China is the world's second-largest emerging economy, and its extensive economic growth led to serious negative externalities in the environment and society in the past. The increasingly exposed poor CSR performance poses a severe challenge to the whole commercial society. Similarly, liability management plays a pivotal role in the development strategy of a firm. Appropriate debt is conducive to the expansion of business scale, however, excessive reliance on operating in debt will lead to corporate debt risk. For a long time, most scholars have been engaged in the research on the economic consequences of CSR such as in the aspect of corporate financial performance [1], shareholder wealth [2], capital cost [3, 4], the credit rating [5] and so on. However, few literatures discuss the relationship and internal mechanism between CSR fulfillment and debt risk.
What determines a company's capital structure? Although there have been many theoretical studies on the structure of debt. Whether CSR fulfilment can alleviate information asymmetry and agency problems between firms and creditors so that firms can raise debt funds from more channels to reduce debt risks? More and more firms regard the implementation of CSR as a business strategy to increase the competitive advantage of the product market and a key means to achieve sustainable development of firms. Whether the fulfillment of CSR will reduce the debt risk of firms by establishing competitive advantages in the product market is worth further discussion. In addition, this paper also tries to explore whether the above mechanism will be different due to the firms with different nature of property rights and firms in different regions?
Based on the above problems, this paper makes use of A-share listed companies in Shanghai and Shenzhen Stock exchanges from 2010 to 2019 as samples to investigate the mechanism of CSR fulfilment affecting firm debt risk. The research results show that: Firstly, fulfillment of CSR is a negative correlation with debt risk, indicating CSR performance can significantly inhibit debt risk. Secondly, CSR performance plays a significant role in restraining debt risk by dispersing the degree of debt concentration and establishing competitive advantages in the product market. Thirdly, in order to ensure the reliability of the research conclusions, we conducted a series of robustness tests, and we replaced measurement method of explanatory variable, intermediary variable and the explained variable in the meantime to test the above two paths respectively; in addition, we used the bootstrap method for verification existence of mediation effects. Finally, in further analysis, we find that in private firms and firms in the eastern region, fulfilment of CSR has a more significant inhibiting effect on debt risk through dispersing the degree of debt concentration and establishing competitive advantages in the product market.
The possible marginal contribution of this article is: Firstly, it has theoretical and practical significance to help us identify the specific path and mechanism of CSR performance affecting debt risk, and it also plays a supplementary role in the study of economic consequences in the field of CSR. Second, the current research on factors affecting the structure of debt is not mature. Existing empirical studies mainly focus on how companies choose different types of debt, but no researches has focused on how the fulfillment of CSR affects firms’ choice of different types of debt, and mitigate the debt risk by reducing the degree of debt concentration. Third, different from the most previous literatures that discussed product market competition as a meso environmental factor in different research frameworks, this paper takes the firm's own competitive advantage as the research object, as it is more targeted to discuss at the micro-level whether the fulfilment of CSR will enhance the competitive position of firms and thus affect the debt risk. In addition, this paper further deepens the understanding of the relationship between CSR fulfilment and debt risk that firms operate under different property rights and in different regions. The rest of this article is arranged as follows. The second part introduces the literature review and research hypothesis. The third part is the research design. The fourth part provides the empirical results. The fifth part provides further study. The last part is the conclusions and policy recommendations.
This paper reviews the research achievements of domestic and foreign scholars in recent years, it is found that there are four main reasons to explain why the fulfilment of social responsibility hurts debt risk: Reducing the cost of debt financing, extending the debt maturity and reducing the strictness of debt contract, and improving the credit rating, to have a restraining effect on debt risk. First, in terms of reducing the cost of debt financing, Goss and Roberts (2011) [4] 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 (2015) [6] found that the more the firms invest in CSR, the fewer the restrictive clauses in debt contracts. Third, in recent years, studies have more focused on the relationship between CSR and credit rating. Attig et al. (2013) [7] showed that credit rating agencies tend to give higher credit ratings to firms that perform well in social responsibility. The above studies all believe that firms that play an active part in CSR can reduce debt risk because of their good corporate image, lower debt financing costs, more relaxed credit conditions and higher credit rating. According to the above conclusion, we deduce the first research hypothesis:
H1: The fulfilment of CSR can inhibit the debt risk faced by firms.
The decentralised debt structure has two sides to the firm. On the positive side, the decentralised debt structure will lead to the difficulty of communication between different creditors, to continue to get support from different types of creditors, and the firm usually will cut back on improper borrowing, which will result in the debt risk of the firm to be low at this time. On the negative side, the firm with a decentralised debt structure means it has different types of creditors at the same time, and different creditors are more likely to have conflicts of interest or free riders. The decentralised debt structure makes it more difficult for different creditors to communicate and negotiate, and the firms need to coordinate the interests of different creditors, thereby reducing creditors’ willingness to learn more about the firm. It also lets managers have the opportunity to borrow heavily so that the debt risk rises. The fulfilment of CSR will increase firm information transparency, thus it helps to reduce the risk of failure of communication between creditors, enabling more investors to be willing to hold firm's debt, when the higher the degree of CSR fulfilment will help firms enlarge the positive side brought by the decentralised debt structure and avoid the negative side. Based on this, we propose a hypothesis:
H2: The degree of debt concentration is the mediating factor that the CSR fulfillment of firms influences debt risk.
With the development of the market economy, firms are facing increasingly fierce competition. The competition among firms has risen from the concrete level of product quality and price to the abstract level of business ethics and moral standards. Enterprises that actively fulfil CSR can handle the relationship with key stakeholders (such as the government, customers and employees) well, and promote firm innovation so that it can build a competitive advantage in product markets. For firms with a competitive advantage in the product market, because of its larger product differentiation or the substitutability of the product is lower, the demand curve for products will be more inelastic. When firms are threatened by rising production costs, they can flexibly transfer the cost shock to the customer, therefore, they can maintain the profitability better and reduce cash flow fluctuation, and thus reduce the possibility of firm debt risk. Based on this, we propose a hypothesis:
H3: Product market competitive advantage is the mediating factor that CSR fulfilment influences debt risk.
This paper takes the Chinese A-share listed companies in Shanghai and Shenzhen stock exchanges from 2010 to 2019 as research samples, and carries out the following processing: (1) remove the samples of listed companies with abnormal trading status such as ST, * ST, PT, etc; (2) the samples with missing main variables were excluded; (3) excluding financial and insurance listed companies; (4) to avoid the influence of extreme outliers, this paper conducts winsorize tail reduction on all continuous variables at the level of 1%, and finally obtains annual observations of 23660 companies. The CSR data of this paper comes from the CSR rating database Hexun.com. The financial data used in this paper are from the CSMAR database.
When Agarwal and Taffler (2008) [8] conducted a cross-border analysis, they found that the Z_score model was superior to the risk-based and market-based prediction model in the accuracy of debt risk prediction. In a recent study, Altman et al. (2017) [9] confirmed the effectiveness of Z_score as a predictor of debt risk.
So in this paper, Altman's (1968) [10] Z_score is adopted to measure a firm's debt risk, and the specific calculation formula is as follows:
Z_score = 1.2 × (Operating funds/Total asset) + 1.4 × (Retained earnings/Total asset) + 3.3 × (Earnings before interest and tax/Total asset) + 0.6 × (Value of equity/Value of liability) + 1 × (Sales revenue/Total asset)
The higher the value of the 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.
The main explanatory variable is CSR, which is the comprehensive score of CSR published by hexun.com from 2010 to 2019. The rating system integrates the CSR fulfillment in five aspects: Shareholders, employees, rights and interests of suppliers, customers and consumers, environment and society of listed companies. The full score is 100, the higher the score, the better the fulfilment of CSR.
Based on the research of Li et al. (2020) [11], the calculation formula for the degree of debt concentration is as follows:
TD is the total liabilities of the firm; TC is the trade credit of the firm, which is the sum of accounts payable, notes payable and advances; BL is the bank loans of the firm; FL is the financing lease of the firm; BP is bonds payable of the firm; Other is other debts of the firm. Loancen which is obtained by standardising SS. Loanconcens are distributed between 0 and 1. The larger the Loanconcen value, the higher the degree of debt concentration.
Referring to Kale and Loon (2011) [12], this paper uses Lerner index ranking to characterise product market competitive advantages. Lerner index (PCM) is calculated as follows:
PCM = (Operating income – Operating cost – Cost of sales – Overheads)/Operating income
Lerner index ranking (RPCM) is ranked according to the PCM value of the firm in the industry from the min to the max, firms in the industry were divided into 10 groups according to this order. RPCM of firms in each group were assigned values from 1 to 10. The higher the RPCM value is, the stronger the bargaining power and more competitive advantage of the firm in the product market.
The following sets of control variables probably affect FDR. Firm's characteristics variables: Firm's scale (Size), firm's age (Age). Firm's financial characteristics variables: Profitability (ROA), management expense ratio (Overhead), non-debt tax shield (NDT), market-to-book ratio of equity (MTB), adequacy of free cash flow (Cash), noncurrent assets to total assets ratio (PPE), the shareholding ratio of the top five shareholders (Lncon), the growth rate of operating income (Growth) and stock returns (RET). Board of directors characteristics variables, independent directors ratio (Indratio), CEO duality (Duality). We also control ΣIndustry (ΣYear) 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 is calculated in section 3.2.1. |
Explanatory variables | CSR | CSR score is obtained from the CSR report of listed companies published in Hexun.com. |
Mediating | Loanconcen | Loanconcen is calculated in the above model section 3.2.3. |
Variables | RPCM | The value of RPCM ranges from 1 to 10. For details, see above. |
Size | Natural logarithm of total assets. | |
Roa | Roa is pretax operating income divided by total assets. | |
Age | Age is equal to inspection year minus listing year. | |
Overhead | Overhead is the management expense happened during the year divided by total assets. | |
Control variables | NDTS | NDTS is the ratio of current year depreciation and amortisation to total assets. |
MTB | MTB is the growth rate of firms and is the ratio of the market value of equity to the book value of equity. | |
Cash | Cash is the adequacy of free cash flow = (Net cash flow from operating activities + Net cash flow from investment activities)/Total assets at beginning of year | |
PPE | The ratio of the total noncurrent asset to total asset. | |
Lncon | Lncon is the combined shareholding of the top five shareholders. | |
Growth | Growth = (Operating income for current year − Operating income for previous year)/Operating income for previous year | |
RET | RET is the firm's average monthly stock return during the year. | |
Indratio | The ratio of the number of independent directors to the number of directors. | |
Duality | Duality is a dummy variable that equals 1 if the same person holds the post of chairman and general manager and 0 otherwise. |
NDT, non-debt tax shield.
According to Baron and Kenny (1986) [13] proposed mediating effect test method and procedure, this paper constructs the research model according to Figure 1.
The explained variable in the model (1) and model (3) is FDR, namely Z_score, explanatory variables are CSR, mediator variables are degree of debt concentration Loanconcen and product market competitive advantage RPCM, respectively. The explained variables in the model (2) were the mediator variables Loanconcen and RPCM, the explained variable was CSR. The mediation effect test process is as follows: Step 1, the coefficient
Table 2 is the descriptive statistics of the main variables. Altman (1968) [10] pointed out that when Z_score is greater than 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 less than 1.81, it indicates that the firm has latent debt risk. When Z_score is between 1.81 and 2.99, it is called ‘grey area’, which indicates that the financial situation of firms is in an unstable state. This paper's main explained variable Z_score's mean value is 6.2083, the maximum value is 63.7491, the minimum value is 0.1730, the 25% percentile is 1.9552, the median value is 3.5302, and the standard deviation is 8.3996. Indicate that the debt risk faced by different firms is quite different, at least 25% of firms are faced with debt risk. The full score of CSR fulfilment published on Hexun.com is 100. According to this table, the mean and median values of CSR are 25.2250 and 22.1200 respectively, with the maximum value of 73.8200 and the minimum value of −2.8200, indicating that the degree of CSR fulfillment in China needs to be further improved. The mean and median values of Loanconcen are 0.3291 and 0.2874 respectively, with a standard deviation of 0.1662, which means the degree of debt concentration between firms varies greatly. The mean and median values of RPCM are 5.4278 and 5.0000 respectively, with a standard deviation of 2.7644, which means the degree of debt concentration between firms varies greatly, these values are similar to those of previous studies.
Descriptive statistics.
Z_score | 20097 | 0.1730 | 6.2083 | 1.9552 | 3.5302 | 6.7077 | 8.3996 | 63.7491 |
Loanconcen | 20097 | 0.0947 | 0.3291 | 0.2069 | 0.2874 | 0.4076 | 0.1662 | 0.9573 |
RPCM | 20097 | 1.0000 | 5.4278 | 3.0000 | 5.0000 | 8.0000 | 2.7644 | 10.0000 |
CSR | 20097 | −2.8200 | 25.2250 | 16.5400 | 22.1200 | 28.1200 | 16.4951 | 73.8200 |
Size | 20097 | 19.4961 | 22.2871 | 21.3812 | 22.1076 | 23.0129 | 1.2774 | 26.0740 |
Roa | 20097 | −0.2147 | 0.0379 | 0.0138 | 0.0348 | 0.0632 | 0.0552 | 0.2069 |
Age | 20097 | 2.0000 | 10.8679 | 5.0000 | 10.0000 | 16.0000 | 6.6695 | 25.0000 |
Overhead | 20097 | 0.0042 | 0.0440 | 0.0244 | 0.0387 | 0.0573 | 0.0279 | 0.1627 |
NDTS | 20097 | 0.0007 | 0.0240 | 0.0123 | 0.0213 | 0.0327 | 0.0156 | 0.0765 |
MTB | 20097 | 0.5909 | 3.3956 | 1.6771 | 2.5835 | 4.1147 | 2.7960 | 19.8846 |
Cash | 20097 | −0.5918 | −0.0207 | −0.0743 | −0.0053 | 0.0489 | 0.1270 | 0.3322 |
PPE | 20097 | 0.0019 | 0.2202 | 0.0905 | 0.1870 | 0.3155 | 0.1646 | 0.7149 |
Lncon | 20097 | 0.2002 | 0.5257 | 0.4145 | 0.5256 | 0.6345 | 0.1507 | 0.8872 |
Growth | 20097 | −0.5576 | 0.1908 | −0.0111 | 0.1124 | 0.2727 | 0.4569 | 3.3170 |
RET | 20097 | −0.0864 | 0.0110 | −0.0173 | 0.0062 | 0.0321 | 0.0421 | 0.2276 |
Indratio | 20097 | 0.3333 | 0.3747 | 0.3333 | 0.3333 | 0.4286 | 0.0537 | 0.5714 |
Duality | 20097 | 0.0000 | 0.2395 | 0.0000 | 0.0000 | 0.0000 | 0.4268 | 1.0000 |
NDT, non-debt tax shield.
Table 3 reports the regression results of the effect of CSR fulfillment on debt risk by affecting the degree of debt concentration and product market competitive advantage. Column (1) is step 1 for mediating effect test, to examine whether the firms’ fulfilment of CSR have effect on debt risk, the estimated coefficient of CSR in the regression result is −0.0132, significantly at the 1% level, it shows that with the improvement of the level of CSR fulfilment, the lower the debt risk the firm faces, the empirical test results support the view of hypothesis H1. Column (2) and column (4) are step 2 of mediating effect test, whether the firms’ fulfilment of CSR has an effect on debt concentration and product market competitive advantage were tested respectively, the estimated coefficient of CSR and Loanconcen is −0.0112, the estimated coefficient of CSR and RPCM is 0.0186, both of them were statistically significant at 1% level, which indicates that the fulfilment of CSR can obviously reduce the degree of debt concentration and enhance the firm's competitive advantage in the product market. Column (3) and column (5) are step 3 of the mediation effect test, the estimated coefficient of intermediary variable Loanconcen and Z_score is 0.2321, and the estimated coefficient of intermediary variable RPCM and Z_score is −0.1209, both of them were significant at 1% level, and it shows that the degree of debt concentration and the competitive advantage of a product market are the key factors affecting the debt risk of firms. In Column (3) and column (5), although the estimated coefficients of CSR and Z_score are −0.0106 and −0.0110 respectively, they are still significant at the 1% level. However, compared with the estimated coefficient of CSR and Z_score in column (1), the estimated coefficient values are changed. The above test results show that the debt concentration and product market competitive advantage have partial mediating effects between the fulfillment of CSR and debt risk. So the influencing mechanism between CSR fulfillment and debt risk is confirmed. Namely, ‘CSR fulfillment-debt concentration/product market competitive advantage-debt risk’, it indicates that CSR fulfilment can reduce the debt risk by reducing the concentration of corporate debt and enhancing the firm competitive advantage in the product market. In addition, to verify the debt concentration degree and product market competitive advantage exit mediating effects between CSR performance and debt risk more accurately. Sobel tests are also carried out in this paper, The Z test values in column (3) and column (5) are −2.7600 and −5.2780, respectively, which are significant at a 1% level. The empirical test results support H1, H2 and H3.
CSR fulfillment and debt risk: based on the mediating effect test of debt concentration and product market competitive advantage (take a negative number of Z_score).
CSR | −0.0132^{***} (−3.67) | −0.0112^{***} (−2.79) | −0.0106^{***} (−3.10) | 0.0186^{***} (15.82) | −0.0110^{***} (−3.03) |
Loanconcen | 0.2321^{***} (5.18) | ||||
RPCM | −0.1209^{***} (−5.60) | ||||
Size | 1.8089^{***} (35.32) | −0.0408^{***} (−34.84) | 1.5572^{***} (29.82) | −0.0102 (−0.61) | 1.8076^{***} (35.32) |
Roa | −34.1504^{***} (−33.24) | 0.2331^{***} (9.93) | −32.7111^{***} (−32.08) | 25.8148^{***} (76.87) | −31.0300^{***} (−26.56) |
Age | 0.0560^{***} (6.40) | 0.0013^{***} (6.26) | 0.0637^{***} (7.35) | −0.0668^{***} (−23.35) | 0.0479^{***} (5.41) |
Overhead | 4.0819^{*} (1.92) | −0.2695^{***} (−5.55) | 2.4178 (1.15) | −12.2106^{***} (−17.57) | 2.6060 (1.22) |
NDTS | 13.7700^{***} (2.78) | −1.0049^{***} (−8.88) | 7.5650 (1.54) | −8.4793^{***} (−5.23) | 12.7451^{**} (2.57) |
MTB | −0.8100^{***} (−35.97) | 0.0019^{***} (3.77) | −0.7980^{***} (−35.78) | 0.0516^{***} (7.01) | −0.8038^{***} (−35.68) |
Cash | −1.6649^{***} (−4.17) | 0.1234^{***} (13.53) | −0.9028^{**} (−2.27) | −0.4065^{***} (−3.11) | −1.7141^{***} (−4.29) |
PPE | 3.2902^{***} (6.69) | −0.0426^{***} (−3.79) | 3.0273^{***} (6.22) | 0.8900^{***} (5.54) | 3.3978^{***} (6.91) |
Lncon | −3.7918^{***} (−10.84) | 0.1463^{***} (18.30) | −2.8884^{***} (−8.27) | −0.0607 (−0.53) | −3.7991^{***} (−10.87) |
Growth | 1.0812^{***} (9.92) | −0.0097^{***} (−3.91) | 1.0212^{***} (9.46) | 0.1997^{***} (5.61) | 1.1054^{***} (10.14) |
RET | −9.9885^{***} (−5.90) | −0.0463 (−1.20) | −10.2741^{***} (−6.13) | 0.0822 (0.15) | −9.9785^{***} (−5.90) |
Indratio | −3.4468^{***} (−3.86) | −0.0472^{**} (−2.31) | −3.7380^{***} (−4.23) | −0.3819 (−1.31) | −3.4929^{***} (−3.91) |
Duality | −0.4317^{***} (−3.73) | 0.0031 (1.18) | −0.4124^{***} (−3.59) | 0.2491^{***} (6.58) | −0.4016^{***} (−3.46) |
Constant | −39.1238^{***} (−32.53) | 1.2306^{***} (44.79) | −31.5255^{***} (−25.25) | 4.9456^{***} (12.58) | −38.5260^{***} (−31.93) |
Year/Industry | Yes | Yes | Yes | Yes | Yes |
N | 20097 | 20097 | 20097 | 20097 | 20097 |
Adj-R^{2} | 0.3661 | 0.1545 | 0.3787 | 0.3748 | 0.3670 |
Z | −2.7600^{***} | −5.2780^{***} | |||
Sobel Test | Std Err | 0.0005 | 0.0004 | ||
P | 0.0058 | 1.305e-07 |
Note: ^{***}, ** and * are significant at 1%, 5% and 10% levels respectively, the same below. NDT, non-debt tax shield.
To ensure the robustness of the empirical results, explanatory variables, intermediate variables and explained variables were replaced at the same time. Referring to the method of Tykvova and Borell (2012), Z_score1 is used to replace the original debt risk index Z_score. The calculation method of Z_score1 is as follows:
Z_score = 0.717 × (Operating funds/Total asset) + 0.847 × (Retained earnings/Total asset) + 3.107× (Earnings before interest and tax/Total asset) + 0.420 × (Value of equity/Value of liability) + 0.998 × (Sales revenue/Total asset)
For facilitating interpretation, Z_score1 in this paper has been negative in the robustness tests.
The results of the robustness test are shown in Table 4, column (1) is the total effect showing that the coefficient of
Robustness test after replace explanatory variables, mediation variables and explained variables.
−0.0087^{***} (−3.48) | 0.0007^{**} (2.57) | −0.0080^{***} (−3.22) | 0.0007^{***} (11.78) | −0.0082^{***} (−3.26) | |
Loantype | −1.0030^{***} (−6.95) | ||||
dum_PCM | −0.7536^{**} (−2.51) | ||||
Controls | Yes | Yes | Yes | Yes | Yes |
Year/Industry | Yes | Yes | Yes | Yes | Yes |
N | 20097 | 20097 | 20097 | 20097 | 20097 |
Adj-R^{2} | 0.3688 | 0.3432 | 0.4090 | 0.4055 | 0.3689 |
Z | −2.5610^{**} | −2.4540^{**} | |||
Sobel test | Std err | 0.0006 | 0.0002 | ||
P | 0.0104 | 0.0141 |
Note: The control variables in Table 4 are the same as those in Table 3.
To ensure the robustness of the conclusions of this study, the bootstrap method, the latest mediation test programme proposed internationally in recent years, is used to test the mediation effect of debt concentration and product market competitive advantage again. Table 5 is the Bootstrap test for the degree of debt concentration. Table 6 is the Bootstrap test for the product market competitive advantage. _bs_1 is the indirect effect, _bs_2 is the direct effect. Both in Tables 5 and 6 the _bs_1 indirect effect does not include 0 in the 95% confidence interval, representing the degree of debt concentration and product market competitive advantage plays an intermediary role between CSR fulfilment and debt risk. Therefore, the empirical research conclusion of this paper is robust.
Bootstrap method was used to test the mediation effect of debt concentration.
_bs_1 (ind_eff) | −0.00141562 | 0.0000239 | 0.00050512 | −0.0025358 | −0.000406 (P) |
−0.0217125 | −0.0003436 (BC) | ||||
_bs_2 (dir_eff) | −0.01463271 | 0.0001333 | 0.00349908 | −0.0024313 | −0.0079729 (P) |
−0.0212825 | −0.007886 (BC) |
Note: P is a confidence interval, BC is a confidence interval after deviation correction.
Bootstrap method was used to test the mediation effect of product market competitive advantage.
_bs_1 (ind_eff) | −0.0047 | 4.01E-05 | 0.000544 | −0.00587 | −0.0036 (P) |
−0.01384 | −0.00098 (P) | ||||
_bs_2 (dir_eff) | −0.0073 | 0.000111 | 0.003209 | −0.00591 | −0.00364 (BC) |
−0.01402 | −0.00129 (BC) |
Note: P is a confidence interval, BC is a confidence interval after deviation correction.
In firms with different property rights, there are great differences in their willingness and tendency to fulfil CSR and ability to deal with debt risks, in this circumstance, the mediating effect of the degree of debt concentration and the product market competitive advantage between the CSR fulfillment and debt risk would quiet difference. According to the property rights of firms, the samples are divided into state-owned firms group and private firms group. Table 7 shows the empirical test results of the mediation effect for state-owned firms, column (1) of Table 7 shows that the estimation coefficients between CSR and Z_score are significantly negative, it shows that fulfilling CSR by state-owned firms can reduce the debt risk the firm faced.
Sample of state-owned enterprises.
CSR | −0.0175^{***} (−5.53) | −0.0002 (−1.49) | −0.0180^{***} (−5.73) | 0.0172^{***} (11.10) | −0.0178^{***} (−5.59) |
Loanconcen | 3.1501^{***} (10.04) | ||||
RPCM | 0.0185 (0.83) | ||||
Controls | Yes | Yes | Yes | Yes | Yes |
Year/Industry | Yes | Yes | Yes | Yes | Yes |
N | 8350 | 8350 | 8350 | 8350 | 8350 |
Adj-R^{2} | 0.3324 | 0.1644 | 0.3403 | 0.3881 | 0.3324 |
Z | −1.4780 | 0.8238 | |||
Sobel test | Std err | 0.0004 | 0.0004 | ||
P | 0.1394 | 0.4081 |
Note: The control variables in Table 7 are the same as those in Table 3.
Column (2) is the second step to test the mediating effect of the degree of debt concentration, and the estimated coefficients between Loanconcen and CSR are not significant, meanwhile, the Z value and P-value in the Sobel test are −1.4780 and 0.1394 respectively, and it shows that the mediation effect of degree of debt concentration does not exist in state-owned firms. Column (5) is the third step of testing the intermediary effect of product market competitive advantage, the estimation coefficient of RPCM and Z_score is not significant, and the Z value and P-value in the Sobel test are 0.8238 and 0.4081 respectively, as it shows that the mediation effect of product market competitive advantage does not exist in state-owned firms. The above empirical test results indicate that the CSR fulfillment by state-owned firms cannot reduce debt risk by dispersing the degree of debt concentration and improving the competitive advantage in the product market.
Table 8 shows the empirical test results of the mediation effect of the private firms, the estimated coefficient between CSR and Z_score in column (1) of Table 8 is −0.0136, which is significant at the 5%, it shows that fulfilling CSR in private firms can mitigate the debt risk. The estimated coefficients of Loanconcen and CSR in column (2) are significantly negative at the 1% level. Column (3) the estimation coefficient between CSR and Z_score is not significant. Meanwhile, the Z value of the Sobel test is −5.3310, which is significant at the level of 1%, it shows that the degree of debt concentration has a complete intermediary effect in private firms. The estimated coefficient of RPCM and CSR in column (4) is 0.0219, which is significant at the 1% level, combined with the test results of column (5), the estimation coefficient between CSR and Z_score is not significant, Z-value of Sobel test is −5.3950, which is significant at the level of 1%. It shows that the product market competitive advantage in private firms has a complete intermediary effect. The above empirical test results indicate that the CSR fulfilment of private firms can reduce debt risk by dispersing the degree of debt concentration and improving the competitive advantage of the product market.
Sample of private enterprises.
CSR | −0.0136^{**} (−2.14) | −0.0232^{***} (−11.35) | −0.0089 (−1.03) | 0.0219^{***} (12.40) | −0.0092 (−1.44) |
Loanconcen | 0.2060^{***} (6.92) | ||||
RPCM | −0.2000^{***} (−5.99) | ||||
Controls | Yes | Yes | Yes | Yes | Yes |
Year/Industry | Yes | Yes | Yes | Yes | Yes |
N | 11646 | 11646 | 11646 | 11646 | 11646 |
Adj-R^{2} | 0.3688 | 0.1675 | 0.3840 | 0.3809 | 0.3707 |
Z | −5.3310^{***} | −5.3950^{***} | |||
Sobel test | Std err | 0.0010 | 0.0008 | ||
P | 5.763e-11 | 6.850e-08 |
Note: The control variables in Table 8 are the same as those in Table 3.
The reason is that state-owned firms have dual operation objectives under the institutional background of China, the first objective is to seek profitability and development for itself, and the second objective is to help local governments share certain social responsibilities, assist local governments in maintaining social stability, promote employment and local economic development, so local governments usually lend a helping hand with tax reduction and exemption, government subsidies and even debt forgiveness to state-owned firms. The protection of ‘fatherism’ behaviour by local government such as policy support and regional barriers, could destruct the positive effects of the competition mechanism so that state-owned firms will no longer be committed to cultivating competitive advantages to enhance competitiveness, and the heavy burden of CSR will also squeeze out the resources that should have been used to enhance the competitive advantage of the product market in state-owned firms. By contrast, private firms do not need to bear the policy burden because there is no natural connection between them and the government. Therefore, private firms can distinguish themselves from their competitors by establishing a reputation through their CSR fulfilment, to deliver positive signals to the government and other key stakeholders to obtain scarce credit resources and obtain the support of stakeholders in the fierce product market competition to alleviate the debt risks.
Enterprises in different regions, no matter the degree of economic activity, the maturity of the financial market or the intensity of market competition, therefore, the impact of CSR fulfillment on debt risk through debt concentration and product market competitive advantage will also be greatly different. In this paper, the sample is divided into eastern regions, central and western regions according to the location of enterprise registration. Table 9 reports the mediating effect of test results of firms domiciled in the eastern regions, and Table 10 shows the mediating effect of test results of the firms registered in central and western regions. As can be seen from column (1) of Table 9, the estimated coefficient between CSR and Z_score is significantly negative at the 5% level, and the estimated coefficients of Loanconcen and CSR in column (2) are significantly negative at the 1% level, the estimation coefficient between CSR and Z_score is not significant in column (3), meanwhile, the Z-value of Sobel test is −4.5060 which is significant at the level of 1%, indicating that the degree of debt concentration has a complete intermediary effect on firms located in eastern regions of China. Table 9 column (4) reports the second step of testing the mediating effect of product market competitive advantage, the estimated coefficient of RPCM and CSR is significantly positive at the 1% level, combined with the test results of column (5), it can be seen that the estimation coefficient between CSR and Z_score is not significant, while that between RPCM and Z_score is significant at 1% level. The Z-value of the Sobel test is −5.2470, significant at the 1% level, the results show that there also exists a complete mediating effect of product market competitive advantage among firms in eastern China.
Sample of firms registered in the eastern region.
CSR | −0.0100^{**} (−2.17) | −0.0303^{***} (−9.54) | −0.0086 (−1.34) | 0.0201^{***} (14.14) | −0.0069 (−1.48) |
Loanconcen | 0.2834^{***} (6.02) | ||||
RPCM | −0.1559^{***} (−5.65) | ||||
Controls | Yes | Yes | Yes | Yes | Yes |
Year/Industry | Yes | Yes | Yes | Yes | Yes |
N | 13755 | 13755 | 13755 | 13755 | 13755 |
Adj-R^{2} | 0.3606 | 0.1750 | 0.3723 | 0.3743 | 0.3620 |
Z | −4.5060^{***} | −5.2470^{***} | |||
Sobel test | Std err | 0.0006 | 0.0006 | ||
P | 2.531e-06 | 1.542e-07 |
Note: The control variables in Table 9 are the same as those in Table 3.
Sample of firms registered in the central and western region.
CSR | −0.0194^{***} (−3.46) | −0.0142^{***} (−4.21) | −0.0153^{***} (−3.08) | 0.0162^{***} (7.75) | −0.0183^{***} (−3.24) |
Loanconcen | 0.2237^{***} (6.28) | ||||
RPCM | −0.0685^{**} (−2.03) | ||||
Controls | Yes | Yes | Yes | Yes | Yes |
Year/Industry | Yes | Yes | Yes | Yes | Yes |
N | 6342 | 6342 | 6342 | 6342 | 6342 |
Adj-R^{2} | 0.3843 | 0.1230 | 0.3986 | 0.3870 | 0.3846 |
Z | −2.2020^{***} | 1.9640^{**} | |||
Sobel test | Std err | 0.0009 | 0.0006 | ||
P | 0.0013 | 0.0496 |
Note: The control variables in Table 10 are the same as those in Table 3.
As can be seen from column (1) of Table 10, the estimated coefficient between CSR and Z_score is significantly negative at the 1% level, column (2) lists the second step of the mediating effect test of the degree of debt concentration, the estimated coefficients of Loanconcen and CSR is also significant negative at the 1% level, the Z value of Sobel test is −2.2020 and the P-value of Sobel test is 0.0013, it shows that partial mediating effect of degree of debt concentration exists in the firms which were registered in middle and western regions. Table 10 column (4) reports the second step of testing the mediating effect of product market competitive advantage, the estimated coefficient of RPCM and CSR is significantly positive at the 1% level.
Compared with column (1), the estimated coefficient between CSR and Z_score changes significantly in column (5), the Z value of the Sobel test is 1.9640, and the P-value of the Sobel test is 0.0496, the results show that the product market competitive advantage has a partial mediating effect to the firms located in the central and western regions.
The above-grouped test results show that CSR fulfilment reduces debt risk more obviously in eastern regions by dispersing the concentration of debt and improving the competitive advantage of the product market.
The higher legal level that persists in the eastern region can make the firm's debt default behaviour be punished in time and provide a strong guarantee for the performance of the debt obligation by borrowers. At the same time, the process of marketisation in the eastern region is faster, the level of economic development is higher, and the competition among enterprises is also becoming more intense. The public pays more attention to the performance of corporate social responsibility which is conducive to the realisation of differentiation strategy and improvement of the competitiveness of firms in the product market, playing a better role in restraining the debt risk of firms.
The central and western regions have a low level of economic development marketisation process and legalisation process are relatively backward, firms are subject to more government intervention, and the government pays more attention to local economic development than CSR. The difficulty of debt financing of firms in the central and western regions not only depends on the fulfilment of CSR but also depends on the ‘government-firm relationship’ and ‘bank-firm relationship’, the financing channels of firms are relatively single, the degree of market competition is also relatively low.
In general, the research conclusions of this paper confirm that CSR fulfillment has an inhibitory effect on debt risk, and use the mediation effect model to analyse the internal mechanism of CSR fulfilment affecting on debt risk, it also expands the research on the economic consequences of CSR fulfillment. The research of this paper also shows that CSR fulfillment can enable firms to obtain debt financing from more channels and make the debt structure more decentralised, it is helpful to understand the formation and determinants of capital structure, and it is found that the degree of debt concentration is an important mediating factor between the fulfillment of CSR and debt risk, has certain theoretical significance. Banks and other financial institutions can incorporate corporate social responsibility performance into their credit evaluation system to help banks build a scientific credit decision-making system. In view of the present situation of CSR, the fulfilment level is generally low in China. The research conclusions of this paper also help the firm to realise that actively fulfilling CSR can enable itself to obtain high-quality resources needed for survival and development on their own and thus establish competitive advantages. Finally, for policymakers, it is necessary to establish and improve the supervision and evaluation mechanism of CSR fulfilment. Policy makers need to improve the information environment, dredge the circulation channel between the enterprise and the resource provider, guide advantageous resources to flow to firms that perform CSR well, and help firms and the whole society achieve sustainable development. Therefore, the research conclusion of this paper has certain practical guiding significance for enterprises, capital providers and policy makers.
CSR fulfillment and debt risk: based on the mediating effect test of debt concentration and product market competitive advantage (take a negative number of Z.score).
CSR | −0.0132 |
−0.0112 |
−0.0106 |
0.0186 |
−0.0110 |
Loanconcen | 0.2321 |
||||
RPCM | −0.1209 |
||||
Size | 1.8089 |
−0.0408 |
1.5572 |
−0.0102 (−0.61) | 1.8076 |
Roa | −34.1504 |
0.2331 |
−32.7111 |
25.8148 |
−31.0300 |
Age | 0.0560 |
0.0013 |
0.0637 |
−0.0668 |
0.0479 |
Overhead | 4.0819 |
−0.2695 |
2.4178 (1.15) | −12.2106 |
2.6060 (1.22) |
NDTS | 13.7700 |
−1.0049 |
7.5650 (1.54) | −8.4793 |
12.7451 |
MTB | −0.8100 |
0.0019 |
−0.7980 |
0.0516 |
−0.8038 |
Cash | −1.6649 |
0.1234 |
−0.9028 |
−0.4065 |
−1.7141 |
PPE | 3.2902 |
−0.0426 |
3.0273 |
0.8900 |
3.3978 |
Lncon | −3.7918 |
0.1463 |
−2.8884 |
−0.0607 (−0.53) | −3.7991 |
Growth | 1.0812 |
−0.0097 |
1.0212 |
0.1997 |
1.1054 |
RET | −9.9885 |
−0.0463 (−1.20) | −10.2741 |
0.0822 (0.15) | −9.9785 |
Indratio | −3.4468 |
−0.0472 |
−3.7380 |
−0.3819 (−1.31) | −3.4929 |
Duality | −0.4317 |
0.0031 (1.18) | −0.4124 |
0.2491 |
−0.4016 |
Constant | −39.1238 |
1.2306 |
−31.5255 |
4.9456 |
−38.5260 |
Year/Industry | Yes | Yes | Yes | Yes | Yes |
N | 20097 | 20097 | 20097 | 20097 | 20097 |
Adj-R^{2} | 0.3661 | 0.1545 | 0.3787 | 0.3748 | 0.3670 |
Z | −2.7600 |
−5.2780 |
|||
Sobel Test | Std Err | 0.0005 | 0.0004 | ||
P | 0.0058 | 1.305e-07 |
Variable definitions.
Explained variables | FDR | Z_score is calculated in section |
Explanatory variables | CSR | CSR score is obtained from the CSR report of listed companies published in Hexun.com. |
Mediating | Loanconcen | Loanconcen is calculated in the above model section |
Variables | RPCM | The value of RPCM ranges from 1 to 10. For details, see above. |
Size | Natural logarithm of total assets. | |
Roa | Roa is pretax operating income divided by total assets. | |
Age | Age is equal to inspection year minus listing year. | |
Overhead | Overhead is the management expense happened during the year divided by total assets. | |
Control variables | NDTS | NDTS is the ratio of current year depreciation and amortisation to total assets. |
MTB | MTB is the growth rate of firms and is the ratio of the market value of equity to the book value of equity. | |
Cash | Cash is the adequacy of free cash flow = (Net cash flow from operating activities + Net cash flow from investment activities)/Total assets at beginning of year | |
PPE | The ratio of the total noncurrent asset to total asset. | |
Lncon | Lncon is the combined shareholding of the top five shareholders. | |
Growth | Growth = (Operating income for current year − Operating income for previous year)/Operating income for previous year | |
RET | RET is the firm's average monthly stock return during the year. | |
Indratio | The ratio of the number of independent directors to the number of directors. | |
Duality | Duality is a dummy variable that equals 1 if the same person holds the post of chairman and general manager and 0 otherwise. |
Descriptive statistics.
Z_score | 20097 | 0.1730 | 6.2083 | 1.9552 | 3.5302 | 6.7077 | 8.3996 | 63.7491 |
Loanconcen | 20097 | 0.0947 | 0.3291 | 0.2069 | 0.2874 | 0.4076 | 0.1662 | 0.9573 |
RPCM | 20097 | 1.0000 | 5.4278 | 3.0000 | 5.0000 | 8.0000 | 2.7644 | 10.0000 |
CSR | 20097 | −2.8200 | 25.2250 | 16.5400 | 22.1200 | 28.1200 | 16.4951 | 73.8200 |
Size | 20097 | 19.4961 | 22.2871 | 21.3812 | 22.1076 | 23.0129 | 1.2774 | 26.0740 |
Roa | 20097 | −0.2147 | 0.0379 | 0.0138 | 0.0348 | 0.0632 | 0.0552 | 0.2069 |
Age | 20097 | 2.0000 | 10.8679 | 5.0000 | 10.0000 | 16.0000 | 6.6695 | 25.0000 |
Overhead | 20097 | 0.0042 | 0.0440 | 0.0244 | 0.0387 | 0.0573 | 0.0279 | 0.1627 |
NDTS | 20097 | 0.0007 | 0.0240 | 0.0123 | 0.0213 | 0.0327 | 0.0156 | 0.0765 |
MTB | 20097 | 0.5909 | 3.3956 | 1.6771 | 2.5835 | 4.1147 | 2.7960 | 19.8846 |
Cash | 20097 | −0.5918 | −0.0207 | −0.0743 | −0.0053 | 0.0489 | 0.1270 | 0.3322 |
PPE | 20097 | 0.0019 | 0.2202 | 0.0905 | 0.1870 | 0.3155 | 0.1646 | 0.7149 |
Lncon | 20097 | 0.2002 | 0.5257 | 0.4145 | 0.5256 | 0.6345 | 0.1507 | 0.8872 |
Growth | 20097 | −0.5576 | 0.1908 | −0.0111 | 0.1124 | 0.2727 | 0.4569 | 3.3170 |
RET | 20097 | −0.0864 | 0.0110 | −0.0173 | 0.0062 | 0.0321 | 0.0421 | 0.2276 |
Indratio | 20097 | 0.3333 | 0.3747 | 0.3333 | 0.3333 | 0.4286 | 0.0537 | 0.5714 |
Duality | 20097 | 0.0000 | 0.2395 | 0.0000 | 0.0000 | 0.0000 | 0.4268 | 1.0000 |
Sample of firms registered in the central and western region.
CSR | −0.0194^{***} (−3.46) | −0.0142^{***} (−4.21) | −0.0153^{***} (−3.08) | 0.0162^{***} (7.75) | −0.0183^{***} (−3.24) |
Loanconcen | 0.2237^{***} (6.28) | ||||
RPCM | −0.0685^{**} (−2.03) | ||||
Controls | Yes | Yes | Yes | Yes | Yes |
Year/Industry | Yes | Yes | Yes | Yes | Yes |
N | 6342 | 6342 | 6342 | 6342 | 6342 |
Adj-R^{2} | 0.3843 | 0.1230 | 0.3986 | 0.3870 | 0.3846 |
Z | −2.2020^{***} | 1.9640^{**} | |||
Sobel test | Std err | 0.0009 | 0.0006 | ||
P | 0.0013 | 0.0496 |
Bootstrap method was used to test the mediation effect of product market competitive advantage.
_bs_1 (ind_eff) | −0.0047 | 4.01E-05 | 0.000544 | −0.00587 | −0.0036 (P) |
−0.01384 | −0.00098 (P) | ||||
_bs_2 (dir_eff) | −0.0073 | 0.000111 | 0.003209 | −0.00591 | −0.00364 (BC) |
−0.01402 | −0.00129 (BC) |
Sample of private enterprises.
CSR | −0.0136^{**} (−2.14) | −0.0232^{***} (−11.35) | −0.0089 (−1.03) | 0.0219^{***} (12.40) | −0.0092 (−1.44) |
Loanconcen | 0.2060^{***} (6.92) | ||||
RPCM | −0.2000^{***} (−5.99) | ||||
Controls | Yes | Yes | Yes | Yes | Yes |
Year/Industry | Yes | Yes | Yes | Yes | Yes |
N | 11646 | 11646 | 11646 | 11646 | 11646 |
Adj-R^{2} | 0.3688 | 0.1675 | 0.3840 | 0.3809 | 0.3707 |
Z | −5.3310^{***} | −5.3950^{***} | |||
Sobel test | Std err | 0.0010 | 0.0008 | ||
P | 5.763e-11 | 6.850e-08 |
Sample of firms registered in the eastern region.
CSR | −0.0100^{**} (−2.17) | −0.0303^{***} (−9.54) | −0.0086 (−1.34) | 0.0201^{***} (14.14) | −0.0069 (−1.48) |
Loanconcen | 0.2834^{***} (6.02) | ||||
RPCM | −0.1559^{***} (−5.65) | ||||
Controls | Yes | Yes | Yes | Yes | Yes |
Year/Industry | Yes | Yes | Yes | Yes | Yes |
N | 13755 | 13755 | 13755 | 13755 | 13755 |
Adj-R^{2} | 0.3606 | 0.1750 | 0.3723 | 0.3743 | 0.3620 |
Z | −4.5060^{***} | −5.2470^{***} | |||
Sobel test | Std err | 0.0006 | 0.0006 | ||
P | 2.531e-06 | 1.542e-07 |
Bootstrap method was used to test the mediation effect of debt concentration.
_bs_1 (ind_eff) | −0.00141562 | 0.0000239 | 0.00050512 | −0.0025358 | −0.000406 (P) |
−0.0217125 | −0.0003436 (BC) | ||||
_bs_2 (dir_eff) | −0.01463271 | 0.0001333 | 0.00349908 | −0.0024313 | −0.0079729 (P) |
−0.0212825 | −0.007886 (BC) |
Robustness test after replace explanatory variables, mediation variables and explained variables.
−0.0087^{***} (−3.48) | 0.0007^{**} (2.57) | −0.0080^{***} (−3.22) | 0.0007^{***} (11.78) | −0.0082^{***} (−3.26) | |
Loantype | −1.0030^{***} (−6.95) | ||||
dum_PCM | −0.7536^{**} (−2.51) | ||||
Controls | Yes | Yes | Yes | Yes | Yes |
Year/Industry | Yes | Yes | Yes | Yes | Yes |
N | 20097 | 20097 | 20097 | 20097 | 20097 |
Adj-R^{2} | 0.3688 | 0.3432 | 0.4090 | 0.4055 | 0.3689 |
Z | −2.5610^{**} | −2.4540^{**} | |||
Sobel test | Std err | 0.0006 | 0.0002 | ||
P | 0.0104 | 0.0141 |
Sample of state-owned enterprises.
CSR | −0.0175^{***} (−5.53) | −0.0002 (−1.49) | −0.0180^{***} (−5.73) | 0.0172^{***} (11.10) | −0.0178^{***} (−5.59) |
Loanconcen | 3.1501^{***} (10.04) | ||||
RPCM | 0.0185 (0.83) | ||||
Controls | Yes | Yes | Yes | Yes | Yes |
Year/Industry | Yes | Yes | Yes | Yes | Yes |
N | 8350 | 8350 | 8350 | 8350 | 8350 |
Adj-R^{2} | 0.3324 | 0.1644 | 0.3403 | 0.3881 | 0.3324 |
Z | −1.4780 | 0.8238 | |||
Sobel test | Std err | 0.0004 | 0.0004 | ||
P | 0.1394 | 0.4081 |
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Mathematical Equations A study on the phenomenon of anaphoric correction in college students’ English conversation Computer Art Design Model Based on Nonlinear Fractional Differential Equations The Optimization Model of Public Space Design Teaching Reform Based on Fractional Differential Equations The Approximate Solution of Nonlinear Vibration of Tennis Based on Nonlinear Vibration Differential Equation Graphical Modular Power Technology of Distribution Network Based on Machine Learning Statistical Mathematical Equation Employment and Professional Education Training System of College Graduates Based on the Law of Large Numbers Economic Research on Multiple Linear Regression in Fruit Market inspection and Management Nonlinear Differential Equations in Preventing Financial Risks Lagrange’s Mathematical Equations in the Sports Training of College Students Simulation Research of Electrostatic Precipitator Power Supply Voltage Control System Based on Finite Element Differential Equation Research on the effect of generative adversarial network based on wavelet transform hidden Markov model on face creation and classification Research on Lightweight Injection Molding (CAE) and Numerical Simulation Calculate of New Energy Vehicle Power Flow Calculation in Smart Distribution Network Based on Power Machine Learning Based on Fractional Differential Equations Demonstration of application program of logistics public information management platform based on fuzzy constrained programming mathematical model Basketball Shooting Rate Based on Multiple Regression Logical-Mathematical Algorithm The Optimal Application of Lagrangian Mathematical Equations in Computer Data Analysis Similarity Solutions of the Surface Waves Equation in (2+1) Dimensions and Bifurcation Optimal decisions and channel coordination of a green supply chain with marketing effort and fairness concerns Game theoretic model for low carbon supply chain under carbon emissions reduction sensitive random demand Limit cycles of a generalised Mathieu differential system Influence of displacement ventilation on the distribution of pollutant concentrations in livestock housing Application of data mining in basketball statistics The nonlinear effects of ageing on national savings rate – An Empirical Study based on threshold model Design of fitness walker for the elderly based on ergonomic SAPAD model AtanK-A New SVM Kernel for Classification Mechanical behaviour of continuous girder bridge with corrugated steel webs constructed by RW Study of a linear-physical-programming-based approach for web service selection under uncertain service quality The Relationship Between College Students’ Taekwondo Courses and College Health Based on Mathematical Statistics Equations Analysis and countermeasures of cultivating independent learning ability in colleges teaching English based on OBE theory A mathematical model of plasmid-carried antibiotic resistance transmission in two types of cells Fractional Differential Equations in the Exploration of Geological and Mineral Construction AdaBoost Algorithm in Trustworthy Network for Anomaly Intrusion Detection Projection of Early Warning Identification of Hazardous Sources of Gas Explosion Accidents in Coal Mines Based on NTM Deep Learning Network Burnout of front-line city administrative law-enforcing personnel in new urban development areas: An empirical research in China Enterprise Financial Risk Early Warning System Based on Structural Equation Model A Study on the Application of Quantile Regression Equation in Forecasting Financial Value at Risk in Financial Markets Fractional Differential Equations in the Model of Vocational Education and Teaching Practice Environment Information transmission simulation of Internet of things communication nodes under collision free probability equation Image denoising model based on improved fractional calculus mathematical equation Random Fourier Approximation of the Kernel Function in Programmable Networks The Complexity of Virtual Reality Technology in the Simulation and Modeling of Civil Mathematical Models University Library Lending System Model Based on Fractional Differential Equations Calculation and Performance Evaluation of Text Similarity Based on Strong Classification Features Intelligent Matching System of Clauses in International Investment Arbitration Cases Based on Big Data Statistical Model Evaluation and Verification of Patent Value Based on Combination Forecasting Model Financial Institution Prevention Financial Risk Monitoring System Under the Fusion of Partial Differential Equations Prediction and Analysis of ChiNext Stock Price Based on Linear and Non-linear Composite Model Calculus Logic Function in Tax Risk Avoidance in Different Stages of Enterprises The Psychological Memory Forgetting Model Based on the Analysis of Linear Differential Equations Optimization Simulation System of University Science Education Based on Finite Differential Equations The Law of Large Numbers in Children's Education Optimization System of Strength and Flexibility Training in Aerobics Course Based on Lagrangian Mathematical Equation Data structure simulation for the reform of the teaching process of university computer courses RETRACTION NOTE Research on the mining of ideological and political knowledge elements in college courses based on the combination of LDA model and Apriori algorithm Research on non-linear visual matching model under inherent constraints of images Good congruences on weakly U-abundant semigroups Can policy coordination facilitate unimpeded trade? An empirical study on factors influencing smooth trade along the Belt and Road Research on the processing method of multi-source heterogeneous data in the intelligent agriculture cloud platform Internal control index and enterprise growth: An empirical study of Chinese listed-companies in the automobile manufacturing industry Research on design of customer portrait system for E-commerce Research on rule extraction method based on concept lattice of intuitionistic fuzzy language Fed-UserPro: A user profile construction method based on federated learning A multi-factor Regression Equation-based Test of Fitness Maximal Aerobic Capacity in Athletes Design and evaluation of intelligent teaching system on basic movements in PE Garment Image Retrieval based on Grab Cut Auto Segmentation and Dominate Color Method Financial Risk Prediction and Analysis Based on Nonlinear Differential Equations Constructivist Learning Method of Ordinary Differential Equations in College Mathematics Teaching Multiple Effects Analysis of Hangzhou Issuing Digital Consumer Coupons Based on Simultaneous Equations of CDM Model Response Model of Teachers’ Psychological Education in Colleges and Universities Based on Nonlinear Finite Element Equations A Hybrid Computational Intelligence Method of Newton's Method and Genetic Algorithm for Solving Compatible Nonlinear Equations Pressure Image Recognition of Lying Positions Based on Multi-feature value Regularized Extreme Learning Algorithm English Intelligent Question Answering System Based on elliptic fitting equation Precision Machining Technology of Jewelry on CNC Machine Tool Based on Mathematical Modeling Application Research of Mathematica Software in Calculus Teaching Computer Vision Communication Technology in Mathematical Modeling Skills of Music Creation Based on Homogeneous First-Order Linear Partial Differential Equations Mathematical Statistics Technology in the Educational Grading System of Preschool Students Music Recommendation Index Evaluation Based on Logistic Distribution Fitting Transition Probability Function Children's Educational Curriculum Evaluation Management System in Mathematical Equation Model Query Translation Optimization and Mathematical Modeling for English-Chinese Cross-Language Information Retrieval The Effect of Children’s Innovative Education Courses Based on Fractional Differential Equations Fractional Differential Equations in the Standard Construction Model of the Educational Application of the Internet of Things Optimization research on prefabricated concrete frame buildings based on the dynamic equation of eccentric structure and horizontal-torsional coupling Optimization in Mathematics Modeling and Processing of New Type Silicate Glass Ceramics Green building considering image processing technology combined with CFD numerical simulation Research on identifying psychological health problems of college students by logistic regression model based on data mining Abnormal Behavior of Fractional Differential Equations in Processing Computer Big Data Mathematical Modeling Thoughts and Methods Based on Fractional Differential Equations in Teaching Research on evaluation system of cross-border E-commerce platform based on the combined model A mathematical model of PCNN for image fusion with non-sampled contourlet transform Nonlinear Differential Equations in Computer-Aided Modeling of Big Data Technology The Uniqueness of Solutions of Fractional Differential Equations in University Mathematics Teaching Based on the Principle of Compression Mapping Financial customer classification by combined model Influence of displacement ventilation on the distribution of pollutant concentrations in livestock housing Recognition of Electrical Control System of Flexible Manipulator Based on Transfer Function Estimation Method Automatic Knowledge Integration Method of English Translation Corpus Based on Kmeans Algorithm Real Estate Economic Development Based on Logarithmic Growth Function Model Design of Tennis Mobile Teaching Assistant System Based on Ordinary Differential Equations Financial Crisis Early Warning Model of Listed Companies Based on Fisher Linear Discriminant Analysis High Simulation Reconstruction of Crowd Animation Based on Optical Flow Constraint Equation Construction of Intelligent Search Engine for Big Data Multimedia Resource Subjects Based on Partial Least Squares Structural Equation 3D Animation Simulation of Computer Fractal and Fractal Technology Combined with Diamond-Square Algorithm Analysis of the Teaching Quality of Physical Education Class by Using the Method of Gradient Difference The Summation of Series Based on the Laplace Transformation Method in Mathematics Teaching Optimal Solution of the Fractional Differential Equation to Solve the Bending Performance Test of Corroded Reinforced Concrete Beams under Prestressed Fatigue Load Animation VR scene mosaic modeling based on generalized Laplacian equation Radial Basis Function Neural Network in Vibration Control of Civil Engineering Structure Optimal Model Combination of Cross-border E-commerce Platform Operation Based on Fractional Differential Equations The influence of accounting computer information processing technology on enterprise internal control under panel data simultaneous equation Research on Stability of Time-delay Force Feedback Teleoperation System Based on Scattering Matrix BIM Building HVAC Energy Saving Technology Based on Fractional Differential Equation Construction of comprehensive evaluation index system of water-saving irrigation project integrating penman Montei the quation Human Resource Management Model of Large Companies Based on Mathematical Statistics Equations Data Forecasting of Air-Conditioning Load in Large Shopping Malls Based on Multiple Nonlinear Regression Analysis of technical statistical indexes of college tennis players under the win-lose regression function equation Automatic extraction and discrimination of vocal main melody based on quadratic wave equation Analysis of wireless English multimedia communication based on spatial state model equation Optimization of Linear Algebra Core Function Framework on Multicore Processors Application of hybrid kernel function in economic benefit analysis and evaluation of enterprises Research on classification of e-commerce customers based on BP neural network The Control Relationship Between the Enterprise's Electrical Equipment and Mechanical Equipment Based on Graph Theory Mathematical Modeling and Forecasting of Economic Variables Based on Linear Regression Statistics Nonlinear Differential Equations in Cross-border E-commerce Controlling Return Rate 3D Mathematical Modeling Technology in Visualized Aerobics Dance Rehearsal System Fractional Differential Equations in Electronic Information Models BIM Engineering Management Oriented to Curve Equation Model Leakage control of urban water supply network and mathematical analysis and location of leakage points based on machine learning Analysis of higher education management strategy based on entropy and dissipative structure theory Prediction of corporate financial distress based on digital signal processing and multiple regression analysis Mathematical Method to Construct the Linear Programming of Football Training Multimedia sensor image detection based on constrained underdetermined equation The Size of Children's Strollers of Different Ages Based on Ergonomic Mathematics Design Application of Numerical Computation of Partial Differential Equations in Interactive Design of Virtual Reality Media Stiffness Calculation of Gear Hydraulic System Based on the Modeling of Nonlinear Dynamics Differential Equations in the Progressive Method Knowledge Analysis of Charged Particle Motion in Uniform Electromagnetic Field Based on Maxwell Equation Relationship Between Enterprise Talent Management and Performance Based on the Structural Equation Model Method Term structure of economic management rate based on parameter analysis of estimation model of ordinary differential equation Influence analysis of piano music immersion virtual reality cooperation based on mapping equation Chinese painting and calligraphy image recognition technology based on pseudo linear directional diffusion equation Label big data compression in Internet of things based on piecewise linear regression Animation character recognition and character intelligence analysis based on semantic ontology and Poisson equation Design of language assisted learning model and online learning system under the background of artificial intelligence Study on the influence of adolescent smoking on physical training vital capacity in eastern coastal areas Application of machine learning in stock selection Comparative analysis of CR of ideological and political education in different regions based on improved fuzzy clustering Action of Aut( G ) on the set of maximal subgroups ofp -groupsThe internal mechanism of corporate social responsibility fulfillment affecting debt risk in China: analysis of intermediary transmission effect based on degree of debt concentration and product market competitive advantage Study on transmission characteristics in three kinds of deformed finlines based on edge-based finite element method Asymptotic stability problem of predator–prey system with linear diffusion Research on loyalty prediction of e-commerce customer based on data mining Algebraic Equations in Educational Model of College Physical Education Course Education Professional English Translation Corpus Under the Binomial Theorem Coefficient Geometric Tolerance Control Method for Precision Machinery Based on Image Modeling and Novel Saturation Function Retrieval and Characteristic Analysis of Multimedia Tester Based on Bragg Equation Semiparametric Spatial Econometric Analysis of Household Consumption Based on Ordinary Linear Regression Model Video adaptive watermark embedding and detection algorithm based on phase function equation English Learning Motivation of College Students Based on probability Distribution Scientific Model of Vocational Education Teaching Method in Differential Nonlinearity Research on mobile Awareness service and data privacy Protection based on Linear Equations computing protocol Vocal Music Teaching Model Based on Finite Element Differential Mathematical Equations Studying a matching method combining distance proximity and buffer constraints The trend and influence of media information Propagation based on nonlinear Differential equation Research on the construction of early warning model of customer churn on e-commerce platform Evaluation and prediction of regional human capital based on optimised BP neural network Study on inefficient land use determination method for cities and towns from a city examination perspective A sentiment analysis method based on bidirectional long short-term memory networks A study of local smoothness-informed convolutional neural network models for image inpainting Mathematical Calculus Modeling in Improving the Teaching Performance of Shot Put Application of Nonlinear Differential Equation in Electric Automation Control System Higher Mathematics Teaching Curriculum Model Based on Lagrangian Mathematical Model Computational Algorithm to Solve Two–Body Problem Using Power Series in Geocentric System Decisions of competing supply chain with altruistic retailer under risk aversion Optimization of Color Matching Technology in Cultural Industry by Fractional Differential Equations The Marketing of Cross-border E-commerce Enterprises in Foreign Trade Based on the Statistics of Mathematical Probability Theory Application of Linear Partial Differential Equation Theory in Guiding Football Scientific Training Nonlinear Channel Estimation for Internet of Vehicles Some Necessary Conditions for Feedback Functions of de Bruijn Sequences The Evolution Model of Regional Tourism Economic Development Difference Based on Spatial Variation Function System Model of Shipping Enterprise Safety Culture Based on Dynamic Calculation Matrix Model An empirical research on economic growth from industrial structure optimisation in the Three Gorges Reservoir area The Inner Relationship between Students' Psychological Factors and Physical Exercise Based on Structural Equation Model (SEM) Analysis and Research on Influencing Factors of Ideological and Political Education Teaching Effectiveness Based on Linear Equation Study of agricultural finance policy information extraction based on ELECTRA-BiLSTM-CRF Fractional Differential Equations in Sports Training in Universities Examination and Countermeasures of Network Education in Colleges and Universities Based on Ordinary Differential Equation Model Innovative research of vertical video creation under the background of mobile communication Higher Education Agglomeration Promoting Innovation and Entrepreneurship Based on Spatial Dubin Model Chinese-English Contrastive Translation System Based on Lagrangian Search Mathematical Algorithm Model Genetic algorithm-based congestion control optimisation for mobile data network