 | 0.0557 | 0.1962 |
Age | 23660 | 0.0000 | 10.0511 | 4.0000 | 9.0000 | 16.0000 | 7.0084 | 25.0000 |
VCF | 23660 | 0.0022 | 0.0453 | 0.0189 | 0.0339 | 0.0586 | 0.0392 | 0.2164 |
Overhead | 23660 | 0.0041 | 0.0447 | 0.0248 | 0.0394 | 0.0581 | 0.0282 | 0.1544 |
NDTS | 23660 | 0.0007 | 0.0238 | 0.0119 | 0.0209 | 0.0325 | 0.0157 | 0.0763 |
MTB | 23660 | 0.5996 | 3.5910 | 1.7365 | 2.6862 | 4.3403 | 3.0321 | 19.1986 |
Div | 23660 | 0.0000 | 0.7555 | 1.0000 | 1.0000 | 1.0000 | 0.4298 | 1.0000 |
PPE | 23660 | 0.0022 | 0.2186 | 0.0889 | 0.1845 | 0.3128 | 0.1656 | 0.7144 |
Lncon | 23660 | 0.2021 | 0.5356 | 0.4230 | 0.5381 | 0.6489 | 0.1523 | 0.8804 |
Growth | 23660 | −0.5395 | 0.1967 | −0.0090 | 0.1159 | 0.2795 | 0.4604 | 3.1335 |
RET | 23660 | −0.0686 | 0.0102 | −0.0188 | 0.0052 | 0.0319 | 0.0421 | 0.1592 |
Indratio | 23660 | 0.3333 | 0.3748 | 0.3333 | 0.3333 | 0.4286 | 0.0536 | 0.5714 |
Duality | 23660 | 0.0000 | 0.2575 | 0.0000 | 0.0000 | 1.0000 | 0.4373 | 1.0000 |
CSR, corporate social responsibility; MTB, market-to-book ratio of equity; NDTS, non-debt tax shield.
In columns 1 and 4 of Table 3, we only control the industry and annual fixed effect for regression. In columns 2 and 5, we not only control the industry and annual fixed effect but also add control variables for multiple regressions. The results show that the regression coefficients of CSR and corporate debt risk Z_score and O_score are significantly negative at the 1% level; that is to say, the higher the level of CSR fulfilment, the lower the debt risk faced by firms, which supports hypothesis 1. In addition, the regression results of the control variables show that Size, Age, PPE and Growth are positively correlated with debt risk. However, ROA, Div, Lncon, RET and Indratio are negatively correlated with debt risk.
CSR fulfilment and debt risk, the moderating effect of product-market competition (Z_score and HHI are negative)
CSR | −0.0169*** (−4.66) | −0.0099*** (−2.73) | −0.0164*** (−3.99) | −0.0398*** (−25.38) | −0.0073*** (−4.61) | −0.0103*** (−5.70) |
HHI | 14.6110*** (10.46) | 4.2472*** (6.93) | ||||
CSR*HHI | −0.0911*** (−3.02) | −0.0435*** (−3.28) | ||||
Size | 2.0913*** (41.76) | 2.0756*** (41.54) | 0.8739*** (39.86) | 0.8697*** (39.68) | ||
ROA | −36.6600*** (−35.63) | −36.1459*** (−35.19) | −26.9191*** (−59.76) | −26.7790*** (−59.45) | ||
Age | 0.0488*** (5.77) | 0.0522*** (6.19) | 0.0215*** (5.82) | 0.0225*** (6.08) | ||
VCF | 10.7848*** (8.71) | 10.7521*** (8.71) | −0.5821 (−1.07) | −0.5788 (−1.07) | ||
Overhead | 4.3665** (2.15) | 5.8658*** (2.89) | −16.1690*** (−18.21) | −15.7934*** (−17.77) | ||
NDTS | 15.1886*** (3.21) | 14.8717*** (3.15) | −20.6733*** (−9.99) | −20.8409*** (−10.08) | ||
MTB | −0.6836*** (−33.75) | −0.6920*** (−34.21) | 0.2599*** (29.32) | 0.2581*** (29.10) | ||
Div | −0.2356* (−1.81) | −0.2202* (−1.70) | −0.3078*** (−5.41) | −0.3027*** (−5.33) | ||
PPE | 4.1707*** (8.84) | 4.1867*** (8.90) | 3.7310*** (18.06) | 3.7347*** (18.10) | ||
Lncon | −4.8438*** (−14.28) | −4.6771*** (−13.81) | −2.7487*** (−18.51) | −2.7058*** (−18.22) | ||
Growth | 1.3257*** (12.81) | 1.3227*** (12.82) | 0.2641*** (5.83) | 0.2626*** (5.80) | ||
RET | −12.8841*** (−7.89) | −11.9855*** (−7.35) | −1.9071*** (−2.67) | −1.6842** (−2.35) | ||
Indratio | −4.2738*** (−4.95) | −4.3505*** (−5.05) | −0.7872** (−2.08) | −0.8201** (−2.17) | ||
Duality | −0.5299*** (−4.84) | −0.5266*** (−4.82) | 0.0088 (0.18) | 0.0095 (0.20) | ||
Constant | −7.2702*** (−14.07) | −46.4121*** (−39.28) | −44.2865*** (−37.10) | −10.0410*** (−44.92) | −28.1203*** (−54.36) | −27.5263*** (−52.57) |
Year/Industry | Yes | Yes | Yes | Yes | Yes | Yes |
N | 23660 | 23660 | 23659 | 23660 | 23660 | 23659 |
Adj- |
0.0977 | 0.3779 | 0.3813 | 0.1443 | 0.3960 | 0.3972 |
F | 86.4271 | 327.5768 | 318.0266 | 133.9788 | 353.5853 | 339.8737 |
Note:
represent significance at the levels of 1%, 5% and 10%, respectively. CSR, corporate social responsibility; HHI, Herfindahl-Hirschman index; MTB, market-to-book ratio of equity; NDTS, non-debt tax shield.
The regression results of columns 3 and 6 (Table 3) show that the regression coefficients of debt risk Z_score and O_score and CSR * HHI are significant at the 1% level, which indicates that the degree of product-market competition has a significant moderating effect on the relationship between CSR fulfilment and debt risk, i.e. the more fierce the product-market competition, the more the inhibitory effect of CSR fulfilment on debt risk can be promoted, and hypothesis 2 is verified.
CSR and debt risk Z_score and O_score are the main variables in this paper, and these may be affected by the inherent differences of the industry. m_CSR, m_Z_score and m_O_score are the industry-adjusted CSR, Z_score and O_score, measured as CSR, Z_score and O_score less the mean values of CSR, Z_score and O_score for all firms in the same industry, respectively.
The results are shown in Table 4. The m_Z_score and m_O_score are significantly negatively correlated with the m_CSR, which is consistent with the regression results in Table 3 concerning the main test analysis, indicating that the above conclusions are robust.
Replacement of main variables (Z_score is negative)
m_CSR | −0.0126*** (−3.49) | −0.0090*** (−5.68) |
Controls | Yes | Yes |
Constant | −40.0503*** (−33.60) | −17.4561*** (−33.27) |
Year/Industry | Yes | Yes |
N | 23660 | 23660 |
Adj- |
0.3019 | 0.3023 |
Note: The control variables in Table 4 are the same as those in Table 3, and to avoid repetition, the results of control variables are omitted.
represent significance at the levels of 1%, 5% and 10%, respectively. CSR, corporate social responsibility.
In conformity with the suggestion of Chen Caiyun [10], we test the robustness of our results by using change in CSR and change in debt risk in the current year and the next year; whole control variables are changes in the current year, and the results are shown in columns 1 and 3 (Table 5). The CSR fulfilment change in the current period and the next period show a negative relationship with the Z_score and O_score changes in the next period at the 1% level, as can be seen in columns 2 and 4 (Table 5). However, the CSR fulfilment change in the next period does not seem to affect the Z_score and O_score changes in the current period.
Dynamic test (Z_score is negative)
ΔCSR |
−0.0131*** (−4.40) | 0.0017 (0.59) | −0.0208*** (−18.17) | −0.0007 (−0.73) |
ΔCSR |
−0.0163*** (−5.27) | −0.0061*** (−5.13) | ||
ΔSize | 0.9445*** (5.55) | 3.1999*** (18.70) | −0.0751 (−1.15) | 2.0405*** (33.96) |
ΔROA | 3.1905*** (3.69) | −16.2485*** (−19.27) | 5.6848*** (17.16) | −15.4860*** (−52.30) |
ΔAge | 0.3425 (0.43) | −1.3515* (−1.69) | −0.0981 (−0.32) | −0.1314 (−0.47) |
ΔVCF | 0.6081 (0.45) | −2.8218** (−2.09) | 0.2477 (0.48) | −0.9724** (−2.05) |
Δoverhead | 12.4276*** (4.08) | −7.0720** (−2.31) | 4.4970*** (3.85) | −10.6482*** (−9.90) |
ΔNDTS | −10.4221 (−1.44) | −13.0303* (−1.79) | 3.2840 (1.18) | −26.0014*** (−10.15) |
ΔMTB | 0.0874*** (4.09) | −0.4907*** (−22.85) | −0.0156* (−1.90) | 0.1604*** (21.28) |
ΔDiv | −0.0005 (−0.01) | −0.2662*** (−2.72) | 0.1689*** (4.49) | −0.3473*** (−10.10) |
ΔPPE | −0.4916 (−0.75) | 5.2796*** (7.98) | 0.0463 (0.18) | 3.4835*** (14.99) |
ΔLncon | −3.5143*** (−4.52) | −6.5829*** (−8.42) | −0.8265*** (−2.77) | −3.6601*** (−13.33) |
ΔGrowth | −0.0156 (−0.23) | 0.4864*** (7.23) | −0.0286 (−1.12) | −0.3487*** (−14.77) |
ΔRET | −1.1422 (−1.17) | −18.2114*** (−18.52) | −1.1966*** (−3.19) | −2.1178*** (−6.13) |
ΔIndratio | −0.6330 (−0.57) | 0.8220 (0.74) | −0.2544 (−0.60) | 0.2334 (0.60) |
ΔDuality | 0.1502 (1.07) | −0.1674 (−1.18) | −0.0247 (−0.46) | −0.0028 (−0.06) |
Constant | −0.3142 (−0.36) | 1.4759* (1.68) | 0.2355 (0.71) | 0.1100 (0.36) |
Year/industry | Yes | Yes | Yes | Yes |
N | 17164 | 17164 | 17164 | 17164 |
0.0872 | 0.2325 | 0.0528 | 0.2586 | |
Adj- |
0.0850 | 0.2306 | 0.0504 | 0.2568 |
Note:
represent significance at the levels of 1%, 5% and 10%, respectively.
CSR, corporate social responsibility.
This shows that changes in fulfilment of CSR in the current period and the next period can affect the change in debt risk in the next period, but the change in fulfilment of CSR in the next period cannot affect the change in debt risk in the current period, which eliminates the endogenous problem caused by the reverse causal relationship between the fulfilment of CSR and debt risk. The above research conclusion is still robust.
The interaction between the dependent variable and the independent variable is also a key factor leading to endogeneity. Since the lag term of the independent variable has occurred, it is ‘predetermined’ (– i.e. from the perspective of the current period, its value has been fixed). The current independent variable is related to it, but the current dependent variable has nothing to do with it. Therefore, the endogenous problem caused by the interaction between dependent variables and independent variables can be properly dealt with by the 1-year lag treatment of the independent variables. Therefore, this paper will replace the original independent variables in model 1 with the 1-year lag treatment of the independent variables, and then carry out the robustness test. The results are shown in columns 1 and 2 (Table 6), where a CSR lag of 1 year shows a negative relationship with the debt risk Z_score and O_score at the 1% level, indicating that after considering the endogenous problems that may be caused by the interaction of the dependent variables and the independent variables, the results are still consistent with the results of the previous main test analysis, which is robust.
Regression results of independent variable lag for one period (Z_score is negative)
CSR |
−0.0174*** (−4.82) | −0.0095*** (−5.67) |
Size |
2.1373*** (39.83) | 0.7652*** (30.88) |
ROA |
−28.8522*** (−25.90) | −19.5183*** (−37.95) |
Age |
0.0127 (1.39) | 0.0117*** (2.76) |
VCF |
8.3963*** (6.47) | −0.2604 (−0.43) |
overhead |
0.6466 (0.31) | −15.3937*** (−15.87) |
NDTS |
12.3036** (2.43) | −17.8428*** (−7.63) |
MTB |
−0.4280*** (−20.11) | 0.2122*** (21.59) |
Div |
0.0453 (0.33) | −0.1449** (−2.27) |
PPE |
3.1000*** (6.15) | 3.0327*** (13.04) |
Lncon |
−4.6787*** (−13.07) | −2.7233*** (−16.48) |
Growth |
0.9543*** (8.88) | 0.2054*** (4.14) |
RET |
−6.0977*** (−3.59) | −3.2185*** (−4.10) |
Indratio |
−4.6850*** (−5.11) | −0.4761 (−1.12) |
Duality |
−0.4769*** (−4.09) | 0.0440 (0.82) |
Constant | −46.6619*** (−37.39) | −25.7190*** (−44.64) |
Year/Industry | Yes | Yes |
N | 20363 | 20363 |
0.3128 | 0.3038 | |
Adj- |
0.3114 | 0.3023 |
Note:
represent significance at the levels of 1%, 5% and 10%, respectively.
CSR, corporate social responsibility; MTB, market-to-book ratio of equity; NDTS, non-debt tax shield.
Considering that the firm’s CSR fulfilment may be inherent to its environment and its own characteristics, the characteristic variables of enterprises with good CSR fulfilment and those with poor CSR fulfilment are significantly different. If these characteristic variables also affect debt risk, then the relationship between firm CSR fulfilment and debt risk observed in the above probabilistic analysis model based on the full sample may affect interference factors, and so the PSM method is used to solve the endogenous problem. This method controls the significant differences in corporate characteristics between the firms with good and poor CSR fulfilment. In order to realise the PSM method, we use matching samples with similar firm characteristics to test the impact of CSR fulfilment on debt risk. This paper matches the firms with higher scores of CSR (higher than the industry median value) with those firms with lower scores (lower than the industry median value). We implement this procedure using the probit method (model 6), and control the following firm’s characteristic variables: Size, Age, ROA, VCF and SOE (Nature of ownership is a dummy variable; if a firm’s ultimate controller is the government, it take the value of 1, and 0 otherwise); at the same time, we also control industry and year fixed effects. The dummy variable of CSR fulfilment is the dependent variable in the probit regression; if the score of CSR fulfilment is higher than the industry median value, then it takes the value of 1, and otherwise the value of 0. We use the nearest neighbour method to match the firms with high scores of CSR (treatment firms) with the firms with low scores of CSR (control firms), and conduct the sampling without putting back. The PSM method produces a matching sample, including 8599 firm annual observations.
Table 7 shows the test results of running the main regression with matched samples. In columns 1 and 2, CSR and debt risk Z_score and O_score are negatively correlated, and these are significant at the level of 1%. This shows that the firms that integrate CSR fulfilment into their business activities and business strategies will face lower debt risk, which is consistent with the results of the previous full sample model regression, thus proving that the conclusion of this study is robust.
PSM (Z_score is negative)
CSR | −0.0166*** (−2.99) | −0.0093*** (−3.79) |
Controls | Yes | Yes |
Constant | −46.7106*** (−23.97) | −28.4039*** (−33.11) |
Year/Industry | Yes | Yes |
N | 8599 | 8599 |
0.3815 | 0.3802 | |
Adj- |
0.3783 | 0.3771 |
Note: The control variables in Table 7 are the same as those in Table 3. To avoid repetition, the results of control variables are omitted.
represent significance at the levels of 1%, 5% and 10%, respectively.
CSR, corporate social responsibility; PSM, propensity score matching.
To sum up, after considering the measurement error of variables, the endogenous problems caused by simultaneity and the interference factors of different CSR fulfilments with the same corporate characteristics, all kinds of robustness test results show that good CSR fulfilment can effectively reduce the debt risk faced by firms. The research conclusion of hypothesis 1 is thus robust.
In order to further test the moderating effect of product-market competition on the relationship between CSR fulfilment and debt risk, this paper divides the samples into a high product-market competition level group and a low product-market competition level group, and on this basis, the results of subsamples’ regression of model 1 are shown in Table 8. In the high product-market competition level group, columns 1 and 3 (Table 8) show that the estimated coefficients of debt risk Z_score and O_score are −0.0236 and −0.0157, respectively, and they are significant at the level of 1%. In the low product-market competition level group, columns 2 and 4 (Table 8), the estimated coefficients of debt risk Z_score and O_score are −0.0030 and −0.0001, respectively, but they are not statistically significant, indicating that the higher the degree of competition in the product market, the more obvious the inhibitory effect of CSR fulfilment on debt risk. The group test results support hypothesis H2.
Grouping by product-market competition intensity (Z_score and HHI are negative)
CSR | −0.0236*** (−4.45) | −0.0030 (−0.60) | −0.0157*** (−6.55) | −0.0001 (−0.02) |
Controls | Yes | Yes | Yes | Yes |
Constant | −51.6314*** (−31.24) | −43.2057*** (−28.27) | −34.0105*** (−45.51) | −26.3189*** (−39.05) |
Year/Industry | Yes | Yes | Yes | Yes |
N | 11830 | 11829 | 11830 | 11829 |
0.3654 | 0.3780 | 0.3770 | 0.3403 | |
Adj- |
0.3641 | 0.3767 | 0.3757 | 0.3390 |
Note: The control variables in Table 8 are the same as those in Table 3. To avoid repetition, the results of control variables are omitted.
represent significance at the levels of 1%, 5% and 10%, respectively.
CSR, corporate social responsibility; HHI, Herfindahl-Hirschman index.
According to Table 3, although we arrive at the conclusion that the fulfilment of CSR will have an inhibitory effect on a firm’s debt risk, according to the CSR scoring system of Hexun, the fulfilment of CSR includes five dimensions: shareholder; employee; rights and interests of suppliers, customers and consumers; environmental; and CSR. In order to test the difference of the inhibitory effect of different dimensions of CSR on corporate debt risk, this paper, based on the inferences drawn by Junshan and Xudong [21], divides the above-mentioned five dimensions of CSR fulfilment into three layers: monetary capital layer (ShareholderR), human capital layer (EmployeeR) and social capital layer (ExternalR). Among them, the monetary capital level is expressed by the score of the shareholder responsibility dimension, the human capital level is expressed by the score of the employee responsibility dimension and the social capital level is expressed by the sum of the three dimensions of supplier, customer and consumer rights responsibility, and environmental responsibility and CSR. Tables 9 and 10 provide the regression results of different layers of CSR fulfilment and debt risk Z_score and O_score, respectively. In columns 1 and 2 (Tables 9 and 10), it can be seen that the fulfilment of CSR in monetary capital layer and human capital layer is negatively correlated with debt risk, and the estimated coefficients are significant at the level of 1%, indicating that the debt risk faced by firms with good CSR fulfilment in these two layers is significantly lower. Debt risk is largely caused by the external financing constraints of firms. From the perspective of monetary capital layer, the fulfilment of CSR at the layer of monetary capital helps firms to better obtain the support of shareholders, creditors and other capital providers, and obtain financing through better channels and more easier credit policies, without regard to the aspect of reducing the cost of equity financing [22] or that of reducing the cost of debt financing. In addition, it also plays a significant role in extending the debt maturity [2], thus alleviating the debt risk faced by firms. From the perspective of human capital layer, employees are one of the key stakeholders of the firm, and human capital is regarded as one of the most critical factors for a firm to succeed in an increasingly competitive environment; to a large extent, these results are in line with the conclusion of Bae et al. [23] that CSR fulfilment in terms of employee treatment fairness has a positive impact on corporate capital structure. From column 3 (Table 9), it can be seen that fulfilment of CSR in social capital layer (ExternalR) and Z_score are negatively correlated, and the estimated coefficient is −0.0067, which is not significant. In column 3, Table 10 displays that the regression results for the fulfilment of CSR in social capital layer (ExternalR) and O_score are also negatively correlated, with an estimated coefficient of −0.0063, although it is significant to the extent of 1%; but it is still remote compared to the coefficient of monetary capital layer CSR fulfilment in column 1 and the coefficient of human capital layer CSR fulfilment in column 2 (Table 10). It can be inferred that the inhibitory effect of CSR fulfilment of social capital on debt risk is significantly weaker than those of monetary capital and human capital. The regression results shown in column 4 (Table 9) also provide direct evidence in support of this conclusion. This shows that the CSR at the social capital layer has little inhibitory effect on the debt risk faced by firms. Column 4 (Tables 9 and 10) shows the regression results of all layers of CSR fulfilment on corporate debt risk, to assess the net impact of CSR fulfilment on corporate debt risk at each level. The regression results are similar to those in columns 1 and 2 (Tables 9 and 10). Similarly, the estimated coefficient of CSR fulfilment of social capital layer is not statistically significant, and this conclusion is consistent with the results of Godfrey et al. [24]. The reason is that the fulfilment of CSR to the main stakeholders (such as fund providers and employees) will create more favourable resource exchange among these groups, which can effectively alleviate the financing constraints of firms, enhance the value of firms and prevent negative economic consequences. It seems that the fulfilment of CSR to the secondary stakeholders cannot create more favourable financing conditions for firms, so as to reduce the debt risk faced by firms [25].
Dimensions of CSR and debt risk (Z_score is negative)
ShareholderR | −0.0775*** (−4.90) | −0.0738*** (−4.58) | ||
EmployeeR | −0.0463*** (−2.79) | −0.0643** (−2.46) | ||
ExternalR | −0.0067 (−1.38) | 0.0121 (1.58) | ||
Controls | Yes | Yes | Yes | Yes |
Constant | −46.1237*** (−39.79) | −46.5026*** (−39.17) | −46.0650*** (−39.11) | −46.5855*** (−39.24) |
Year/Industry | Yes | Yes | Yes | Yes |
N | 23660 | 23660 | 23660 | 23660 |
Adj- |
0.3783 | 0.3779 | 0.3777 | 0.3784 |
328.1829 | 327.5895 | 327.3737 | 314.1067 |
Note: The control variables in Table 9 are the same as those in Table 3. To avoid repetition, the results of control variables are omitted.
represent significance at the levels of 1%, 5% and 10%, respectively.
CSR, corporate social responsibility.
Dimensions of CSR and debt risk O_score
ShareholderR | −0.0775*** (−4.90) | −0.0738*** (−4.58) | ||
EmployeeR | −0.0463*** (−2.79) | −0.0643** (−2.46) | ||
ExternalR | −0.0067 (−1.38) | 0.0121 (1.58) | ||
Controls | Yes | Yes | Yes | Yes |
Constant | −27.8747*** (−54.94) | −28.0681*** (−53.99) | −27.9260*** (−54.14) | −28.1411*** (−54.16) |
Year/Industry | Yes | Yes | Yes | Yes |
23,660 | 23,660 | 23,660 | 23,660 | |
Adj- |
0.3783 | 0.3779 | 0.3777 | 0.3784 |
328.1829 | 327.5895 | 327.3737 | 314.1067 |
Note: The control variables in Table 10 are the same as those in Table 3. To avoid repetition, the results of control variables are omitted.
represent significance at the levels of 1%, 5% and 10%, respectively.
CSR, corporate social responsibility.
Based on the CSR score data published in Hexun from 2010 to 2019 for A-share listed companies in the Shanghai and Shenzhen stock exchanges, this paper makes an empirical study on the impact of CSR fulfilment on debt risk faced by firms under the background of China’s economic system transformation, and assesses whether product-market competition can strengthen the effect of CSR fulfilment on debt risk. First, we find that CSR is helpful to restrain debt risk; this conclusion is still valid after fully considering the endogenous problems caused by variable measurement error and missing important variables. Second, product-market competition can improve the internal governance of firms, reduce the degree of information asymmetry and promote the inhibitory effect of CSR on debt risk; this conclusion is still valid after grouping the degree of product-market competition. Third, there are significant differences in the impact of different layers of CSR fulfilment on the debt risk faced by firms. The inhibition effect of CSR fulfilment in monetary capital layer and human capital layer on debt risk is significantly stronger than that in social capital layer. Therefore, firms should fully understand the positive significance of fulfilment of CSR, strive to promote the integration of CSR fulfilment and firm strategy, give full play to the positive role of CSR in the survival and development of firms, promote the harmonious unity of social interests and firm interests through the implementation of CSR strategy and ultimately realise sustainable development.
Regression results of independent variable lag for one period (Z.score is negative)
CSR |
−0.0174 |
−0.0095 |
Size |
2.1373 |
0.7652 |
ROA |
−28.8522 |
−19.5183 |
Age |
0.0127 (1.39) | 0.0117 |
VCF |
8.3963 |
−0.2604 (−0.43) |
overhead |
0.6466 (0.31) | −15.3937 |
NDTS |
12.3036 |
−17.8428 |
MTB |
−0.4280 |
0.2122 |
Div |
0.0453 (0.33) | −0.1449 |
PPE |
3.1000 |
3.0327 |
Lncon |
−4.6787 |
−2.7233 |
Growth |
0.9543 |
0.2054 |
RET |
−6.0977 |
−3.2185 |
Indratio |
−4.6850 |
−0.4761 (−1.12) |
Duality |
−0.4769 |
0.0440 (0.82) |
Constant | −46.6619 |
−25.7190 |
Year/Industry | Yes | Yes |
N | 20363 | 20363 |
0.3128 | 0.3038 | |
Adj- |
0.3114 | 0.3023 |
CSR fulfilment and debt risk, the moderating effect of product-market competition (Z.score and HHI are negative)
CSR | −0.0169 |
−0.0099 |
−0.0164 |
−0.0398 |
−0.0073 |
−0.0103 |
HHI | 14.6110 |
4.2472 |
||||
CSR*HHI | −0.0911 |
−0.0435 |
||||
Size | 2.0913 |
2.0756 |
0.8739 |
0.8697 |
||
ROA | −36.6600 |
−36.1459 |
−26.9191 |
−26.7790 |
||
Age | 0.0488 |
0.0522 |
0.0215 |
0.0225 |
||
VCF | 10.7848 |
10.7521 |
−0.5821 (−1.07) | −0.5788 (−1.07) | ||
Overhead | 4.3665 |
5.8658 |
−16.1690 |
−15.7934 |
||
NDTS | 15.1886 |
14.8717 |
−20.6733 |
−20.8409 |
||
MTB | −0.6836 |
−0.6920 |
0.2599 |
0.2581 |
||
Div | −0.2356 |
−0.2202 |
−0.3078 |
−0.3027 |
||
PPE | 4.1707 |
4.1867 |
3.7310 |
3.7347 |
||
Lncon | −4.8438 |
−4.6771 |
−2.7487 |
−2.7058 |
||
Growth | 1.3257 |
1.3227 |
0.2641 |
0.2626 |
||
RET | −12.8841 |
−11.9855 |
−1.9071 |
−1.6842 |
||
Indratio | −4.2738 |
−4.3505 |
−0.7872 |
−0.8201 |
||
Duality | −0.5299 |
−0.5266 |
0.0088 (0.18) | 0.0095 (0.20) | ||
Constant | −7.2702 |
−46.4121 |
−44.2865 |
−10.0410 |
−28.1203 |
−27.5263 |
Year/Industry | Yes | Yes | Yes | Yes | Yes | Yes |
N | 23660 | 23660 | 23659 | 23660 | 23660 | 23659 |
Adj- |
0.0977 | 0.3779 | 0.3813 | 0.1443 | 0.3960 | 0.3972 |
F | 86.4271 | 327.5768 | 318.0266 | 133.9788 | 353.5853 | 339.8737 |
Dynamic test (Z.score is negative)
ΔCSR |
−0.0131 |
0.0017 (0.59) | −0.0208 |
−0.0007 (−0.73) |
ΔCSR |
−0.0163 |
−0.0061 |
||
ΔSize | 0.9445 |
3.1999 |
−0.0751 (−1.15) | 2.0405 |
ΔROA | 3.1905 |
−16.2485 |
5.6848 |
−15.4860 |
ΔAge | 0.3425 (0.43) | −1.3515 |
−0.0981 (−0.32) | −0.1314 (−0.47) |
ΔVCF | 0.6081 (0.45) | −2.8218 |
0.2477 (0.48) | −0.9724 |
Δoverhead | 12.4276 |
−7.0720 |
4.4970 |
−10.6482 |
ΔNDTS | −10.4221 (−1.44) | −13.0303 |
3.2840 (1.18) | −26.0014 |
ΔMTB | 0.0874 |
−0.4907 |
−0.0156 |
0.1604 |
ΔDiv | −0.0005 (−0.01) | −0.2662 |
0.1689 |
−0.3473 |
ΔPPE | −0.4916 (−0.75) | 5.2796 |
0.0463 (0.18) | 3.4835 |
ΔLncon | −3.5143 |
−6.5829 |
−0.8265 |
−3.6601 |
ΔGrowth | −0.0156 (−0.23) | 0.4864 |
−0.0286 (−1.12) | −0.3487 |
ΔRET | −1.1422 (−1.17) | −18.2114 |
−1.1966 |
−2.1178 |
ΔIndratio | −0.6330 (−0.57) | 0.8220 (0.74) | −0.2544 (−0.60) | 0.2334 (0.60) |
ΔDuality | 0.1502 (1.07) | −0.1674 (−1.18) | −0.0247 (−0.46) | −0.0028 (−0.06) |
Constant | −0.3142 (−0.36) | 1.4759 |
0.2355 (0.71) | 0.1100 (0.36) |
Year/industry | Yes | Yes | Yes | Yes |
N | 17164 | 17164 | 17164 | 17164 |
0.0872 | 0.2325 | 0.0528 | 0.2586 | |
Adj- |
0.0850 | 0.2306 | 0.0504 | 0.2568 |
PSM (Z.score is negative)
CSR | −0.0166 |
−0.0093 |
Controls | Yes | Yes |
Constant | −46.7106 |
−28.4039 |
Year/Industry | Yes | Yes |
N | 8599 | 8599 |
0.3815 | 0.3802 | |
Adj- |
0.3783 | 0.3771 |
Variable definitions
Explained variables | FDR | Z_score as calculated in |
O_score as calculated in |
||
Explanatory variables | CSR | CSR score is obtained from the CSR reports of listed companies published in Hexun. |
Control variables | Size | Natural logarithm of total assets at the end of the year. |
ROA | ROA is equal to pretax operating income divided by total assets. | |
Age | Age is equal to inspection year minus listing year. | |
VCF | Three year volatility of the ratio of cash flow to total assets at the end of the year. | |
Overhead | Overhead is the management expense that happened during the current year divided by total assets. | |
NDTS | NDTS is the ratio of current year depreciation and amortisation to total assets. | |
MTB | MTB is the growth rate of firms, and it is the ratio of the market value of equity at the end of the year to the book value of equity at the end of the year. | |
Div | Div represents weather the enterprise has had dividend payouts in the current year; if yes it takes the value of 1 and 0 otherwise. | |
PPE | The ratio of total noncurrent assets to total assets. | |
Lncon | Lncon is the combined shareholding of the top five shareholders. | |
Growth | Growth is the growth rate of operating income that equals change in sales revenue of the current year compared to the previous year, and then divided by the previous year’s operating income. | |
RET | RET is the firm’s average monthly stock return during the year. | |
Indratio | The proportion of independent directors to the total number of directors. | |
Duality | Duality is a dummy variable that equals 1 if chairman and the general manager are in one position and 0 otherwise. |
Dimensions of CSR and debt risk (Z.score is negative)
ShareholderR | −0.0775 |
−0.0738 |
||
EmployeeR | −0.0463 |
−0.0643 |
||
ExternalR | −0.0067 (−1.38) | 0.0121 (1.58) | ||
Controls | Yes | Yes | Yes | Yes |
Constant | −46.1237 |
−46.5026 |
−46.0650 |
−46.5855 |
Year/Industry | Yes | Yes | Yes | Yes |
N | 23660 | 23660 | 23660 | 23660 |
Adj- |
0.3783 | 0.3779 | 0.3777 | 0.3784 |
328.1829 | 327.5895 | 327.3737 | 314.1067 |
Dimensions of CSR and debt risk O.score
ShareholderR | −0.0775 |
−0.0738*** (−4.58) | ||
EmployeeR | −0.0463 |
−0.0643** (−2.46) | ||
ExternalR | −0.0067 (−1.38) | 0.0121 (1.58) | ||
Controls | Yes | Yes | Yes | Yes |
Constant | −27.8747 |
−28.0681 |
−27.9260*** (−54.14) | −28.1411*** (−54.16) |
Year/Industry | Yes | Yes | Yes | Yes |
23,660 | 23,660 | 23,660 | 23,660 | |
Adj- |
0.3783 | 0.3779 | 0.3777 | 0.3784 |
328.1829 | 327.5895 | 327.3737 | 314.1067 |
Descriptive statistics
Z_score | 23660 | 0.1785 | 6.7777 | 2.0313 | 3.7837 | 7.4065 | 8.8820 | 55.5422 |
O_score | 23660 | −27.3073 | −11.5968 | −13.3983 | −10.7945 | −8.8855 | 3.9466 | −5.0486 |
CSR | 23660 | −3.1500 | 24.8365 | 16.5800 | 22.1300 | 27.8000 | 16.0305 | 74.5200 |
Size | 23660 | 19.7510 | 22.1602 | 21.2268 | 21.9870 | 22.8968 | 1.2861 | 25.8845 |
ROA | 23660 | −0.2157 | 0.0394 | 0.0147 | 0.0368 | 0.0657 | 0.0557 | 0.1962 |
Age | 23660 | 0.0000 | 10.0511 | 4.0000 | 9.0000 | 16.0000 | 7.0084 | 25.0000 |
VCF | 23660 | 0.0022 | 0.0453 | 0.0189 | 0.0339 | 0.0586 | 0.0392 | 0.2164 |
Overhead | 23660 | 0.0041 | 0.0447 | 0.0248 | 0.0394 | 0.0581 | 0.0282 | 0.1544 |
NDTS | 23660 | 0.0007 | 0.0238 | 0.0119 | 0.0209 | 0.0325 | 0.0157 | 0.0763 |
MTB | 23660 | 0.5996 | 3.5910 | 1.7365 | 2.6862 | 4.3403 | 3.0321 | 19.1986 |
Div | 23660 | 0.0000 | 0.7555 | 1.0000 | 1.0000 | 1.0000 | 0.4298 | 1.0000 |
PPE | 23660 | 0.0022 | 0.2186 | 0.0889 | 0.1845 | 0.3128 | 0.1656 | 0.7144 |
Lncon | 23660 | 0.2021 | 0.5356 | 0.4230 | 0.5381 | 0.6489 | 0.1523 | 0.8804 |
Growth | 23660 | −0.5395 | 0.1967 | −0.0090 | 0.1159 | 0.2795 | 0.4604 | 3.1335 |
RET | 23660 | −0.0686 | 0.0102 | −0.0188 | 0.0052 | 0.0319 | 0.0421 | 0.1592 |
Indratio | 23660 | 0.3333 | 0.3748 | 0.3333 | 0.3333 | 0.4286 | 0.0536 | 0.5714 |
Duality | 23660 | 0.0000 | 0.2575 | 0.0000 | 0.0000 | 1.0000 | 0.4373 | 1.0000 |
Replacement of main variables (Z.score is negative)
m_CSR | −0.0126 |
−0.0090 |
Controls | Yes | Yes |
Constant | −40.0503 |
−17.4561 |
Year/Industry | Yes | Yes |
N | 23660 | 23660 |
Adj- |
0.3019 | 0.3023 |
Grouping by product-market competition intensity (Z.score and HHI are negative)
CSR | −0.0236 |
−0.0030 (−0.60) | −0.0157 |
−0.0001 (−0.02) |
Controls | Yes | Yes | Yes | Yes |
Constant | −51.6314 |
−43.2057 |
−34.0105 |
−26.3189 |
Year/Industry | Yes | Yes | Yes | Yes |
N | 11830 | 11829 | 11830 | 11829 |
0.3654 | 0.3780 | 0.3770 | 0.3403 | |
Adj- |
0.3641 | 0.3767 | 0.3757 | 0.3390 |
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normal random variables in supply chain risk management Linear fractional differential equations in bank resource allocation and financial risk management model Construction and reform of art design teaching mode under the background of the integration of non-linear equations and the internet Spatial–temporal graph neural network based on node attention A contrastive study on the production of double vowels in Mandarin Financial accounting measurement model based on numerical analysis of rigid normal differential equation and rigid generalised functional equation Research of cascade averaging control in hydraulic equilibrium regulation of heating pipe network Mathematical analysis of civil litigation and empirical research of corporate governance Health monitoring of Bridges based on multifractal theory College students’ innovation and entrepreneurship ability based on nonlinear model Health status diagnosis of the bridges based on multi-fractal de-trend fluctuation analysis Mathematical simulation analysis of optimal testing of shot puter's throwing path Performance evaluation of college laboratories based on fusion of decision tree and BP neural network Application and risk assessment of the energy performance contracting model in energy conservation of public buildings The term structure of economic management rate under the parameter analysis of the estimation model based on common differential equation Sensitivity analysis of design parameters of envelope enclosure performance in the dry-hot and dry-cold areas The Spatial Form of Digital Nonlinear Landscape Architecture Design Based on Computer Big Data The improvement of museum information flow based on paste functional mapping method The art design of industrialised manufacturing furniture products based on the simulation of mathematical curves TOPSIS missile target selection method supported by the posterior probability of target recognition The incentive contract of subject librarians in university library under the non-linear task importance Modelling and Simulation of Collaborative Innovation System in Colleges and Universities Based on Interpreted Structural Equation Model Small amplitude periodic solution of Hopf Bifurcation Theorem for fractional differential equations of balance point in group competitive martial arts The Optimal Solution of Feature Decomposition Based on the Mathematical Model of Nonlinear Landscape Garden Features Composite mechanical performance of prefabricated concrete based on hysteresis curve equation Higher education innovation and reform model based on hierarchical probit Application of Fuzzy Mathematics Calculation in Quantitative Evaluation of Students’ Performance of Basketball Jump Shot The teaching of sports science of track and field-based on nonlinear mathematical equations Visual error correction of continuous aerobics action images based on graph difference function Ecological balance model of effective utilization of agricultural water resources based on fractional differential equations Application of Higher Order Ordinary Differential Equation Model in Financial Investment Stock Price Forecast Precision algorithms in second-order fractional differential equations Application of Forced Modulation Function Mathematical Model in the Characteristic Research of Reflective Intensity Fibre Sensors Fractional differential equations in National Sports Training in Colleges and Universities Radioactive source search problem and optimisation model based on meta-heuristic algorithm Application of mathematical probabilistic statistical model of base – FFCA financial data processing Research on a method of completeness index based on complex model Distribution network monitoring and management system based on intelligent recognition and judgement Fake online review recognition algorithm and optimisation research based on deep learning Research on the sustainable development and renewal of Macao inner harbour under the background of digitisation Support design of main retracement passage in fully mechanised coal mining face based on numerical simulation Study on the crushing mechanism and parameters of the two-flow crusher Topological optimisation technology of gravity dam section structure based on ANSYS partial differential equation operation Interaction design of financial insurance products under the Era of AIoT Modeling the pathway of breast cancer in the Middle East Corporate social responsibility fulfilment, product-market competition and debt risk: Evidence from China ARMA analysis of the green innovation technology of core enterprises under the ecosystem – Time series data Reconstruction of multimodal aesthetic critical discourse analysis framework Image design and interaction technology based on Fourier inverse transform What does students’ experience of e-portfolios suggest Research on China interregional industrial transformation slowdown and influencing factors of industrial transformation based on numerical simulation The medical health venture capital network community structure, information dissemination and the cognitive proximity The optimal model of employment and entrepreneurship models in colleges and universities based on probability theory and statistics A generative design method of building layout generated by path Analysis of the causes of the influence of the industrial economy on the social economy based on multiple linear regression equation Research of neural network for weld penetration control Engineering project management based on multiple regression equation and building information modelling technology Research on predictive control of students’ performance in PE classes based on the mathematical model of multiple linear regression equation Beam control method for multi-array antennas based on improved genetic algorithm The influence of X fuzzy mathematical method on basketball tactics scoring Mathematical model of back propagation for stock price forecasting Application of regression function model based on panel data in bank resource allocation financial risk management Application of Logical Regression Function Model in Credit Business of Commercial Banks Research on aerobics training posture motion capture based on mathematical similarity matching statistical analysis Application of Sobolev-Volterra projection and finite element numerical analysis of integral differential equations in modern art design Research on motion capture of dance training pose based on statistical analysis of mathematical similarity matching Application of data mining in basketball statistics Application of B-theory for numerical method of functional differential equations in the analysis of fair value in financial accounting Research on the influence of fuzzy mathematics simulation model in the development of Wushu market Study on audio-visual family restoration of children with mental disorders based on the mathematical model of fuzzy comprehensive evaluation of differential equation Difference-in-differences test for micro effect of technological finance cooperation pilot in China Application of multi-attribute decision-making methods based on normal random variables in supply chain risk management Exploration on the collaborative relationship between government, industry, and university from the perspective of collaborative innovation The impact of financial repression on manufacturing upgrade based on fractional Fourier transform and probability AtanK-A New SVM Kernel for Classification Validity and reliability analysis of the Chinese version of planned happenstance career inventory based on mathematical statistics Visual positioning system for marine industrial robot assembly based on complex variable function Mechanical behaviour of continuous girder bridge with corrugated steel webs constructed by RW Application of Lane-Emden differential equation numerical method in fair value analysis of financial accounting Regression function model in risk management of bank resource allocation Application of numerical method of functional differential equations in fair value of financial accounting Optimal solution of fractional differential equations in solving the relief of college students’ mental obstacles Risk contagion in financial markets based on copula model Calculating university education model based on finite element fractional differential equations and macro-control analysis Educational research on mathematics differential equation to simulate the model of children's mental health prevention and control system Analysis of enterprise management technology and innovation based on multilinear regression model Verifying the validity of the whole person model of mental health education activities in colleges based on differential equation RETRACTION NOTE Calculation of tourism development income index based on finite element ordinary differential mathematical equation Adoption of deep learning Markov model combined with copula function in portfolio risk measurement Radar system simulation and non-Gaussian mathematical model under virtual reality technology Comparison of compression estimations under the penalty functions of different violent crimes on campus through deep learning and linear spatial autoregressive models Research and application of constructing football training linear programming based on multiple linear regression equation Research on management evaluation of enterprise sales cash flow percentage method based on the application of quadratic linear regression equations Mathematical simulation analysis of optimal detection of shot-putters’ best path Determination of the minimum distance between vibration source and fibre under existing optical vibration signals: a study Mathematical modelling of enterprise financial risk assessment based on risk conduction model Nonlinear differential equations based on the B-S-M model in the pricing of derivatives in financial markets Mathematical simulation experiment based on optimisation of heat treatment process of aluminium alloy materials Mathematical model of transforming image elements to structured data based on BP neural network Educational reform informatisation based on fractional differential equation MCM of Student’s Physical Health Based on Mathematical Cone Sports health quantification method and system implementation based on multiple thermal physiology simulation Research on visual optimization design of machine–machine interface for mechanical industrial equipment based on nonlinear partial equations Informationisation of teaching model for track and field education based on finite element higher-order fractional differential equation Research on identifying psychological health problems of college students by logistic regression model based on data mining Information technology of preschool education reform of fine arts based on fractional differential equation Information Teaching Model of Preschool Art Education in Colleges and Universities Based on Finite Element Higher-Order Fractional Differential Equation A mathematical model of PCNN for image fusion with non-sampled contourlet transform Application of artificial intelligence algorithm in mathematical modelling and solving College Students’ Mental Health Climbing Consumption Model Based on Nonlinear Differential Equations Differential equation to verify the validity of the model of the whole-person mental health education activity in Universities Optimisation of Modelling of Finite Element Differential Equations with Modern Art Design Theory Analysis and Prediction of College Students’ Mental Health Based on K-means Clustering Algorithm Mathematical function data model analysis and synthesis system based on short-term human movement Human gait modelling and tracking based on motion functionalisation Analysis and synthesis of function data of human movement Energy-saving technology of BIM green buildings using fractional differential equation Study on the training model of football movement trajectory drop point based on fractional differential equation Financial Accounting Measurement Model Based on Numerical Analysis of Rigid Normal Differential Equation and Rigid Functional Equation User online consumption behaviour based on fractional differential equation Differential equation model of financial market stability based on Internet big data Multi-attribute Decision Method Based on Normal Random Variable in Economic Management Risk Control Children’s cognitive function and mental health based on finite element nonlinear mathematical model Dichotomy model based on the finite element differential equation in the educational informatisation teaching reform model Nonlinear Dissipative System Mathematical Equations in the Multi-regression Model of Information-based Teaching Stock price analysis based on the research of multiple linear regression macroeconomic variables Fractional Linear Regression Equation in Agricultural Disaster Assessment Model Based on Geographic Information System Analysis Technology