The Relationship between Female Top Managers and Corporate Social Responsibility in China: The Moderating Role of the Marketization Level

: This study links the gender diversity of the top management team (TMT) to corporate social responsibility (CSR) and examines the moderating role of the marketization level in their relationship. According to the token theory, females are “tokens” and have di ﬃ culty playing their roles when they are rare in groups, where their presence is used for providing legitimacy. Meanwhile, CSR is implemented to gain legitimacy. Therefore, we predicted that there was a negative relationship between female top managers and CSR, and that the marketization level positively moderated their relationship. The hypotheses were supported by the data from 17,032 manager-year observations of listed companies in China. The results indicated that the female top managers’ presence and CSR performance had the same function of gaining legitimacy. With limited resources, ﬁrms added females at the expense of decreasing investment in CSR when under the external pressure of increasing female top managers. Furthermore, this negative relationship was stronger in ﬁrms with a less-developed institutional environment because ﬁrms with weak institutions have strong incentives to ﬁnd alternatives to ﬁll the institutional void, which helps to gain access to resources and reduce transaction costs.


Introduction
Although the composition of the top management team is an essential subject in the literature, the relationship between the gender diversity of top management teams (TMTs) and corporate social responsibility (CSR) remains a relatively under-researched area. Some scholars explore the influence of gender diversity on CSR; however, the existing articles present inconsistent results. Some studies show that gender diversity has a positive influence on CSR [1][2][3][4][5][6], some find no salient relationship between them [7], and a few find that gender diversity has a negative influence on CSR [8].
The studies mentioned above are implemented in different contexts, and almost all of them explore Western countries. With the increasing importance of the transitional economy, this calls for research on China. Generally, women remain underrepresented in firms' top management teams, and the process of board diversity is slow in China. In the sample of 220 listed companies in China surveyed by Deloitte, there were 2247 seats on the board of directors, of which 245 were female directors, accounting for 10.90%, which is less than half of the proportion of female directors in Europe in 2017 [9].
Kanter defines the rarity of females or minorities in a skewed group as "tokens," where tokens are viewed as out-groups by the majority and will relieve societal pressure by hiring them [10]. Due to the tremendous pressure of adding females to the boards, firms add women to their organization with the inherent and original motivation of gaining legitimacy [11].
With the longstanding debate about CSR, most managers and scholars are against the traditional view that states that a firm's sole objective is profit maximization. However, they approve of the stakeholder view and regard CSR performance as a reflection of a firm's legitimacy [12].
This study examined the relationship between female directors and CSR performance using Chinese public firms' panel data. According to the token theory, the tokens' presence is due to a need for legitimacy, and it is hard for them to play their role. Meanwhile, in consideration of the same function played by female directors and CSR, namely, gaining legitimacy, we suggest that CSR is negatively related to the addition of female top managers.
Furthermore, the importance of the means used to gain legitimacy varies with different institutional environments. In other words, the value of CSR initiatives is greater in countries with weaker market institutions because firms can adopt CSR activities to fill institutional voids [13]. Therefore, we suggest that the level of the institutional environment will weaken the negative relationship between CSR and female top managers.
Our research makes several significant contributions. First, it contributes to the top management team diversity. Most studies about female top managers pay great attention to females' functions [3,14,15], but they do not explore the general situation most female managers may face in real life. One exception is the study by Knippen, Shen, and Zhu [16], where they found that firms are more likely to increase female directors if they are under more substantial external pressure for greater board gender diversity by adding new positions, and male directors may have a gender bias against them. However, they did not specifically mention females' token role and that the firms' aim when increasing female directors is to gain legitimacy while tending to ignore the separation within boards. In contrast, our study investigated the current female managers' situation in China and explored the relationship between female top managers and CSR.
Our study also contributes to the application of the token theory. We point out that most Chinese public firms still treat females as tokens as they are rare in the top management teams, and this kind of quantitative disadvantage puts them in an inferior position. Thus, unfortunately, they may only be a means to gain legitimacy.
Finally, our study has important implications for research on organizational responses to external pressure to adopt socially desirable practices. Firms will respond to the external pressure from stakeholders to gain legitimacy, but they have the motivation to increase one form of legitimacy while decreasing another. Firms in a high-level institutional environment or a more transparent market will care less about gaining legitimacy because the ways to gain legitimacy are more critical for firms from regions with an institutional void.

CSR and Legitimacy
There is a long-standing debate between two classical views on whether a firm should engage in CSR [17,18]. The early scholars that were advocates of shareholder theory and neoclassical economic theory believed that the only social responsibility for executives is maximizing the firm's profits, within the rules of the game of obeying the law [19], and the spending of resources on CSR would inevitably damage the profit [20], which will make the firms who shoulder CSR less competitive in the market. Furthermore, Friedman [21] believes that engaging in CSR is an agency problem or a conflict between managers and shareholders' interests. He argues that managers use CSR to improve their own social, political, or career progress at the expense of shareholders.
Meanwhile, many scholars who hold the stakeholder view propose that multiple stakeholder groups should be considered during strategy development and decision-making [22]. Stakeholders are commonly defined as "any group or individual who can affect or is affected by the achievements of the organization's objectives" [22], which including customers, employees, suppliers, community groups, governments, and some stockholders, especially institutional shareholders [17].
Stakeholder theory has become the dominant paradigm in CSR, although CSR's influence on a firm's financial performance or value is underexplored [17]. The authors of two meta-analyses [23,24] have concluded that the existing empirical evidence supports a modest positive association between corporate social performance and corporate financial performance. Sajko et al. [25] found that high CSR investment helped firms to experience fewer losses in the short run and took less time to recover from the 2008 global financial crisis. They think that CSR contributes to organizational resilience, which helps organizations to anticipate, avoid, and adjust to shocks in their environment [26] by building stability and flexibility. In addition, according to the resource-based view, corporate responsibility performance constitutes an organizational resource that can help firms to develop new intangibles that can be sources of competitive advantages [27], which further improve a firm's performance [28].
With its development in society and academia, CSR performance has long been viewed as reflecting a firm's moral legitimacy [12]. This kind of legitimacy is given by the firm's various stakeholders and thus is defined as the extent to which its stakeholders accept the firm as a moral corporate citizen.
Modern CSR was ushered into China in the late 1990s and is developing here now. Based on the experience in developed countries, CSR development is a long process. El et al. [13] found that the CSR initiatives' value is greater in countries with weaker market institutions because firms can adopt CSR activities to fill institutional voids. Lin [29] points that in the early stage of development, it is reasonable to expect that there is a gap between the words promised in the CSR initiatives and the real implementation of the CSR measures. At this stage in China, we still view CSR measures as the basic means to gain legitimacy rather than the structural change.

Gender Diversity
Two organization theories, namely, resource dependence theory and agency theory, provide the general theoretical underpinnings for how gender diversity in a firm influences its CSR performance. The resource dependence theory views organizations as operating in an open system, and the resources organizations depend on are crucial to firms' development. Female top managers can provide unique and rare resources to the firm compared with their male counterparts [11,30,31]. Hillman et al. [11] found that women are more than twice as likely as men to hold a doctoral degree, which would help them to provide more expertise during work. They also found that those female directors are more likely than male directors to have expert backgrounds outside of the business, which helps to gain more professional advice and counsel from diverse perspectives. Daily and Dalton [30] assert that increasing board gender diversity can enhance decision-making because females' participation brings broader perspectives, and more results will be analyzed. Women can also help to prevent decisions that are too risky as women are generally more financially risk-averse than men [31]. Meanwhile, women's most common paths to reach the boardroom are through community services and academia [31].
Another essential resource female directors can bring is legitimacy [11]. The public has recently called for corporations to add more women to their boards. Many countries (e.g., Norway, Spain, Italy, France, and Sweden) are using quotas to drive up numbers, and the percentage of women on boards is far more than 15% (except India's 13.8%). With the great pressure from society, the addition of female directors increases legitimacy.
Agency theory describes the potential for conflicts of interest that arise from the separation of ownership and control in organizations [32,33]. When ownership and control are separated, managers may pursue their self-interest at the expense of profit maximization, creating "agency" costs in the process [32]. Gender diversity helps to reduce the "agency" costs [8]. As mentioned before, gender diversity enhances both the decision process by broadening the perspectives while making decisions and the quality of decisions by providing more professional advice and counsel. Therefore, gender diversity reduces agency costs by enhancing the quality of decisions.

The Influence of Gender Diversity on CSR
The influence of gender diversity on CSR has not reached a unified conclusion yet. Many scholars have found that gender diversity has a positive impact on CSR [1][2][3][4][5][6], some find no salient relationship between them [7], a few have found that gender diversity has a negative influence on CSR [8].
Though empirical research results are mixed, most scholars approve the view that gender diversity has a positive influence on CSR because of women's unique characteristics. Zhang et al. [3] examined the relationship between female directors and CSR using a sample of over 500 of the largest listed companies on the U.S. and found empirical evidence showing that a more significant presence of female directors is linked to a better CSR performance within a firm's industry. They suggest that female directors possess specific psychological characteristics that push them to enhance stakeholder claims. Usually, women are affectionate, helpful, kind, sympathetic, interpersonally sensitive, nurturing, and concerned about others' welfare [34]. Setó-Pamies [2] further contended that men and women have different values where CSR is concerned. That is to say, women are more prone to relationships, to respond to the needs of others, and feel responsible for not causing harm.
In addition to women's inherent characteristics, the resources female directors possess also help organizations do better regarding their CSR performance. The resource dependence theory serves as the base of the boards' provision of resources function [35], including providing legitimacy, advice, and counsel. Zhang et al. [3] contended that female directors may offer unique firm resources due to their ability to connect to specific stakeholder groups and obtain acceptance. Because firms with female directors will usually be viewed as diversity friendly firms, they will have more favorable CSR ratings [4].
However, the positive influence of female directors on CSR can be affected by the context. Rodriguez-Ariza et al. [1] analyzed a panel of 550 international firms for the period 2004 to 2010 to compare the role of female directors in family and non-family firms in promoting responsible practices; they found that the positive effect of the presence of female directors on the degree of socially responsible commitment was much less in family firms than in non-family firms, as females tend to behave in accordance with the family orientation toward CSR. In other words, because of the female invisibility and their assigned role as family delegates, they cannot put forward their advice and instead have to follow the family's decision.

Tokenism and Token Theory
Kanter [10] defined the rarity of females or minorities in a skewed group as "tokens," and if the group's absolute size is small, tokens can also be solitary individuals. He further contended that tokens will meet three perceptual phenomena: visibility, polarization, and assimilation. In response to performance pressure brought about by high visibility, tokens choose either overachievement or limit their visibility. However, most of them try to be less visible. To cope with the boundary heightening deriving from polarization, tokens either accept isolation or try to become insiders. To deal with role entrapment caused by assimilation, it is often easier for tokens to accept stereotyped roles with self-distortion. Due to their limited visibility, isolation, and self-distortion, the tokens' performance will be negatively affected.
In a word, "tokens" are viewed as part of the out-group by the majority and will receive much pressure from them [10]. Due to the tremendous pressure of adding females to the boards, firms add women to their organization with the inherent and original motivation of gaining legitimacy [11].
Situations will shift only when the number of minorities in a group reaches the "critical mass" [36]. The critical mass theory suggests that shifts in a group's heterogeneity can result in shifts in the group's overall behavior [37]. The critical mass theory posits that "one is a token, two is a presence, and three is a voice" [38].
Empirically, many scholars find that tokens cannot play their intended roles in practice [39][40][41]. Torchia, Calabrò, and Huse [39] used a sample of 317 Norwegian firms to test whether "at least three women" could constitute the desired critical mass by identifying different minorities of women directors (one woman, two women, and at least three women). The results suggest that tokens have no salient impact on firm innovation and that attaining critical mass, i.e., going from one or two women (a few tokens) to at least three women (consistent minority), makes it possible to enhance the level of firm innovation. Erkut et al. [40] investigated top managers from Fortune 1000 United States companies and found that the tokens' influence on the board is small, and three women constitute a critical mass on a corporate board. The same result was proposed in China. Liu, Wei, and Xie [41] examined the effect of board gender diversity on firm performance in China's listed firms' boards from 1999 to 2011, and the results show that boards with three or more female directors had a more substantial impact on firm performance than boards with two or fewer female directors, which is consistent with the critical mass theory.
From the above, we conclude that the influence of tokens on a group's decision is small, and under such circumstances, the presence of females in a group is due to the legitimacy that they bring as tokens. That is to say, the initial motivation for a firm to increase female directors or female top managers is to gain legitimacy. Combined with CSR's function to gain legitimacy, we suggest that under the external pressure of increasing females in the top management teams, the firms will add females at the expense of decreasing investment in CSR. Therefore, we hypothesized the following: Hypothesis H1: The presence of females in a firm's top management team is negatively related to its CSR performance.

The Moderating Role of the Marketization Level
The marketization level captures the process of institutional development in Chinese provinces. Fan et al. [42][43][44] evaluated the marketization level of each province and municipality in China from five aspects: (1) the relationship between the government and the marketplace, (2) the development of the non-state economy, (3) the development of the product market, (4) the development of the factor market, and (5) the development of agent organization and the legal and institutional environment; they then aggregated the scores into a generalized marketization index. The marketization index shows that the process of marketization is unbalanced across the nation.
El et al. [13] found that a CSR initiative's value is greater in countries with weaker market institutions. They posit that firms in the countries where institutional voids increase transaction costs have strong incentives to reduce transaction costs. Furthermore, CSR can reduce transaction costs and increases access to resources, such as capital [13,45] and reputation [46]. Hence, the strategic value of CSR is greater in countries with a less developed institutional environment.
In accordance with the view of El et al. [13], we posit that the value of CSR is greater in provinces with weak market institutions within China. The underlying mechanism is as follows. When capital markets, regulatory systems, and contract enforcement mechanisms are absent or weak, firms must develop strategic responses to overcome these voids [47]. CSR initiatives [13] and the addition of minorities [10,16], such as women, are strategic responses to the public. Furthermore, firms in provinces with weaker institutions are eager to adjust their strategies to gain the best approaches to achieving resources and legitimacy with lower costs. Therefore, we hypothesized the following: Hypothesis H2: The negative relationship between females in TMT and CSR performance is stronger for firms in less developed markets than for firms in developed markets.

Sample and Data Collection
Our sample came from the companies listed on China's Shanghai and Shenzhen Stock Exchanges between 2011 and 2017. The number of companies listed on China's Shanghai and Shenzhen Stock Exchanges increased from 2342 in 2011 to 3485 in 2017. The composition of the study sample was based on the information in three databases: (a) a Wind data set for the accounting and financial information (such as return on equity, total assets, leverage, and the ownership of the firm) provided in consolidated financial statements; (b) the China Stock Market and Accounting Research (CSMAR) database for the information of senior managers (such as the gender of senior managers) and the value of Tobin's Q, which is known as the value of a company; (c) the Hexun.com dataset for CSR data.
As one of the largest databases on Chinese listed firms, CSMAR serves as the primary source of information on Chinese stock markets and the financial statements of China's exchange-listed firms. It was designed and developed by GTA Information Technology, one of the foremost providers of data related to Chinese companies. Wind and Hexun.com are leading financial data, information, and software service enterprises in mainland China. They provide timely updates on stock trading information to meet the needs of investors and researchers. Data from WIND, CSMAR, and Hexun.com have been widely used in prior research in the finance and strategy areas [8,[48][49][50].
The following sampling procedure was used: (a) calculate the number of senior managers, including executive team members, board directors, and supervisors for every company; (b) combine the data from the three datasets and drop the observations with missing values; (c) exclude companies with delisting risk warnings because those companies are abnormal in terms of their profitability and enterprise value; (d) drop the financial companies since their equity characteristics make them non-comparable with non-financial firms [1]. Following this procedure, our sample was composed of 3245 non-financial listed companies for the period of 2011-2017.
The sample with 17,032 observations was unbalanced because there were newly listed companies that entered every year and data were not available for all companies for the entire study period. These firms were active in sixteen different sectors, as classified by China Securities Regulatory Commission (CSRC). Table 1 presents the sample distribution, specifying the number of firms by industries, showing that most firms were active in manufacturing. It can be seen from the table that the manufacturing companies were the most active in our sample, accounting for 64.51% of the total sample. This is in line with the country's situation, which is famous for manufacturing, indicating that our sample was quite reasonable.

Dependent Variable
The level of CSR performance was represented by a construct addressing all the related activities that were carried out, especially those in the social and environmental spheres [51]. Information in this area was obtained from the Hexun.com database, following many previous studies in this field [52,53]. The professional evaluation system of the social responsibility report of listed companies established by the Hexun.com database was evaluated from five aspects: shareholder, employee, customer and consumer's rights and interests, environment, society, where each aspect had second-and third-level indicators to comprehensively evaluate social responsibility. Among them, there were 13 secondary indicators and 37 tertiary indicators (see Appendix A).
The CSR's professional evaluation system began with the social responsibility reports and annual reports to get the original data. Then, the weight of each indicator was adjusted according to the nature and characteristics of the industry. This evaluation system is quite comprehensive and covers almost all the related stakeholders.

Independent Variable
According to Chinese company law, a company's top management team comprises the board of directors, the board of supervisors, and the senior management team. Therefore, in our study, women in a firm's top management team included females on the board of directors, females on the board of supervisors, and females in the top management team. To roughly study the effects of women's presence in a firm's top management team, we created the variable "female," which was coded as "1" if there was at least one woman, and "0" otherwise. To precisely study the effects of women's presence in a firm's top management team, we calculated the number of females as the independent variable female for a robust test. The distribution of the number of females can be seen in Figure 1. The figure shows that the mean of female top managers was less than 3, including the female top managers from three panels: the board of directors, the senior management team, and the board of supervisors.

Dependent Variable
The level of CSR performance was represented by a construct addressing all the related activities that were carried out, especially those in the social and environmental spheres [51]. Information in this area was obtained from the Hexun.com database, following many previous studies in this field [52,53]. The professional evaluation system of the social responsibility report of listed companies established by the Hexun.com database was evaluated from five aspects: shareholder, employee, customer and consumer's rights and interests, environment, society, where each aspect had secondand third-level indicators to comprehensively evaluate social responsibility. Among them, there were 13 secondary indicators and 37 tertiary indicators (see Appendix A).
The CSR's professional evaluation system began with the social responsibility reports and annual reports to get the original data. Then, the weight of each indicator was adjusted according to the nature and characteristics of the industry. This evaluation system is quite comprehensive and covers almost all the related stakeholders.

Independent Variable
According to Chinese company law, a company's top management team comprises the board of directors, the board of supervisors, and the senior management team. Therefore, in our study, women in a firm's top management team included females on the board of directors, females on the board of supervisors, and females in the top management team. To roughly study the effects of women's presence in a firm's top management team, we created the variable "female," which was coded as "1" if there was at least one woman, and "0" otherwise. To precisely study the effects of women's presence in a firm's top management team, we calculated the number of females as the independent variable female for a robust test. The distribution of the number of females can be seen in Figure 1. The figure shows that the mean of female top managers was less than 3, including the female top managers from three panels: the board of directors, the senior management team, and the board of supervisors.

Moderating Variable
The market index reflects the level of marketization level of a region and was collected from the book "China Market Index," which was published by Fan et al. [54]. This market index comprehensively compares the marketization process of all provinces, autonomous regions, and municipalities in China from different aspects. This book has been updating China's market index year by year since 2010. The same index system was used to continuously measure the marketization process of each region, thus providing a stable observation framework reflecting the marketization change, and the objective index was used to measure the depth and breadth of the marketization reform of each province, autonomous region, and municipality directly under the central government, which effectively avoided subjective evaluations. Because of its stability and reliability, the marketization index is regarded as a good variable for reflecting China's market environment by many researchers [52,53].

Control Variables
We included several typical firm characteristics as controls related to the firm solvency, the firm value, the ownership of the firm, the firm size, and the firm profitability. We obtained accounting data from the WIND dataset. Solvency means the ability to afford the debt; therefore, we used the debt-to-equity ratio (leverage). Leverage is equal to the total liabilities divided by the total assets. Bertrand and Scholar [55] defined Tobin's Q as the ratio of the market value of an enterprise's assets to the replacement cost (or book value). Therefore, we calculated it as the market value of a firm's equity plus the market value of liabilities and then divided by the year-end book value of its total assets. The firm size was measured as the logarithm of the firm's assets, including all debt and equity, and the asset data were from the public annual fiscal reports of each company. The return on equity (ROE) reflects the profitability of a firm and was also from the company's public annual financial statements.
We included state ownership as a firm attribute, which is a special and essential characteristic of companies in China. The research shows that state-owned enterprises (SOEs) donate no more than non-SOEs [56]. If a company's ultimate controller was the central or local state government or government subsidiary, the SOE code was "1"; otherwise, it is "0." In addition, we also controlled for the top management team's attributes, such as the size of the team (team size). Finally, the results were controlled by year and industry to prevent it from biasing the results.
We substituted the female dummy variables with the number of females to do a robust test and add a firm's age variable to our model in the robust test as well. Details of the variable descriptions and sources are presented in Table 2.

Estimation Approach and the Econometric Model
In order to reduce the endogeneity, we used a fixed-effect model to explore the relationship between female participation in top management teams and CSR performance, as well as the moderating effects of firm size, ROE, and the market index. The independent variable and control variables were lagged by one year to better reflect the causal relationship between female top managers and CSR. (1) Equation (1) reveals the main effect of our research. The dependent variable CSR it+1 was measured one year later to examine the causal relationship between female top managers and CSR. β 1 , defined as the coefficient of the independent variable female, was expected to be significantly negative. The marketization level (marketindex it ) was the moderator. According to the literature mentioned before, we predicted the sign of the interaction term of centralized marketization level and female dummy (β 3 ) to be positive. CV it , composed of the leverage, top management team size, firm's value (TobinsQ it ), firm size (firmsize it ), profitability (ROE it ), and nature of the state ownership, was the vector of control variables. λ is composed of control variables' coefficients Industry it , defined as a set of dummy variables describing the industry's classification, whose details can be found in Table 1, was added to the formula to control for the industrial effect. η is the coefficient of industry and the ε it is an error term

Descriptive Statistics and Correlations
The descriptive statistics and a correlation matrix of all variables, except the industry dummy, are presented in Table 3. With the exception of the leverage variable, the other explanatory variables were significantly correlated with CSR. From Table 3, the highest significant correlation coefficient among the independent variables was 0.375. As suggested by Damodar [57], unless the correlation coefficients among regressors exceed 0.80, multi-collinearity will not be a severe problem for multivariate analysis. Thus, there was no problem with multi-collinearity among the regressors included in our regression models. In an additional analysis, we conducted a multicollinearity diagnostic for variables in the model using variance inflation factors (VIFs). The results show that the highest VIF was 1.33, and the average of the VIFs was 1.10, suggesting that multicollinearity may not be a problem in this study.

Multivariate Regression Analysis
We report the results of the CSR regression models pertaining to females in Table 4. Both the independent variables and moderating variables were lagged by one year to examine the causal relationship between female top managers and CSR. Model 1 includes all the control variables and the moderator. As expected, the firm's leverage (b = −1.604, p < 0.01) and market index (b = −4.835, p < 0.01) were negatively related to CSR. Tobin's Q (b = 0.037, p < 0.01), firm size (b = 1.101, p < 0.01), and ROE (b = 0.026, p < 0.01) had a significantly positive relationship with CSR. Then, we entered the independent variable female into model 2 and the interaction terms into model 3. To eliminate the influence of dimensional difference and observation variations, all variables were centralized before the interaction. Hypothesis 1 proposed that the females' presence in the firm's top management team would have a negative effect on CSR. The results for model 2 in Table 4 show that the impact of females on CSR was negative (b = −2.383, p < 0.05). Thus, hypothesis 1 was supported by the results. This was because female directors in most companies are rare, and they tend to be viewed as tokens. Therefore, companies add female top managers for the sake of gaining legitimacy [35]. Meanwhile, CSR has long been viewed as moral legitimacy. Thus, the addition of female top managers and investment in CSR are both used for gaining legitimacy, and firms may choose female top managers while decreasing the investment in CSR, which will undoubtedly cause a low CSR performance.
The market index was added in model 3 as the moderating variable. Hypothesis 2 proposed that the negative relationship between female top managers and CSR would be stronger for firms with low marketization than for firms with a high marketization level. The results for model 3 in Table 4 show that the coefficient of the interaction term of the market index and female was positive (b = 0.755, p < 0.1), which means that the negative relationship was weaker as the market index increased. Therefore, hypothesis 2 was supported. Furthermore, this corresponds with El et al.'s [13] finding that the value of the CSR initiatives is greater in countries with weaker market institutions because firms can adopt CSR activities to fill institutional voids. Therefore, firms in a market with a low marketization level care more about the means to gain legitimacy, and the negative relationship between female top managers and CSR is stronger.

Robustness Tests
Another measure of women's presence in a firm's top management team is the number of female top managers (NumFemale), which was used to strengthen our analyses. Because our sample was confined to firms with female top managers in the robust test, a simple regression of CSR on the number of female top managers may not be suitable. That is to say, the firms that have female top managers may have distinct characteristics from those who do not. Therefore, it is possible that factors that affect the presence of female top managers could also be related to the dependent variable, CSR. This suggests that the coefficients of the terms associated with the presence of female top managers would be correlated with the error term. Thus, the multiple regression estimates of those coefficients would be biased.
The effect of female top managers on CSR was estimated using the Heckman selection model to avoid such a sample selection bias [58]. The Heckman selection model includes two equations. The first (selection) equation estimates the likelihood that firms have female top managers by applying a probit model to the entire sample of firms. An adjustment term called the "inverse Mills ratio" (λ) was calculated at this stage. In the second equation, the sample was restricted to the sample of firms having female top managers. The CSR model was re-estimated in this equation, with the "inverse Mills ratio" included as a control variable. The Heckman two-stage model thus corrected for the sample selection bias based on information representing all companies in the population.
The descriptive statistics and the correlation matrix are presented in Table 5. Panel A of Table 5 includes the variables used in the first-stage probit model of the two-stage Heckman analysis. The mean (0.949) shows that most firms in our sample had female top managers. As expected, the market index, the firm's ownership nature, and the firm size were significantly correlated to the likelihood of the presence of female top managers. The descriptive statistics and correlation matrix for the key variables used in the second stage of the Heckman analysis are presented in panel B of Table 5. Most variables were the same as the model we mentioned before, and the correlations were similar to before. Panel B presents the descriptive statistics and matrix of correlations for the main variables used in the second stage of the Heckman analysis. As seen in panel B, among the 12,281 observations of public firms, the mean was 25.86 and the standard deviation was 0.15, indicating that the overall CSR level was not high and varied slightly. On average, the top management teams had 19.47 members and had 3.52 female top managers, which means female top managers were rare in top management teams. The inverse Mills ratio had significant relationships with all other variables. The other variables are similar to before. Table 6 shows the results of the first-stage Heckman selection model, which was a probit regression of female's presence against factors thought to influence whether a firm has female top managers. A one-year lag was used between the dependent and the independent variables. Model 1 was a baseline model that consisted of firm and industry level predictors. Model 2 introduced firm age as an additional independent variable, which was expected to have an impact on a firm's decision regarding having or not having female top managers. The change in λ 2 (13.47, p < 0.01) at the bottom of Table 6 indicates that model 2 had a better fit. Thus, the results from model 2 were used to formulate the inverse Mills ratio for the multiple regression estimates presented in the second-stage CSR model. Table 6. Probit estimates for Heckman first-stage model: female's presence regressed on the firm and industry predictors 1 .  Table 7 provides the outcomes from the Heckman model's second-stage estimation using the inverse Mills ratio from the probit model in Table 6 (model 2) to account for the selection bias in the female dummy data. The regression models were the same as before, except for adding the inverse Mills ratio as the control variable. Model 1 in Table 7 reports the impacts of several fundamental control variables. Model 2 added NumFemale as an independent variable. The results of model 2 show that the number of females in top management was negatively related to CSR (b = −0.229, p < 0.05). The results from model 2 were similar to our main model mentioned before, which strongly supports our hypotheses and reinforces our empirical research.

Variables
In addition, in order to explore whether there was a U-shaped relationship between the number of females in a firm's top management team and CSR performance, we created model 3. The results from model 3 show that the number of females in a firm's top management team did not have a U-shaped relationship with CSR. Table 7. Estimates for the Heckman second-stage model: NumFemale regressed on the firm and industry predictors 1 .

Discussion and Conclusions
Many extant types of research try to identify the unique characteristics of females that help the firm's success and justify increasing the presence of females in a firm's top management to show they are treating female managers properly. However, few companies give females a stage to show their talents without bias and stereotypes and treat them as equals with males. On the contrary, most firms are controlled by men, who treat women as outgroup members and make females less likely to serve on major board committees [16], and only increase female top managers in order to gain legitimacy. Our study described the general situation in China because the data we used were all normal A-share listed companies.
Consistent with our results, Jia and Zhang [8] used a sample of privately-owned listed Chinese firms and their response to the Wenchuan earthquake on 12 May 2008 and found that women on boards of directors had a negative association with corporate philanthropic contributions to disaster relief. They explained the result from the perspectives of agency cost, and that women would be less likely to participate in the selfish and risky activities of corruption. They held the view that because a corporate philanthropic disaster response (CPDR) contains considerable agency costs, and they proposed that women on boards increase corporate governance efficiency and female directors evaluate the benefits of CPDR for shareholders, they restrain the agency costs of CPDR, and consequently, respond negatively to CPDR. However, they did not realize the token position of female top managers in the Chinese context. Although women exist in companies, they are not necessarily able to play a role.
Our study focused on most ordinary enterprises and investigated the effect of female top managers as a substitute for corporate social responsibility. In practice, female directors are tokens in most listed firms in China. In addition, the roles females actually play is far from what we intend them to be. In other words, although the number of female directors is increasing, the bias and stereotypes of women still exist. As for CSR, legitimacy theory is frequently used when taking the firm's motivation to engage in CSR into consideration. Furthermore, the CSR measures implemented by Chinse firms are far from its definition and initiatives set out by the government [29]. From the perspective of the original purposes, we proposed that women's presence on top management and the CSR measures implemented by firms are both means to gain legitimacy in practice. Therefore, firms under external pressure for gender diversity would choose to reduce the firm's CSR investment, resulting in worse CSR performance.
Furthermore, we tested the moderate variables related to the effect of female top managers as a substitute for CSR. The results supported our hypothesis that the negative relationship between female top managers and CSR will be stronger for firms in a market with a low marketization level because firms with less-developed institutional environments tend to have more motivation to substitute two measures in order to gain legitimacy and fill the institutional void.
Our research makes several significant contributions. First, it contributes to the top management team diversity. Most studies about women's top managers pay great attention to females' roles [3,14,15], but they do not explore the general situation most women managers may face in real life and work situations. One exception is the study by Knippen, Shen, and Zhu [16]. They found that firms are more likely to increase female directors if they are under more substantial external pressure for greater board gender diversity by adding new positions, and male directors may have gender bias against them. However, they did not specifically mention that the firms' essential purpose of increasing female directors is to gain legitimacy and tend to ignore the separation within boards. In contrast, our study presents the current general situation of female managers in China and explores the relationship between female top managers and CSR for firms in different institutional environment levels.
Our study also contributes to the application of the token theory. We pointed out that most Chinese public firms still treat females as tokens as they are rare in top management teams, and this kind of quantitative disadvantage puts them in an inferior position. Thus, unfortunately, they may only be the means to gain legitimacy.
Finally, our study has important implications for research on organizational responses to external pressure in the adoption of socially desirable practices. Firms will respond to the external pressure from stakeholders to gain legitimacy, but with limited resources, they have the motivation to increase one, while decreasing another that has the same function. In addition, firms' responses will be impacted by the marketization level. Firms in a low-level institutional environment or a less transparent market will care more about the means to gain legitimacy because the ways to gain legitimacy are more critical for firms with an institutional void.
Practically, our research shows the situation that female top managers are still underrepresented in most Chinese public firms, and females are rare in top management teams. Under such circumstances, females are unable to play their intended roles. Therefore, it is important for firms and governments to make some efforts to improve female top managers' inferior situation. Our research also indicated that it is not enough for enterprises to increase the number of female executives internally, but also pay attention to the environment. Outside investors and the public need to spare no effort to monitor enterprises to create a transparent market such that they have the motivation to increase the number of female executives and CSR measures to a higher level simultaneously.
We note several limitations as well. First, our sample was unbalanced panel data due to the deletion of some observations with missing values and abnormal values. Thus, our conclusions might not apply to firms with incomplete financial information. In addition, some vital but unobservable variables might have been omitted by our studies when examining both the main effect and the moderating effects, which may, to some extent, affect our conclusion.
Further research could be conducted to improve our research by taking manager-level, firm-level, and region-level factors into consideration to figure out females' roles in different contexts. At the manager level, as proposed by Kanter in 1977 [10], females would respond differently to the performance pressure, boundary heightening, and role entrapment. Therefore, it is likely that the specific characteristics of female top managers will change their token role and have an influence on CSR. Manager-level characteristics, such as age, education, and skills [59], may be taken into consideration.
At a firm level, corporate governance and corporate visibility are two main research directions. Corporate governance includes two key dimensions: policy and board structure [7,60]. First, corporate governance can be viewed from the policy perspective. For example, a firm's corporate governance is expected to oversee the development of long-term strategy, but also specific policy, such as CEO hiring/firing and compensation, information disclosure and transparency, and responses to strategic issues, such as CSR [59]. The board structure refers to characteristics, such as board size, separation of the CEO and board chairperson roles, use of committees, and ownership [61]. The factors mentioned above could be taken into consideration to examine whether governance can mitigate the token problem such that diversity complements CSR instead of substituting CSR.
Corporate visibility has been identified as an essential company attribute in a variety of studies. More visible organizations will be prompted to take leading roles in managing impacts and stakeholders [62]. Thus, visible organizations may respond to the public pressure of adding female top managers differently to invisible ones.
As for region-level factors that may influence the effect of female top managers on CSR, the development level differences between countries is a key variable. In the data from Western countries, gender diversity improves CSR [1][2][3][4][5][6] due to the high marketization level, and the effects in our study disappear or even work in the opposite direction. Thus, a comparative study between countries is of great theoretical and practical value.