Commitment of Independent and Institutional Women Directors to Corporate Social Responsibility Reporting

This paper examines how independent and institutional women directors on boards affect corporate social responsibility (hereafter CSR) reporting. Most of the previous empirical evidence has shown a linear association between female directors and CSR disclosure, but to the best of our knowledge, no research has investigated the individual effect of independent and institutional female directors on CSR reporting. Therefore, the analysis of how the disclosure of CSR information is affected by independent and institutional women directors in a separate way merits our attention. Thus, we posit that there is a nonlinear association, concretely quadratic, between independent and institutional female directors on boards and CSR reporting. Our results demonstrate that, in line with the monitoring hypothesis, as the presence of independent and institutional women directors on boards increases, the CSR disclosure improves, but when their presence on boards reaches a tipping point (20.47% and 13.32%, respectively), CSR reporting decreases, which is consistent with the collusion hypothesis. This research contributes to the existing literature on the relationship between board gender diversity and CSR disclosure by suggesting that board structures formed by institutional and independent female directors have an effect on CSR reporting. Hence, female directors play a relevant role on boards since they may influence the CSR disclosure.


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PUCHETA-MARTíNEZ ET Al. disclosure, board gender diversity has received growing interest from scholars. Board gender diversity may imply a variety of opinions and ideas, which may affect the CSR disclosure because a firm's stakeholders are not a homogeneous group (Catalyst, 1995). Women empathise with stakeholders and show a higher sensitivity towards their demands and needs, thus demonstrating a greater concern for social and environmental matters. Taking these views into consideration and given that the female leadership style differs from that of males (e.g., Alonso-Almedia, Perramon, & Bagur-Femenias, 2017;Manzoor & Abrar, 2011), we expect that female and male directors will behave in different ways regarding the CSR disclosure.
Past research has examined the impact of independent (Cuadrado-Ballesteros, Rodríguez-Ariza, & García-Sánchez, 2015a) and institutional directors (Dimson, Karakaş, & Li, 2015) on the CSR disclosure, but it has not differentiated between female and male directors. Researchers have also paid little attention to the effect of female directors' typology on CSR reporting. As far as we know, a few authors, such as Cabeza-García, Fernández-Gago, and Nieto (2017), have attempted to analyse the effect of outside female directors and independent female directors on the CSR disclosure, but no research has investigated the individual effect of independent and institutional women directors on CSR reporting. These female directors are not directly involved in the management activities of companies, but there are some differences among them and, therefore, their incentives and engagement with CSR reporting may differ. Accordingly, the examination of how the reporting of CSR matters is affected by outside female directors (independent and institutional) in a separate way also merits our attention.
Combining a nonlinear association, women directors' typology, and CSR disclosure, we aim to explore whether there is a nonlinear relationship between independent and institutional female directors and the reporting of CSR information. Hence, the paper addresses the following research question: How does the presence of female directors on the board affect CSR reporting?
Our results show that as the proportions of independent and institutional female directors on boards grow, CSR reporting also increases, which is consistent with the monitoring hypothesis; however, with the inclusion of additional independent and institutional women directors beyond a tipping point (20.47% and 13.32%, respectively), the CSR disclosure decreases, which is in line with the collusion hypothesis. Thus, our findings suggest a nonlinear association between outside women directors and CSR disclosure. This evidence confirms the importance of outside female directors (independent and institutional women directors) for CSR disclosure in Spain, where there are still high levels of ownership concentration, a lack of protection for minority shareholders, and a lack of transparency in the financial and nonfinancial information disclosure.
Therefore, the most relevant innovation of this paper, in comparison to the preceding research that reports that independent female directors affect the CSR disclosure either positively or negatively (a linear association), or that does not explore the effect of institutional female directors on CSR reporting, is that Spanish boards of listed firms made up by independent and institutional women directors will encourage or discourage CSR reporting depending on their representativeness on boards, which is consistent with a nonlinear relationship.
This study contributes to the growing CSR and gender diversity literature in several ways. Firstly, examining board structures with institutional and independent directors extends the knowledge of the types of female directors and their representativeness on boards that leads to better CSR reporting. Our paper is, to the best of our knowledge, the first to investigate the individual impact of both types of women directors on the CSR disclosure in a nonlinear way. Secondly, by analysing how diverse types of female directors on boards impact CSR reporting, we have tried to heed the call for exploring the effect of board gender diversity on CSR commitments in order to extend the scope of this analysis beyond the Anglo-Saxon context (Jain & Jamali, 2016). Thirdly, we contribute to the debate on how independent and institutional female directors may impact CSR reporting, by combining two competing views (agency theory and social identity theory) and by reconciling past paradoxical findings regarding female involvement on boards and CSR disclosure. Prior literature has focused on different theoretical perspectives to analyse board gender diversity and CSR reporting, but it seems to have disregarded social and psychological aspects, which indicate that female and male directors behave differently when making business decisions. Finally, our evidence may alert listed nonfinancial firms' shareholders, potential investors, policymakers, stakeholders, and managers to the most appropriate gender representation on boards for encouraging the CSR disclosure.

| THEORE TIC AL FR AME WORK
There are several competing views of the effect of women directors on the CSR disclosure. Among them, the most common are the agency and resource dependency approaches. In this sense, the agency theory postulates that the efficient supervisory role performed by female directors on boards will reduce information asymmetries, increasing the CSR disclosure and, consequently, mitigating agency problems between the managers and stakeholders (e.g., Reguera-Alvarado, Fuentes, & Laffarga, 2015). The resource dependence approach argues that female directors, given their capacity to maintain outside connections with stakeholders and organisations, will positively affect the CSR disclosure because their presence on boards is a relevant tool for firms to gain legitimacy with stakeholders and society (Lückerath-Rovers, 2013). Theories which explore board gender diversity and CSR disclosure from a social, behavioural, and psychological perspective have been disregarded by some of the prior research, but they provide relevant theoretical arguments for examining such a relationship. The gender socialisation theory suggests that a female leadership style is more ethical and social than that of males and is thus more likely to be orientated towards stakeholders, therefore increasing CSR reporting (e.g., Landry, Bernardi, & Bosco, 2016). However, the social identity theory posits that when the presence of women directors on boards goes from moderate to higher levels, they will be more likely to reduce CSR reporting because they will be classified as out-group members (boards with males and females) instead of in-group members (boards with a majority of males), performing better in-group than out-group (e.g., Nielsen & Huse, 2010).
Our viewpoint, which is in line with Thomsen and Conyon (2012), is that most of these different perspectives are more complementary than contradictory. In this regard, from the agency, resource dependence, and gender socialisation theories, a positive linear association can be predicted between board gender diversity and CSR disclosure, while a negative linear association can be predicted from the social identity approach, and an inverted U-shaped curvilinear association can be expected from an integration of agency theory, for instance, through the social identity approach (Ali, Ng, & Kulik, 2014). Thus, the positive or negative effect of female directors on the CSR disclosure will depend, according to the theoretical integration employed, on the representativeness of female directors on boards (Ali et al., 2014;Richard, Murthi, & Ismail, 2007).
A relevant stream of empirical research supports the thesis that there is a positive or negative linear relationship between female directors and CSR reporting (e.g., Alonso-Almedia et al., 2017;Dobbin & Jung, 2011;Fernández-Feijoo, Romero, & Ruiz, 2012;Fernández-Feijoo, Romero, & Ruiz, 2014a) or there is no significant association (e.g., Shukeri, Ong, & Shaari, 2012). This inconclusive evidence suggests that research should be based on contrasting approaches (a positive and negative linear association), which will propose a curvilinear relationship (Ali et al., 2014). To the best of our knowledge, there is no research focused on exploring a nonlinear relationship that is concretely curvilinear between board gender diversity and CSR disclosure, which can be supported by the integration of the agency theory with the social identity theory. Thus, against such a backdrop, we wonder whether there is a nonlinear association between women directors and CSR disclosure.
Corporate governance codes and laws, particularly those in Spain, generally classify board directors' typology between insiders and outsiders, who can be represented by women and men. According to the Spanish Unified Code of Corporate Governance (UCCG, 2006), which was updated by the Good Governance Code of Listed Companies (GGC, 2015), insiders are executive directors directly involved in a firm's management, and outside directors can be split between independent and institutional directors, who have different agendas and incentives for controlling managers. Independent directors are professionals in a workplace totally outside the company and are interested in showing the responsible behaviour of the firms. They do not have social relationships with the firms or the families that run them, except in a professional capacity, and therefore they can perform their tasks without pressure from the firm, managers, and dominant shareholders. Additionally, independent directors represent minority shareholders' interests or dispersed ownership, protecting their rights with respect to the agency costs of controlling shareholders (Ferrarini & Filippelli, 2013). Independent directors are interested in protecting their reputation and credibility, which will depend on the extent to which companies are socially responsible and, accordingly, they will be more likely to disclose CSR information that signals to the stakeholders their engagement with CSR matters. Institutional directors represent controlling shareholders and might have professional or personal relations with the companies. Given the high ownership concentration of the Spanish listed firms, dominant shareholders take important positions on boards, have a long-term horizon, and have a strong influence on the management (e.g., Pucheta-Martínez & López-Zamora, 2018). The role performed by institutional investors who serve as directors on boards allows them to take part in the decision-making process of the firms as shareholders and directors (e.g., Weinstein & Yafeh, 1998). These directors are considered strategic directors (e.g., Oh, Chang, & Martynov, 2011) since they may provide experience and guidance, connect the firms with relevant stakeholders or significant external agents, obtain external resources, and formulate strategic or other important decisions of the firms (Shaukat, Qiu, & Trojanowski, 2015). Thus, institutional directors are concerned with disclosing more company information in order to maintain the prestige and public image of a company, and therefore they tend to demonstrate active behaviour towards CSR matters by integrating environmental, social, and ethical issues into businesses (Wen, 2009) in order to demonstrate their commitment to the stakeholders.
Hence, they will try to satisfy stakeholders' needs by encouraging the management team to report CSR issues.
Based on the agency theory, shareholders may demand external mechanisms such as voluntary CSR disclosure (Fernández-Feijoo et al., 2014a;Jo, Song, & Tsang, 2016) in order to monitor managers' functions and obtain greater transparency of financial or nonfinancial information. In this sense, the agency approach assigns the board the traditional role of representing the shareholders and protecting them from managers (Griffin, 2017). In this regard, board composition has a relevant role in the decision-making process (Hassan, Miglietta, Paltrinieri, & Floreani, 2018) since it reduces agency costs and encourages CSR disclosure. Specifically, outside directors (independent and institutional) do not have a link with the company, so they tend to disclose more social and environmental information to society and other stakeholders because they are not usually aligned with managers. In addition to outsiders, the agency theory also postulates that board gender diversity is a key attribute, as female directors on boards tend to be more transparent and accountable (Luoma & Goodstein, 1999). This renders women directors as a relevant corporate governance mechanism for controlling managers (Carter, Simkins, & Simpson, 2003) since they will be more likely to mitigate agency problems (Hillman & Dalziel, 2003), thus reducing information asymmetries through the disclosure of CSR issues. This approach also argues that board gender diversity may provide a greater variety of opinions, ideas, values, expertise, experience, and backgrounds, as well as different perceptions and sensitivity to CSR matters. This might have an impact on the disclosure of CSR information since stakeholders linked with a company comprise a heterogeneous group (Catalyst, 1995).
Given that stakeholders' interests differ and are not always aimed in the same direction, as the presence of women directors increases on boards, they will become more heterogeneous, which will therefore make it possible to better understand stakeholders' needs (Ayuso & Argandoña, 2007). According to Eagly, Johannesen-Schmidt, and Engen (2003) and Cuadrado-Ballesteros, Rubio, and Ferrero (2015b), | 293 PUCHETA-MARTíNEZ ET Al. women directors are characterised by their empathy, communication skills, participation, and cooperation, which lead them to have greater concern for social and environmental matters, which may positively impact CSR reporting (e.g., Kesner, 1988). Thus, when female directors on boards rise from low to moderate levels, the benefits go on improving, in line with that suggested by Knouse and Dansby (1999), and female directors on boards might have a positive impact on CSR reporting (e.g., Fernández-Feijoo, Romero, & Ruiz, 2014b;Liao, Lin, & Zhang, 2018) because they are considered to be more benevolent and less power-orientated than their male counterparts (Adams & Funk, 2012).
Nevertheless, when the percentage of female directors increases from moderate to higher levels, they will categorise themselves and others, given that gender diversity is considered a demographic factor (Lau & Murnighan, 1998), as either in-group (board directors with the same demographic group: normally the majority, males) or out-group (board directors with a different demographic group: female and male directors) (e.g., Nielsen & Huse, 2010;Terjesen, Sealy, & Singh, 2009), which is consistent with the social identity theory. Individuals who are considered part of the out-group find it more difficult to join with those who are in-group (Tajfel & Turner, 1986). Individuals who are part of the in-group tend to interact and perform better than those who are in the out-group because they consider themselves as supe- (the in-group) behaviours towards the out-group will be negative.
Traditionally, boards have been dominated by males, and therefore, as Nielsen and Huse (2010) indicate, "women are likely to be perceived as out-group members" because they are the minority on most boards, performing worse than if they were part of the in-group. Outgroup members tend to stereotype and negatively assess the skills of their cohort, creating a bias that causes members to undervalue the contributions of minorities such as female directors (Mackie, 1987;Miller & Brewer, 1996). The interaction between board members generates an intergroup dynamic, which impacts the development and outcome of the group, depending on the effects that the heterogeneous relations may cause, such as coalitions, divergences, conflicts, cooperation, confrontation, and polarisation, among others, as the social identity theory suggests (Tajfel & Turner, 1986). Therefore, male directors who share seats on boards with women directors might demonstrate uncooperative behaviour, resulting in intergroup divergence or decreasing intergroup support, communication, and collaboration (Kravitz, 2003;Pelled, 1996). These negative attitudes reduce board effectiveness because intergroup interactions are unproductive, consequently leading to reduced CSR disclosure. Thus, as women directorship increases, male directors will have to share power with their female counterparts, who possess different abilities and social competences, which may cause divergent processes and dissatisfaction with the organisation. Consequently, this might lead to negative individual performances (e.g., reduced productivity or sales), resulting in adverse group repercussions that negatively affect company outcomes, such as CSR disclosure.
Hence, drawing on the integration of the agency perspective with the social identity approach, as the presence of outside female directors (independent and institutional) increases, firms become more likely to disclose CSR information. However, beyond a certain inflection point, more independent and institutional women directors on boards will reduce the disclosure of CSR information. Thus, from low to moderate levels of gender diversity, it will be beneficial, but from moderate to high levels of gender diversity, it will be detrimental.

| Independent female directors and CSR reporting
The UCCG (2006) and the GGC (2015) claim that independent directors should not have any relationship with a company in such a way that might influence their opinions or functions. Independent directors are a key mechanism for monitoring and controlling firms' managers and board effectiveness (Wang, Xie, & Zhu, 2015). For this reason, the inclusion of independent directors on boards can be considered a link between a company and its environment and can promote CSR reporting, thus improving a firm's long-term success. Harjoto and Jo (2011) and Fernández-Gago, Cabeza-García, and Nieto (2016) demonstrate that independent directors on boards can put pressure on firms in order to ensure congruence between organisational values and social activities, thus contributing to an increase of both CSR disclosure and market value. Additionally, independent directors will be willing to show their commitment to stakeholders through the reporting of CSR information because they are concerned about their image, legitimation, and reputation. We extend these perspectives to independent female directors since the agency approach suggests that women directors may reduce agency costs by disclosing CSR information. Papers by Al-Shaer and Zaman (2016) and Hyun, Yang, Jung, and Hong (2016) show that independent female directors have a positive effect on CSR issues, showing a linear relationship between independent women directors and CSR reporting. This evidence suggests that as the presence of independent female directors increases, there is a higher likelihood of reporting CSR information.
However, according to the social identity theory, the addition of independent female directors beyond a certain threshold may result in a decrease of reporting of CSR matters since they will be categorised as the out-group, performing worse than if they were classified as part of the in-group, suggesting a nonlinear relationship between independent female directors and CSR reporting. In addition to this, Fligstein (1991) also suggests that the financial know-how of independent directors is one of the main reasons for appointing them. Moreover, independent directors do not maintain investment or business links with companies and their shareholders. Thus, these directors are better able to analyse financial issues than other information, such as CSR matters.
Consequently, board independence may be negatively associated with the CSR disclosure, as supported by Cuadrado-Ballesteros, Rodríguez-Ariza, et al. (2015a). Garcia-Sanchez, Cuadrado-Ballesteros, and Sepulveda (2014) provide evidence that independent directors disagree with disclosing CSR information since this could affect their professional reputation, especially given that they are not experts in CSR matters, as Haniffa and Cooke (2005) and Mohamad, Abdullah, Mokhtar, and Kamil (2011) also show. Thus, when the proportion of independent female directors on boards exceeds a certain threshold, it might be detrimental for addressing CSR matters, not only because they are categorised as the out-group, but also because independent female directors may be perceived by their male counterparts as not having the appropriate expertise related to CSR issues. As far as we know, no prior research has explored a nonlinear association between independent women directors and CSR reporting. Therefore, we have attempted to fill this gap by integrating the agency theory with the social identity theory, and accordingly, we formulate the following hypothesis: Hypothesis 1: As the proportion of independent female directors on boards increases, CSR reporting is increased; however, beyond a tipping point, more independent women directors will have a negative impact on CSR reporting.

| Institutional female directors and CSR reporting
Institutional directors on boards represent dominant investors, such as institutional investors. According to the agency theory, these investors become actively involved with management activities, leaving their passive roles regarding the supervision of managers (Ivanova, 2017). Additionally, institutional investors constitute one of the most important elements in the corporate decision-making process (Ruiz- With regard to the CSR disclosure, institutional investors guarantee sustainable actions of the firms in the longer term (Bolton, Becht, & Röell, 2002) and enhance CSR reporting (Harjoto, Laksmana, & Lee, 2015;Hwang, Titman, & Wang, 2015), which help achieve long-term success and benefits for the company. Dyck, Links, Roth, and Wagner (2015) find that institutional investors prefer to represent companies involved with CSR issues because one of their main priorities is to consider CSR responsibilities in the investment decisions of firms, instead of prioritising firms' economic benefits. In addition, institutional investors tend to secure changes in CSR-related shareholder proposals (Del Guercio & Tran, 2012) and voting engagements on CSR issues (Dimson et al., 2015). Dhaliwal, Li, Tsang, and Yang (2011) documented that voluntary CSR disclosure in companies tends to attract institutional investors, who play monitoring and governance roles and have long investment horizons. Authors such as Neubaum and Zahra (2006), Zattoni (2011), and Pucheta-Martínez and López-Zamora (2018) find that institutional directors encourage CSR reporting.
However, the relation between institutional investors and CSR disclosure may be negative. Arora and Dharwadkar (2011) and Ghabayen, Mohamada, and Ahmadb (2015) show that institutional shareholding has a significant and negative effect on CSR reporting, since institutional investors may engage in opportunistic behaviours in order to enjoy private benefits; they may work together with managers and, as a consequence, may reduce the monitoring functions in their governance. Furthermore, Chava (2014) reports that firms' environmental issues are negatively affected by institutional ownership.
Thus, according to this literature, we argue that effective control mechanisms on boards by institutional investors may have both positive and negative effects on CSR disclosure in a linear way. However, Feng and Song (2013) demonstrate a nonlinear association, specifically a quadratic arrangement, between institutional investors and CSR disclosure, as a combined result of the monitoring and entrenchment hypotheses. Harjoto et al. (2015) also find a nonlinear association between institutional ownership and CSR disclosure, suggesting that active institutional investors exert a quadratic influence on CSR reporting. Thus, when institutional directorship is low, the monitoring hypothesis prevails, as it is positively associated with CSR reporting and, as a consequence, institutional directors perform an active role in encouraging managers and other directors to disclose CSR information. However, if the proportion of institutional directors on boards reaches a certain threshold, the entrenchment or collusion hypothesis prevails, and they are negatively associated with the CSR disclosure, given that they prefer to achieve absolute control of firms, which may unfavourably impact the CSR disclosure.
We extend the above views to the role of institutional female directors on boards. To the best of our knowledge, there is no prior evidence on how institutional women directors on boards affect CSR reporting. Drawing on the agency perspective, we expect a positive effect of institutional female directors on CSR reporting as their presence on boards increases since they will play a role in supervising and monitoring the respective managers' behaviour. However, institutional women directors will negatively affect the disclosure of CSR information when their representation exceeds a tipping point, according to the social identity theory, given that they will be classified as an out-group, performing worse than if they were the in-group.
Accordingly, we propose the following hypothesis:

Hypothesis 2: As the proportion of institutional female directors on boards increases, CSR reporting is increased;
however, beyond a tipping point, more institutional women directors will negatively impact on CSR reporting.

| Sample
The sample is composed of 152 Spanish nonfinancial listed firms over the period 2004-2014. Financial companies were excluded from the sample because they use unique accounting, which is difficult to compare with industrial companies, and because they are regulated by financial authorities using special norms. Thus, the final sample includes a panel data of 1,312 firm-year observations. As Arellano | 295 PUCHETA-MARTíNEZ ET Al.
(2003) shows, our unbalanced panel data might report findings that are as consistent as those provided by the balanced panel data.
We built our database from the following sources. The CSR data were obtained from the GRI web page and from the corporate web pages of the companies. The GRI is considered a relevant instrument for providing important information concerning financial, environmental, and social issues (Fernández-Feijoo et al., 2014a). Then, we collected the CSR information from two sources: the GRI web page and companies' web pages. The financial data (ROA, LEV, and SIZE) were collected from the "Sistemas de Análisis de Balances Ibéricos"

| Variables
Our dependent variable is defined as CSR_INDEX and is measured as an average score derived from the ratio between the aggregation of the following five items of CSR-each one measured as a dummy variable-and the total five items analysed: (a) disclosure of CSR information by any means-that is, this item will be given a value of 1 if a firm discloses information on social and environmental matters on its home page using its own reports and/or discloses this information using the GRI report, with 0 given when firms do not report CSR information in any case; (b) disclosure of CSR information through non-GRI reports-i.e., this item will be given a value of 1 if a firm does not disclose CSR information using the GRI reports (firms do not follow the pattern or format of report recommended by the GRI), but it does provide this information according to its own criterion and on its own home page with its own report, with 0 given otherwise; (c) disclosure of CSR information through the GRI reports-that is, this item will be given a value of 1 if a firm discloses social and environmental information using the format or pattern of report recommended by the GRI, but the companies may also provide this information by other means, with 0 given otherwise; (d) the CSR report is certified (checked) by the GRI-that is, this item will be given a value of 1 if the GRI report used by a firm to disclose social and environmental information is checked by the GRI, with 0 given otherwise; and (e) the CSR information is also audited by an external and independent body (external assurance)-that is, this item will be given a value of 1 if the CSR information disclosed by a firm is audited by an independent and external body, with 0 given otherwise. This measure has been created according to the method of analysis of CSR used by Alonso-Almeida, Perramon, and Bagur defined as SIZE, is also controlled for (Li & Chen, 2018). Finally, we have taken into account the business sector, defined as SEC, which is calculated as a dummy variable that equals 1 if the company belongs to the sector analysed, with 0 otherwise. We have used the industry classification set up by the CNMV, described in Table 2, where we offer a summary of all the variables employed and the way in which they have been operationalised.
Thus, we propose the following model: where year and firm fixed effects are represented by µ it and the error by ε it . Firm fixed effects take into account regular and non-observable features of the firms that may be associated with CSR reporting.
The most suitable methodology for estimating this model is the Tobit regression for panel data because it allows us to consider a dependent variable with limits on the left or right censoring. The dependent variable in our research, CSR_INDEX, ranges between 0 and 1, inclusive. Accordingly, this variable is censored on two sides (0-1), and

TA B L E 1 CSR disclosure classification
Index score Classification 0 CSR information is not disclosed by firms 0.1-0.5 CSR information disclosed by firms is moderate 0.6-0.9 CSR information disclosed by firms is significant 1 CSR information disclosed by firms is full Source. Own elaboration Electronic copy available at: https://ssrn.com/abstract=3587837 therefore, the most appropriate regression for testing our hypotheses is a Tobit model.

| Descriptive statistics and correlations
The descriptive statistics of the dependent, independent, and control variables are presented in Table 3. This table reports that the CSR disclosure of Spanish nonfinancial listed firms is, on average, 0.15 out of 1. This value shows that the level of CSR information disclosed by Spanish listed firms is moderate. According to board composition, we can observe that the proportions of independent and institutional directors represent, on average, 30.27% and 44.70%, respectively, while the proportions of independent and institutional women directors on boards represent, on average, 3.18% and 4.55%, respectively.
These results suggest that institutional directors and institutional women directors have more representation on boards than independent directors and independent female directors. The ownership concentration represents, on average, 43.67%, the board size is, on average, 10.20 members, and the firm size is, on average, 10.56 (log of the total sales, expressed in thousands of euros). Moreover, the return on assets is, on average, 2.56%, and the leverage of firms is, on average, 53.20%.
With regard to industries, on average, the "other" manufacturing industry is the highest represented sector, with 23.55%, and the least represented sector is agriculture and fisheries, with 1.60%.
For the sake of brevity, the correlation coefficients for all the variables used in this analysis in order to check for multicollinearity are not reported. The correlations in pairs of all the variables are not greater than 0.80 (Carcello & Neal, 2000). Therefore, based on these results, we can affirm that multicollinearity concerns do not arise. Table 4 presents the results of the Tobit regression. As you can see, we built two models and they are statistically significant. In Model 1, we analyse how independent women directors on boards affect the CSR disclosure, while in Model 2, we investigate the relationship between institutional women directors on boards and CSR reporting.

| Regression results
In Model 1, the variables denoting independent women directors on boards in a linear (INDEP_WOM) and nonlinear way Note. Mean, standard deviation, and percentiles. Panels A and B show the continuous and dummy variables, respectively. CSR_INDEX is measured as the ratio between the aggregation of the five items of CSR considered, measured each one as a dummy variable and the total items (5); INDEP_WOM is the proportion of independent female directors on board; INST_WOM is the proportion of institutional female directors on board.; INDEP is the proportion of independent directors on the boards; INST is the proportion of institutional directors on boards; OWNCON is the ownership concentration in the firm; BDSIZE is the number of directors on boards; ROA is the operate income before interests and taxes over total assets; LEV is the debt over total assets; SIZE is the log of total sales; SEC1 1 if the company operates in the metalworking sector and 0, otherwise; SEC2 1 if the company operates in other manufacturing industries sector and 0, otherwise; SEC3 1 if the company operates in the new technologies sector and 0, otherwise; SEC4 1 if the company operates in the basic metal sector and 0, otherwise; SEC5 1 if the company operates in the mass media sector and 0, otherwise; SEC6 1 if the company operates in the real estate sector and 0, otherwise; SEC7 1 if the company operates in the chemical industry sector and 0, otherwise; SEC8 1 if the company operates in the financing and insurance sector and 0, otherwise; SEC9 1 if the company operates in the energy and water sector and 0, otherwise; SEC10 1 if the company operates in the construction sector and 0, otherwise; SEC11 1 if the company operates in the commerce and other services sector and 0, otherwise; SEC12 1 if the company operates in the cement, glass, and construction material sector and 0, otherwise; SEC13 1 if the company operates in the transport and communications sector and 0, otherwise; SEC14 1 if the company operates in the agriculture and fishing sector and 0, otherwise. Significant at *** for 99% confidence level, ** for 95%, and * for 90%. consistent with the collusion hypothesis, which may not be in line with promoting the CSR disclosure. Consequently, it will be more likely that CSR reporting decreases.
In Model 2, the variables of institutional women directors on boards present a linear (INST_WOM) and nonlinear (INST_WOM 2 ) relation, exhibiting the expected signs, and are statistically significant. Hence, our empirical findings are consistent with Hypothesis 2, which suggests that the disclosure of CSR information improves as the proportion of institutional women directors on boards increases, but only up to a point (13.32%), beyond which further increases are associated with decreases in the CSR disclosure. This idea is confirmed by Frink, Robinson, Reithel, Arthur, and Ammeter (2003), who show that the optimal proportion of women directors on boards occurs when it is balanced. In line with institutional directors, authors such as Feng and Song (2013) and Harjoto et al. (2015) report a nonlinear relationship between institutional ownership and CSR reporting because they consider social activities as a priority in their investment decisions. In line with the findings obtained for independent female directors, our evidence also supports the monitoring and collusion hypotheses with institutional female directors. In this regard, as the presence of institutional female directors on boards increases, there is a higher probability that they positively influence the CSR disclosure; but when their presence on boards reaches a turning point, this situation will invert (collusion hypothesis) and they may support executive teams' decisions focused on other socioeconomic decisions that do not consider the CSR disclosure as a main strategy to increase firm performance.
Regarding control variables, we can appreciate that independent We also control for the potential endogeneity concerns between independent female directors, institutional female directors, and CSR reporting, given that these problems might appear in research such as this (Villalonga & Amit, 2006). Specifically, we would like to assess whether the proportion of independent and institutional women directors on boards leads to more or less CSR disclosure, or whether companies with more or less CSR disclosure may be more or less attractive for independent and institutional women directors. The causality between CSR reporting and these female directors is probably in the direction from directors to CSR disclosure, but it is also possible that the disclosure of CSR matters might impact board structure. The causality issue has been addressed by lagging the measures of the independent variables, which is consistent with Hartzell and Starks (2003) and Ozkan (2007), who support the use of lagged explanatory variables to reduce potential endogeneity problems. The findings, not provided for the sake of brevity, are in line with the results obtained in the baseline model-that is, the estimates of the models with lagged explanatory variables confirm the earlier findings. Thus, the results suggest that the potential endogeneity is not a problem in our research.

| Sensitivity analysis
To test the robustness of our findings, we ran the model using three different dependent variables: (a) the CSR_INDEX calculated as the aggregation of the five items of CSR considered, each one measured as a dummy variable; (b) the CSR_INDEX calculated as the ratio between each of six items-the five items considered in the dependent variable used in the baseline model plus an additional item-and the total six items (each item is computed as a dummy variable; the additional and sixth item takes into account whether the assurance scope refers to the entire CSR report; thus, this item will be given a value of 1 if the whole CSR report is verified, with 0 otherwise); and (c) the CSR_INDEX calculated as the aggregation of the six items of CSR considered in point (b), with each one measured as a dummy variable. The findings obtained, which are not reported for the sake of brevity, corroborate our predictions regarding the curvilinear relationship between independent and institutional female directors and CSR disclosure. Hence, our findings are robust since they do not depend on the way that CSR reporting is measured in this research. ters. In conclusion, our findings suggest that the representation of institutional and independent female directors below the inflection point drives their efforts towards engaging in CSR issues to meet all stakeholders' expectations. These female directors may play an active and effective monitoring role and will tend to align their representatives' interests with those of the other shareholders, trying to guarantee management involvement in CSR matters, avoiding negative and opportunistic disclosures and supporting those that benefit a broad range of stakeholders. However, the monitoring role played by institutional and independent female directors will be less effective and weaker when their presence on boards is higher than the critical point since they will tend to enforce their own interests at the expense of other directors-specifically, male directors. Their aim will not be the enhancement of the CSR disclosure, but rather obtaining private benefits and supervising male counterparts in order to hinder them from fulfilling their own aims. Therefore, institutional and independent female directors will be likely to collude with managers, supporting their decisions, and will be less willing to challenge the managers with regard to the CSR disclosure. Managers may provide benefits to those institutional and independent female directors who do not hinder their decisions, such as limiting the reporting of CSR issues. Hence, this research offers sound guidance on the inclusion of independent and institutional female directors on boards and its effect on the CSR disclosure. Several limitations of this research should be noted. Firstly, in this analysis, we do not consider affiliate directors as outsiders, which is in contrast to other research (e.g., Samara & Berbegal-Mirabent, 2017).

| IMPLI C ATI ON S , LIMITATI ON S , AND SUG G E S TI ON S FOR FUTURE RE S E ARCH DIREC TIONS
Affiliates can be defined as directors who maintain or may maintain personal connections with companies and/or family owners. These include solicitors, financial advisors, and experts, among others (e.g., Arosa, Iturralde, & Maseda, 2010), but they are not employees of the firm. The types of directors who made up Spanish listed firms' boards, insiders or outsiders (independent or institutional), are provided in the annual corporate governance reports that these firms have had to disclose since 2003. The fact that Spanish laws and corporate governance codes do not consider affiliate directors may explain why annual corporate governance reports do not provide information on these directors. For this reason, in this research, we only focus on independent female and institutional female directors, although both types of women directors might also be affiliate directors. Secondly, our database was built using industrial companies, so our results cannot be used to interpret the results of the financial companies.
Thirdly, our CSR reporting measure may be considered simplistic since it provides little information on the content, quality, and extent of the reporting. Ultimately, in this research, we only consider the CSR disclosure towards external stakeholders, but internal social responsibility (towards employees), as Samara and Arenas (2017) suggest, can be as meaningful as external social responsibility (towards the environment).
Hence, we suggest the following future research avenues. Firstly, as Jamali, Lund- Thomsen, and Jeppesen (2017) suggest, it would be interesting to analyse the role of informal firms and micro-firms in CSR, as well as the informal aspects of CSR activities in small to medium-sized enterprises, combining this topic with board gender diversity. Secondly, the development of a more thorough CSR reporting measure, increasing the content, quality, and extent of the reporting, also merits the attention of the researchers. Finally, we encourage scholars to explore CSR reporting towards internal stakeholders (employees) because internal social responsibility is as relevant as external social responsibility.

ACK N OWLED G EM ENTS
The authors acknowledge the financial support from the Spanish Ministry of Economy, Industry and Competitiveness for the research project ECO 2017-82259-R. Furthermore, they would like to thank the two anonymous reviewers for their valuable comments and suggestions to improve the quality of the paper. Finally, they would also like to thank the Editor-in-Chief, Prof. Dima Jamali, and the Associate Editor, Prof. Georges Samara, for their generous and constructive comments, which helped them improve the final version of the paper, and for their support during the review process.

1
We have estimated Models 1 and 2 using other control variables, but the two models used to test the hypotheses are the most significant.