Equity Incentive Model, Source of Subject Matter and Enterprise Performance: Modification Effect Based on Equity Incentive Intensity

. For modern enterprises, equity incentive is an important means to solve the principal-agent problem, the choice of incentive mode and the source of the incentive is an inevitable issue in the implementation of an equity incentive scheme. Based on the sample data of A-share listed companies from 2010 to 2020, this paper constructs a panel two-way fxed efect model, combining regression analysis and three interactions with diferential equations (PDE), which empirically explores the relationship between two incentive models of stock option and restricted stock, the source of subject matter and enterprise performance. Te study shows that the restricted stock incentive model signifcantly improved the performance of enterprises, and the intensity of incentives played a signifcant inverted U -shaped moderating role between the enterprise’s performance and the diferent incentive models. After adding the subject matter incentive source, it is further found that repurchase, as the source of subject matter, has a positive moderating efect on restricted stock and a negative moderating efect on stock option. Te intensity of equity incentives moderates the relationship between stock option incentive models and enterprise performance when enterprises use repurchases as the source. Te results of the above-given research provide some reference for enterprises to give appropriate incentive intensities, objective selection of the subject matter source under diferent equity incentive models based on their characteristics, and facilitation of more efcient use of equity incentive tools.


Introduction
Te equity incentive mechanism started to be implemented in China in 2006. It gradually became a regular arrangement for listed enterprises to solve the principal-agent problem, which is essential to accelerate the convergence of owners and operators of enterprises to a community of interests [1]. Since the promulgation of the Measures for the Administration of Share Incentives of Listed Companies (hereinafter referred to as the Measures), there has been an explosion in academic research on equity incentives, with the number of articles published in core journals rising from 273 to 2715 according to statistics. Incremental improvements in the market economy tend to supplement the essential contractual components of enterprises' equity incentives, and researchers' research on equity incentives has been extended. Some researchers believed that setting the core contractual elements was an integral part of whether the equity incentive scheme can efectively resolve the moral hazard and adverse selection problems arising from the principal agent, and in the setting of contract elements, the choice of incentive model and incentive object is critical [2]. Presently, domestic enterprises mainly focus on two models of equity incentive, namely, stock option incentive and restricted stock incentive, and the source of subject matter incentive is mostly through repurchasing stock and issuing shares. So how does the heterogeneous nature of these two incentive models and the source of the subject matter afect the promotion of interest convergence between shareholders and managers and afect the performance of the enterprise? Tis is a question that warrants further study. At this stage, scholarly research on the relationship between equity incentive models and enterprise performance can be grouped into two main categories. Some academics argued that the restricted stock incentive model is directly related to the rewards received by executives, urging them to think carefully when making risky investments and infuencing them to make decisions. It is thus argued that restricted shares will be superior to stock option and that listed companies should be guided and encouraged in their policies to choose the restricted stock incentive model [3]. Taking entity enterprises as an example, Haiyan [4] explored the relationship between equity incentives and innovation performance in innovative frms from the perspective of equity incentives. It was found that for senior management, implementing a performance-based equity incentive model was more motivating than implementing a share price-based incentive model. Tis characteristic gives it a stronger incentive efect since the restricted stock is generally punitive in nature. For example, executives cannot unlock and sell their stock freely if they do not meet the agreed performance or fail a test. Wenzhe [5] introduced a framework of game theory analysis and conducted empirical testing using data from 2006 to 2017 on equity incentive plans for A-share listed companies. Te results showed that frms with high executive power also tend to choose restricted shares, the reason being that executives could make greater private gains through restricted shares granted at a discount. Based on the perspective of two incentive models, stock options and restricted stock, Songwen [6] used an extension test to show that restricted stock equity incentives had an inverted U-shaped relationship with corporate innovation investment. Trough an investigation of the infuence of incentive targets on the choice of equity incentive methods in listed companies, Shufang [7] conducted a three-step binary logistic regression on the sample and found that when the proportion of leaders among incentive targets was greater, frms did not select stock options that were more suitable for executives, but the more likely they were to select restricted stocks with higher profitability and equal rights and duties, and this was more apparent in frms with more managerial power. When the equity incentive plan meets the incentive characteristics, restricted stocks can play a better incentive efect and promote enterprise performance. Other academics had argued that the stock option model enhances corporate risk-taking more than the restricted stock model. Te incentive efect of stock option was superior to restricted stock. And, enterprise performance signifcantly improved with the intensity of equity incentives in companies that implement stock option. Lihui [8] selected typical listed companies using stock option and restricted stock incentive models in China for comparative analysis and conducted an empirical test with a sample of companies that frst implemented equity incentive plans in the A-share market from 2013 to 2016. It found that equity incentives did not have a signifcant positive contribution to the operating performance of listed companies in China, comparing with the restricted equity incentive model of stock, stock option have a better incentive efect. Xuelui [9] used a DID model to analyse a matched sample and the results showed that the stock option model can better enhance corporate risk-taking than the restricted stock model and directed oferings promoted corporate risk-taking more signifcantly than repurchase style stock sources.
Obviously, the fndings of domestic and international scholars are highly biased due to the diferences between the samples, variables, and methods selected at the time of the study. Te stock option model has long been the mainstream choice of foreign companies for equity incentives. Tere is a general consensus in the literature that stock option is more efective as incentives and better at mitigating agency problems than restricted stock. Bryan et al. [10], Lambert and Larcker [11], Chourou et al. [12], and Kadan and Swinkels [13] had argued extensively that in the context of time-based incentive conditions, incentive recipients of options would have a stronger incentive to risk investing for high returns, while restricted shares were granted to incentive recipients for free and were less motivating. Dechow and Sloan [14] and Core and Guay [15] argued that stock options had the advantage of better embellishment of proft statements and that poorer performing companies would prefer stock options. Te choice of incentive model, however, remains an unanswered question as far as our practice is concerned in China. Stock repurchases are also an important tool for frms to stabilize their stock price and information transmission, and they have an enormous impact on enterprise performance. Te existing literature rarely associates repurchase with equity incentives, and the literature on equity incentives that use repurchase as the source of incentives is even rarer.
Te innovation of this paper is to refne the impact of the equity incentive model, incentive intensity, and interaction term on enterprise performance in the context of principalagent theory and executive rights theory by adding the source of the subject matter equity incentive as an infuencing factor based on the existing literature. Tis provides a basis for listed companies to choose the appropriate incentive intensity and subject matter when implementing equity incentives.
In this study, we took data from listed frms in China's A-share market from 2010 to 2020 as our samples. A twoway panel fxed efects regression was conducted using the pattern of equity incentives implemented by the sample companies as the explanatory variables, and on this basis, the interaction terms of incentive intensity, source of incentive targets, and both were introduced to analyse the impact of the pattern of equity incentives, incentive intensity, and source of incentive targets on frm performance. Te GMM, replacement variables, and simple slope method were also used to conduct robustness tests. Finally, the empirical results were summarised and the shortcomings and future directions of this study were pointed out to provide theoretical reference for diferent types of listed companies in choosing their equity incentive models.

Theoretical Analysis and Research Hypothesis
Stock option and restricted stock, the two most common incentive models of equity incentive scheme in China's listed frms, must be exercised by the incentive recipients when they reach their assessment targets. Tis means that whichever incentive model to choose, in order to obtain lucrative incentive return, they must strive to make investment success, improve enterprise performance, and on this basis to achieve the assessment objectives. However, there are also clear diferences between the two incentive models. Firstly, there are diferences between how they are granted. Under the stock option model, the incentive recipient is not required to pay any money on the grant date. If the appraisal target is not met, the registered stock options are simply cancelled without any loss. In principle, if the valuation target is met, the listed company will directly pay the incentive recipient cash equivalent to the value of the stock options to complete the award. Lambert and Larcker [11] shows that in the restricted stock model the incentive recipient must pay a lump sum of money on the date of the grant in order to purchase all of the shares granted in real terms, and typically the incentive recipient must raise fnance and bear interest costs. If the appraisal target is not met, the listed company repurchases the corresponding shares at a price no greater than the grant price plus interest on bank deposits for the same period of time, which of course does not cover the fnancing costs borne by the recipient of the incentive. Te incentive recipient will beneft from selling the unlocked shares if the valuation target is met. But where the recipient of the incentive is a director or supervisor of the frm, the sale of shares will face some regulatory restrictions. Terefore, the incentive recipients of restricted stock face more constraints and it takes longer to realise the benefts [5]. Secondly, these two models have their obvious characteristics in essence. From the perspective of rights and duties derived from both, there is a symmetrical relationship between the rights and obligations of restricted stock. Under the premise of satisfying the conditions for granting, the incentive object can obtain stock, and the rise or fall of the stock price is directly related to the interests of the incentive object. Executives, as the incentive recipients, whose decision-making directly afects the enterprise, can invest in high-risk projects. If the investment success of high-risk projects leads to higher stock prices, they will achieve tremendous gains. On the contrary, once the project falls into a huge loss or even leads to the abnormal sales/revenue of corporate funds, the stock price will fall, resulting in executives being unable to obtain high returns or facing severe losses. Tat is, the constrained model of stock incentives will restrain executives, allowing executives to pursue enterprise value maximization when making decisions to promote enterprise performance (see Figure 1). Te rights and obligations of a stock option are not symmetrical. Te option holder has the right to choose to exercise but does not have to do so. Finally, from the perspective of incentives and constraints on incentive objects, there are also signifcant diferences between stock option and restricted stock. Under the restricted stock incentive model, the risk of the company releasing shares is efectively controlled by the setting of the lock-up condition. And, for incentive recipients, the setting of the lock-up period also discourages executive short-sightedness to a certain extent [8]. Furthermore, frms may impose harsh release conditions to fnancially sanction the incentive. However, incentive recipients under the stock option model can escape such penalties by forfeiting the exercise of their options.
In addition to the incentive model, the equity incentive plan includes exercise price, incentive intensity, award quantity, incentive recipients, expiry date, and grant conditions. Te robust design of these elements can contribute to improving enterprise performance. Several studies have concluded that the intensity of equity incentives signifcantly impacts enterprise performance when considering models of equity incentives. With the increase of incentive intensity, management will be more concerned about the company's long-term development, which is more conducive to enterprise performance [16]. Guo [17] concluded that equity incentives had a significant efect on enterprise performance through propensity score matching analysis, indicating that the higher the intensity of equity incentives, the more signifcant the performance improvement. In an empirical study, Jianfeng [18] found a signifcant and positive relationship between the intensity of managerial equity incentives and enterprise performance. As the intensity of managerial equity incentives increased, management became more focused on the long-term development of the frm and was more motivated to increase investment in R&D, which in turn improved enterprise performance. For example, Shengjun [19] used the diference between the return on total assets three years after equity incentives were implemented and the return on total assets three years prior to implementation as a measure of the performance of the frm. It showed that equity incentive intensity was positively related to frm performance up to the 18% level. A few other earlier studies have shown that because of the low intensity of equity incentive implementation in Chinese companies, the efect on frm performance improvement is not signifcant enough [20]. Tis paper argues that when listed companies implement equity incentive scheme, giving appropriate incentives to incentive objects is conducive to promote enterprise performance. However, if the incentive intensity is too strong, it will lead to a larger share held by management, making its control and infuence in the company uncontrolled. Exceeding the critical point of incentive intensity will continue to weaken the Mathematical Problems in Engineering efect of equity incentives. Excessive incentives will waste corporate resources and ultimately are unfavorable for improving enterprise performance. Based on the above-given analysis, this paper proposes hypotheses H1 and H2.
H1: the restricted stock incentive model has a better impact on enterprise performance than the stock option when implementing an equity incentive scheme H2: incentive intensity has an inverted U-shaped moderating efect between equity incentive patterns and enterprise performance In terms of the source of subject matter, issuing shares and stock repurchase are the two most prominent methods. A gap exists in the literature regarding the selection of two diferent sources of subject matter for listed frms when implementing equity incentives. Te number of stocks repurchased by a listed company has no efect on the control of the benefcial owner's control, but at the same time, the earnings EPS increases to a certain level of proft, thereby enhancing the value of the company. Equity repurchases can also reduce paid-in capital, increase asset-liability ratio and save tax by increasing debt, which in turn promotes better use of "fnancial leverage" and has a positive impact on enterprise performance [21]. Skinner [22] examined time series data on US-listed companies and found that proft factors were becoming increasingly assertive in explaining stock repurchase behaviour, with enterprises with lower EPS having a greater incentive to undertake stock repurchases. When there is a large discrepancy between the current debt ratio and the optimal position of a publicly listed enterprise, there is a strong willingness to carry out stock repurchases, primarily through the form of debt to repurchase stocks [23]. Te executive perspective suggests that when changes in capital structure afect executive control, executives prefer to repurchase, for it is only in this way that the threat of dilution can be lessened. Besides, listed companies may also use share repurchases as a signal of value transmission if they believe that external investors do not have a realistic understanding of the company's current situation and result in their value being undervalued. An announcement of a stock repurchase will lead investors who have received negative news to have a new positive perception of the enterprise's surplus, increasing their trust in the company, thus promoting investors to invest more in the company's stock price to generate excess returns, which has a positive efect on enterprise performance [24]. Te root cause of the principal-agent problem is a potential confict of interest between the owner and the manager of the business. Lin and Liu [16] believed that shareholders do not want to add high agency costs, whereas managers may choose to invest in projects with suboptimal returns or even harmful returns based on their goals of interest. In this case, if the company carried out a stock repurchase, it can reduce the idle cash fow, increase shareholder wealth, and reduce the risk of managers' arbitrary control of liquid capital. Similarly, Jagannathan et al. [25] showed that listed companies could use large amounts of idle free cash fow through share repurchases as a way to reduce agency costs for listed companies and to prevent operators from using funds at their discretion. Based on the above-given studies, it appears that the use of repurchases as a source of incentive for listed frms is more benefcial to frm performance. Terefore, this paper advances hypotheses H3 and H4.
H3a: the stock option incentive model is benefcial in promoting enterprise performance when repurchases are used as the source of the subject matter H3b: the restricted stock incentive model is benefcial in promoting enterprise performance when repurchases are used as the source of the subject matter H4a: when repurchasing is used as the source of the subject matter, there is a positive moderating efect of incentive intensity between the stock option incentive model and the enterprise's performance H4b: when repurchasing is used as the source of the subject matter, there is a negative moderating efect of incentive intensity between the stock option incentive model and the enterprise's performance H4c: when repurchasing is used as the source of the subject matter, there is a positive moderating efect of incentive intensity between the restricted stock incentive model and the enterprise's performance H4d: when repurchasing is used as the source of the subject matter, there is a negative moderating efect of incentive intensity between the restricted stock incentive model and the enterprise's performance

Sample Selection and Data Sources.
Te sample used in this paper consists of data from 2010 to 2020 for enterprises listed on the Chinese A stock market. Also, the data in the sample were fltered as follows to ensure the accuracy and validity of the data: (1) exclude listed companies in the fnancial and insurance industries. (2) Exclude enterprises that have terminated their listing. (3) Exclude listed companies that use a combination of both incentive models. (4) Exclude enterprises that have suspended or ended the implementation of equity incentives. In addition, all nondummy variables are Winsorize scaled at the 1% and 99% levels in this article to avoid the potential confounding of this study by extreme values. For the purposes of this paper, the data sources are primarily CSMAR and WIND databases, with the missing data coming from Python big data crawlers, and the fnal 1876 observations obtained through data fltering by Excel; the empirical analysis was carried out by Stata.

Explained Variables
(1) Enterprise Performance (ROA). Te indicators used in the studies to measure enterprise performance primarily include accounting and market indicators. Accounting indicators mainly include return on equity (ROE) and return on total assets (ROA). Market indicators mainly include earnings per share (EPS), Tobin Q (TQ), price-earnings ratio (P/E), market book ratio (M/B). Market indicators are often used by foreign academics to measure enterprise performance in their studies, but given the gulf between the development of China's capital market and that of foreign countries, and low capital market efciency, market indicators may not correspond to actual market conditions, the rationality of the use of market indicators to measure enterprise performance is open to dispute [26]. On the other hand, market indicators are usually linked to stock prices, and because of the frequency of stock price movements and weak market validity in our market, the use of market indicators is usually not an accurate measure of enterprise performance. At this stage, when scholars in China study this issue, the indicators selected by most studies are still dominated by return on equity (ROE) and return on total assets (ROA). Trough a synthesis of previous studies and the requirements of the Administrative Measures on Equity Incentives for Listed Companies, in this paper, we choose the return on average annual total assets (ROA) to measure enterprise performance and use the return on average annual equity (ROE) as the regressor in the robustness test.

Explanatory Variables
(1) Equity Incentive Models. Listed companies implementing both stock option and restricted stock incentive models were selected. Dummy variables were set: the implementation of the stock option incentive took the value of 1 and the restricted stock incentive took the value of 0.
(2) Incentive Intensity. It is defned as the percentage of total equity capital to be incentivized by the equity incentive scheme for publicly traded enterprises that implement the equity incentive scheme; as the value approaches 1, the intensity of the equity incentive increases.
(3) Te Source of the Incentive Matter. It refers to the object of the equity incentive in the equity incentive scheme in what manner; the value is 1 by stock repurchase and 0 by issuing shares.

Control Variables.
Enterprise performance is also confounded by other factors, such as its size, operating capacity, debt capacity, growth capacity, and governance. For the purposes of this paper, enterprise size (Size), total asset sales/revenue (Operate), debt capacity (Lev), equity concentration (Shrhfd1), the growth rate of total assets (Growth), and the presence of two jobs in one (Both). Corporate donations (donation) are chosen as control variables. Defnitions and explanations of each variable can be seen in Table 1.

Construction of the Model.
In light of the above theories and hypotheses, in order to verify the relationship between the equity incentive model and enterprise performance and consider the moderating efect of equity incentive intensity and the source of incentive subject matter. Te Explained variable is the continuous variable ROA; ROE is used for robustness testing. Te equity incentive model and the source of incentive matter are bipartite dummy variables, respectively. Five regression models were constructed as follows: Models (1) and (2) are used to explore the impact of the two incentive models on enterprise performance. Te restricted stock incentive model, which is expected to be signifcant and lower than zero. It means more conducive to improved enterprise performance. Model (3) considers the role of equity incentive intensity between the two models. If α 24 is signifcant and disagrees with the sign of the α 23 coefcient, it indicates that there is an inverted U-shaped moderation of incentive intensity between the stock equity incentive model and enterprise performance.
In order to validate H 3 and H 4 , the relationship between the incentive model and enterprise performance and the moderating role of incentive intensity between the two when the source of the incentive comes from repurchases. Set models (4) and (5) Table 2 shows the results of the descriptive analysis of each variable, and the sample will be analysed in fve dimensions: mean (Mean), standard deviation (Sd), minimum (Min), median (Median), and maximum (Max). Among them, return on total assets (ROA), equity incentive intensity (Strength), enterprise size (Size), total asset sales/revenue (Operation), total asset growth rate (Growth), debt capacity (Lev), equity concentration (Shrhfd1), and corporate donations (donation) are continuous variables; equity incentive model (Mode), source of equity incentive underlying (Source) and control of two positions (Both) are dummy variables.

Descriptive Statistical Analysis.
Specifcally, it appears that among the A-share listed companies implementing equity incentives: the mean value of ROA is 6.95% with a standard deviation of 0.054. Te ROA of 1820 out of 1876 samples was positive, which leads to the conclusion that most listed enterprises implementing equity incentives have better efects on profts and the distribution of enterprise performance (see Figure 2).
On the choice of incentive model (Mode): the mean value of listed companies is 0.2521, and the median value is also biased toward 0, providing evidence that executives of listed companies in China prefer the restricted stock incentive model at this stage.
For the source of the subject matter (Source): as stipulated in the Rules for the Implementation of Share Repurchase by Listed Companies on Shenzhen Stock Exchange and the Rules for the Implementation of Share Repurchase by Listed Companies on Shanghai Stock Exchange, if the listed companies have been listed for less than one year to implement the equity incentive, or if the stock repurchase method is used that causes the company will reach less than 25% of the total number of shares of the companies, thus not satisfying the listing conditions, only issuing shares can be used as the source of the subject matter of the equity incentive. Moreover, all of the announced equity incentive schemes of the GEM companies use issuing shares as the source of subject matter, as most of the GEM companies have been listed for less than one year and thus cannot use repurchase as the source of the subject matter for the implementation of equity incentives. In terms of the data, the mean value tends to be zero for the source of the subject matter (Source), which is consistent with the fact that most listed companies choose targeted issuance as the primary source of the subject matter equity incentives.
Among the listed companies implementing the equity incentive scheme, the mean value of equity incentive strength (Strength) is 2.32%, the minimum value is 0.1515%, and the maximum value is 8.75%. In 422 of these samples, the equity incentive intensity was less than or equal to 1%, and 127 had a greater than 5% equity incentive intensity with an equity incentive intensity distribution (see Figure 3). Te overall picture from the data shows that the intensity of equity incentives in China is low at this stage and that there is a wide gap in the intensity of incentives between diferent companies. In foreign countries, the incentive intensity is typically between 10% and 15%, whereas in China it is typically less than 10%, making our equity incentive intensity somewhat conservative in comparison.

Analysis of Correlation.
When the Pearson correlation coefcient test was performed, the absolute values of the correlation coefcients were all less than 0.4, and the test passed (See Table 3). In addition, the VIF test is used further to illustrate the problem of multicollinearity in the model. Te maximum value of VIF for all variables is 3.01, which indicates no serious multicollinearity problems.  (2), the adjusted R 2 is 0.3264, which is a substantial increase from the value of R 2 in model (1). It is indicative of a further increase in the explanatory power of the equation.
Hypothesis H 1 was further tested. It indicates that restricted stock is the more preferred option in listed frms' incentive covenants under incentive-based performance conditions. Because publicly traded frms are more willing to make risky investments under the stock option model. If the investment fails and the frm's stock price falls, managers will avoid damage to their own interests by forgoing the exercise of their options. Conversely, if the project is successful and generates signifcant returns, the stock price will rise rapidly and managers will naturally be able to exercise their options for more substantial returns. When managers make decisions to invest in high-risk projects, the enterprise needs to take on substantial risks, which increases the probability of gains and losses [27]. Te probability of loss is much greater than the probability of proft in a competitive market. If managers only consider their own interests and increase risky investments, this will infuence enterprise performance (ROA). In the restricted stock incentive model, managers are required to meet performance evaluation criteria before they can sell their shares. During this period, if their investment decisions fail, the share price falls, and the managers will also sufer losses [28], so there is a stronger constraint on a risky investment in the equity incentive model. Some studies have shown that the value of the restricted stock is negatively correlated with frm risk, and this model will aggravate the risk aversion level of executives, the risk-aversion efect of restricted stock incentives is considerably stronger than the stock option model [29]. Te above-given research results are consistent with the conclusions of Haiyan [4], Wenzhe [5], and Shufang [7]. Table 5 shows the moderating efect of the strength of the equity incentive (Strength) on the incentive model (Mode) and enterprise performance (ROA). Te primary term of Mode × Strength has a positive coefcient, but the secondary term of Mode × Strength 2 has a signifcantly negative coefcient. It indicates an inverted U-shaped relationship between the intensity of equity incentives and enterprise performance relative to the equity incentive model. Xiaowu [30] showed that listed frms implement equity incentives among their managers, the intensity of which is less than a critical threshold level, and equity incentives are benefcial in promoting long-term improvements in enterprise performance. However, as the intensity of the equity incentive increases, the proportion of shares owned by management increases, which in turn enables them to increase their control and infuence within the frm, and above the threshold the performance enhancing efect of the equity incentive is continuously lost. Excessive   Mathematical Problems in Engineering equity incentives can also waste corporate resources and are ultimately detrimental to the improvement and enhancement of listed enterprises' performance. It is clear from this that it is not the case that the greater the incentive intensity, the better the incentive efect. H 2 tests the hypothesis. Te results in column 2 of Table 5 show that there is no signifcant association between the source of the subject matter and enterprise performance. But the coefcient in column 3 is −0.0349, which passes the test at the 1% signifcance level. It indicates that the incentive underlying the repurchase method has a negative moderating efect on the relationship between stock option and enterprise performance, and a positive moderating efect on restricted stock. Kahle [31] found, in a large number of case studies of share repurchases, that companies with signifcant stock-based equity incentives prefer to use share repurchases rather than cash dividends as a corporate payment policy. Te stock required for equity incentive and employee stock ownership plans can be obtained through the issuing of shares and stock repurchases. Tis method of the stock repurchase is more fexible than the issuing shares that will dilute the frm's equity. Hypothesis H 3b was tested. At the same time, this paper adds the primary and secondary terms of equity incentive strength to the source of the subject matter incentive. Te secondary term coefcient is not signifcant. Te regression results suggest that there is an isotropic rather than an inverted U-shaped moderating efect of equity incentive intensity between the source of the subject matter incentive and enterprise performance. Te results are shown in columns 4 and 5 in Table 5. Tis would also mean that the higher the intensity of the repurchase, it is more benefcial to enterprise performance, consistent with the results of the literature described above.

Tests for Moderating Efects. Column 1 of
Column 6 of Table 5 regresses the interaction terms of the three parts (Mode × Source × Strength). But the regression results show signifcant multicollinearity in the model. For Mode and Source are dummy variables which take the value of either 0 or 1, the result of the crossmultiplication term will be zero if one takes 0. If one of the policies takes a large sample with a value of 0, the efect of the other two values will be overwritten due to the limitations of the sample data, and the process is shown as follows: (3) Te original dummy variables in this paper are fxed as follows: Mode � 1 for the stock option incentive model, Mode � 0 for the restricted stock incentive model, Source � 1 for incentive source matter selection of stock repurchase, and Source � 0 for issuing shares. Te root cause of multicollinearity in the data presented above is the small sample size, but the problem of small sample size cannot be resolved due to the late start of the development of China's equity incentive scheme and the unavailability of additional data.

Mathematical Problems in Engineering
Taking the partial derivative of the above-deformed equation with respect to X 1 X 2 yields: If the values of Mode and Source are swapped, Mode � 1 is the restricted stock incentive model, and Mode � 0 is the stock option incentive model. Source � 1 is when the incentive source is chosen issuing shares, and Source � 0 corresponds to when the incentive source matter is chosen as stock repurchase.
In light of this, one can see that the regression results are equal when the values of the two dummy variables are traded simultaneously. Te table shows the results after swapping the values of the dummy variables. Our analysis shows that at the 1% signifcance level when the enterprise selects the equity incentive model and uses repurchase as the underlying source; that is, incentive intensity has a suppressing efect on the relationship between the incentive model of stock option and enterprise performance. As the intensity of stock repurchases increases, the suppressive efect on the negative relationship between the stock option incentive model and enterprise performance increases, at which point R 2 rises from 0.3277 to 0.3374, and the ft is better. H 4b was verifed.

Robustness Tests.
In this paper, the national economic growth index (ln gdp), the fxed asset investment growth index (ln invest), the per capita disposable income growth index (ln output), and the per capita consumption index (ln cost) are used as instrumental variables in addressing the indigeneity issue. At the same time, considering that changes in any economic factor are inherently inertial, the results of the previous period usually have an impact on the results of the later period and there is a lagging efect on the enterprise performance of each listed company. For this reason, this paper uses the generalized method of moments (GMM) estimation to estimate a dynamic panel data model that is robust to potential endogenous issues (see Table 6). Te regression results pass the stability test at the 1% level, and the sign of the coefcients is consistent with the above, P -values for Hansen's test were 0.493 and 0.715, respectively. Te GMM endogeneity test passes.
To ensure the accuracy and consistency of the above fndings, the explained variable ROA was replaced with ROE in the model to test the above results. Table 7 was mainly used to test the relationship between the equity incentive model and enterprise performance, and the regression coefcient was −0.0147, signifcant and negative, which is consistent with the above fndings.
In this paper, two methods are used to test the moderating efect of incentive strength: the simple slope method with selected points [32] and replacing the explained variables. Te moderating efects of the three interaction terms are After variation, it is obtained that Te coefcient of M (α 5 X 1 + (α 6 + α 7 X 1 )X 2 ) refects how the relationship between X 1 and Y is moderated by the variable M. Te slope subscale types in (4) in Figure 4, all others are main scale types. It is intuitive from the graph that stock repurchase is positively related to corporate performance as the intensity of equity incentives increases. Tis is contrary to the regression results for H 3b , indicating that incentive intensity has a dampening efect between the stock option incentive model and enterprise performance when repurchases are used as the source of subject matter.    Note. * * * , * * , * indicate signifcant at the 1%, 5%, 10% levels.
Substitution of ROA for ROE as the explained variable resulted in a regression coefcient of 0.3002, signifcant and positive in line with the results above (See Table 8).

Conclusions and Recommendations
Te above-given study empirically analyzes the relationship among the equity incentive model, incentive intensity, and source of subject matter and enterprise performance and concludes the following: (1) restricted stock incentive model has a positive impact on enterprise performance. (2) Incentive intensity positively moderates between the restricted stock incentive model and enterprise performance is negatively moderates between the stock option incentive model and enterprise performance. (3) Te restricted options from the repurchase have contributed to improved enterprise performance. (4) Tere is a signifcant positive moderating efect between incentive intensity and enterprise performance when repurchased restricted stock is the source of the incentive.
Tis study is based on the perspective of shareholders of listed companies and does not fully consider factors such as exercise costs, personal income tax, dividend distribution, and opportunistic behavior that are directly related to equity incentive returns. At the same time, China's capital market started late. Although the market efciency has been greatly improved, it has not yet reached semistrong efectiveness, and it inevitably afects the efectiveness of equity incentives. Considering that China's equity incentive scheme needs to be further developed in the market, this paper does not further explore the relationship of incentive model, subject source, and enterprise performance in combination with the unique characteristics of the Chinese market, which is also the content that needs to be improved in the follow-up of this study.
Te impact of equity incentive schemes on the performance of listed enterprises, as an important means of resolving principal-agent relations, has been the subject of a contentious debate. Compared to most of the developed foreign capital markets, the development of China's capital market is relatively late, and the exploration of the practical application of the equity incentive model should be combined with the analysis specifc to the real situation. Combined with the above research fndings, listed enterprises in China should pay attention when implementing the equity incentive scheme: frstly, the choice of equity incentive model and the diferent sources of incentive targets will make a diference to the performance of the enterprise, and listed enterprises should choose diferent incentive models in conjunction with the sources of the targets. Although the stock option incentive model can have a signifcant negative efect on enterprise performance, for listed companies that are under more capital pressure and choose public issues as the source of the subject matter, the choice of the stock option incentive model is more conducive to enterprise performance. Secondly, when implementing equity incentives, the heterogeneity of the moderating efect of equity incentive intensity between the two incentive models and enterprise performance should be carefully considered.
If listed companies choose restricted stock as the equity incentive model, they can appropriately increase the equity incentive intensity to achieve the efect of increasing enterprise performance. Of course, in addition to drawing the above conclusions in practical application, it is also important to give due consideration to the applicability of the equity incentive scheme. Optimal enterprise performance can only be achieved with a superior external environment and a good internal structure. From the conclusions drawn in this paper, the restricted stock incentive model appears to be more advantageous for listed companies. However, for the incentives, the risk of receiving high returns is much higher under the restricted stock incentive model than under the stock option. Terefore, listed companies should consider the incentive targets' personal characteristics, risk appetite, and external environment in selecting incentive models. Only in this way can the agency problem in corporate governance be solved and corporate value maximized as soon as possible.

Data Availability
All the data used to support the fndings of this study are included within the article.

Conflicts of Interest
Te authors declare that there are no conficts of interest regarding the publication of this paper.