As a Warning to Others or Do the Same?——A Study on the Spillover Effect of Punishment against Interlocking Company

: Based on the theory of organizational penalty spillover, this paper discusses whether the punishment against interlocking company will affect the accounting information quality of the observing company through the channel of interlocking directors. The research results show that the observing company significantly improves the accounting information comparability within two years after interlocking company is punished when compared horizontally with an interlocking company that is not punished. The observing company also significantly improve the accounting information comparability within two years after the interlocking company is punished when compared longitudinally with before an interlocking company is punished. The findings show that the punishment against listed companies by CSRC and other regulatory authorities have spillover effect, the punishment is not only an act of correcting deviations after the event, but also an attempt to improve the accounting information quality of unpunished companies by punishment that is a Warning to Others. when the dependent variables is Dcompm ,the coefficients on Post*Treat is significantly positive, significance test. The result still

that the punishments against listed company has spillover effect.
The contributions of this paper may be as follows: (1) The paper enriches the study of the consequences of punishments against listed company. The previous literatures mainly investigate the direct consequences of regulatory punishment and the contagious spillover effect caused by punishment, but few papers pay attention to the contrast spillover effect of punishment. We think that the punishment against listed companies by regulatory authorities can have a knock-on effect on the observing company through the channel of interlocking directors, which shows that the purpose of punishments against listed companies by regulatory authorities is not only to expose the illegalities of listed companies and effectively curb their re-occurrence, but also to improving the behavior of unpunished observing company by playing an exemplar role.
(2) The paper enriches the research on the influencing factors of accounting information comparability. The research on the influencing factors of accounting information comparability in the previous literatures is mainly based on the assumption of independent decision-making and does not consider the interaction between companies. As a matter of fact, many companies' decisions affect each other. We use the external factors that bear on interlocking companies to absorb the impact of the illegalities that are punished, according to the method of De Franco (2011) [27] to estimate the degree of change of accounting information comparability, and study the impact of interlocking company on the accounting information comparability of observing company.

Literature review and research hypothesis
Firstly, we review the relevant literatures from three aspects: the interlocking directors, the spillover effect of punishment and the accounting information comparability. Secondly, we analyze the interlocking directors and that transfer of the punishment experienced to observing company as a channel and how it improves the accounting information comparability of observing company.

Interlocking directors
At present, with the popularity of interlocking directors, the corporate networks based on interlocking directors are commonly established. The previous literatures show that interlocking directors can help company to achieve information transmission. Battiston et al. (2003) [16] find that corporate decision-making information would be disseminated through shared directors of different companies. Kang (2008) [7] believes that voluntary payment of stock option grants may be driven by social influence and learning within directors networks. Bizjak et al.(2009) [21] find that if directors had previously engaged in similar backdating behavior in other companies, the possibility of backdating stock options would be greatly increased. Chiu et al.(2013) [28] find that if a company is linked to another company through interlocking directors, and the interlocking company has had financial restatement events in the same year or two years ago, then the company has a greater probability of financial restatement. Fracassi (2016) [23] finds that managers' financial decisions are influenced by peers with social connections, and the more connections between two companies, the more similar decisions they make.
Domestic research on the information transmission of interlocking directors is also very rich. Li Minna and Wang Tieman (2014) [17] point out that company can learn from companies with good salary incentive practices through directors' network to adjust their salary incentive policies. Liu Yongtao et al. (2015) [18] study the impact of interlocking directors on the choice of accounting policies through information transmission mechanism, and find that company with interlocking relationships are more likely to choose the accounting policy of capitalization of development expenditure. Han Jie et al. (2015) [22] find that the company would learn and imitate the R&D investment decisions of the interlocking companies. Chen Yunsen and Zheng Dengjin (2017) [24] examine the impact of directors' network on the convergence of investment between companies. If there are interlocking directors between two companies, the investment level and investment changes between companies are more similar. Han Jie et al. (2017) [25] find that there is a connection between two companies, accounting methods, including inventory valuation and depreciation methods were similar, which showed that the choice of accounting methods could be spread through director linkage. Zhou Xiaosu et al. (2017) [19] find that there was inter-organizational imitation in the choice of accounting policies.
It can be seen that interlocking directors are cost-free and reliable channels of information transmission among companies, which can become the dissemination mechanism of inter-company practice.

Spillover effect of punishment
Spillover effect originally means that when a solution exceeding its capacity is added to a container, the solution overflow affects other instruments outside the container. That is, when an organization carries out an activity, it will not only produce the expected effect on the activity, but also have an impact on other person or organization, and its essence is an external effect [29] . Trevino (1992) [5] holds that punishment is a social event and studies the influence of punishment on the observer. It shows that punishment will not only have an impact on the punished company, but also have an impact on the unpunished organizations or individuals associated with the punished company, that is, the punishment has spillover effect. Lang and Stula (1992) [30] find that spillover effect of punishment can be divided into contagious effect and contrast effect, contagious effect means that punishment has a negative impact on the punished, but also on other unpunished company, and contrast effect means that the punishment behavior has the opposite, positive effect on other unpunished company.
Many scholars have paid attention to the contagious effect of punitive behavior. Fich and Shivdasani (2007) [6] investigate the impact of financial fraud on the reputation of external directors and find that interlocking company with the same directors also showed a decline in valuation in litigation applications. Kang (2008) [7] find that reputational punishment may spread from the accused company to the interlocking company through the interlocking directors' network. The market value of accused companies will also fall on the day -that is market value of the accused companies decline. Yin Li and Chen Shou (2010) [8] find that group member companies with the financial crisis will have a negative externality impact on affiliated member companies. Beatty(2013) [9] believes that regulatory punishment decisions not only have a significant negative impact on the punished company, but also affect unpunished individuals or organizations. Zhang Yue et al.(2018) [4] find that the company and other stakeholders showed strong negative reactions to the announcement of illegal filing before and after the announcement of illegal listed companies,.
In addition, some literatures argue that spillover effect of punishment not only has a similar effect on other organizations and sometimes has a contrasting positive effect. Jennings et al. [31] (2011) find that company reduce discretionary accrued earnings after peer companies in the same industry were investigated by SEC for manipulation of earnings. Zhong et al. (2017) [32] find that directors subject to regulatory sanctions in another company were more likely to attend board meetings and play supervisory role more effective. Liu Wenjun et al. (2017) [13] find that the auditors with common work experience with punished auditors more incline to issue non-standard audit opinions to customers in the future because of their common audit experience. Yang Jinfeng et al. (2018) [15] find that compared with the unpunished certified public accountant, the audit quality of the punished certified public accountant and his colleagues has been improved using the CSRC administrative punishment decision. Brown et al. (2018) [33] find that if SEC comments on the disclosure of risk factors of industry leaders, competitors or peers, companies that did not receive any comments largely revised their disclosures the following year.
To sum up, the spillover effect of punishment is manifested in the capital market performance and behavior of peers, both contagion effect and contrast effect are rich, but there are also shortcomings. First, most of the channel of spillover effect of punishment revolve around the same region and industry, and there is little discussion about interlocking directors as the path of spillover effect. Second, there are few literatures that study the spillover effect of punishment against listed companies on their accounting information quality.

Accounting information comparability
Accounting information comparability is one of the important quality characteristics of accounting information, which means that different company accounting systems should produce similar accounting information for the same or similar economic business. On the contrary, accounting information should fully reflect the difference when the economic business is different.FASB No.8 (2010) defines the accounting information comparability as the second level of the useful financial information quality feature hierarchy: improving quality.
The research on the economic consequences of the accounting information comparability is very rich. De Franco et al. (2011) [27] believe that the increase of the accounting information comparability can reduce the information collection and treatment cost of the investors, and can reduce the risk and cost of the value evaluation of the participants in the equity capital market. Kim et al. (2013) [34] believe that the accounting information comparability can help to reduce the uncertainty of the perceived risk of bond and CDS market participants, thereby reducing the cost of debt financing. Yang Zhonghai et al. (2015) [35] think that the improvement of the financial report comparability can significantly lower the equity capital cost. Jiang Xuanyu et al. (2017) [36] find that the accounting information comparability can help to overcome the market friction and promote companies innovation. Xie Hongshuang et al.(2017) [37] find that improvement of the accounting information comparability can significantly improve the dynamic adjustment speed of the capital structure. Yuan Zhenchao and Rao Pingui (2018) [38] find that the comparable performance of accounting information can effectively alleviate the information asymmetry faced by companies. It can be seen that the improvement of the accounting information comparability can help the company to transmit positive signals in the capital market, and can also help the information users to improve the decision-making usefulness of accounting information.
The previous literatures show that influencing factors of the accounting information comparability mainly include standard convergence, strategic differences, internal control, CEO tenure and so on. Wan Peng and Chen Xiangyu (2017) [39] find that the international convergence of accounting standards indirectly affects the information disclosure behavior of the company through the accounting information comparability, and the international convergence of accounting standards improves the financial statements comparability. Zhou Donghua and Yang Xiaokang (2018) [40] show that insider trading can significantly reduce the accounting information comparability. Zhang Xianzhi et al.(2018) [41] find that the more the company strategy deviates from the conventional strategy of the industry, the lower the financial reports comparability, and the improvement of the quality of internal control can lead to improving the financial reports comparability. Chen Guohui and Yin Jian (2018) [42,43] examine that CEO tenure and CFO experience significantly affect the accounting information comparability.
Most of the studies focus on how the corporate independent decision-making affects the accounting information comparability, and few literatures discusses the external factors that affect the accounting information comparability. We study the relationship between the external shock that punishment against interlocking company and accounting information comparability of observing company.

Spillover effect of punishment against interlocking company on accounting information comparability of observing company
It conveys the signal of its operation and financial problems to the market when interlocking company is punished, which will be paid special attention by investors. Observing company which has same director with interlocking company will also be re-examined by investors [7] . Compared with the unpunished companies, the observing company need to take positive action to highlight its advantages in order to reduce the negative investor sentiment caused by punishment against interlocking company and maintain their image in the corporate network.
First, the observing company will avoid violations. Trevino(1992) [5] believes that punishment has a deterrent effect, that enhances the risk perception of observers, and reduces similar violations in the future. When the observing company which has interlocking relationship with the punished interlocking company observes that the interlocking company is punished because the illegal behavior through the interlocking directors, it will subconsciously improve the risk perception of illegal behavior, and consider the potential punishment cost caused by illegal behavior to avoid the re-occurrence of illegal behavior, so as to reduce the uncertainty of accounting treatment and improve the quality of accounting information.
Second, the observing company will send a positive signal to the capital market. According to the signal theory of Spence (2002) [26] , under the condition of asymmetric information, company needs to adopt appropriate signals to transmit information. If the signal is cheap and easy to imitate, the signal clarification is less reliable, the clarification effect is poor and limited. Only by adopting a way that imitators can not emulate can send credible signals to investors, the clarification effect is good, and it is easier to form a contrast positive effect. So in order to maintain the image and enhance the confidence of investors, the observing company will choose the behavior and signal that other companies are difficult to imitate, and send a positive signal to the capital market.
The accounting information comparability can help to transfer high-quality signals to the capital market as a "improve quality characteristic" in the hierarchical structure of useful financial information. The FASB points out that if comparable accounting information is not available, it is not possible to make investment and credit decisions in a rational and effective manner. If the capital market is not complete, the investors need to identify the relative investment value and risk of the company more clearly by comparing the financial statement, operating results and cash flow of the observing company with other companies. Compared with the other accounting information quality characteristics such as the correlation, the robustness and the earnings quality, the accounting information comparability can determine the quality of the accounting information of the observing company through the horizontal comparison among the companies in the industry, so as to be more consistent with the decision-making characteristics of the investors. In addition, compared with other accounting information characteristics, the comparability is a relative index, which needs to be compared with the similar accounting information of other companies and the measure is consistent as far as possible. This makes it difficult for information to be manipulated through choosing the independent accounting policies and method selections. Thus, the accounting information comparability is an imitative information feature. In general, when the interlocking company is punished, the observing company may choose to improve the accounting information comparability to highlight its advantages and increase the investor's confidence.
The above discussion leads to first hypothesis: Hypothesis 1: Compared with the companies that interlocking company is not punished, the observing company that interlocking company is punished will improve the accounting information comparability.
Some studies have shown that there is a negative correlation between the quality of t board and financial reporting fraud [44,45] , so the punishment against listed companies increases the uncertainty of the effective supervision of the punished board, and the directors' supervise and advise ability is likely to be questioned. At the same time, Srinivasan (2005) [46] finds that directors who had experienced accounting re-statement were severely punished by the labor market. Fich and Shivdasani (2007) [6] find that the number of board seats on external directors decreased significantly after financial fraud litigation. The regulatory authorities announce the illegal acts, investigation results and punishment decisions of listed companies on the media (such as the Shanghai Stock Exchange or Stock Exchange website) or the company home page, that will bring multi-dimensional punishment for reputation and qualification to the directors involved, and affect the career of the directors. Fama (1980) [47] , Fama and Jensen (1983) [48] believe that directors are constrained by the human capital market and have the motivation to perform their duties well and convey their reputation to the outside. Therefore, in order to make up for the heavy reputation damage suffered in the punished company, the directors who experience punishment have a strong motivation, not only to the punished company, but also to the other companies they also serve, to supervise and advise effectively.
The key to the effective implementation of supervision and advice by interlocking directors is to improve the ability of supervision and advice. According to the cognitive learning theory, Chen Guoquan and Sun Rui (2013) [49] put forward that the behavior corrector will correct the bad action, establish the cognitive reconstruction, and then shape the new behavior according to their experience. The interlocking directors are the bearers of the punishment of the interlocking company or the participants in the illegal behavior. They have a deep understanding about the business operation, financial situation and other information of the interlocking company, and know the cause, process and result of the violation. According to the experience accumulated in the punishment and knowledge and information acquired in the punishment, the interlocking directors establish cognitive reconstruction, that actively corrects the wrong behavior, and learns new methods and knowledge in order to improve their ability to supervise and advise. Hillman and Dalziel(2003) [50] believe that directors' experience and professional knowledge are an important part of board capital, which is conducive to the improvement of board supervision and consultation function. In addition, according to the information transmission function of interlocking directors, the interlocking directors will pass on the experience and corrective behavior accumulated in the punishment against interlocking company to the observing company, so that the interlocking directors can implement effective supervision suggestions in the observing company. Chen Yunsen et al. (2018) [51] think that improving the directors' ability of supervision and suggestion is helpful to the improvement of company perform, while Peasnell et al. (2005) [52] and Chen et al. (2015) find that directors strengthen corporate governance and play a key role in the quality of financial reporting, Faleye and Hoitash (2011) [53] think that the supervision function of the board is mainly reflected in the financial reporting quality. Zhong (2017) [32] also shows that interlocking directors with supervision experience and punishment experience can serve to improve the financial reporting quality.
As mentioned before, compared with other accounting information quality characteristics, the accounting information comparability can reveal the value of the company more deeply and provide more meaningful information to the investors. Therefore, improving the accounting information comparability is one of the key levels to improve the quality of the financial report. In sum, we think that interlocking directors improve the ability of supervision and suggest through performance correction that the interlocking directors experience the company punishment, acts to improve the corporate governance level of the observing company, and can improve the accounting information comparability of the observing company further.
Overall, this leads us to second hypothesis. Hypothesis 2: Compared with before interlocking company is punished, the observing company will improve the accounting information comparability after interlocking company is punished.

Sample and data
We obtain the data used to measure the accounting information comparability from 2008 to 2019 from the CSMAR database, the Wind database and the Ruisi database, and the data on the directors of all A-share listed companies in Shanghai and Shenzhen and the data on the punishment of all A-share listed companies in Shanghai and Shenzhen are obtained from the CSMAR database. Because the research object of this paper is the spillover effect brought by the punished interlocking company, the type of punishment and the institution for implementing the punishment are not divided in the data treatment process (Shanghai Stock Exchange, Shenzhen Stock Exchange, China Securities Regulatory Commission and the Ministry of Finance).
The data of this paper eliminate the following samples in the process of treatment: (1) excludes samples without interlocking companies; (2) removes the samples of all financial industries; (3) all the observing companies that are punished during the sample period are deleted because we examines the spillover effect of punishment against interlocking company, that is, the impact of regulatory punishment on the relevant unpunished company; (4) the owners' equity is negative, and the IPO company and the company with lack of data are excluded. In the end, we got 6034 observations. In order to control the outlier problem, all continuous variables are winsorized at bottom 1% and top 99%. The econometric analysis software of this paper is Stata15.0.

Dependent variable--The degree of change of accounting information comparability
In this paper, the degree of change of the accounting information comparability of the observing company from the previous period (t -1) to the current period of (t) (Dcomp) is taken as the dependent variable. The calculation process is as follows: First of all, calculate the accounting information comparability of the observing company. Following De Franco (2011) [27] , we measure accounting information comparability using data for 16 consecutive quarters, and use Basu's (1997) [54] model to control the effects of earnings recognition conservatism, that is, the asymmetry between the recognition of good news and bad news. We estimate equation (1) Re Re (1) where Earningsit is the adjusted accounting earnings that offset the fair value gains and losses that they included of company i in period t. Returnit is the stock price return of company i in period t. Negit is defined as a dummy variable; if the annual stock return is negative, it equals one; otherwise, it equals zero. Under the framework in equation (1) (2) and equation (3), where E(Earningsiit) is the predicted accounting earnings of company i given company i's function and company i's return in period t, and E(Earningsijt) is the predicted accounting earnings of company j given company j's function and company i's return in period t.
The accounting information comparability between companies i and j (Compijt) during period t is defined as the negative value of the average absolute difference between the predicted earnings using company i's and company j's functions, calculated by the following equation (4) (4) where Compijt is the accounting information comparability for each company i-company j combination for j companies within the same industry in year t. Higher values indicate higher accounting information comparability. We rank all j values of Compijt for each company i from highest to lowest and calculate the average Compijt of the four company j's with the highest comparability with company i (Comp4) during period t , the average Compijt of the ten company j's with the highest comparability with company i (Comp10) during period t, the median Compijt for all companies in the same industry as company i during period t (Compm) and the mean Compijt for all companies in the same industry as company i during period t (Compa).
Secondly, we measure the change degree of the accounting information comparability in t period (Dcomp), that is, the accounting information comparability in period t minus the accounting information comparability in period t-1, and the calculation method is such as formula (5).
Dcomp is positive, that is to say, the accounting information comparability in period t is higher than that in period t-1, which indicates that the companies improves the accounting information comparability, on the contrary, it means that the accounting information comparability is weakened. We measure the degree of change of the accounting information comparability using degree of change of Comp4 (Dcomp4), degree of change of Compm (Dcompm), degree of change of Comp10 (Dcomp10) and degree of change of Compa(Dcompa).

Horizontal angle
Horizontal angle means that the accounting information comparability of the observing company that the interlocking company is punished significantly higher than that of the interlocking company that is not punished, that is hypothesis 1.In order to test hypothesis 1, we establish the independent variable P_after.P_after is s a dummy variable, which represents whether the observing company occurs the event that interlocking company is punished . If the observing company occurs the event that the interlocking company is punished for the first time during the sample period, the P_after is equal to1 in the two years after the year, which the interlocking company is punished, otherwise P_after is equal to 0. In the year which interlocking company is punished, it will not have an impact on the behavior of the observing company, so P_after is equal to 0. If the observing company doesn't occur the event that the interlocking company is punished during the sample period, P_after is equal to 0. Two years is due to the short duration of the market disciplinary mechanism, and we find that the impact of interlocking company on the accounting information comparability of the observing company will be weakened after more than two years of punishment.

Longitudinal angle
Longitudinal angle means that the accounting information comparability of the observing company that the interlocking company is punished is significantly higher than that before that the interlocking company is punished, that is hypothesis 2. In order to test hypothesis 2 and set the independent variable, After as a dummy variable, due to the limited impact of market disciplinary mechanism on the accounting information comparability, we only choose the window period of two years before and after the punishment against interlocking company, which can be divided into the following five times:-2, -1, 0, 1,2. Among them, "-" represents the time before the interlocking company is punished,"0" represents the year that the interlocking company is punished. " +" represents the time after the interlocking company is punished. In period 1 and 2, After is equal to 1,otherwise After is equal to 0.The reason why After was 0 in period 0 is that the punishment announcement of the interlocking company will not have a substantial impact on the behavior of the observing company.

Control variables
According to Fang Hongxing (2017) [55] , Zhou Donghuan and Yang xiaokai [40] , Chen   [42] ,we select control variables that may affect the accounting information comparability of listed companies. There are some variables that representing the basic characteristics of Listed Company, such as debt assets ratio (Lev), company size (Size), price to book ratio (Mb) and growth rate of revenue(Grow), return on total assets( ROA), earning management (DA), List age(Age) and State ownership(Soe) ,and some variables that represent the internal governance mechanism of listed companies, including CEO duality (Dual), Ownership concentration (H1), Proportion of independent directors (Indepen) and Board size (Board). In addition, the model also controls year and industry effects respectively.

Horizontal angle
we used the following regression model (6) in order to test the Hypothesis 1:

3.3.2Horizontal angle
we used the following regression model (7) in order to test the Hypothesis 2: Among them, the difference between model (6) and model (7) is that model (6) takes all listed companies (including punished interlocking company and unpunished interlocking company) as the research object, while model (7) only takes the punished companies of interlocking company as the sample. Table 2 shows the summary statistics, including observations, mean, standard deviation, minimum, median and maximum. The observations in this paper are 6034. Among them, the independent variable is the difference between period t and period t-1, so our sample contains observation 4974 in the last. The average and median of the four indicators (Dcompa, Dcomp4, Dcompm and Dcomp10) are basically 0, which indicates that the degree of improving the accounting information comparability in the whole sample is very limited. The average value of return on assets (Roa) is 0.043, the maximum value is 0.211, the minimum value is -0.142; the average company size (Size) is 22.48; the average Lev is 0.467, which conforms to the reality of China; the average annual growth rate of revenue (Grow) of sample companies is 0.153, the maximum value is 2.475, and the minimum value is -0.522, which is in line with the reality of China. The difference of growth among companies is relatively large; the average level of earnings management (DA) is 0.066, the maximum value is 0.467, the minimum value is 0.001, and the degree of earnings manipulation among companies is also quite different. The average ratio of independent directors (Indepen) is 0.371, which accord with the relevant regulations of Chinese listed companies.  Table 3 is the basic regression result of model (6). The coefficient on P_after is significantly positive, it shows that the accounting information comparability of the observing company that interlocking company is punished is indeed significantly improved compared with the companies that interlocking company is not punished, and hypothesis 1 is supported. About the control variables, Age, Grow and Indepen has a significant positive impact on the accounting information comparability, which indicates that the better the operating ability of the company, the longer the listed age and the higher the proportion of independent directors, the more likely to improve the accounting information comparability, but Lev has a significant negative impact, indicating that the higher the debt ratio, the more likely to reduce the accounting information comparability.  Table 4 is the basic regression result for the model (7). The regression coefficient on After is significantly positive when the dependent variable was Dcompa and Dcompm, and the regression coefficient on After was positive but not significant when the dependent variable was Dcomp4 and Dcomp10, which may be due to the fact that the Dcomp4 and Dcomp10 is only mean value of the top four and ten companies ,the measurement method of comparability is very strict, so the improvement of this index is not significant. However, the results show that the accounting information comparability of the observing company is obviously improved after the interlocking company is punished, and the hypothesis of the longitudinal angle is also supported. About the control variable, Age has a significant positive effect, the longer the listed company age, the more likely the company is to improve the accounting information comparability. But Size and Lev have a significant negative impact. The larger the size of the company, the higher the proportion of the debt, the more likely the companies can lower the accounting information comparability.

4.3.1Propensity-score matching
The model (6) support hypothesis 1, which refers to the control group of interlocking company without punishment, but there may be endogenous problems arising from sample selection. For example, the company's improvement of accounting information comparability may be determined by its own situation. Therefore, in order to control the sample selection bias, we adopt the propensity-score matching method.
The first step is to divide the whole sample into two groups according to the P_all variable. The sample that P_all is equal to 1 constitutes the treatment group and the sample that P_all is equal to 0 constitutes the control group. Because matching is to find the closest matching company in the year when the sample company occur the event that the interlocking company is punished for the first time, only the observation which P_once is equal to 1 is selected for the treatment group, and these observation are combined with the control group to form the observation value for calculating the propensity-score. Model (8) Logit regression: Where Control is a matching co-variable, unlike the control variable of model (6), the model (6) uses the value of the lag period and the model (8) uses the current value.
In the second step, run the logit model, calculate the propensity-score of all samples, and then match it year by year, find out the matching company which has the closest propensity-score with the observing company that the interlocking company is punished, and specify the hypothetical treatment year for the matching company. For example, observing company A occur the event that the interlocking company is punished for the first time in 2010, and after finding the closest company B in 2010, company B was designated 2010 as the hypothetical treatment year. In addition to the closest propensity-score, the following conditions should be considered when pairing: (1) matching year by year; (2) matching with replacement method in the same year; (3) matching with no-replacement method between years, that is, the observation that have been selected as matched samples in this year will not participate in the matching in future years.
In the third step, after obtaining the matching group, the matched results and the observation of the treatment group are combined, and the information of the relevant variables is obtained by re-merging with the pre-pairing data. At this point, the matching group is marked as Treat is equal to 0, and the treatment group is marked as Treat is equal to1. Since both groups of samples have treatment years, the event window can be determined according to the difference between the natural year and the treatment year.
On this basis, we define a similar P_after variable for the control group. As mentioned earlier, we limit the sample to the window period [+1,+2]. If the observation period is two years after the specified treatment year, the P_after is equal to 1, otherwise, the P_after is equal to 0. For the control group, window period [+1,+2] refers to the control group for two years after the interlocking company is punished, which is counterfactual. Figures 1 and 2 show the p-score of the treatment and the control group before and after matching, respectively. Before matching, the p-score of the treatment group is higher than that of the control group, and after matching, the p-score of the two groups are basically the same. The results showed that the treatment group and the control group satisfy the common support criteria after propensity-score matching.
The fourth step, regression analysis examines the coefficient on P_after. As can be seen from Table 5, the coefficient on P_after is still significantly positive. The results show that the accounting information comparability of the observing company is still significantly improved after propensity-score matching.

PSM-DID
Although both hypothesis 1 and hypothesis 2 are supported, there are still some shortcomings in basic regression. The difference of accounting information comparability before and after the interlocking company is punished may be the trend of the observing company itself, not because of the impact of interlocking company is punished. In order to solve this problem, we use difference-in-difference estimation based on the previous propensity-score matching.
Because we need to examine the degree of change of accounting information comparability before and after punishment of interlocking company, we still choose the same window period [-2,+2] as model (7). On this basis, we define post variables for treatment group and control group, Post is equal to 1 after the treatment year (for control group, the treatment year is the designated treatment year), otherwise Post is equal to 0. Thereby, there are Treat and Post variables in the model, and the regression coefficient on their interaction terms is the estimator. The model is follows:  (9) Table6 shows the results of psm-did. Three results are reported for four indicators (Dcompa, Dcomp4, Dcompm and Dcomp10) to improve the accounting information comparability. Although only when the dependent variables is Dcompm ,the coefficients on Post*Treat is significantly positive, other dependent variable fail to pass the significance test. The result still shows that after the interlocking company is punished, the observing company will significantly improve its accounting information comparability. Hypothesis 2 has been significantly supported.
Based on the spillover effect of punishment and the theory of interlocking directors, this paper explores whether the punishment against listed companies by the regulatory authorities has spillover effect on the observing company which have interlocking relationship with punished interlocking company using the sample of A-share listed companies in Shanghai and Shenzhen stock markets from 2008 to 2019: Firstly, the observing company significantly improve the accounting information comparability within two years after interlocking company is punished when compared horizontally with the company that interlocking company is not punished. After controlling the bias of sample selection, the conclusion of horizontal angle after propensity score matching is still valid.
Secondly, he observing company also significantly improve the accounting information comparability within two years after the interlocking company is punished when compared vertically with before interlocking company is punished. This conclusion is proved again using psm-did.
Based on the above results, we believe that the observing company will improve the accounting information comparability after the punishment against interlocking company by the regulatory authorities, which shows that the punishment against listed companies will have a contrast spillover effect to other companies through the channel of interlocking directors.
This study has the following enlightenments: (1) The impact of punishment against Listed Companies with interlocking relations indirectly provides supporting evidence for the effectiveness of securities market regulation. Therefore, the regulatory authorities should continue to strengthen the supervision and punishment of capital market irregularities, so as to strengthen the role of the listed companies' punishment, and improve the quality of information disclosure of Listed Companies in China. This will reduce the information asymmetry between investors and listed companies. (2) Another enlightening factor is to play the role of information transmission of interlocking directors actively, while studying the convergence of interlocking directors 'behavior. Also, we should also pay attention to the contrast effect of information transmission of interlocking directors, and provide operational suggestions for companies to establish a good image that transmit positive signals in the company network.