Dynamic Panel Threshold Model-Based Analysis on Equity Restriction and Enterprise Performance in China

This paper takes China’s A-share listed companies of the mixed ownership of state-owned enterprises from 2007 to 2016 as a sample, and examines the impact of state-owned business mixed reform on corporate performance. Research shows that under different equity restriction ratios, there exists a difference in the connection between corporate performance and equity restriction ratio. Corporate performance reduces with the subjoin of equity restriction ratio, and they are negatively correlated when the stockholding ratio of the largest stockholder is less than 25%; on the condition that the stockholding ratio of the largest stockholder is in the range of 25 and 40% and 40 and 60%, it presents an “inverted U-shaped” connection between corporate performance and equity restriction ratio. At this time, the threshold value of the optimal equity restriction ratio is 1.1336 and 0.7297, respectively. On the condition that the stockholding ratio of the largest stockholder is equal to or more than 60%, there exists no threshold value for equity restriction ratio. However, the regression results present that corporate performance increases with the increase of equity restriction ratio, and the two are positively correlated.


Introduction
China's mixed ownership reform's initial purpose is to increase global competitiveness and deepen state-owned business' reform. Mixed ownership's reform is also the deep participation in the reform of state-owned business of the non-public economy. It uses state-owned enterprises' mature platform, brand, technology, and channels, linked to the flexible mechanism and internal driving force of private enterprises to improve the achievements of the enterprise by optimizing the governance structure and ownership structure. In order to further promote the state-owned enterprises' mixed reform, the National Development and Reform Commission released a term, that is "Opinions on Deepening the Several Policies for the Reform of Mixed Ownership Reform Pilots" in 2018, which attracted widespread attention from academic and practical circles. Statistics show that between 2007 and 2016, the largest stockholder's average stockholding ratio of China's state-owned mixed-ownership enterprises was 0.3959, with a median of 0.3904. These statistics indicates that among the state-owned mixed-ownership companies in China, the largest shareholder shareholding ratio is relatively high, and this phenomenon of "one shareholder holding the largest share" is common. Meanwhile, it also shows that the benefit conflicts between managements and shareholders, majority shareholders and minority shareholders exist in China's state-owned mixed-ownership enterprises. Then, how to effectively control the two types of agency costs to improve company performance becomes a problem worth studying when two types of agent conflicts of interest coexist.
The essence of state-owned enterprise mixed reform is to improve the ownership structure. The purpose is to balance the equity and create an efficient governance structure to improve company performance. The study on corporate performance and ownership structure began with the separate theory in two rights proposed by Berle and Means [1]. They hold the opinion that when the firm's equity is scattered, benefit conflicts between managements and shareholders are likely to occur; that is, the first type of agency problem. Some scholars believe that the existence of the first type of agent will lead to the failure to achieve optimal corporate performance. Demsetz and Villalonga [2] found that there was no scientific connection between company performance and ownership structure. However, La Porta et al. [3] proposed a different view from Berle and Means 1. They believe that the equity of modern enterprises is not scattered but relatively concentrated, and most enterprises generally have large stockholders holding stocks, that is, the second kind of agency conflict. Lückoff [4] discussed the conflicts of interest in delegated management as well as efficiency mechanisms. Since then, more research has shifted from the first type of agency conflict to the second type of agency conflict and has begun to focus on agency conflicts in the large stockholders and the minority stockholders. The principal-agent theory indicates the direct formation of the contract formation process under information dissymmetry, and explores under what condition can the principal design a mechanism at a low cost to promote the agent to put their shoulder to the wheel to make full use of the utility of the principal. The first type of agency problem exists in the principal and the agent. The former pursues the greatest increase in personal assets generated by the maximization of the company's value, and the agent pursues the maximization of self-interest. This difference caused the truth that the conductor who actually controls the control deviates from the principle of maximizing the interests of the owner in the process of business management. The second type of agency problem is essentially a matter of interest between the largest stockholder and the minority stockholders. The largest stockholder can manipulate the enterprise according to its cash flow rights and control advantages, and embezzle the benefits of the enterprise or other stockholders. Gomes and Novaes [5] and Berkman et al. [6] found that equity restriction is beneficial to alleviate the two types of agents. When the company has multiple major shareholders, it can not only supervise the management, but also effectively alleviate the interest encroachment of the controlling shareholders.
The so-called "Equity Restriction" is mainly manifested in the supervision and restriction relationship formed among several large shareholders. They jointly participate in significant decisions and share control rights, thereby avoiding the situation that one of the shareholders has absolute control, and other shareholders are difficult to supervise and control. Foreign authors generally hold that equity restriction can effectively monitor and restrict controlling shareholders and improve corporate performance [7,8]. The government financial institutions contribute negatively, while investors in other countries contribute positively to company performance in accordance with profitability [9]. However, the conclusions drawn by domestic scholars are often not consistent with those drawn abroad, these are the three main situations: (1) company performance is related with equity restriction ratio: Wang et al. [10] took Chinese family enterprises as research samples, and the test results showed that the Equity restriction ratio of large shareholders of Chinese family enterprises could improve corporate performance. (2) Corporate performance is unrelated to equity restriction ratio: using the data of the Shanghai-based equipment, machinery instrument, and listed companies in 2005-2008, Liu et al. [11] found a negative connection between corporate performance and equity restriction ratio. (3) The connection between company performance and equity restriction ratio is nonlinear: Chen and Bian [12] take the statistics of A-share private listed firms from 2007 to 2013 as the subject, the final outcome indicates that the improvement of equity restriction ratio in private listed companies can effectively alleviate the second kind of agency conflict, reduce the minority shareholders' asset encroachment behavior, and the connection between company performance and equity restriction ratio have an inverted "N" relationship. Yang et al. [13] utilized the data of the family business located in A-shares from 2010 to 2014 as a sample regression test. The research found that the equity restriction ratio of the family business and Tobin-Q's connection is not strictly inverted U-shaped, but a non-smooth symmetry curve and the impact of equity restriction ratio on Tobin-Q varies with threshold variables.
Thus, it can be seen that although scholars across the world have conducted various kinds of studies, but no consistent conclusion has been reached [14]. Cheng [15] found that firms with larger boards have lower variability of corporate performance. Sirgy [16] found that corporate performance is related to business ethics to some degree. Moreover, it can be seen from domestic literature based on the relationship of company performance and equity restriction ratio that few types of literature discuss the influence of firm performance reaction to equity restriction ratio from the perspective of state-owned mixed ownership enterprises. What is the connection between company performance and equity restriction ratio in China's state-owned mixed enterprises? Positively correlated or negatively correlated? Linear or nonlinear? Is the connection between company performance and equity restriction ratio affected by the stockholding ratio of the largest stockholder? When the stockholding ratios of the controlling stockholders are different (equity decentralization, the relative and absolute holding of the largest stockholder), will the connection between company performance and equity restriction ratio change? Is there an optimal equity restriction ratio? These are the starting points of this study.
The outcome indicates that it presents a conspicuous inverted U-shaped connection between company performance and equity restriction ratio, which shows that a moderate equity restriction ratio is promotive to completing the monetary performance of state-owned mixed ownership enterprises, while excessive equity restriction ratio will bring state-owned mixed ownership enterprises opposite company performance. In the course of the article's research, the whole sample was grouped according to the stockholding ratio of the largest stockholder. The threshold regression test shows that the impact of equity restriction ratio on firm performance is different under different ownership concentration. If the stockholding ratio of the largest stockholder is short of 25%, firm performance decreases with the subjoin of the equity restriction ratio; if the stockholding ratio of the largest stockholder is from 25 to 60%, company performance and equity restriction ratio are in an inverted U-shape; if the stockholding ratio of the largest stockholder is equal to or more than 60%, the firm performance increases with the rise of the equity restriction ratio.
This study may have the following contributions: (1) innovation in research perspectives. The research objects of this study are state-owned A-share listed companies with mixed ownership, these companies are taken as samples for research separately, China's mixed ownership enterprises' particularity is also be considered. From the perspective of equity restriction ratio, this study discusses its impact on the performance of state-owned mixed ownership firms and provides a new perspective and research conclusions for the research in existing state-owned mixed ownership companies, which may play a complementary role in this field. (2) Improvements in research methods. This study uses the threshold regression model to explore the connection between company performance and equity restriction ratio and considers the influence of ownership concentration. The threshold regression test of the influence of equity restriction ratio on corporate performance is carried out in accordance with the discrete degree of ownership, and the result shows that the impact of equity restriction ratio on company performance is different under different ownership concentration. Research based on the classification and refinement of samples can make the regression results more targeted, accurate, and closer to the actual situation of enterprises. (3) The previous literature mainly focuses on the influence of the largest shareholder on company performance and explores the issue of optimal equity restriction ratio. For example, Xu and Wang [17] used the listed companies as research objects and found that the stockholding ratio of the largest stockholder is limited to 50-60%, and is optimal for improving corporate performance. Based on previous research, this study mainly explores whether there is an optimal equity restriction ratio under the different stockholding ratio of the largest stockholder.
The outcome shows that when the shareholding ratio of the largest stockholder is from 25 to 60%, there is an optimal equity restriction ratio of the threshold value, which is 1.1336 and 0.7297, respectively.
The follow-up arrangements of this article are scheduled as below. The second part is the research hypothesis and theoretical analysis. The third part is the research design, including model design, variable description, and sample selection. The fourth part is empirical analysis, including descriptive statistical analysis, correlation analysis, and regression analysis. The fifth part is further research, and we conclude the study in the final section.

Theoretical Framework and Hypothesis
In accordance with the principal-agent theory, when an enterprise develops to a particular scale, owners no longer directly take part in the management and operation of the firm but hire workers to manage and operate the company on their behalf. The dissociation of management and ownership rights of the enterprise results in the principal-agent relationship [1]. When the various types of information of the principal are known by the agent, the principal usually does a better job in all aspects [18]. In the principal-agent relationship, the former pays attention to the maximization of his wealth, however, the agent focuses on the bonus, salary, on-the-job consumption, and leisure time as much as possible. Due to the essential difference between the utility functions of the two, conflicts of interests will inevitably be created in the company's daily operations, which lead to the generation of agency costs [19]. The cost of the loss of shareholders' interests caused by the manager's pursuit of self-interested behavior and excessive investment, such as in-service consumption and leisure time, is called the first type of agency cost. The controlling shareholders adopt the pyramid structure, and the large shareholders use the "tunnel behavior" to seek self-interests and encroach on the benefits of the minority stockholders. We claim the loss of the benefits of the minority stockholders caused by these reasons is the second type of agency cost.
As the phenomenon of "one shareholder holding the largest share" in state-owned mixed ownership enterprises is widespread, non-public capital is often in a weak position, so it is easier and more common for controlling stockholders to graft the benefits of the minority stockholders. In addition, since the controlling shareholders of state-owned mixed ownership enterprises are usually the state or local government, the board of supervisors is often in a virtual state, and internal control and external supervision are ineffective. At this point, if there are other large shareholders, whether they collude with the controlling shareholders or form supervision and checks on them, the cost of encroachment of the controlling shareholders will increase [20]. Therefore, we hold the opinion that if there are lots of large shareholders at the same period, that is, when there is a moderate degree of equity restriction ratio, it can not only restrain the large stockholders from misappropriating the benefits of the minority stockholders, but also improve corporate performance and cut back the second type of agency cost. The reasons are as follows. First, other large shareholders supervise the encroachment of the controlling shareholders, alleviate the problem of "one shareholder holding the largest share," and restrict the self-interested behavior of large shareholders [21,22]. Second, the large shareholders will supervise and restrict each other, thus reducing the occurrence of encroachment behavior [23]. Third, competition or cooperation between multiple large shareholders can also restrict the encroachment of large stockholders on the minority stockholders. In order to obtain support and trust from other shareholders, large shareholders make commitments and guarantees committed to improving corporate performance. Last, even if several large stockholders conspire to occupy the benefits of the minority stockholders, all such forms of collusion will not exist for a long time because the benefits of each stockholder are inconsistent and it is not easy to unify and coordinate [24]. In short, the ameliorating of the equity restriction can cut back the two types of agency cost and improve firm performance.
In general, if the controlling stockholders' supervision of the manager is effective, the first type of agency cost is usually lower. However, due to the diversification of capital entities in state-owned mixed-ownership companies, the complexity of principal hierarchy and the contractual relationship is not market-oriented. The powers and responsibilities between shareholders' meetings, boards of directors, and managers are not clear. Thus, the behavior of manager's pursuing on-the-job consumption and increasing leisure time cannot be effectively supervised and restricted. The concept of "equity restriction" was proposed, which mainly reflected the constraints of other major shareholders on the decision-making of the largest stockholder in the firm. The strength of equity restriction will directly affect the behavior of the largest stockholder and further affect firm performance [25]. If there are other large shareholders in the enterprise, that is, with the improvement of the equity restriction ratio, other large shareholders will supervise and intervene in the decision-making behavior of the controlling shareholders. Although compared with the low degree of equity restriction ratio, the controlling shareholders will have less time and energy to supervise managers. However, due to the participation of other large shareholders, they will also pay attention to the behaviors and decisions of managers, supervise managers together with the controlling stockholders, and cut back the occurrence of colluding behaviors between the controlling stockholders and managers [26]. Therefore, the first type of agency cost will be reduced appropriately if the equity restriction ratio is increased, which promotes the amelioration of firm performance. Whereas if the equity restriction ratio is too high, vicious competition between the large shareholders and the controlling shareholders may occur. Ignorance of the supervision of managers may create an opportunity for operators, leading to the agency cost rise of the first type [27]. At the same time, vicious competition may lead to the shareholders' pursuing self-interest without balancing the interests of the company and eventually result in the decrease of firm performance [28]. In addition, excessive equity restriction ratio will weaken the influence and decision-making efficiency of the controlling stockholders in the firm's business decisions, and reduce their enthusiasm to upgrade the firm's performance. To sum up, we believe that when the equity restriction ratio increases, it is beneficial to cut back the agency cost of the first type and increase corporate performance. However, if the equity restriction ratio passes a certain critical value, the increase of the equity restriction ratio will subjoin the agency costs of the first type, which will have an adverse influence on company performance.
The popular view holds that equity restriction can decline the infringing ability of the controlling shareholder, and can enhance the efficiency of the firm and the value of the enterprise [29,30]. In summary, on the condition that the equity restriction ratio is improved, not only can the controlling shareholders and the management be supervised, but also the first type of agency cost can be reduced; the problem of "one stockholder holding the largest share" can be alleviated, the benefits of minority stockholders can be protected, and the second type of agency cost can be lowered. Therefore, a moderate equity restriction ratio is conducive to reducing both types of agency costs and improving corporate performance [31,32] However, if the equity restriction ratio is too high, the controlling shareholders can be restrained from "tunneling" the company and embezzlement behavior, reducing the second type of agency cost. However, excessive equity restriction ratio will weaken the influence and decision-making efficiency of controlling shareholders in the company's business decisions, and reduce their enthusiasm and efforts to improve corporate performance. Moreover, vicious competition between other large shareholders and controlling shareholders easily occurs, thus neglecting the supervision of managers, leading to the rise of agency cost of the first type, and causing negative effects on corporate performance. In view of the stated analysis, the hypothesis of our paper is posed: In the state-owned mixed ownership enterprises, the equity restriction ratio and the overall corporate performance are in an "inverted U-shaped" relationship.

Sample Selection and Data Source
This study used A-share state-owned listed firms with mixed ownership from 2007 to 2016 as the subject. In this study, the selected data were screened as follows: (1) excluding the influence of extreme values, the data of S, ST, *ST, and S*ST (* and the letter as a whole represents a meaning) companies were excluded (S means that the firm has not completed the share reform; ST means that the firm has sustained losses in two consecutive years and its shares have been specially treated; *ST means that the firm's three-year loss has the risk of delisting or due to major events resulting in insolvency and delisting; S*ST means that the firm's three consecutive years of loss suffered from early warning of delisting and the share reform has not been completed).
(2) Considering the particularity of financial enterprises, the data of all financial enterprises were excluded. (3) Excluding enterprise data with an asset-liability ratio greater than 1. (4) Excluding other sample companies with missing values. (5) Searching the equity nature of the top 10 shareholders of the remaining sample companies from Shanghai and Shenzhen Stock Exchange, and excluding the listed companies with the top 10 shareholders as state-owned shares. Finally, the balance panel data of 533 firms were obtained, with 5330 observed values in total. Data in our study mostly originated from the CSMAR database. Additionally, Stata14.0 was used for data processing in this study. So as to exclude the impact of outliers, Winsorize on 1% of continuous variables was carried out.

Explained Variable
Company performance: the factors affecting firm performance mostly contained external elements (law, policy, culture, and environment, etc.) and internal factors (business management, organizational form, corporate culture, and innovation ability, etc.) [33]. This study only discusses the internal factors that affect enterprise performance. Generally, foreign authors apply the Tobin-Q value (market value of enterprises/replacement cost of assets) to measure firm performance. Considering the premise of using the Tobin-Q value is that the market is efficient, and the replacement cost of assets is complicated, it is not reasonable to use this index to measure company performance in China. Domestic scholars tend to use a single financial accounting index, such as return on total assets (ROA, net profit/average balance of total assets) or rate of return on common stockholders' equity (ROE, net profit/average balance of net assets) to measure firm performance. Given the availability and quantification of indicators, this study draws on the references [34], and use the rate of return on common stockholders' equity (ROE) as the proxy variable of firm performance.

Explanatory Variable
Balance degree of ownership: the existing methods to measure equity restriction ratio in existing literature mainly include (sum of squares) the stockholding ratio of the second to the fifth (or the tenth) stockholders; the stockholding ratio of the second to the fifth largest stockholder (or the tenth largest stockholder)/the stockholding ratio of the first largest stockholder. This study used the stockholding ratio of the second to the tenth largest stockholder/the stockholding ratio of the largest stockholder to measure the equity restriction ratio. Ownership concentration (Largest): this study took the stockholding ratio of the largest stockholder as the proxy variable of ownership concentration.

Control Variable
According to former research, this study controlled different factors that influence corporate performance, including enterprise size equal natural logarithm of operating income; capital structure (Lev) equal total liabilities/total assets, that is, the leverage level of the company, which indicates the solvency of the company. In general, the higher the leverage level is, the lower the solvency of the enterprise is, and the greater the risk enterprise it takes, the more difficult it is for the corporate performance to improve. Asset turn over equal operating income/average balance of total assets, which reflects the operating capacity of the enterprise; enterprise growth equal (total assets ending value of the present period minus total assets initial value of the current period) divide by total assets initial value of the current period, namely, total assets growth rate, which reflects the enterprise's development ability. In addition, dummy variables like year and industry are set. The specific definition is shown in Table 1.

Model Design
Learning from the current practice of Xu and Wang [17] and Liu [11] in the research on equity restriction ratio, corporate performance, and considering the endogenous problems raised by Xu [27], this study constructs the following dynamic panel models (1) to (4) to examine the impact of equity restriction ratio on firm performance. Among them, model (1) examines the impact of equity restriction ratio on firm performance without adding control variables; model (2) invests in control variables, but does not take into account of the impact of ownership concentration, and examines the connection between equity restriction ratio and company performance; model (3) is to examine the connection between equity restriction ratio and firm performance after adding control variables and ownership concentration; model (4) is based on the previous model, while adding ownership concentration (Largest), the squared term of the ownership concentration (Largest 2 ) and the control variables, test the connection between equity restriction ratio and company performance.
where A is the correlation coefficient of the nth variable, ε i,t is the random disturbance term; ROE i,t−1 and ROE i,t represent the return on net assets of the previous period and the current period respectively; Largest i,t is the ownership concentration, that is, the stockholding ratio of the largest shareholder; Largesr i,t 2 represents the square of the stockholding ratio of the first largest stockholder; Balance i,t represents equity restriction ratio, that is, the sum of the shareholding ratio of the second to tenth largest stockholders/the stockholding ratio of the largest stockholder; Balance i,t 2 represents the square of (the sum of the stockholdings of the second to tenth largest stockholder/the largest stockholder)/the stockholding ratio of the largest stockholder; Control i,t is the control variable. It shows that the mean return of the net assets of the sample company is 8.28%, and the return on net assets is slightly changed, and the corporate's performance is relatively stable. The average return on assets (ROA) is 0.0399, with a median of 0.0322 and a standard deviation of 00438. It represents that the average return of the sample corporate's total assets is 3.99%; the maximum value is 0.1973, and the minimum value of ROA is negative value 0.0792, indicating that the difference in total return on assets is small. The mean stockholding ratio of the largest stockholder (Largest) is 0.3959, the median is 0.3904, and the standard deviation is 0.1486, showing that in China's state-owned mixed ownership companies, the concentration of ownership has not changed much but is generally high. The phenomenon of "one shareholder holding the largest share" is widespread. The mean value of the equity restriction ratio is 0.5349, the median is 0.3272, the minimum is 0.0242, and the maximum is 2.6139. The maximum and minimum gaps are large, but the standard deviation is 0.5365. The degree of dispersion is not high, indicating that the equity restriction ratio is ubiquitous in the sample enterprises.

Descriptive Statistics
Control variable: the maximum value is 0.8845, the minimum value of Lev is 0.0974, which shows that there is a big difference in the asset-liability ratio of state-owned mixed ownership enterprises, and some enterprises have higher debt ratios. However, the average value of Lev is 0.5204, the median is 0.5376, and the standard deviation is 0.1879, which shows that the leverage level of most state-owned mixed ownership enterprises is within a reasonable range and will not face excessive debt repayment pressure. The minimum growth rate of enterprise growth is negative value 0.2291, and the maximum value is 0.9440, which shows that the growth rate of operating income of state-owned mixed ownership enterprises is significant, but the average value of 0.1300 indicates that the overall growth is at a relatively high and reasonable level. The average size of the enterprises (Size) is 22.5754, the minimum value is 20.0828, and the maximum value is 26.4828, no obvious difference in the size of state-owned mixed ownership enterprises was found. The mean value of Asset turnover is 0.7589, the maximum value is 2.8123, the minimum value is 0.0604, which indicates that the total asset turnover rate of state-owned mixed ownership enterprises is quite different. The overall performance of the assets is at a medium level, which needs further improvement.

Correlation Analysis
Before the regression analysis, the study first tested the correlation of each variable, and the Pearson correlation coefficient table is represented in Table 3. We can see from Table 3 that the correlation coefficient in ROE and L.ROE is obviously positive, showing that the ROE of the first phase is highly correlated with the ROE of the current period. The correlation coefficient in equity restriction ratio and firm performance is 0.0539, which is significantly positive at the 1% level, showing that it is at least a positive relation between firm performance and equity restriction ratio, but whether there is an inverted U-type relationship or other non-linear relationship between the two requires further verification.  Note: ***, **, and * indicate significant levels at 1, 5, and 10%, respectively.
For the control variable of this paper: the correlation coefficient in firm performance and capital structure (Lev) is −0.06, which is obviously negative, showing that the higher the company's asset-liability ratio, the greater the risk faced by the company and the lower the company's performance. Apart from that, the correlation coefficients of company growth, company size, and Asset-turnover with company performance are significantly positive (0.3309, 0.1443, and 0.1701, respectively), indicating that they are significantly positively related with company performance. The rapid growth of the enterprise indicates the rapid increase of operating income, while the growth of operating income indicates the proper operating condition of the company and enhances the improvement of corporate performance. The extension of company size is promotive to the formation of scale effect, the more conducive to the company to reduce costs, create more profits, and thereby improve company performance. The improvement of the turnover rate of total assets indicates the increase of business income in the case that there is no substantial change in the total assets, which straightly promotes the performance of companies. The control variables selected in this study are significantly related with firm performance at the level of 1%, which proves that the selection of control variables in our study is reasonable in a sense. Additionally, the relation coefficient between all variables is relatively small, indicating that there is little possibility of multicollinearity, which to some extent guarantees the rationality of the model setting in this study and the reliability of the regression results.

Regression Analysis
This study intended to use OLS (OLS means Ordinary least squares) regression to examine the hypothesis in our study, and the test consequences are represented in Table 4. The regression consequences from model (1) shows that when there are no control variables, ownership concentration (Largest) and the square of the ownership concentration (Largest 2 ), the equity restriction ratio (Balance) (ROE) and firm performance coefficient is 0.0146, obviously positive at the degree of 1%, while the square of equity restriction ratio (Balance 2 ) and firm performance (ROE) coefficient is 0.0047, obviously negative at the degree of 5%. The symbols of Balance and Balance 2 are opposite, and the symbols of the former are obviously positive, while the symbols of the latter are obviously negative, showing that the equity restriction ratio in state-owned mixed ownership companies has an obvious inverted U-shaped connection with firm performance for the most part. The results of the model (2) show that after the addition of factors of control variables, the coefficient of Balance is 0.0133, which is significantly positive, and the coefficient of Balance 2 is negative value 0.0042, which is significantly negative. The test results of adding Largest in model (3), adding Largest and Largest 2 in model (4) show that the coefficients of Balance were 0.0310 and 0.0305 respectively, which were still significantly positive, and the coefficients of Balance 2 are negative value 0.0086 and negative value 0.0079 respectively, which are significantly negative at the degree of 1%.
The test consequences in Table 1 show that, whether or not the influence of ownership concentration is taken into account, there is an obvious inverted U-shaped connection in equity restriction ratio and company performance of state-owned mixed ownership companies on the whole. The result means that the moderate level of equity restriction ratio acts as a certain role of supervision and incentive to the controlling shareholders of state-owned mixed ownership enterprises, which alleviates the negative effects brought by "one shareholder holding the largest share", reduces the self-interest of the management, reduces the agency cost, and promotes the ameliorating of company performance. However, the excessive degree of equity restriction weakens the decision-making efficiency and enthusiasm of the controlling shareholders and may lead to vicious competition among large shareholders and increase agency cost, thus adversely affecting the performance of state-owned mixed ownership corporates. The results support the hypothesis in this study.
In the control variables, except for the obvious negative relation coefficient between company performance and capital structure, the correlation coefficients among company size, growth, and total asset turnover and company performance are all significantly positive, which indicates that if company debt level rises, company risk increases as well and company performance decreases. If ownership concentration rises, the expansion of company size, the rise of growth level, and the acceleration of total asset turnover, company performance will improve accordingly.

Robustness Checks
To make the above conclusions more reliable, robustness checks were carried out in this study (see Tables 5 and 6). First, we undertook other measures of major variables. For the measurement of corporate performance, we replaced ROE (rate of return on equity) in the models (1) to (4) with ROA (return on total assets), then checked the model again. The regression results are represented in Table 5. Second, the Balance coefficients of the models (1) to (4) are all significantly positive, and the Balance 2 coefficients are all significantly negative. The adverse results of them indicate that the equity restriction ratio exists an "inverted U-shaped" connection with company performance. The regression results are in accordance with the original results, showing that the regression results are robust. Third, we considered the endogenetic problem of variables. Considering the endogenous problem between company performance and ownership concentration, in other words, whether the equity restriction ratio affects the corporate performance, or the corporate performance affects the equity restriction ratio.
In order to control the endogenous problem, we took the current corporate performance (ROE/ROA) as the explained variable, the corporate performance in a lag period (L.ROE/L.ROA), and the equity restriction ratio in a lag period (L. Balance) as the explained variable for a new regression test, and the regression results show that the lag issue of equity restriction ratio has an obvious influence on the current company performance. Taking the equity restriction ratio in the current period as the explained variable, and taking the equity restriction ratio in the lag period as the explanatory variable, the regression consequences show that the performance of the company in a lag period has no significant impact on the equity restriction ratio in the current period.  Note: ***, **, and * indicate significant levels at 1, 5, and 10%, respectively.

Dynamic Panel Threshold Analysis
From the literature all over the world on the existing research on company performance and equity restriction ratio, most theoretical and empirical studies pay close attention to explore the connection between company performance and ownership concentration, and try to find the optimal stockholding ratio of the largest stockholder. For example, Xu and Wang 17 used the listed firms as research objects and the result shows that the stockholding ratio of the largest stockholder is limited to 50-60%, which is most promotive to improve company performance. From literature research on company performance and equity restriction ratio, most of them only prove the existence of equity restriction, and there are a few kinds of literature that analyze the reasonable range of equity restriction ratio. We know from the above research that have an inverted U-shaped connection between company performance and equity restriction ratio of state-owned mixed ownership companies. Therefore, this study takes the equity restriction ratio (Balance) as the threshold variable and explanatory variable, the company performance (ROE) as the explanatory variable, the capital structure (Lev), the company size (Size), the growth (Growth), and the total asset turnover rate (TA-turnover) as control variables, and performs a threshold regression test with full sample data, trying to find the optimal threshold for the equity restriction ratio. However, the results in our test show that there is no threshold value for the equity restriction ratio. Is the relationship between company performance and equity restriction ratio not obvious, or is the model not perfect? According to the research methods used by Mcconnell and Servaes [35], and Li et al. [36], this study differentiates the whole object companies into groups in accordance with the stockholding ratio of the largest stockholders, and investigates the connection between equity restriction ratio and company performance. In addition, from the above analysis we can see that there may be a nonlinear connection in the influence of equity restriction ratio on the performance of state-owned mixed ownership companies. Therefore, this study refers to Hansen's [37] idea of the threshold regression model and constructs the dynamic panel threshold model grouping to test whether there is an optimal value of equity restriction ratio.
In accordance with most scholars' research, if the largest stockholder ratio is more than 25%, it is usually in the dominant voting position. Worldwide, the necessary stockholding ratio of controlling stockholders is often confined from 20 to 25%. Xu and Wang [17] believe that if the largest stockholder controls less than 20% of the stocks, it is equity participation, and the equity structure is decentralized. If the largest stockholder's stockholding ratio is between 20 and 50%, it is relatively controlling. However, Li et al. 37 believe that if the largest stockholder controls more than 40% of the stocks, it can form absolute control over the enterprise. Therefore, this paper further tests the data according to the size of the stockholding ratio of the largest stockholder. According to the size of the largest stockholder, the stockholding structure has three types: equity decentralization, relative holding, and absolute holding.
Group I (equity decentralization): the stockholding ratio of the largest stockholder is (0-25%). Group II (relative holding): the stockholding ratio of the largest stockholder is (25%-40%). Group III (absolute holding): the stockholding ratio of the largest stockholder is (40%-100%). In China's state-owned mixed ownership firms, the number of firms where the largest stockholder holding ratio is more than 60% is less than 10% of the total number of companies. Therefore, as to make the test consequences more targeted, we divided the data of the largest shareholder holding ratio more than or equal to 40% into two groups: the largest stockholder holding ratio between 40% and 60% and the largest stockholder holding ratio more than or equal to 60%. The results are divided into the following four groups.

Panel Threshold Regression Model
The method of panel threshold model with the individual effect minimizes the sum of residual squares to determine the threshold value and tests the prominence of the threshold value. The specific idea is select a certain variable as the threshold variable, and divide the regression model into multiple intervals according to the searched threshold. The regression equations of each interval are expressed differently, and the other sample values are classified according to the interval divided by the threshold.Take the panel threshold regression model as an example: where u it is the individual effect, y it is the explained variable, θ i the coefficient, x it the explanatory variable, q it is the threshold variable, I(•) is the indicator function, γ is the threshold value, ε it the residual. The basic idea to determine the threshold value is as follows: by eliminating the individual effect in model (5), and then minimizing the sum of squares of residuals in the model without individual effect S 1 (γ) on this basis, searching the optimal estimate value of the threshold ∧ γ, that is ∧ γ = argminS 1 (γ). Firstly, the threshold effect test was carried out on the model. The bootstrap method was used to obtain the asymptotic distribution, and the threshold effect was determined by the LM test (LM means Lagrangian Multiplier Test) F statistic and the associated p value. If the p value is small enough, it indicates the existence of a threshold effect and rejects the null hypothesis that no threshold effect exists. Then, continue to test whether there are two or three threshold values, until p is no longer significant, to determine the number of threshold values.

Dynamic Panel Threshold Regression Model Design and Threshold Existence Effect Test
Taking the analysis of 300 equity sampling as the threshold variable, the results show below Table 7. when the stockholding ratio of the largest stockholder is less than 25%: the F value of the LM statistic is 13.68, and the corresponding p value is 0.0433, which is obvious at the 5% level. Therefore, the null hypothesis that no threshold effect exists is wrong. The first possible threshold value (γ = 0.8705) is found, and the corresponding residual sum of squares is the smallest. A further test for whether there are two thresholds: in this case, the F value of the LM statistic is 5.62, and the associated p value is 0.55, it is not significant, indicating that the double threshold assumption should be rejected, that is, only a single threshold exists. (2) When the stockholding ratio of the largest stockholder is between 25% and 40%, the F value of the LM statistic is 12.02, and the corresponding p value is 0.06, which is obvious at the 10% level. Therefore, the null hypothesis that no threshold effect exists is wrong. The first possible threshold value (γ = 1.1336) is found, and the corresponding residual sum of squares is the smallest. A further test for whether there are two threshold values: at this point, the F value of the LM statistic is 6.8, and the corresponding p value is 0.4033, it is not significant, indicating that the hypothesis of the double threshold should be rejected; that is, only a single threshold value exists. (3) When the stockholding ratio of the largest stockholder is between 40% and 60%: the F value of the LM statistic is 13.62, and the corresponding p value is 0.03, which is obvious at the 5% level. Therefore, the null hypothesis that there is no threshold effect is wrong. The first possible threshold value (γ = 0.7297) is found, the corresponding residual sum of squares is the smallest. A further test for whether there are two threshold values: at this point, the F value of the LM statistic is 6.88, and the corresponding p value is 0.31, it is not significant, indicating that the hypothesis of the double threshold should be rejected; that is, only a single threshold value exists. (4) When the stockholding ratio of the largest stockholder is equal to or more than 60%: the F value of the LM statistic is 6.88, and the corresponding p value is 0.31, it is not significant, indicating that the assumption of no threshold should not be rejected, and there is no threshold value of the equity restriction ratio within this range.
When the stockholding ratio of the first largest stockholder is less than 25%, between 25 and 40%, and 40 and 60%, there is only a single threshold value, and when the stockholding ratio of the first largest stockholder is equal to or more than 60%, there are several threshold values. Therefore, in this study, only the dynamic panel threshold model with a single threshold (6) is constructed in the first three intervals, and the threshold regression test is performed as follows: where µ i is the intercept term, θ n is the correlation coefficient of the variable, ε it is the residual, i is the listed company, t is the year, X it is the control variable, γ is the threshold value, I(•) is the indicator function. Note: ***, **, and * indicate significant levels at 1%, 5%, and 10% respectively.
The corresponding threshold values and confidence interval estimation results under different equity concentration levels are shown in Table 8, which shows that when the equity concentration is in the range of (0,25%), (25%,40%), and (40%,60%), there are three thresholds for the equity balance respectively. The first is 0.8705, the second is 1.1336, and the third is 0.7297.

Dynamic Panel Threshold Regression Analysis
The results of the dynamic panel threshold regression are shown in Table 9. The results are as follows: (1) when the stockholding ratio of the first largest stockholder is less than 25%, and the equity restriction ratio is less than the threshold value of 0.8705, the coefficient of Balance1 is −0.0405. On this occasion, it is an obvious negative correlation between corporate performance and equity restriction ratio at the 1% level; under the condition that the equity restriction ratio is greater than the threshold value of 0.8705, the coefficient of Balance 2 is −0.0014, but it is not significant. It can be seen that when there exists low ownership concentration, and the ownership is distracted, company performance is negatively related with the equity restriction ratio. Therefore, under the condition that the stockholding ratio of the first largest stockholder is less than 25%, there is no optimal threshold value for the equity restriction ratio. At this time, the equity restriction ratio is generally higher, and it should be appropriately reduced. (2) Under the condition that the stockholding ratio of the largest stockholder is between 25 and 40% and the stockholding balance degree is less than the threshold value of 1.1336, the coefficient of Balance1 is 0.0272, and the company performance is obviously and positively related with the equity restriction ratio at the level of 5%. Under the condition that the equity restriction ratio is greater than the threshold value of 1.1336, the coefficient of Balance 2 is negative value 0.0055, corporate performance is negatively correlated with the equity restriction ratio, but it is not significant. It is indicated that in this interval when the equity restriction ratio is less than 1.1336, company performance rises when the equity restriction ratio increases; and when the equity restriction ratio is greater than 1.1336, company performance decreases when the equity restriction ratio increases. The optimal threshold value for the equity restriction ratio is 1.1336. It can be seen that in the case of relatively concentrated equity, the equity restriction ratio should be appropriately increased, the supervision and balance of the largest shareholder should be exerted, the supervision of the management should be strengthened, and the corporate performance should be improved. However, excessively improved equity restriction ratio will have an adverse effect on corporate performance, and the two have an inverted U-shaped relationship. (3) Under the condition that the stockholding ratio of the first largest stockholder is between 40 and 60% and the equity restriction ratio is less than the threshold value of 0.7297, the coefficient of Balance1 is 0.0589, and the corporate performance and equity restriction ratio are in a significant positive correlation at the level of 5%; under the condition that the equity restriction ratio is greater than the threshold value of 0.7297, with a coefficient of Negative value 0.0185, corporate performance is negatively related with equity restriction ratio, but it is not significant. After comparison, it shows that when the concentration of equity is high, similar to the case of relative concentration of equity, and when the equity restriction ratio is below the critical value, the corporate performance rises when the equity restriction ratio rises; when the equity restriction ratio exceeds the critical value, the company performance deceased with the rise of equity restriction ratio, and the two show an inverted U-shaped relationship. Within this interval, the equity restriction ratio's optimal value is 0.7292. (4) In the case where the stockholding ratio of the first largest stockholder is equal to or more than 60%, although there is no threshold value, it can be seen that the coefficient of Balance1 is obviously positive at the 1% degree, it is a positive relation between company performance and equity restriction ratio. To analyze the reasons, we can explore the following aspects: First, under the condition that the stockholding ratio of the first largest stockholder is less than 25%, since the stockholding ratio of the largest stockholder is not high, and the equity is scattered. At this time, the equity restriction ratio is generally too high. Excessive equity restriction ratio leads to vicious competition among multiple large shareholders, neglecting supervision of managers, leading to an increase in the cost of the first type of agency; in addition, over-supervision will limit the flexibility of decision-making and the enthusiasm of improving corporate performance will be reduced by controlling shareholders of the state-owned mixed ownership enterprises, resulting in inefficient decision-making and finally lead to a decline in corporate performance. This is different from the results drawn by Li et al. 37. They take private listed companies as the object and the results show that the lower the stockholding ratio of the largest stockholder, the stronger the mechanism of supervision and balance of other large stockholders on the controlling stockholders. Moreover, it is more effective to upgrade company performance.
Second, under the condition that the stockholding ratio of the largest stockholder is between 25 and 40%, there are two situations at this time: if the stockholding of the enterprise is dispersed, the largest shareholder can completely control the enterprise. Due to the existence of "entrenchment effects", the motives and encroachment of shareholders "tunneling" enterprises and encroaching on the benefits of minority stockholders increased as their stockholding ratio increased [26]. In this condition, if the stockholding ratio of other large stockholders is high, it is conducive to promoting the completing of company performance by supervising and restricting the bad behavior of the controlling shareholders. However, when several other large stockholders hold a high proportion of shares and even threaten the position of the controlling stockholders, it is easy to form vicious competition among largest stockholders, thus allowing operators to increase agency cost. At the same time, vicious competition may lead to the pursuit of private stockholders without taking into account the interests of the company, which will lead to the decline of firm performance.
Third, under the condition that the stockholding ratio of the largest stockholder is between 40 and 60%, the first major stockholder can form absolute control over the enterprise. Within this interval, it is possible to form a "tunneling defense effect," and it is also possible to form an "interest equalization effect." Due to the high stockholding ratio of the largest stockholder, it has the power to make decisions on major issues to a certain extent. If there is a moderate degree of equity restriction ratio, other large shareholders will intervene and correct the improper decision of the controlling shareholders, improve the correctness of the decision, limit the self-interest of the large shareholders, and then improve the corporate performance. However, if the equity restriction ratio is too high, it may lead to vicious competition among several large shareholders, which may also weaken the influence of the controlling stockholders in the firm's business decision-making and reduce its enthusiasm for improving the company's performance, leading to a decline in firm performance.
Fourth, under the condition that the stockholding ratio of the largest stockholder is equal to or more than 60%, it has absolute control over the enterprise and fully grasps the decision-making power and the right to speak on major issues. Although there is a "convergence effect of interests" at this time, the largest shareholder will naturally make unremitting efforts to improve corporate performance, but the phenomenon of encroaching on the benefits of minority stockholders, manipulating stock prices, and providing false information, still exists 22. Therefore, the higher of the equity restriction ratio, the more effectively it can alleviate the problem of "one shareholder holding the largest share" of state-owned enterprises, limit the self-interested behavior of large stockholders, and the more favorable it is to improve corporate performance, They are positive correlations. Note: ***, **, and * indicate obvious levels at 1, 5, and 10% respectively.

Comparative Analysis of the Equity Restriction Ratio of State-Owned Mixed Ownership Enterprises
Comparing the threshold regression results with the actual situation of equity restriction ratio in current China's state-owned mixed ownership enterprises, from Table 10, we can see that (1) Under the condition that the largest stockholder's stockholding ratio is less than 25%, the average value of the equity restriction ratio is 1.1587. From previous analysis, we can see that the company performance of this interval is negatively related with the equity restriction ratio, and the threshold value of the threshold regression result is 0.8705. Therefore, the equity restriction ratio of the current mixed ownership enterprises should be appropriately reduced. (2) Under the condition that the stockholding ratio of the largest stockholder is between 25 and 40%, the average value of the equity restriction ratio is 0.6213, which is significantly lower than the optimal threshold of 1.1336 in the interval of the above regression results; under the condition that the largest stockholder's stockholding ratio is between 40 and 60%, the average equity balance is 0.2605, which is also a certain distance compared with the optimal threshold of 0.7297. Therefore, it is necessary to increase the equity restriction ratio in these two areas appropriately, and it is most conducive to promote the improvement of company performance. (3) As can be seen from the above, under the condition that the stockholding ratio of the largest stockholder is equal to or more than 60%, the company performance in this area increases with the increase of equity restriction ratio, and the actual average of equity restriction ratio is only 0.1134. Moreover, because the ratio of the largest stockholder in the interval is relatively high, improving the equity restriction ratio is not enough to form an influence that can compete with it. Therefore, we should not only pay attention to internal supervision and checks and balances but also strengthen external supervision to protect the interests of other minority shareholders.
These research conclusions are also in line with the reality of China's current state-owned companies. If the controlling stockholder of Chinese state-owned companies is effective in supervising managers, the first type of agency costs is usually lower. However, due to the diversification of investment entities in China's state-owned mixed-ownership enterprises, the level of principals is complex, and the contractual relationship is not market-oriented. The powers and responsibilities between shareholders' meetings, boards of directors, and managers are not clear, leading managers to pursue on-the-job consumption and increase leisure time. The behavior cannot be effectively supervised and restricted. If the company has other major shareholders, that is, with the improvement of the equity restriction, other major stockholders will supervise and intervene in the decision-making behavior of the controlling stockholder. Although controlling shareholder's time and energy for the supervision of the managers will be relatively reduced compared with the lower equity restriction ratio, they will also pay attention to the behavior and decision-making of the managers due to the participation of other major stockholders 29. Therefore, under the condition that the equity restriction ratio is increased, the first type of agency costs will be appropriately reduced, which in turn will increase the improvement of company performance. If the equity restriction ratio is too high, the other major stockholders and the controlling stockholder are prone to vicious competition, neglecting the supervision of the manager, thus giving the operators an opportunity to take advantage of the first type of agency costs. At the same time, vicious competition may lead shareholders to seek their own benefits without taking into account the benefits of the company, so that corporate performance declines. In addition, excessive equity restriction ratio will weaken the influence and decision-making efficiency of controlling shareholders in the company's business decisions, and reduce their enthusiasm for improving the company's performance.

Conclusions
This study took the state-owned A-share listed firms with mixed-ownership in China's stock market as objects and conducted an OLS regression test to explore the connection between company performance and equity restriction ratio. The consequences indicate that there is not a simple linear relationship between equity restriction ratio and company performance in state-owned mixed ownership listed companies, but an overall "inverted U-shaped" curve relationship. In addition, we set a dynamic panel threshold regression model, grouped in accordance with the size of the largest stockholder stockholding, and used the equity restriction ratio as a threshold variable to conduct a threshold regression test to examine whether there is a difference in the connection between company performance and equity restriction ratio under different equity concentration levels and whether there is an optimal equity restriction ratio. The regression results show that under the different stockholding ratios of the first largest stockholder, the relationship between equity restriction ratio and company performance is different. The specific performance is as follows: under the condition that the stockholding ratio of the largest stockholder is less than 25%, there is a negative relation between the equity restriction ratio and company performance; under the condition that the stockholding ratio of the largest stockholder is between 25 and 40% and 40 and 60%, the two have an "inverted U-shaped" relationship, there is an optimal equity restriction ratio, it is 1.1336 and 0.7297, respectively; under the condition that the stockholding ratio of the largest stockholder is equal to or more than 60%, the equity restriction ratio is positively related with company performance. Therefore, this paper believes that if the equity restriction ratio increases, it will help to cut back the first type of agency costs and increase the performance of the enterprise; and if the equity restriction ratio is too high and even exceeds a certain threshold, the rise of the equity restriction ratio will cause a rise in the first type of agency costs and has a negative influence on company performance.
The following policy recommendations are proposed: First, from the perspective of the connection between equity restriction ratio and company performance: the equity restriction ratio of listed companies in China and the performance of state-owned mixed ownership firms are generally in the "inverted U-shaped" relationship. Therefore, we must not only improve the equity restriction ratio, but also the macroeconomic control of the controlling power, so that a large number of major shareholders can form a balance between mutual restraint and supervision. The equity restriction ratio cannot be overstated because it may adversely influence the performance of the firm. Second, the connection between equity restriction ratio and company performance is different when under different ownership concentration. Under the condition that the ownership of the enterprise is dispersed (the largest stockholder holds less than 25%), the equity restriction ratio should be appropriately reduced. Under the condition that the equity is relatively concentrated (the proportion of the largest stockholder is between 25 and 40%), based on preventing excessive equity restriction ratio, the equity restriction ratio of the enterprise should be appropriately increased, making the equity restriction ratio close to 1.1336. Under the condition that the stockholding ratio of the largest stockholder is between 40% and 60% makes the equity restriction ratio close to 0.7297. Under the condition that the stockholding ratio is very concentrated (the largest stockholder holds equal to or more than 60%), and the total control is achieved, it is not only necessary to improve the equity restriction ratio within the enterprise, but more attention should be paid to external auditing and strengthening of external supervision of enterprises.